TSTP Solution File: SCT042-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT042-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:00:28 EDT 2024
% Result : Unsatisfiable 3.99s 0.94s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1204
% Syntax : Number of formulae : 2333 ( 757 unt; 0 def)
% Number of atoms : 5531 (1351 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 5607 (2409 ~;2518 |; 0 &)
% ( 680 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 10 ( 1 avg)
% Number of predicates : 722 ( 720 usr; 682 prp; 0-3 aty)
% Number of functors : 48 ( 48 usr; 8 con; 0-5 aty)
% Number of variables : 4082 (4082 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15260,plain,
$false,
inference(avatar_sat_refutation,[],[f830,f835,f840,f845,f850,f855,f860,f865,f870,f875,f880,f885,f890,f895,f900,f905,f910,f915,f920,f925,f930,f935,f940,f945,f950,f955,f960,f965,f970,f975,f980,f985,f990,f995,f1000,f1005,f1010,f1015,f1020,f1025,f1030,f1035,f1040,f1045,f1050,f1055,f1060,f1065,f1070,f1075,f1080,f1085,f1090,f1095,f1100,f1105,f1110,f1115,f1119,f1123,f1127,f1131,f1135,f1139,f1143,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1179,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1211,f1215,f1219,f1223,f1227,f1231,f1235,f1239,f1243,f1247,f1251,f1255,f1259,f1272,f1276,f1280,f1284,f1288,f1292,f1296,f1300,f1304,f1308,f1312,f1316,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1380,f1386,f1405,f1410,f1414,f1418,f1422,f1426,f1430,f1434,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1523,f1527,f1531,f1535,f1539,f1594,f1633,f1637,f1641,f1645,f1649,f1653,f1657,f1661,f1665,f1669,f1673,f1677,f1681,f1685,f1689,f1693,f1697,f1701,f1705,f1709,f1713,f1717,f1721,f1725,f1729,f1733,f1737,f1741,f1803,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2120,f2137,f2182,f2209,f2213,f2217,f2221,f2225,f2229,f2233,f2237,f2243,f2247,f2251,f2255,f2259,f2263,f2267,f2271,f2275,f2279,f2283,f2287,f2291,f2295,f2299,f2303,f2308,f2312,f2316,f2320,f2324,f2328,f2332,f2404,f2510,f2576,f2580,f2584,f2588,f2592,f2596,f2600,f2604,f2608,f2612,f2616,f2621,f2625,f2629,f2633,f2637,f2641,f2645,f2649,f2653,f2657,f2662,f2666,f2884,f3011,f3015,f3019,f3023,f3027,f3031,f3035,f3041,f3045,f3049,f3053,f3057,f3061,f3065,f3069,f3073,f3077,f3084,f3088,f3092,f3096,f3100,f3104,f3108,f3112,f3116,f3120,f3125,f3129,f3133,f3137,f3141,f3145,f3149,f3153,f3157,f3161,f3165,f3379,f3585,f3673,f3678,f3682,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3714,f3718,f3722,f3726,f3730,f3734,f3738,f3742,f3746,f3750,f3754,f3759,f3763,f3767,f3771,f3775,f3779,f3783,f3787,f3791,f3795,f3800,f3804,f3808,f3812,f3816,f3820,f3824,f3828,f3832,f4671,f4892,f4896,f4900,f4904,f4908,f4912,f4916,f4920,f4924,f4928,f4932,f4936,f4940,f4944,f4948,f4952,f4956,f4960,f4964,f4968,f4972,f4976,f4980,f4984,f4988,f4992,f4996,f5000,f5004,f5008,f5180,f5539,f5825,f5905,f5909,f5913,f5917,f5921,f5925,f5929,f5933,f5937,f5941,f5945,f5949,f5953,f5957,f5961,f5965,f5969,f5973,f5977,f5981,f5985,f5989,f5994,f5998,f6142,f6233,f6288,f6347,f6351,f6355,f6359,f6363,f6368,f6396,f6400,f6404,f6408,f6412,f6416,f6420,f6424,f6428,f6433,f6438,f6988,f6992,f7038,f7042,f7046,f7050,f7054,f7058,f7062,f7066,f7071,f7075,f7079,f7083,f7311,f7535,f7539,f7552,f7556,f7560,f7564,f7568,f7572,f7576,f7580,f7584,f7588,f7593,f7597,f7601,f7605,f7609,f7613,f7617,f7621,f7625,f7629,f7633,f7637,f7641,f7645,f7649,f7653,f7657,f7662,f7667,f7673,f7688,f8488,f8492,f8496,f8500,f8504,f8607,f8611,f8615,f8619,f8623,f8627,f8631,f8635,f8639,f8643,f8647,f8651,f8655,f8659,f9165,f9169,f9173,f9248,f9252,f9256,f9260,f9264,f9268,f9272,f9276,f9280,f9286,f9541,f9545,f9549,f9553,f9557,f9561,f9565,f9569,f9573,f9577,f9581,f9585,f9839,f10030,f10103,f10107,f10111,f10115,f10119,f10123,f10127,f10131,f10135,f10140,f10264,f10384,f10539,f10546,f10550,f10554,f10558,f10920,f10924,f10928,f11015,f11019,f11023,f11027,f11031,f11289,f11295,f11299,f11303,f11371,f11410,f11414,f11556,f11561,f11565,f11570,f11661,f11779,f11853,f11937,f11941,f12139,f12143,f12267,f12405,f12562,f12566,f12570,f12574,f12578,f12582,f13149,f13153,f13157,f13161,f13165,f13169,f13173,f13177,f13181,f13185,f13189,f13193,f13202,f13206,f13210,f13215,f13220,f13224,f13228,f13232,f13236,f13240,f13244,f13248,f13252,f13256,f13260,f13264,f13268,f13272,f13694,f13761,f13887,f14118,f14141,f14145,f14149,f14153,f14157,f14161,f14166,f14170,f14174,f14178,f14201,f14206,f14210,f14214,f14218,f14222,f14226,f14230,f14234,f14238,f14242,f14246,f14250,f14254,f14258,f14262,f14266,f14271,f14275,f14279,f15123,f15127,f15131,f15164,f15168,f15172,f15176,f15180,f15184,f15188,f15192,f15196,f15200,f15204,f15208,f15212,f15216,f15222,f15226,f15230,f15234,f15238,f15242,f15246,f15250,f15254,f15258,f15259]) ).
fof(f15259,plain,
( spl0_58
| ~ spl0_445
| ~ spl0_660 ),
inference(avatar_split_clause,[],[f15217,f15174,f6986,f1112]) ).
fof(f1112,plain,
( spl0_58
<=> v_a____ = v_b____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f6986,plain,
( spl0_445
<=> ! [X9,X1] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f15174,plain,
( spl0_660
<=> ! [X0] : ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f15217,plain,
( v_a____ = v_b____
| ~ spl0_445
| ~ spl0_660 ),
inference(resolution,[],[f15175,f6987]) ).
fof(f6987,plain,
( ! [X1,X9] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f6986]) ).
fof(f15175,plain,
( ! [X0] : ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_660 ),
inference(avatar_component_clause,[],[f15174]) ).
fof(f15258,plain,
( spl0_680
| ~ spl0_47
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3499,f3082,f1057,f15256]) ).
fof(f15256,plain,
( spl0_680
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,X1,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f1057,plain,
( spl0_47
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f3082,plain,
( spl0_302
<=> ! [X9,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = c_Divides_Odiv__class_Omod(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3499,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,X1,tc_Int_Oint)
| ~ spl0_47
| ~ spl0_302 ),
inference(resolution,[],[f3083,f1059]) ).
fof(f1059,plain,
( class_Divides_Osemiring__div(tc_Int_Oint)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f3083,plain,
( ! [X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = c_Divides_Odiv__class_Omod(X1,X9,X0) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f3082]) ).
fof(f15254,plain,
( spl0_679
| ~ spl0_18
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3498,f3082,f912,f15252]) ).
fof(f15252,plain,
( spl0_679
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f912,plain,
( spl0_18
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f3498,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_18
| ~ spl0_302 ),
inference(resolution,[],[f3083,f914]) ).
fof(f914,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f15250,plain,
( spl0_678
| ~ spl0_256
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3384,f3047,f2326,f15248]) ).
fof(f15248,plain,
( spl0_678
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f2326,plain,
( spl0_256
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f3047,plain,
( spl0_294
<=> ! [X4,X3,X14] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3384,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
| ~ spl0_256
| ~ spl0_294 ),
inference(resolution,[],[f3048,f2327]) ).
fof(f2327,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2326]) ).
fof(f3048,plain,
( ! [X3,X14,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3047]) ).
fof(f15246,plain,
( spl0_677
| ~ spl0_257
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3347,f3043,f2330,f15244]) ).
fof(f15244,plain,
( spl0_677
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f2330,plain,
( spl0_257
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3043,plain,
( spl0_293
<=> ! [X4,X3,X14] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3347,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) )
| ~ spl0_257
| ~ spl0_293 ),
inference(resolution,[],[f3044,f2331]) ).
fof(f2331,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2330]) ).
fof(f3044,plain,
( ! [X3,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3043]) ).
fof(f15242,plain,
( spl0_676
| ~ spl0_132
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2919,f2614,f1436,f15240]) ).
fof(f15240,plain,
( spl0_676
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1436,plain,
( spl0_132
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f2614,plain,
( spl0_271
<=> ! [X9,X0,X5,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X9,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2919,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_132
| ~ spl0_271 ),
inference(duplicate_literal_removal,[],[f2912]) ).
fof(f2912,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_132
| ~ spl0_271 ),
inference(resolution,[],[f2615,f1437]) ).
fof(f1437,plain,
( ! [X0,X8,X5] :
( c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1436]) ).
fof(f2615,plain,
( ! [X0,X1,X9,X5] :
( ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0)
| c_lessequals(X5,X9,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2614]) ).
fof(f15238,plain,
( spl0_675
| ~ spl0_133
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2918,f2614,f1440,f15236]) ).
fof(f15236,plain,
( spl0_675
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1440,plain,
( spl0_133
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f2918,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_133
| ~ spl0_271 ),
inference(duplicate_literal_removal,[],[f2913]) ).
fof(f2913,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X2,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_133
| ~ spl0_271 ),
inference(resolution,[],[f2615,f1441]) ).
fof(f1441,plain,
( ! [X0,X8,X5] :
( c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X8,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f15234,plain,
( spl0_674
| ~ spl0_132
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f2900,f2610,f1436,f15232]) ).
fof(f15232,plain,
( spl0_674
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f2610,plain,
( spl0_270
<=> ! [X9,X0,X5,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X1,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2900,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_132
| ~ spl0_270 ),
inference(duplicate_literal_removal,[],[f2893]) ).
fof(f2893,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_132
| ~ spl0_270 ),
inference(resolution,[],[f2611,f1437]) ).
fof(f2611,plain,
( ! [X0,X1,X9,X5] :
( ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0)
| c_lessequals(X5,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f2610]) ).
fof(f15230,plain,
( spl0_673
| ~ spl0_133
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f2899,f2610,f1440,f15228]) ).
fof(f15228,plain,
( spl0_673
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X1,X3)
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f2899,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X1,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_133
| ~ spl0_270 ),
inference(duplicate_literal_removal,[],[f2894]) ).
fof(f2894,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X1,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_133
| ~ spl0_270 ),
inference(resolution,[],[f2611,f1441]) ).
fof(f15226,plain,
( spl0_672
| ~ spl0_129
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2570,f2330,f1424,f15224]) ).
fof(f15224,plain,
( spl0_672
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1424,plain,
( spl0_129
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2570,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_129
| ~ spl0_257 ),
inference(superposition,[],[f2331,f1425]) ).
fof(f1425,plain,
( ! [X3,X4] : c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f15222,plain,
( spl0_671
| ~ spl0_129
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2553,f2326,f1424,f15220]) ).
fof(f15220,plain,
( spl0_671
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f2553,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_129
| ~ spl0_256 ),
inference(superposition,[],[f2327,f1425]) ).
fof(f15216,plain,
( spl0_670
| ~ spl0_129
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2462,f2261,f1424,f15214]) ).
fof(f15214,plain,
( spl0_670
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f2261,plain,
( spl0_240
<=> ! [X5,X8,X7] :
( X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2462,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
| X1 = X2 )
| ~ spl0_129
| ~ spl0_240 ),
inference(superposition,[],[f2262,f1425]) ).
fof(f2262,plain,
( ! [X8,X7,X5] :
( c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X8,tc_nat)
| X7 = X8 )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2261]) ).
fof(f15212,plain,
( spl0_669
| ~ spl0_171
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2442,f2249,f1679,f15210]) ).
fof(f15210,plain,
( spl0_669
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1679,plain,
( spl0_171
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f2249,plain,
( spl0_237
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X8,X5,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2442,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0) )
| ~ spl0_171
| ~ spl0_237 ),
inference(duplicate_literal_removal,[],[f2433]) ).
fof(f2433,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_171
| ~ spl0_237 ),
inference(resolution,[],[f2250,f1680]) ).
fof(f1680,plain,
( ! [X0,X8,X5] :
( c_lessequals(X8,X5,X0)
| c_lessequals(X5,X8,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1679]) ).
fof(f2250,plain,
( ! [X0,X8,X5] :
( ~ c_lessequals(X8,X5,X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X8 )
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2249]) ).
fof(f15208,plain,
( spl0_668
| ~ spl0_171
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2419,f2241,f1679,f15206]) ).
fof(f15206,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f2241,plain,
( spl0_235
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2419,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0) )
| ~ spl0_171
| ~ spl0_235 ),
inference(duplicate_literal_removal,[],[f2410]) ).
fof(f2410,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_171
| ~ spl0_235 ),
inference(resolution,[],[f2242,f1680]) ).
fof(f2242,plain,
( ! [X0,X8,X5] :
( ~ c_lessequals(X5,X8,X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X5 )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2241]) ).
fof(f15204,plain,
( spl0_667
| ~ spl0_136
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2393,f2231,f1452,f15202]) ).
fof(f15202,plain,
( spl0_667
<=> ! [X0,X3,X2,X1] : c_List_Odrop(X0,c_List_Oappend(c_List_Oreplicate(X0,X1,X2),X3,X2),X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f1452,plain,
( spl0_136
<=> ! [X5,X0,X3] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X5,X0),tc_List_Olist(X0)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f2231,plain,
( spl0_233
<=> ! [X13,X0,X12] : c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2393,plain,
( ! [X2,X3,X0,X1] : c_List_Odrop(X0,c_List_Oappend(c_List_Oreplicate(X0,X1,X2),X3,X2),X2) = X3
| ~ spl0_136
| ~ spl0_233 ),
inference(superposition,[],[f2232,f1453]) ).
fof(f1453,plain,
( ! [X3,X0,X5] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X5,X0),tc_List_Olist(X0)) = X3
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f2232,plain,
( ! [X0,X12,X13] : c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X13
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2231]) ).
fof(f15200,plain,
( spl0_666
| ~ spl0_144
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2380,f2223,f1484,f15198]) ).
fof(f15198,plain,
( spl0_666
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1484,plain,
( spl0_144
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X3,tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f2223,plain,
( spl0_231
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2380,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_144
| ~ spl0_231 ),
inference(superposition,[],[f2224,f1485]) ).
fof(f1485,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X3,tc_nat) = X4
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1484]) ).
fof(f2224,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2223]) ).
fof(f15196,plain,
( spl0_665
| ~ spl0_143
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2379,f2223,f1480,f15194]) ).
fof(f15194,plain,
( spl0_665
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f1480,plain,
( spl0_143
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X3,tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f2379,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_143
| ~ spl0_231 ),
inference(superposition,[],[f2224,f1481]) ).
fof(f1481,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X3,tc_nat) = X4
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f15192,plain,
( spl0_664
| ~ spl0_136
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2357,f2215,f1452,f15190]) ).
fof(f15190,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_List_Oreplicate(X0,X1,X2) = c_List_Olist_ONil(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f2215,plain,
( spl0_229
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2357,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_List_Oreplicate(X0,X1,X2) = c_List_Olist_ONil(X2) )
| ~ spl0_136
| ~ spl0_229 ),
inference(superposition,[],[f2216,f1453]) ).
fof(f2216,plain,
( ! [X0,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2215]) ).
fof(f15188,plain,
( spl0_663
| ~ spl0_157
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2055,f1881,f1537,f15186]) ).
fof(f15186,plain,
( spl0_663
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f1537,plain,
( spl0_157
<=> ! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1881,plain,
( spl0_192
<=> ! [X3,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X3,tc_nat),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f2055,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) )
| ~ spl0_157
| ~ spl0_192 ),
inference(resolution,[],[f1882,f1538]) ).
fof(f1538,plain,
( ! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f1882,plain,
( ! [X3,X14,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X3,tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1881]) ).
fof(f15184,plain,
( spl0_662
| ~ spl0_166
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1817,f1671,f1659,f15182]) ).
fof(f15182,plain,
( spl0_662
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X0,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f1659,plain,
( spl0_166
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1671,plain,
( spl0_169
<=> ! [X9,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1817,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X0,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_166
| ~ spl0_169 ),
inference(resolution,[],[f1672,f1660]) ).
fof(f1660,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1659]) ).
fof(f1672,plain,
( ! [X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1671]) ).
fof(f15180,plain,
( spl0_661
| ~ spl0_166
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1809,f1667,f1659,f15178]) ).
fof(f15178,plain,
( spl0_661
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f1667,plain,
( spl0_168
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1809,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_166
| ~ spl0_168 ),
inference(resolution,[],[f1668,f1660]) ).
fof(f1668,plain,
( ! [X0,X8,X5] :
( ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1667]) ).
fof(f15176,plain,
( spl0_660
| ~ spl0_59
| ~ spl0_653 ),
inference(avatar_split_clause,[],[f15101,f14277,f1117,f15174]) ).
fof(f1117,plain,
( spl0_59
<=> ! [X5] : ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Olist_OCons(X5,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f14277,plain,
( spl0_653
<=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f15101,plain,
( ! [X0] : ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_59
| ~ spl0_653 ),
inference(superposition,[],[f1118,f14278]) ).
fof(f14278,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_653 ),
inference(avatar_component_clause,[],[f14277]) ).
fof(f1118,plain,
( ! [X5] : ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Olist_OCons(X5,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1117]) ).
fof(f15172,plain,
( spl0_659
| ~ spl0_166
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1798,f1663,f1659,f15170]) ).
fof(f15170,plain,
( spl0_659
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f1663,plain,
( spl0_167
<=> ! [X9,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1798,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_166
| ~ spl0_167 ),
inference(resolution,[],[f1664,f1660]) ).
fof(f1664,plain,
( ! [X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1663]) ).
fof(f15168,plain,
( spl0_658
| ~ spl0_164
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1789,f1659,f1651,f15166]) ).
fof(f15166,plain,
( spl0_658
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1651,plain,
( spl0_164
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1789,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) )
| ~ spl0_164
| ~ spl0_166 ),
inference(resolution,[],[f1660,f1652]) ).
fof(f1652,plain,
( ! [X0,X8,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X8,X0) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1651]) ).
fof(f15164,plain,
( spl0_657
| ~ spl0_165
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1788,f1659,f1655,f15162]) ).
fof(f15162,plain,
( spl0_657
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1655,plain,
( spl0_165
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1788,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) )
| ~ spl0_165
| ~ spl0_166 ),
inference(resolution,[],[f1660,f1656]) ).
fof(f1656,plain,
( ! [X0,X8,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X8,X0) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1655]) ).
fof(f15131,plain,
( ~ spl0_20
| spl0_656
| ~ spl0_159
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1774,f1643,f1631,f15129,f922]) ).
fof(f922,plain,
( spl0_20
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f15129,plain,
( spl0_656
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f1631,plain,
( spl0_159
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1643,plain,
( spl0_162
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1774,plain,
( ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
| c_lessequals(X1,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_159
| ~ spl0_162 ),
inference(resolution,[],[f1644,f1632]) ).
fof(f1632,plain,
( ! [X0,X8,X5] :
( c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X8,X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1631]) ).
fof(f1644,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4 )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1643]) ).
fof(f15127,plain,
( spl0_655
| ~ spl0_114
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1400,f1366,f1346,f15125]) ).
fof(f15125,plain,
( spl0_655
<=> ! [X0,X1] :
( c_List_Orotate1(X0,X1) = c_List_Oremdups(c_List_Orotate1(X0,X1),X1)
| ~ c_List_Odistinct(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f1346,plain,
( spl0_114
<=> ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1366,plain,
( spl0_119
<=> ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1400,plain,
( ! [X0,X1] :
( c_List_Orotate1(X0,X1) = c_List_Oremdups(c_List_Orotate1(X0,X1),X1)
| ~ c_List_Odistinct(X0,X1) )
| ~ spl0_114
| ~ spl0_119 ),
inference(resolution,[],[f1367,f1347]) ).
fof(f1347,plain,
( ! [X0,X12] :
( c_List_Odistinct(c_List_Orotate1(X12,X0),X0)
| ~ c_List_Odistinct(X12,X0) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f1367,plain,
( ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) = X12 )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1366]) ).
fof(f15123,plain,
( spl0_654
| ~ spl0_116
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1398,f1366,f1354,f15121]) ).
fof(f15121,plain,
( spl0_654
<=> ! [X0,X1] :
( c_List_Orev(X0,X1) = c_List_Oremdups(c_List_Orev(X0,X1),X1)
| ~ c_List_Odistinct(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f1354,plain,
( spl0_116
<=> ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1398,plain,
( ! [X0,X1] :
( c_List_Orev(X0,X1) = c_List_Oremdups(c_List_Orev(X0,X1),X1)
| ~ c_List_Odistinct(X0,X1) )
| ~ spl0_116
| ~ spl0_119 ),
inference(resolution,[],[f1367,f1355]) ).
fof(f1355,plain,
( ! [X0,X12] :
( c_List_Odistinct(c_List_Orev(X12,X0),X0)
| ~ c_List_Odistinct(X12,X0) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1354]) ).
fof(f14279,plain,
( spl0_653
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5746,f4986,f1424,f1318,f1197,f14277]) ).
fof(f1197,plain,
( spl0_79
<=> ! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1318,plain,
( spl0_107
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f4986,plain,
( spl0_391
<=> ! [X5,X0,X3] : c_List_Olist_OCons(X5,c_List_Oreplicate(X3,X5,X0),X0) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f5746,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391 ),
inference(forward_demodulation,[],[f5745,f1198]) ).
fof(f1198,plain,
( ! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f5745,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,X1)
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391 ),
inference(forward_demodulation,[],[f5703,f1425]) ).
fof(f5703,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X1)
| ~ spl0_107
| ~ spl0_391 ),
inference(superposition,[],[f4987,f1319]) ).
fof(f1319,plain,
( ! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X5,X0)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f4987,plain,
( ! [X3,X0,X5] : c_List_Olist_OCons(X5,c_List_Oreplicate(X3,X5,X0),X0) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0)
| ~ spl0_391 ),
inference(avatar_component_clause,[],[f4986]) ).
fof(f14275,plain,
( spl0_652
| ~ spl0_93
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5713,f4986,f1253,f14273]) ).
fof(f14273,plain,
( spl0_652
<=> ! [X2,X0,X1] : c_List_Olist_ONil(X2) != c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f1253,plain,
( spl0_93
<=> ! [X38,X0,X24] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X24,X38,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f5713,plain,
( ! [X2,X0,X1] : c_List_Olist_ONil(X2) != c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X2)
| ~ spl0_93
| ~ spl0_391 ),
inference(superposition,[],[f1254,f4987]) ).
fof(f1254,plain,
( ! [X38,X0,X24] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X24,X38,X0)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f14271,plain,
( spl0_651
| ~ spl0_80
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5712,f4986,f1201,f14269]) ).
fof(f14269,plain,
( spl0_651
<=> ! [X2,X0,X1] : c_List_Omember(X0,c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1201,plain,
( spl0_80
<=> ! [X13,X0,X5] : c_List_Omember(X5,c_List_Olist_OCons(X5,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f5712,plain,
( ! [X2,X0,X1] : c_List_Omember(X0,c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X2),X2)
| ~ spl0_80
| ~ spl0_391 ),
inference(superposition,[],[f1202,f4987]) ).
fof(f1202,plain,
( ! [X0,X5,X13] : c_List_Omember(X5,c_List_Olist_OCons(X5,X13,X0),X0)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1201]) ).
fof(f14266,plain,
( spl0_650
| ~ spl0_79
| ~ spl0_103
| ~ spl0_129
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5694,f4978,f1424,f1302,f1197,f14264]) ).
fof(f14264,plain,
( spl0_650
<=> ! [X0,X1] : c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil(X0),X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f1302,plain,
( spl0_103
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f4978,plain,
( spl0_389
<=> ! [X5,X0,X27] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X27,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X27,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f5694,plain,
( ! [X0,X1] : c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil(X0),X0),tc_List_Olist(X0))
| ~ spl0_79
| ~ spl0_103
| ~ spl0_129
| ~ spl0_389 ),
inference(forward_demodulation,[],[f5693,f1198]) ).
fof(f5693,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil(X0),X0),tc_List_Olist(X0))
| ~ spl0_103
| ~ spl0_129
| ~ spl0_389 ),
inference(forward_demodulation,[],[f5594,f1425]) ).
fof(f5594,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,c_List_Olist_ONil(X0),X0),tc_List_Olist(X0))
| ~ spl0_103
| ~ spl0_389 ),
inference(superposition,[],[f4979,f1303]) ).
fof(f1303,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0))
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1302]) ).
fof(f4979,plain,
( ! [X0,X27,X5] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X27,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X27,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f4978]) ).
fof(f14262,plain,
( spl0_649
| ~ spl0_75
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5622,f4978,f1181,f14260]) ).
fof(f14260,plain,
( spl0_649
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1181,plain,
( spl0_75
<=> ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X6,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f5622,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_75
| ~ spl0_389 ),
inference(superposition,[],[f1182,f4979]) ).
fof(f1182,plain,
( ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X6,tc_nat),X6,tc_nat)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f14258,plain,
( spl0_648
| ~ spl0_156
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5614,f4978,f1533,f14256]) ).
fof(f14256,plain,
( spl0_648
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f1533,plain,
( spl0_156
<=> ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f5614,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1)),tc_nat)
| ~ spl0_156
| ~ spl0_389 ),
inference(superposition,[],[f1534,f4979]) ).
fof(f1534,plain,
( ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f14254,plain,
( spl0_647
| ~ spl0_150
| ~ spl0_281
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4755,f3802,f2655,f1508,f14252]) ).
fof(f14252,plain,
( spl0_647
<=> ! [X2,X0,X1] :
( c_List_Odistinct(c_List_Otl(c_List_Odrop(X0,X1,X2),X2),X2)
| ~ c_List_Odistinct(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1508,plain,
( spl0_150
<=> ! [X6,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Odrop(X6,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2655,plain,
( spl0_281
<=> ! [X0,X12,X3] : c_List_Odrop(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Odrop(X3,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f3802,plain,
( spl0_358
<=> ! [X0,X12,X3] : c_List_Odrop(X3,c_List_Otl(X12,X0),X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f4755,plain,
( ! [X2,X0,X1] :
( c_List_Odistinct(c_List_Otl(c_List_Odrop(X0,X1,X2),X2),X2)
| ~ c_List_Odistinct(X1,X2) )
| ~ spl0_150
| ~ spl0_281
| ~ spl0_358 ),
inference(forward_demodulation,[],[f4730,f2656]) ).
fof(f2656,plain,
( ! [X3,X0,X12] : c_List_Odrop(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Odrop(X3,X12,X0),X0)
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f2655]) ).
fof(f4730,plain,
( ! [X2,X0,X1] :
( c_List_Odistinct(c_List_Odrop(X0,c_List_Otl(X1,X2),X2),X2)
| ~ c_List_Odistinct(X1,X2) )
| ~ spl0_150
| ~ spl0_358 ),
inference(superposition,[],[f1509,f3803]) ).
fof(f3803,plain,
( ! [X3,X0,X12] : c_List_Odrop(X3,c_List_Otl(X12,X0),X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0)
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f3802]) ).
fof(f1509,plain,
( ! [X0,X6,X12] :
( c_List_Odistinct(c_List_Odrop(X6,X12,X0),X0)
| ~ c_List_Odistinct(X12,X0) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f14250,plain,
( spl0_646
| ~ spl0_149
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f4675,f3798,f1504,f14248]) ).
fof(f14248,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( ~ c_List_Odistinct(c_List_Orotate1(c_List_Olist_OCons(X1,X0,X2),X2),X2)
| c_List_Odistinct(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1504,plain,
( spl0_149
<=> ! [X13,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f3798,plain,
( spl0_357
<=> ! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X36),X36),X36) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f4675,plain,
( ! [X2,X0,X1] :
( ~ c_List_Odistinct(c_List_Orotate1(c_List_Olist_OCons(X1,X0,X2),X2),X2)
| c_List_Odistinct(X0,X2) )
| ~ spl0_149
| ~ spl0_357 ),
inference(superposition,[],[f1505,f3799]) ).
fof(f3799,plain,
( ! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X36),X36),X36)
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f3798]) ).
fof(f1505,plain,
( ! [X0,X12,X13] :
( ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0)
| c_List_Odistinct(X12,X0) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f14246,plain,
( spl0_645
| ~ spl0_105
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4573,f3777,f1310,f14244]) ).
fof(f14244,plain,
( spl0_645
<=> ! [X0,X3,X2,X1] : c_List_Ohd(c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1310,plain,
( spl0_105
<=> ! [X12,X5,X0] : c_List_Ohd(c_List_Olist_OCons(X5,X12,X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f3777,plain,
( spl0_352
<=> ! [X5,X13,X0,X12] : c_List_Oappend(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Oappend(X12,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f4573,plain,
( ! [X2,X3,X0,X1] : c_List_Ohd(c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3) = X0
| ~ spl0_105
| ~ spl0_352 ),
inference(superposition,[],[f1311,f3778]) ).
fof(f3778,plain,
( ! [X0,X5,X12,X13] : c_List_Oappend(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Oappend(X12,X13,X0),X0)
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f3777]) ).
fof(f1311,plain,
( ! [X0,X5,X12] : c_List_Ohd(c_List_Olist_OCons(X5,X12,X0),X0) = X5
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f14242,plain,
( spl0_644
| ~ spl0_120
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f4341,f3748,f1370,f14240]) ).
fof(f14240,plain,
( spl0_644
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f1370,plain,
( spl0_120
<=> ! [X21] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f3748,plain,
( spl0_345
<=> ! [X3,X4,X14] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f4341,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ spl0_120
| ~ spl0_345 ),
inference(superposition,[],[f1371,f3749]) ).
fof(f3749,plain,
( ! [X3,X14,X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat)
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f3748]) ).
fof(f1371,plain,
( ! [X21] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1370]) ).
fof(f14238,plain,
( spl0_643
| ~ spl0_222
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4221,f3744,f2001,f14236]) ).
fof(f14236,plain,
( spl0_643
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2001,plain,
( spl0_222
<=> ! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f3744,plain,
( spl0_344
<=> ! [X5,X7,X8] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f4221,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_222
| ~ spl0_344 ),
inference(superposition,[],[f2002,f3745]) ).
fof(f3745,plain,
( ! [X8,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat)
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f3744]) ).
fof(f2002,plain,
( ! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat),tc_nat)
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f14234,plain,
( spl0_642
| ~ spl0_106
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3644,f3155,f1314,f14232]) ).
fof(f14232,plain,
( spl0_642
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) = c_List_Osko__List__Xneq__Nil__conv__1__2(X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1314,plain,
( spl0_106
<=> ! [X5,X0,X12] : c_List_Otl(c_List_Olist_OCons(X5,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f3155,plain,
( spl0_320
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_OCons(c_List_Osko__List__Xneq__Nil__conv__1__1(X12,X0),c_List_Osko__List__Xneq__Nil__conv__1__2(X12,X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3644,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) = c_List_Osko__List__Xneq__Nil__conv__1__2(X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_106
| ~ spl0_320 ),
inference(superposition,[],[f1315,f3156]) ).
fof(f3156,plain,
( ! [X0,X12] :
( c_List_Olist_OCons(c_List_Osko__List__Xneq__Nil__conv__1__1(X12,X0),c_List_Osko__List__Xneq__Nil__conv__1__2(X12,X0),X0) = X12
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f1315,plain,
( ! [X0,X5,X12] : c_List_Otl(c_List_Olist_OCons(X5,X12,X0),X0) = X12
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f14230,plain,
( spl0_641
| ~ spl0_105
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3643,f3155,f1310,f14228]) ).
fof(f14228,plain,
( spl0_641
<=> ! [X0,X1] :
( c_List_Ohd(X0,X1) = c_List_Osko__List__Xneq__Nil__conv__1__1(X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f3643,plain,
( ! [X0,X1] :
( c_List_Ohd(X0,X1) = c_List_Osko__List__Xneq__Nil__conv__1__1(X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_105
| ~ spl0_320 ),
inference(superposition,[],[f1311,f3156]) ).
fof(f14226,plain,
( spl0_640
| ~ spl0_106
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3625,f3151,f1314,f14224]) ).
fof(f14224,plain,
( spl0_640
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) = c_List_Osko__List__Xlist__Xexhaust__1__2(X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f3151,plain,
( spl0_319
<=> ! [X0,X8] :
( c_List_Olist_ONil(X0) = X8
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X0),c_List_Osko__List__Xlist__Xexhaust__1__2(X8,X0),X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f3625,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) = c_List_Osko__List__Xlist__Xexhaust__1__2(X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_106
| ~ spl0_319 ),
inference(superposition,[],[f1315,f3152]) ).
fof(f3152,plain,
( ! [X0,X8] :
( c_List_Olist_OCons(c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X0),c_List_Osko__List__Xlist__Xexhaust__1__2(X8,X0),X0) = X8
| c_List_Olist_ONil(X0) = X8 )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f3151]) ).
fof(f14222,plain,
( spl0_639
| ~ spl0_105
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3624,f3151,f1310,f14220]) ).
fof(f14220,plain,
( spl0_639
<=> ! [X0,X1] :
( c_List_Ohd(X0,X1) = c_List_Osko__List__Xlist__Xexhaust__1__1(X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f3624,plain,
( ! [X0,X1] :
( c_List_Ohd(X0,X1) = c_List_Osko__List__Xlist__Xexhaust__1__1(X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_105
| ~ spl0_319 ),
inference(superposition,[],[f1311,f3152]) ).
fof(f14218,plain,
( spl0_638
| ~ spl0_106
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3606,f3147,f1314,f14216]) ).
fof(f14216,plain,
( spl0_638
<=> ! [X0,X1] :
( c_List_Otl(X0,X1) = c_List_Osko__List__Xlist__Xnchotomy__1__2(X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f3147,plain,
( spl0_318
<=> ! [X18,X0] :
( c_List_Olist_ONil(X0) = X18
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xnchotomy__1__1(X18,X0),c_List_Osko__List__Xlist__Xnchotomy__1__2(X18,X0),X0) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f3606,plain,
( ! [X0,X1] :
( c_List_Otl(X0,X1) = c_List_Osko__List__Xlist__Xnchotomy__1__2(X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_106
| ~ spl0_318 ),
inference(superposition,[],[f1315,f3148]) ).
fof(f3148,plain,
( ! [X0,X18] :
( c_List_Olist_OCons(c_List_Osko__List__Xlist__Xnchotomy__1__1(X18,X0),c_List_Osko__List__Xlist__Xnchotomy__1__2(X18,X0),X0) = X18
| c_List_Olist_ONil(X0) = X18 )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3147]) ).
fof(f14214,plain,
( spl0_637
| ~ spl0_105
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3605,f3147,f1310,f14212]) ).
fof(f14212,plain,
( spl0_637
<=> ! [X0,X1] :
( c_List_Ohd(X0,X1) = c_List_Osko__List__Xlist__Xnchotomy__1__1(X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f3605,plain,
( ! [X0,X1] :
( c_List_Ohd(X0,X1) = c_List_Osko__List__Xlist__Xnchotomy__1__1(X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_105
| ~ spl0_318 ),
inference(superposition,[],[f1311,f3148]) ).
fof(f14210,plain,
( spl0_636
| ~ spl0_188
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3383,f3047,f1865,f14208]) ).
fof(f14208,plain,
( spl0_636
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f1865,plain,
( spl0_188
<=> ! [X6,X14,X15] :
( c_HOL_Oord__class_Oless(X6,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f3383,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_188
| ~ spl0_294 ),
inference(resolution,[],[f3048,f1866]) ).
fof(f1866,plain,
( ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X14,tc_nat)
| c_HOL_Oord__class_Oless(X6,X14,tc_nat) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1865]) ).
fof(f14206,plain,
( spl0_635
| ~ spl0_155
| ~ spl0_621 ),
inference(avatar_split_clause,[],[f14112,f13758,f1529,f14203]) ).
fof(f14203,plain,
( spl0_635
<=> c_List_Odistinct(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1529,plain,
( spl0_155
<=> ! [X5,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Olist_OCons(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f13758,plain,
( spl0_621
<=> c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f14112,plain,
( c_List_Odistinct(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_155
| ~ spl0_621 ),
inference(resolution,[],[f13760,f1530]) ).
fof(f1530,plain,
( ! [X0,X5,X12] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X5,X12,X0),X0)
| c_List_Odistinct(X12,X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f13760,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_621 ),
inference(avatar_component_clause,[],[f13758]) ).
fof(f14201,plain,
( spl0_634
| ~ spl0_221
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3350,f3043,f1997,f14199]) ).
fof(f14199,plain,
( spl0_634
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f1997,plain,
( spl0_221
<=> ! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X4,X6,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f3350,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_221
| ~ spl0_293 ),
inference(resolution,[],[f3044,f1998]) ).
fof(f1998,plain,
( ! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X4,X6,tc_nat),tc_nat),tc_nat)
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f1997]) ).
fof(f14178,plain,
( ~ spl0_20
| spl0_633
| ~ spl0_99
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f2896,f2610,f1286,f14176,f922]) ).
fof(f14176,plain,
( spl0_633
<=> ! [X0,X1] :
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1286,plain,
( spl0_99
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2896,plain,
( ! [X0,X1] :
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X1,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_99
| ~ spl0_270 ),
inference(superposition,[],[f2611,f1287]) ).
fof(f1287,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f14174,plain,
( spl0_632
| ~ spl0_75
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2567,f2330,f1181,f14172]) ).
fof(f14172,plain,
( spl0_632
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f2567,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_75
| ~ spl0_257 ),
inference(resolution,[],[f2331,f1182]) ).
fof(f14170,plain,
( spl0_631
| ~ spl0_219
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2493,f2277,f1989,f14168]) ).
fof(f14168,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) != X1
| c_List_Olist_ONil(X2) = c_List_Otake(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1989,plain,
( spl0_219
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2277,plain,
( spl0_244
<=> ! [X0,X12,X3] : c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Odrop(X3,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2493,plain,
( ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) != X1
| c_List_Olist_ONil(X2) = c_List_Otake(X0,X1,X2) )
| ~ spl0_219
| ~ spl0_244 ),
inference(superposition,[],[f1990,f2278]) ).
fof(f2278,plain,
( ! [X3,X0,X12] : c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Odrop(X3,X12,X0),X0) = X12
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2277]) ).
fof(f1990,plain,
( ! [X0,X12,X13] :
( c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f1989]) ).
fof(f14166,plain,
( spl0_630
| ~ spl0_218
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2492,f2277,f1985,f14164]) ).
fof(f14164,plain,
( spl0_630
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) != X1
| c_List_Olist_ONil(X2) = c_List_Odrop(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1985,plain,
( spl0_218
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2492,plain,
( ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) != X1
| c_List_Olist_ONil(X2) = c_List_Odrop(X0,X1,X2) )
| ~ spl0_218
| ~ spl0_244 ),
inference(superposition,[],[f1986,f2278]) ).
fof(f1986,plain,
( ! [X0,X12,X13] :
( c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0)
| c_List_Olist_ONil(X0) = X13 )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f14161,plain,
( ~ spl0_20
| spl0_629
| ~ spl0_99
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2422,f2245,f1286,f14159,f922]) ).
fof(f14159,plain,
( spl0_629
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f2245,plain,
( spl0_236
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2422,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_99
| ~ spl0_236 ),
inference(superposition,[],[f2246,f1287]) ).
fof(f2246,plain,
( ! [X0,X8,X5] :
( c_Orderings_Oord__class_Omin(X5,X8,X0) != X5
| c_lessequals(X5,X8,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2245]) ).
fof(f14157,plain,
( spl0_628
| ~ spl0_125
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2358,f2219,f1408,f14155]) ).
fof(f14155,plain,
( spl0_628
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f1408,plain,
( spl0_125
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f2219,plain,
( spl0_230
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2358,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) )
| ~ spl0_125
| ~ spl0_230 ),
inference(resolution,[],[f2220,f1409]) ).
fof(f1409,plain,
( ! [X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1408]) ).
fof(f2220,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2219]) ).
fof(f14153,plain,
( spl0_627
| ~ spl0_129
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2174,f1993,f1424,f14151]) ).
fof(f14151,plain,
( spl0_627
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1993,plain,
( spl0_220
<=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2174,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_220 ),
inference(superposition,[],[f1994,f1425]) ).
fof(f1994,plain,
( ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f1993]) ).
fof(f14149,plain,
( spl0_626
| ~ spl0_78
| ~ spl0_615 ),
inference(avatar_split_clause,[],[f13890,f13254,f1193,f14147]) ).
fof(f14147,plain,
( spl0_626
<=> ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1193,plain,
( spl0_78
<=> ! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f13254,plain,
( spl0_615
<=> ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f13890,plain,
( ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1)
| ~ spl0_78
| ~ spl0_615 ),
inference(superposition,[],[f13255,f1194]) ).
fof(f1194,plain,
( ! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f13255,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X2),X2)
| ~ spl0_615 ),
inference(avatar_component_clause,[],[f13254]) ).
fof(f14145,plain,
( spl0_625
| ~ spl0_136
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2125,f1921,f1452,f14143]) ).
fof(f14143,plain,
( spl0_625
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_List_Oreplicate(X0,X1,X2) = c_List_Olist_ONil(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f1921,plain,
( spl0_202
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2125,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_List_Oreplicate(X0,X1,X2) = c_List_Olist_ONil(X2) )
| ~ spl0_136
| ~ spl0_202 ),
inference(superposition,[],[f1922,f1453]) ).
fof(f1922,plain,
( ! [X0,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0))
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f14141,plain,
( spl0_624
| ~ spl0_129
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2013,f1865,f1424,f14139]) ).
fof(f14139,plain,
( spl0_624
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2013,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_129
| ~ spl0_188 ),
inference(superposition,[],[f1866,f1425]) ).
fof(f14118,plain,
( ~ spl0_20
| spl0_623
| ~ spl0_157
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1744,f1631,f1537,f14116,f922]) ).
fof(f14116,plain,
( spl0_623
<=> ! [X0] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1744,plain,
( ! [X0] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_157
| ~ spl0_159 ),
inference(resolution,[],[f1632,f1538]) ).
fof(f13887,plain,
( spl0_622
| ~ spl0_549
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f13017,f11559,f10262,f13885]) ).
fof(f13885,plain,
( spl0_622
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_Int_Oint),X1,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f10262,plain,
( spl0_549
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f11559,plain,
( spl0_572
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f13017,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_Int_Oint),X1,tc_Int_Oint) = X0
| ~ spl0_549
| ~ spl0_572 ),
inference(superposition,[],[f11560,f10263]) ).
fof(f10263,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Int_Oint)
| ~ spl0_549 ),
inference(avatar_component_clause,[],[f10262]) ).
fof(f11560,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f11559]) ).
fof(f13761,plain,
( spl0_621
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_605 ),
inference(avatar_split_clause,[],[f13216,f13212,f4986,f1424,f1318,f1197,f13758]) ).
fof(f13212,plain,
( spl0_605
<=> c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f13216,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_605 ),
inference(forward_demodulation,[],[f13214,f5746]) ).
fof(f13214,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_605 ),
inference(avatar_component_clause,[],[f13212]) ).
fof(f13694,plain,
( spl0_620
| ~ spl0_549
| ~ spl0_554 ),
inference(avatar_split_clause,[],[f12862,f10552,f10262,f13692]) ).
fof(f13692,plain,
( spl0_620
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f10552,plain,
( spl0_554
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f12862,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_549
| ~ spl0_554 ),
inference(superposition,[],[f10553,f10263]) ).
fof(f10553,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0
| ~ spl0_554 ),
inference(avatar_component_clause,[],[f10552]) ).
fof(f13272,plain,
( spl0_619
| ~ spl0_78
| ~ spl0_108
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f6842,f6406,f1322,f1193,f13270]) ).
fof(f13270,plain,
( spl0_619
<=> ! [X2,X0,X1] : c_List_Olist_ONil(X2) = c_List_Odrop(X0,c_List_Otake(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f1322,plain,
( spl0_108
<=> ! [X0,X12] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f6406,plain,
( spl0_437
<=> ! [X4,X0,X12,X3] : c_List_Otake(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(X4,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f6842,plain,
( ! [X2,X0,X1] : c_List_Olist_ONil(X2) = c_List_Odrop(X0,c_List_Otake(X0,X1,X2),X2)
| ~ spl0_78
| ~ spl0_108
| ~ spl0_437 ),
inference(forward_demodulation,[],[f6823,f1323]) ).
fof(f1323,plain,
( ! [X0,X12] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0)
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f6823,plain,
( ! [X2,X0,X1] : c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Odrop(X0,X1,X2),X2) = c_List_Odrop(X0,c_List_Otake(X0,X1,X2),X2)
| ~ spl0_78
| ~ spl0_437 ),
inference(superposition,[],[f6407,f1194]) ).
fof(f6407,plain,
( ! [X3,X0,X4,X12] : c_List_Otake(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(X4,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),X0)
| ~ spl0_437 ),
inference(avatar_component_clause,[],[f6406]) ).
fof(f13268,plain,
( spl0_618
| ~ spl0_77
| ~ spl0_99
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f6783,f6398,f1286,f1189,f13266]) ).
fof(f13266,plain,
( spl0_618
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1189,plain,
( spl0_77
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f6398,plain,
( spl0_435
<=> ! [X6,X4,X3] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X4,X6,tc_nat),c_HOL_Ominus__class_Ominus(X3,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X4,X3,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f6783,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat)
| ~ spl0_77
| ~ spl0_99
| ~ spl0_435 ),
inference(forward_demodulation,[],[f6749,f1287]) ).
fof(f6749,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_77
| ~ spl0_435 ),
inference(superposition,[],[f6399,f1190]) ).
fof(f1190,plain,
( ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,X4,tc_nat)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f6399,plain,
( ! [X3,X6,X4] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X4,X6,tc_nat),c_HOL_Ominus__class_Ominus(X3,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X4,X3,tc_nat),X6,tc_nat)
| ~ spl0_435 ),
inference(avatar_component_clause,[],[f6398]) ).
fof(f13264,plain,
( spl0_617
| ~ spl0_77
| ~ spl0_98
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f6778,f6398,f1282,f1189,f13262]) ).
fof(f13262,plain,
( spl0_617
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1282,plain,
( spl0_98
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f6778,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_77
| ~ spl0_98
| ~ spl0_435 ),
inference(forward_demodulation,[],[f6738,f1283]) ).
fof(f1283,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f6738,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| ~ spl0_77
| ~ spl0_435 ),
inference(superposition,[],[f6399,f1190]) ).
fof(f13260,plain,
( spl0_616
| ~ spl0_77
| ~ spl0_108
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f6253,f5979,f1322,f1189,f13258]) ).
fof(f13258,plain,
( spl0_616
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Otl(c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f5979,plain,
( spl0_419
<=> ! [X0,X12,X3] : c_List_Otl(c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f6253,plain,
( ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Otl(c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1)
| ~ spl0_77
| ~ spl0_108
| ~ spl0_419 ),
inference(forward_demodulation,[],[f6238,f1323]) ).
fof(f6238,plain,
( ! [X0,X1] : c_List_Otl(c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Otl(X0,X1),X1)
| ~ spl0_77
| ~ spl0_419 ),
inference(superposition,[],[f5980,f1190]) ).
fof(f5980,plain,
( ! [X3,X0,X12] : c_List_Otl(c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X12,X0),X0)
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f5979]) ).
fof(f13256,plain,
( spl0_615
| ~ spl0_71
| ~ spl0_391 ),
inference(avatar_split_clause,[],[f5710,f4986,f1165,f13254]) ).
fof(f1165,plain,
( spl0_71
<=> ! [X5,X0,X12] : ~ c_List_Onull(c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f5710,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X2),X2)
| ~ spl0_71
| ~ spl0_391 ),
inference(superposition,[],[f1166,f4987]) ).
fof(f1166,plain,
( ! [X0,X5,X12] : ~ c_List_Onull(c_List_Olist_OCons(X5,X12,X0),X0)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1165]) ).
fof(f13252,plain,
( spl0_614
| ~ spl0_120
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5612,f4978,f1370,f13250]) ).
fof(f13250,plain,
( spl0_614
<=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f5612,plain,
( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(c_List_Olist_OCons(X2,X0,X1),tc_List_Olist(X1))
| ~ spl0_120
| ~ spl0_389 ),
inference(superposition,[],[f1371,f4979]) ).
fof(f13248,plain,
( spl0_613
| ~ spl0_377
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5416,f4934,f4930,f13246]) ).
fof(f13246,plain,
( spl0_613
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f4930,plain,
( spl0_377
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f4934,plain,
( spl0_378
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f5416,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1) )
| ~ spl0_377
| ~ spl0_378 ),
inference(duplicate_literal_removal,[],[f5383]) ).
fof(f5383,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_377
| ~ spl0_378 ),
inference(resolution,[],[f4935,f4931]) ).
fof(f4931,plain,
( ! [X10,X0,X1,X9] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_lessequals(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f4930]) ).
fof(f4935,plain,
( ! [X10,X0,X1,X9] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0)
| ~ c_lessequals(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f4934]) ).
fof(f13244,plain,
( ~ spl0_20
| spl0_612
| ~ spl0_159
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4422,f3583,f1631,f13242,f922]) ).
fof(f13242,plain,
( spl0_612
<=> ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f3583,plain,
( spl0_325
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f4422,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_159
| ~ spl0_325 ),
inference(resolution,[],[f3584,f1632]) ).
fof(f3584,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f3583]) ).
fof(f13240,plain,
( spl0_611
| ~ spl0_371
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f5260,f4914,f4906,f13238]) ).
fof(f13238,plain,
( spl0_611
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f4906,plain,
( spl0_371
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f4914,plain,
( spl0_373
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f5260,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_371
| ~ spl0_373 ),
inference(duplicate_literal_removal,[],[f5227]) ).
fof(f5227,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_371
| ~ spl0_373 ),
inference(resolution,[],[f4915,f4907]) ).
fof(f4907,plain,
( ! [X10,X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f4906]) ).
fof(f4915,plain,
( ! [X10,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f4914]) ).
fof(f13236,plain,
( spl0_610
| ~ spl0_93
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4572,f3777,f1253,f13234]) ).
fof(f13234,plain,
( spl0_610
<=> ! [X0,X3,X2,X1] : c_List_Olist_ONil(X3) != c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f4572,plain,
( ! [X2,X3,X0,X1] : c_List_Olist_ONil(X3) != c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3)
| ~ spl0_93
| ~ spl0_352 ),
inference(superposition,[],[f1254,f3778]) ).
fof(f13232,plain,
( spl0_609
| ~ spl0_80
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4571,f3777,f1201,f13230]) ).
fof(f13230,plain,
( spl0_609
<=> ! [X0,X3,X2,X1] : c_List_Omember(X0,c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f4571,plain,
( ! [X2,X3,X0,X1] : c_List_Omember(X0,c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3)
| ~ spl0_80
| ~ spl0_352 ),
inference(superposition,[],[f1202,f3778]) ).
fof(f13228,plain,
( spl0_608
| ~ spl0_80
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3641,f3155,f1201,f13226]) ).
fof(f13226,plain,
( spl0_608
<=> ! [X0,X1] :
( c_List_Omember(c_List_Osko__List__Xneq__Nil__conv__1__1(X0,X1),X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f3641,plain,
( ! [X0,X1] :
( c_List_Omember(c_List_Osko__List__Xneq__Nil__conv__1__1(X0,X1),X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_80
| ~ spl0_320 ),
inference(superposition,[],[f1202,f3156]) ).
fof(f13224,plain,
( spl0_607
| ~ spl0_80
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3622,f3151,f1201,f13222]) ).
fof(f13222,plain,
( spl0_607
<=> ! [X0,X1] :
( c_List_Omember(c_List_Osko__List__Xlist__Xexhaust__1__1(X0,X1),X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f3622,plain,
( ! [X0,X1] :
( c_List_Omember(c_List_Osko__List__Xlist__Xexhaust__1__1(X0,X1),X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_80
| ~ spl0_319 ),
inference(superposition,[],[f1202,f3152]) ).
fof(f13220,plain,
( spl0_606
| ~ spl0_80
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3603,f3147,f1201,f13218]) ).
fof(f13218,plain,
( spl0_606
<=> ! [X0,X1] :
( c_List_Omember(c_List_Osko__List__Xlist__Xnchotomy__1__1(X0,X1),X0,X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f3603,plain,
( ! [X0,X1] :
( c_List_Omember(c_List_Osko__List__Xlist__Xnchotomy__1__1(X0,X1),X0,X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_80
| ~ spl0_318 ),
inference(superposition,[],[f1202,f3148]) ).
fof(f13215,plain,
( spl0_605
| ~ spl0_155
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f2995,f2659,f1529,f13212]) ).
fof(f2659,plain,
( spl0_282
<=> c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__1,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2995,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_155
| ~ spl0_282 ),
inference(resolution,[],[f2661,f1530]) ).
fof(f2661,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__1,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f2659]) ).
fof(f13210,plain,
( spl0_604
| ~ spl0_78
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2569,f2330,f1193,f13208]) ).
fof(f13208,plain,
( spl0_604
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2569,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_78
| ~ spl0_257 ),
inference(superposition,[],[f2331,f1194]) ).
fof(f13206,plain,
( spl0_603
| ~ spl0_91
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2522,f2293,f1245,f13204]) ).
fof(f13204,plain,
( spl0_603
<=> ! [X2,X0,X1] :
( c_List_Oappend(c_List_Olist_ONil(X0),X2,X0) != X1
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1245,plain,
( spl0_91
<=> ! [X5,X0] : c_List_Oappend(c_List_Olist_ONil(X0),X5,X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f2293,plain,
( spl0_248
<=> ! [X13,X0,X12,X28] :
( X13 = X28
| c_List_Oappend(X12,X13,X0) != c_List_Oappend(X12,X28,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2522,plain,
( ! [X2,X0,X1] :
( c_List_Oappend(c_List_Olist_ONil(X0),X2,X0) != X1
| X1 = X2 )
| ~ spl0_91
| ~ spl0_248 ),
inference(superposition,[],[f2294,f1246]) ).
fof(f1246,plain,
( ! [X0,X5] : c_List_Oappend(c_List_Olist_ONil(X0),X5,X0) = X5
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1245]) ).
fof(f2294,plain,
( ! [X28,X0,X12,X13] :
( c_List_Oappend(X12,X13,X0) != c_List_Oappend(X12,X28,X0)
| X13 = X28 )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2293]) ).
fof(f13202,plain,
( spl0_602
| ~ spl0_90
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2514,f2289,f1241,f13200]) ).
fof(f13200,plain,
( spl0_602
<=> ! [X2,X0,X1] :
( c_List_Oappend(X2,c_List_Olist_ONil(X1),X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f1241,plain,
( spl0_90
<=> ! [X0,X12] : c_List_Oappend(X12,c_List_Olist_ONil(X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f2289,plain,
( spl0_247
<=> ! [X13,X0,X12,X28] :
( X13 = X28
| c_List_Oappend(X13,X12,X0) != c_List_Oappend(X28,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2514,plain,
( ! [X2,X0,X1] :
( c_List_Oappend(X2,c_List_Olist_ONil(X1),X1) != X0
| X0 = X2 )
| ~ spl0_90
| ~ spl0_247 ),
inference(superposition,[],[f2290,f1242]) ).
fof(f1242,plain,
( ! [X0,X12] : c_List_Oappend(X12,c_List_Olist_ONil(X0),X0) = X12
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1241]) ).
fof(f2290,plain,
( ! [X28,X0,X12,X13] :
( c_List_Oappend(X13,X12,X0) != c_List_Oappend(X28,X12,X0)
| X13 = X28 )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2289]) ).
fof(f13193,plain,
( spl0_601
| ~ spl0_79
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2470,f2265,f1197,f13191]) ).
fof(f13191,plain,
( spl0_601
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f2265,plain,
( spl0_241
<=> ! [X4,X3,X14] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2470,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
| X0 = X1 )
| ~ spl0_79
| ~ spl0_241 ),
inference(superposition,[],[f2266,f1198]) ).
fof(f2266,plain,
( ! [X3,X14,X4] :
( c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X14,tc_nat)
| X3 = X4 )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2265]) ).
fof(f13189,plain,
( spl0_600
| ~ spl0_78
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2460,f2261,f1193,f13187]) ).
fof(f13187,plain,
( spl0_600
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f2460,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
| X0 = X1 )
| ~ spl0_78
| ~ spl0_240 ),
inference(superposition,[],[f2262,f1194]) ).
fof(f13185,plain,
( spl0_599
| ~ spl0_90
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2394,f2231,f1241,f13183]) ).
fof(f13183,plain,
( spl0_599
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Odrop(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f2394,plain,
( ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Odrop(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1)
| ~ spl0_90
| ~ spl0_233 ),
inference(superposition,[],[f2232,f1242]) ).
fof(f13181,plain,
( spl0_598
| ~ spl0_75
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2046,f1877,f1181,f13179]) ).
fof(f13179,plain,
( spl0_598
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1877,plain,
( spl0_191
<=> ! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X4,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2046,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ spl0_75
| ~ spl0_191 ),
inference(resolution,[],[f1878,f1182]) ).
fof(f1878,plain,
( ! [X6,X4,X15] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X4,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f13177,plain,
( spl0_597
| ~ spl0_75
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2028,f1869,f1181,f13175]) ).
fof(f13175,plain,
( spl0_597
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1869,plain,
( spl0_189
<=> ! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X15,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2028,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat)
| ~ spl0_75
| ~ spl0_189 ),
inference(resolution,[],[f1870,f1182]) ).
fof(f1870,plain,
( ! [X6,X4,X15] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X15,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1869]) ).
fof(f13173,plain,
( spl0_596
| ~ spl0_83
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1860,f1727,f1213,f13171]) ).
fof(f13171,plain,
( spl0_596
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) != X0
| c_List_Olist_ONil(X1) = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1213,plain,
( spl0_83
<=> ! [X0,X12] : c_List_Orev(c_List_Orev(X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1727,plain,
( spl0_183
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orev(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1860,plain,
( ! [X0,X1] :
( c_List_Olist_ONil(X1) != X0
| c_List_Olist_ONil(X1) = c_List_Orev(X0,X1) )
| ~ spl0_83
| ~ spl0_183 ),
inference(superposition,[],[f1728,f1214]) ).
fof(f1214,plain,
( ! [X0,X12] : c_List_Orev(c_List_Orev(X12,X0),X0) = X12
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f1728,plain,
( ! [X0,X12] :
( c_List_Olist_ONil(X0) != c_List_Orev(X12,X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1727]) ).
fof(f13169,plain,
( spl0_595
| ~ spl0_83
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1850,f1711,f1213,f13167]) ).
fof(f13167,plain,
( spl0_595
<=> ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1711,plain,
( spl0_179
<=> ! [X13,X0,X12] :
( X12 = X13
| c_List_Orev(X12,X0) != c_List_Orev(X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1850,plain,
( ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 )
| ~ spl0_83
| ~ spl0_179 ),
inference(superposition,[],[f1712,f1214]) ).
fof(f1712,plain,
( ! [X0,X12,X13] :
( c_List_Orev(X12,X0) != c_List_Orev(X13,X0)
| X12 = X13 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f13165,plain,
( spl0_594
| ~ spl0_129
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1844,f1703,f1424,f13163]) ).
fof(f13163,plain,
( spl0_594
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1703,plain,
( spl0_177
<=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1844,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_177 ),
inference(superposition,[],[f1704,f1425]) ).
fof(f1704,plain,
( ! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1703]) ).
fof(f13161,plain,
( spl0_593
| ~ spl0_129
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1821,f1675,f1424,f13159]) ).
fof(f13159,plain,
( spl0_593
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1675,plain,
( spl0_170
<=> ! [X5,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1821,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_129
| ~ spl0_170 ),
inference(superposition,[],[f1676,f1425]) ).
fof(f1676,plain,
( ! [X1,X5] :
( c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1675]) ).
fof(f13157,plain,
( spl0_592
| ~ spl0_159
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1811,f1667,f1631,f13155]) ).
fof(f13155,plain,
( spl0_592
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1811,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) )
| ~ spl0_159
| ~ spl0_168 ),
inference(duplicate_literal_removal,[],[f1810]) ).
fof(f1810,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_159
| ~ spl0_168 ),
inference(resolution,[],[f1668,f1632]) ).
fof(f13153,plain,
( spl0_591
| ~ spl0_150
| ~ spl0_589 ),
inference(avatar_split_clause,[],[f13125,f12580,f1508,f13151]) ).
fof(f13151,plain,
( spl0_591
<=> ! [X0,X1] :
( c_List_Odistinct(c_List_Otl(X0,X1),X1)
| ~ c_List_Odistinct(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f12580,plain,
( spl0_589
<=> ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f13125,plain,
( ! [X0,X1] :
( c_List_Odistinct(c_List_Otl(X0,X1),X1)
| ~ c_List_Odistinct(X0,X1) )
| ~ spl0_150
| ~ spl0_589 ),
inference(superposition,[],[f1509,f12581]) ).
fof(f12581,plain,
( ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_589 ),
inference(avatar_component_clause,[],[f12580]) ).
fof(f13149,plain,
( spl0_590
| ~ spl0_121
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1773,f1643,f1374,f13147]) ).
fof(f13147,plain,
( spl0_590
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f1374,plain,
( spl0_121
<=> ! [X3] : c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1773,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X0
| ~ spl0_121
| ~ spl0_162 ),
inference(resolution,[],[f1644,f1375]) ).
fof(f1375,plain,
( ! [X3] : c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1374]) ).
fof(f12582,plain,
( spl0_589
| ~ spl0_79
| ~ spl0_81
| ~ spl0_129
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4737,f3802,f1424,f1205,f1197,f12580]) ).
fof(f1205,plain,
( spl0_81
<=> ! [X0,X12] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f4737,plain,
( ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_79
| ~ spl0_81
| ~ spl0_129
| ~ spl0_358 ),
inference(forward_demodulation,[],[f4736,f1198]) ).
fof(f4736,plain,
( ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0,X1)
| ~ spl0_81
| ~ spl0_129
| ~ spl0_358 ),
inference(forward_demodulation,[],[f4703,f1425]) ).
fof(f4703,plain,
( ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,X1)
| ~ spl0_81
| ~ spl0_358 ),
inference(superposition,[],[f3803,f1206]) ).
fof(f1206,plain,
( ! [X0,X12] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) = X12
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1205]) ).
fof(f12578,plain,
( spl0_588
| ~ spl0_71
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f4569,f3777,f1165,f12576]) ).
fof(f12576,plain,
( spl0_588
<=> ! [X2,X0,X1,X3] : ~ c_List_Onull(c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f4569,plain,
( ! [X2,X3,X0,X1] : ~ c_List_Onull(c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3)
| ~ spl0_71
| ~ spl0_352 ),
inference(superposition,[],[f1166,f3778]) ).
fof(f12574,plain,
( spl0_587
| ~ spl0_73
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3640,f3155,f1173,f12572]) ).
fof(f12572,plain,
( spl0_587
<=> ! [X0,X1] :
( c_List_Osko__List__Xneq__Nil__conv__1__2(X0,X1) != X0
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1173,plain,
( spl0_73
<=> ! [X5,X0,X39] : c_List_Olist_OCons(X5,X39,X0) != X39 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f3640,plain,
( ! [X0,X1] :
( c_List_Osko__List__Xneq__Nil__conv__1__2(X0,X1) != X0
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_73
| ~ spl0_320 ),
inference(superposition,[],[f1174,f3156]) ).
fof(f1174,plain,
( ! [X39,X0,X5] : c_List_Olist_OCons(X5,X39,X0) != X39
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f12570,plain,
( spl0_586
| ~ spl0_73
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3621,f3151,f1173,f12568]) ).
fof(f12568,plain,
( spl0_586
<=> ! [X0,X1] :
( c_List_Osko__List__Xlist__Xexhaust__1__2(X0,X1) != X0
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f3621,plain,
( ! [X0,X1] :
( c_List_Osko__List__Xlist__Xexhaust__1__2(X0,X1) != X0
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_73
| ~ spl0_319 ),
inference(superposition,[],[f1174,f3152]) ).
fof(f12566,plain,
( spl0_585
| ~ spl0_73
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3602,f3147,f1173,f12564]) ).
fof(f12564,plain,
( spl0_585
<=> ! [X0,X1] :
( c_List_Osko__List__Xlist__Xnchotomy__1__2(X0,X1) != X0
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f3602,plain,
( ! [X0,X1] :
( c_List_Osko__List__Xlist__Xnchotomy__1__2(X0,X1) != X0
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_73
| ~ spl0_318 ),
inference(superposition,[],[f1174,f3148]) ).
fof(f12562,plain,
( spl0_584
| ~ spl0_191
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2541,f2326,f1877,f12560]) ).
fof(f12560,plain,
( spl0_584
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2541,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
| ~ spl0_191
| ~ spl0_256 ),
inference(resolution,[],[f2327,f1878]) ).
fof(f12405,plain,
spl0_583,
inference(avatar_split_clause,[],[f786,f12403]) ).
fof(f12403,plain,
( spl0_583
<=> ! [X4,X0,X12,X3] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X4,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X4,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f786,plain,
! [X3,X0,X4,X12] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X4,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X4,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),X0),
inference(forward_demodulation,[],[f715,f698]) ).
fof(f698,plain,
! [X3,X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),tc_List_Olist(X0)),
inference(definition_unfolding,[],[f225,f413]) ).
fof(f413,axiom,
! [X3,X0,X12] : c_List_Orotate(X3,X12,X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__drop__take_0) ).
fof(f225,axiom,
! [X3,X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate(X3,X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate_0) ).
fof(f715,plain,
! [X3,X0,X4,X12] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X4,c_Nat_Osize__class_Osize(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),tc_List_Olist(X0)),tc_nat),c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X4,c_Nat_Osize__class_Osize(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),tc_List_Olist(X0)),tc_nat),c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),
inference(definition_unfolding,[],[f405,f413,f413,f413]) ).
fof(f405,axiom,
! [X3,X0,X4,X12] : c_List_Orotate(X4,c_List_Orotate(X3,X12,X0),X0) = c_List_Orotate(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).
fof(f12267,plain,
spl0_582,
inference(avatar_split_clause,[],[f793,f12265]) ).
fof(f12265,plain,
( spl0_582
<=> ! [X0,X12,X3] : c_List_Orev(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orev(X12,X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orev(X12,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f793,plain,
! [X3,X0,X12] : c_List_Orev(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orev(X12,X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orev(X12,X0),X0),X0),
inference(forward_demodulation,[],[f721,f272]) ).
fof(f272,axiom,
! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).
fof(f721,plain,
! [X3,X0,X12] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(c_List_Orev(X12,X0),tc_List_Olist(X0)),tc_nat),c_List_Orev(X12,X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(c_List_Orev(X12,X0),tc_List_Olist(X0)),tc_nat),c_List_Orev(X12,X0),X0),X0) = c_List_Orev(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),
inference(definition_unfolding,[],[f323,f413,f413]) ).
fof(f323,axiom,
! [X3,X0,X12] : c_List_Orotate(X3,c_List_Orev(X12,X0),X0) = c_List_Orev(c_List_Orotate(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rev_0) ).
fof(f12143,plain,
spl0_581,
inference(avatar_split_clause,[],[f713,f12141]) ).
fof(f12141,plain,
( spl0_581
<=> ! [X0,X12,X3] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f713,plain,
! [X3,X0,X12] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),
inference(definition_unfolding,[],[f182,f413,f413]) ).
fof(f182,axiom,
! [X3,X0,X12] : c_List_Orotate(X3,X12,X0) = c_List_Orotate(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__conv__mod_0) ).
fof(f12139,plain,
spl0_580,
inference(avatar_split_clause,[],[f425,f12137]) ).
fof(f12137,plain,
( spl0_580
<=> ! [X31,X0,X29,X30] :
( c_List_Otake(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0) != X29
| c_List_Otake(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0) != X30
| c_List_Oappend(X30,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) = c_List_Oappend(X29,X31,X0)
| c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) != X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f425,axiom,
! [X31,X29,X0,X30] :
( c_List_Otake(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0) != X29
| c_List_Otake(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0) != X30
| c_List_Oappend(X30,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) = c_List_Oappend(X29,X31,X0)
| c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) != X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
fof(f11941,plain,
( spl0_579
| ~ spl0_90
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2385,f2227,f1241,f11939]) ).
fof(f11939,plain,
( spl0_579
<=> ! [X0,X1] : c_List_Otake(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2227,plain,
( spl0_232
<=> ! [X13,X0,X12] : c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2385,plain,
( ! [X0,X1] : c_List_Otake(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0
| ~ spl0_90
| ~ spl0_232 ),
inference(superposition,[],[f2228,f1242]) ).
fof(f2228,plain,
( ! [X0,X12,X13] : c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X12
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2227]) ).
fof(f11937,plain,
spl0_578,
inference(avatar_split_clause,[],[f699,f11935]) ).
fof(f11935,plain,
( spl0_578
<=> ! [X0,X12,X3] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) = c_List_Orotate1(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f699,plain,
! [X3,X0,X12] : c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) = c_List_Orotate1(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0),
inference(definition_unfolding,[],[f420,f413,f314,f413]) ).
fof(f314,axiom,
! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f420,axiom,
! [X3,X0,X12] : c_List_Orotate(c_Suc(X3),X12,X0) = c_List_Orotate1(c_List_Orotate(X3,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__Suc_0) ).
fof(f11853,plain,
spl0_577,
inference(avatar_split_clause,[],[f783,f11851]) ).
fof(f11851,plain,
( spl0_577
<=> ! [X0,X12,X3] : c_List_Orotate1(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orotate1(X12,X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orotate1(X12,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f783,plain,
! [X3,X0,X12] : c_List_Orotate1(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orotate1(X12,X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),c_List_Orotate1(X12,X0),X0),X0),
inference(forward_demodulation,[],[f707,f227]) ).
fof(f227,axiom,
! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
fof(f707,plain,
! [X3,X0,X12] : c_List_Orotate1(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(c_List_Orotate1(X12,X0),tc_List_Olist(X0)),tc_nat),c_List_Orotate1(X12,X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(c_List_Orotate1(X12,X0),tc_List_Olist(X0)),tc_nat),c_List_Orotate1(X12,X0),X0),X0),
inference(definition_unfolding,[],[f500,f413,f413]) ).
fof(f500,axiom,
! [X3,X0,X12] : c_List_Orotate1(c_List_Orotate(X3,X12,X0),X0) = c_List_Orotate(X3,c_List_Orotate1(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
fof(f11779,plain,
spl0_576,
inference(avatar_split_clause,[],[f809,f11777]) ).
fof(f11777,plain,
( spl0_576
<=> ! [X0,X14,X12,X5] :
( c_List_Olist__update(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X14,X5,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist__update(X12,X14,X5,X0),X0)
| c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f809,plain,
! [X0,X14,X5,X12] :
( c_List_Olist__update(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X14,X5,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist__update(X12,X14,X5,X0),X0)
| c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14 ),
inference(forward_demodulation,[],[f753,f389]) ).
fof(f389,axiom,
! [X0,X6,X5,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X12,X6,X5,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).
fof(f753,plain,
! [X0,X14,X5,X12] :
( c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist__update(X12,X14,X5,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist__update(X12,X14,X5,X0),X0) = c_List_Olist__update(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X14,X5,X0) ),
inference(definition_unfolding,[],[f284,f282,f282]) ).
fof(f282,axiom,
! [X0,X12] : c_List_Obutlast(X12,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__conv__take_0) ).
fof(f284,axiom,
! [X0,X14,X5,X12] :
( c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Obutlast(c_List_Olist__update(X12,X14,X5,X0),X0) = c_List_Olist__update(c_List_Obutlast(X12,X0),X14,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_1) ).
fof(f11661,plain,
( spl0_575
| ~ spl0_433
| ~ spl0_571 ),
inference(avatar_split_clause,[],[f11557,f11554,f6366,f11659]) ).
fof(f11659,plain,
( spl0_575
<=> ! [X13,X0,X12] :
( c_List_Oappend(X12,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X13,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Oappend(X12,X13,X0),X0)
| c_List_Olist_ONil(X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f6366,plain,
( spl0_433
<=> ! [X13,X0,X12] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f11554,plain,
( spl0_571
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(X12,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f11557,plain,
( ! [X0,X12,X13] :
( c_List_Oappend(X12,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X13,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Oappend(X12,X13,X0),X0)
| c_List_Olist_ONil(X0) = X13 )
| ~ spl0_433
| ~ spl0_571 ),
inference(forward_demodulation,[],[f11555,f6367]) ).
fof(f6367,plain,
( ! [X0,X12,X13] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0))
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f6366]) ).
fof(f11555,plain,
( ! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(X12,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X13,X0),X0) )
| ~ spl0_571 ),
inference(avatar_component_clause,[],[f11554]) ).
fof(f11570,plain,
( spl0_574
| ~ spl0_178
| ~ spl0_335
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f11566,f11563,f3708,f1707,f11568]) ).
fof(f11568,plain,
( spl0_574
<=> ! [X5,X0,X12] :
( c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) = c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Olist_OCons(X5,X12,X0),X0)
| c_List_Olist_ONil(X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1707,plain,
( spl0_178
<=> ! [X5,X0,X12] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f3708,plain,
( spl0_335
<=> ! [X0,X12,X3] : c_Nat_Osize__class_Osize(c_List_Odrop(X3,X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f11563,plain,
( spl0_573
<=> ! [X5,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X12,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f11566,plain,
( ! [X0,X5,X12] :
( c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) = c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Olist_OCons(X5,X12,X0),X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_178
| ~ spl0_335
| ~ spl0_573 ),
inference(forward_demodulation,[],[f11564,f3981]) ).
fof(f3981,plain,
( ! [X2,X0,X1] : c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X0,X1,X2),tc_List_Olist(X2)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_178
| ~ spl0_335 ),
inference(superposition,[],[f3709,f1708]) ).
fof(f1708,plain,
( ! [X0,X5,X12] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = X12
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1707]) ).
fof(f3709,plain,
( ! [X3,X0,X12] : c_Nat_Osize__class_Osize(c_List_Odrop(X3,X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat)
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f3708]) ).
fof(f11564,plain,
( ! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X12,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) )
| ~ spl0_573 ),
inference(avatar_component_clause,[],[f11563]) ).
fof(f11565,plain,
spl0_573,
inference(avatar_split_clause,[],[f735,f11563]) ).
fof(f735,plain,
! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X12,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ),
inference(definition_unfolding,[],[f585,f282,f282]) ).
fof(f585,axiom,
! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Obutlast(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Obutlast(X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
fof(f11561,plain,
( spl0_572
| ~ spl0_46
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2131,f1941,f1052,f11559]) ).
fof(f1052,plain,
( spl0_46
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1941,plain,
( spl0_207
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2131,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0
| ~ spl0_46
| ~ spl0_207 ),
inference(resolution,[],[f1942,f1054]) ).
fof(f1054,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f1942,plain,
( ! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = X1 )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f1941]) ).
fof(f11556,plain,
spl0_571,
inference(avatar_split_clause,[],[f734,f11554]) ).
fof(f734,plain,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(X12,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X13,X0),X0) ),
inference(definition_unfolding,[],[f499,f282,f282]) ).
fof(f499,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Obutlast(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(X12,c_List_Obutlast(X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).
fof(f11414,plain,
spl0_570,
inference(avatar_split_clause,[],[f235,f11412]) ).
fof(f11412,plain,
( spl0_570
<=> ! [X24,X23,X9,X0,X10,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X24,X23,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f235,axiom,
! [X10,X0,X1,X9,X24,X23] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X24,X23,X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
fof(f11410,plain,
spl0_569,
inference(avatar_split_clause,[],[f218,f11408]) ).
fof(f11408,plain,
( spl0_569
<=> ! [X24,X23,X9,X0,X10,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X24,X23,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f218,axiom,
! [X10,X0,X1,X9,X24,X23] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X24,X23,X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
fof(f11371,plain,
spl0_568,
inference(avatar_split_clause,[],[f791,f11369]) ).
fof(f11369,plain,
( spl0_568
<=> ! [X5,X0,X12] : c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f791,plain,
! [X0,X5,X12] : c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0),
inference(forward_demodulation,[],[f719,f389]) ).
fof(f719,plain,
! [X0,X5,X12] : c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0),
inference(definition_unfolding,[],[f283,f282,f282]) ).
fof(f283,axiom,
! [X0,X5,X12] : c_List_Obutlast(X12,X0) = c_List_Obutlast(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_0) ).
fof(f11303,plain,
spl0_567,
inference(avatar_split_clause,[],[f807,f11301]) ).
fof(f11301,plain,
( spl0_567
<=> ! [X0,X14,X12,X8] :
( c_List_Orev(c_List_Olist__update(X12,X14,X8,X0),X0) = c_List_Olist__update(c_List_Orev(X12,X0),c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X8,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f807,plain,
! [X0,X8,X14,X12] :
( c_List_Orev(c_List_Olist__update(X12,X14,X8,X0),X0) = c_List_Olist__update(c_List_Orev(X12,X0),c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X8,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
inference(forward_demodulation,[],[f162,f355]) ).
fof(f355,axiom,
! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f162,axiom,
! [X0,X8,X14,X12] :
( ~ c_HOL_Oord__class_Oless(X14,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Orev(c_List_Olist__update(X12,X14,X8,X0),X0) = c_List_Olist__update(c_List_Orev(X12,X0),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X14,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__update_0) ).
fof(f11299,plain,
( spl0_566
| ~ spl0_50
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2129,f1933,f1072,f11297]) ).
fof(f11297,plain,
( spl0_566
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_Int_Oint) = c_Orderings_Oord__class_Omin(X1,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1072,plain,
( spl0_50
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1933,plain,
( spl0_205
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2129,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_Int_Oint) = c_Orderings_Oord__class_Omin(X1,X0,tc_Int_Oint)
| ~ spl0_50
| ~ spl0_205 ),
inference(resolution,[],[f1934,f1074]) ).
fof(f1074,plain,
( class_Orderings_Olinorder(tc_Int_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1934,plain,
( ! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X8,X5,X0) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1933]) ).
fof(f11295,plain,
spl0_565,
inference(avatar_split_clause,[],[f771,f11293]) ).
fof(f11293,plain,
( spl0_565
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) != c_Power_Opower__class_Opower(X9,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f771,plain,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) != c_Power_Opower__class_Opower(X9,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
inference(definition_unfolding,[],[f390,f314,f314]) ).
fof(f390,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,c_Suc(X3),X0) != c_Power_Opower__class_Opower(X9,c_Suc(X3),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
fof(f11289,plain,
spl0_564,
inference(avatar_split_clause,[],[f708,f11287]) ).
fof(f11287,plain,
( spl0_564
<=> ! [X0,X12,X3] : c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Odrop(X3,X12,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Odrop(X3,X12,X0),X0) = c_List_Odrop(X3,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f708,plain,
! [X3,X0,X12] : c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Odrop(X3,X12,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Odrop(X3,X12,X0),X0) = c_List_Odrop(X3,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0),
inference(definition_unfolding,[],[f463,f282,f282]) ).
fof(f463,axiom,
! [X3,X0,X12] : c_List_Obutlast(c_List_Odrop(X3,X12,X0),X0) = c_List_Odrop(X3,c_List_Obutlast(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
fof(f11031,plain,
spl0_563,
inference(avatar_split_clause,[],[f806,f11029]) ).
fof(f11029,plain,
( spl0_563
<=> ! [X0,X12,X3] :
( c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) = c_List_Orotate1(c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(X3,X12,X0),X0),c_List_Otake(X3,X12,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f806,plain,
! [X3,X0,X12] :
( c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) = c_List_Orotate1(c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(X3,X12,X0),X0),c_List_Otake(X3,X12,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
inference(forward_demodulation,[],[f750,f521]) ).
fof(f521,axiom,
! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X36),X36),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
fof(f750,plain,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(X3,X12,X0),X0),c_List_Olist_ONil(X0),X0),X0) = c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ),
inference(definition_unfolding,[],[f205,f314]) ).
fof(f205,axiom,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(X3,X12,X0),X0),c_List_Olist_ONil(X0),X0),X0) = c_List_Otake(c_Suc(X3),X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__hd__drop_0) ).
fof(f11027,plain,
spl0_562,
inference(avatar_split_clause,[],[f749,f11025]) ).
fof(f11025,plain,
( spl0_562
<=> ! [X0,X12,X6,X1] :
( ~ c_HOL_Oord__class_Oless(X6,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X12,X6,X1,X0) = c_List_Oappend(c_List_Otake(X6,X12,X0),c_List_Olist_OCons(X1,c_List_Odrop(c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f749,plain,
! [X0,X1,X6,X12] :
( ~ c_HOL_Oord__class_Oless(X6,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X12,X6,X1,X0) = c_List_Oappend(c_List_Otake(X6,X12,X0),c_List_Olist_OCons(X1,c_List_Odrop(c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0),X0) ),
inference(definition_unfolding,[],[f206,f314]) ).
fof(f206,axiom,
! [X0,X1,X6,X12] :
( ~ c_HOL_Oord__class_Oless(X6,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X12,X6,X1,X0) = c_List_Oappend(c_List_Otake(X6,X12,X0),c_List_Olist_OCons(X1,c_List_Odrop(c_Suc(X6),X12,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).
fof(f11023,plain,
spl0_561,
inference(avatar_split_clause,[],[f698,f11021]) ).
fof(f11021,plain,
( spl0_561
<=> ! [X0,X12,X3] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f11019,plain,
spl0_560,
inference(avatar_split_clause,[],[f160,f11017]) ).
fof(f11017,plain,
( spl0_560
<=> ! [X0,X13,X12,X5,X3] :
( c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X3,X5,X0) = c_List_Oappend(X12,c_List_Olist__update(X13,c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f160,axiom,
! [X3,X0,X5,X12,X13] :
( c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X3,X5,X0) = c_List_Oappend(X12,c_List_Olist__update(X13,c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_1) ).
fof(f11015,plain,
( spl0_559
| ~ spl0_20
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2128,f1933,f922,f11013]) ).
fof(f11013,plain,
( spl0_559
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2128,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X1,X0,tc_nat)
| ~ spl0_20
| ~ spl0_205 ),
inference(resolution,[],[f1934,f924]) ).
fof(f924,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f10928,plain,
spl0_558,
inference(avatar_split_clause,[],[f769,f10926]) ).
fof(f10926,plain,
( spl0_558
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_Power_Opower__class_Opower(X9,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f769,plain,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_Power_Opower__class_Opower(X9,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ),
inference(definition_unfolding,[],[f248,f314,f314]) ).
fof(f248,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),c_Power_Opower__class_Opower(X9,c_Suc(X3),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
fof(f10924,plain,
spl0_557,
inference(avatar_split_clause,[],[f732,f10922]) ).
fof(f10922,plain,
( spl0_557
<=> ! [X0,X12,X3] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f732,plain,
! [X3,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) ),
inference(definition_unfolding,[],[f537,f413]) ).
fof(f537,axiom,
! [X3,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orotate(X3,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
fof(f10920,plain,
spl0_556,
inference(avatar_split_clause,[],[f156,f10918]) ).
fof(f10918,plain,
( spl0_556
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X9,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f156,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X9,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
fof(f10558,plain,
spl0_555,
inference(avatar_split_clause,[],[f752,f10556]) ).
fof(f10556,plain,
( spl0_555
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f752,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f322,f314,f314,f314]) ).
fof(f322,axiom,
! [X3,X4] :
( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) = X3
| c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
fof(f10554,plain,
( spl0_554
| ~ spl0_46
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2126,f1925,f1052,f10552]) ).
fof(f1925,plain,
( spl0_203
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X9,X0),X9,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2126,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0
| ~ spl0_46
| ~ spl0_203 ),
inference(resolution,[],[f1926,f1054]) ).
fof(f1926,plain,
( ! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X9,X0),X9,X0) = X1 )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f10550,plain,
spl0_553,
inference(avatar_split_clause,[],[f725,f10548]) ).
fof(f10548,plain,
( spl0_553
<=> ! [X0,X12,X3] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f725,plain,
! [X3,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) ),
inference(definition_unfolding,[],[f569,f413]) ).
fof(f569,axiom,
! [X3,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orotate(X3,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
fof(f10546,plain,
spl0_552,
inference(avatar_split_clause,[],[f722,f10544]) ).
fof(f10544,plain,
( spl0_552
<=> ! [X0,X12,X3] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f722,plain,
! [X3,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),X0) ),
inference(definition_unfolding,[],[f568,f413]) ).
fof(f568,axiom,
! [X3,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orotate(X3,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
fof(f10539,plain,
spl0_551,
inference(avatar_split_clause,[],[f702,f10537]) ).
fof(f10537,plain,
( spl0_551
<=> ! [X5,X0,X12] : c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f702,plain,
! [X0,X5,X12] : c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X12,
inference(definition_unfolding,[],[f511,f282]) ).
fof(f511,axiom,
! [X0,X5,X12] : c_List_Obutlast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
fof(f10384,plain,
( spl0_550
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_547 ),
inference(avatar_split_clause,[],[f10136,f10133,f4986,f1424,f1318,f1197,f10382]) ).
fof(f10382,plain,
( spl0_550
<=> ! [X0,X12] :
( c_List_Oappend(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Olast(X12,X0),X0),X0) = X12
| c_List_Olist_ONil(X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f10133,plain,
( spl0_547
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),c_List_Olist_OCons(c_List_Olast(X12,X0),c_List_Olist_ONil(X0),X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f10136,plain,
( ! [X0,X12] :
( c_List_Oappend(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Olast(X12,X0),X0),X0) = X12
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_547 ),
inference(forward_demodulation,[],[f10134,f5746]) ).
fof(f10134,plain,
( ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),c_List_Olist_OCons(c_List_Olast(X12,X0),c_List_Olist_ONil(X0),X0),X0) = X12 )
| ~ spl0_547 ),
inference(avatar_component_clause,[],[f10133]) ).
fof(f10264,plain,
( spl0_549
| ~ spl0_36
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2106,f1893,f1002,f10262]) ).
fof(f1002,plain,
( spl0_36
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1893,plain,
( spl0_195
<=> ! [X5,X0,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2106,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Int_Oint)
| ~ spl0_36
| ~ spl0_195 ),
inference(resolution,[],[f1894,f1004]) ).
fof(f1004,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f1894,plain,
( ! [X0,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X5,X0) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1893]) ).
fof(f10140,plain,
spl0_548,
inference(avatar_split_clause,[],[f748,f10138]) ).
fof(f10138,plain,
( spl0_548
<=> ! [X0,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Otake(X3,X12,X0) = c_List_Otake(X3,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f748,plain,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Otake(X3,X12,X0) = c_List_Otake(X3,c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ),
inference(definition_unfolding,[],[f61,f282]) ).
fof(f61,axiom,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Otake(X3,c_List_Obutlast(X12,X0),X0) = c_List_Otake(X3,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__butlast_0) ).
fof(f10135,plain,
spl0_547,
inference(avatar_split_clause,[],[f736,f10133]) ).
fof(f736,plain,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),c_List_Olist_OCons(c_List_Olast(X12,X0),c_List_Olist_ONil(X0),X0),X0) = X12 ),
inference(definition_unfolding,[],[f478,f282]) ).
fof(f478,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(c_List_Obutlast(X12,X0),c_List_Olist_OCons(c_List_Olast(X12,X0),c_List_Olist_ONil(X0),X0),X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
fof(f10131,plain,
spl0_546,
inference(avatar_split_clause,[],[f493,f10129]) ).
fof(f10129,plain,
( spl0_546
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f493,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
fof(f10127,plain,
spl0_545,
inference(avatar_split_clause,[],[f492,f10125]) ).
fof(f10125,plain,
( spl0_545
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f492,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
fof(f10123,plain,
spl0_544,
inference(avatar_split_clause,[],[f467,f10121]) ).
fof(f10121,plain,
( spl0_544
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f467,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
fof(f10119,plain,
spl0_543,
inference(avatar_split_clause,[],[f466,f10117]) ).
fof(f10117,plain,
( spl0_543
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f466,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
fof(f10115,plain,
spl0_542,
inference(avatar_split_clause,[],[f433,f10113]) ).
fof(f10113,plain,
( spl0_542
<=> ! [X5,X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(c_List_Ohd(X13,X0),c_List_Osplice(X12,c_List_Otl(X13,X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f433,axiom,
! [X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(c_List_Ohd(X13,X0),c_List_Osplice(X12,c_List_Otl(X13,X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_1) ).
fof(f10111,plain,
( spl0_541
| ~ spl0_78
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2011,f1865,f1193,f10109]) ).
fof(f10109,plain,
( spl0_541
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2011,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
| ~ spl0_78
| ~ spl0_188 ),
inference(superposition,[],[f1866,f1194]) ).
fof(f10107,plain,
spl0_540,
inference(avatar_split_clause,[],[f26,f10105]) ).
fof(f10105,plain,
( spl0_540
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f26,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
fof(f10103,plain,
spl0_539,
inference(avatar_split_clause,[],[f1,f10101]) ).
fof(f10101,plain,
( spl0_539
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
fof(f10030,plain,
spl0_538,
inference(avatar_split_clause,[],[f414,f10028]) ).
fof(f10028,plain,
( spl0_538
<=> ! [X0,X14,X12,X5] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist__update(X12,X14,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f414,axiom,
! [X0,X14,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist__update(X12,X14,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__list__update_1) ).
fof(f9839,plain,
( spl0_537
| ~ spl0_132
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1760,f1635,f1436,f9837]) ).
fof(f9837,plain,
( spl0_537
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f1635,plain,
( spl0_160
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1760,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) )
| ~ spl0_132
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1757]) ).
fof(f1757,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_132
| ~ spl0_160 ),
inference(resolution,[],[f1636,f1437]) ).
fof(f1636,plain,
( ! [X0,X8,X5] :
( ~ c_lessequals(X5,X8,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1635]) ).
fof(f9585,plain,
spl0_536,
inference(avatar_split_clause,[],[f770,f9583]) ).
fof(f9583,plain,
( spl0_536
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f770,plain,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),c_HOL_Oone__class_Oone(X0),X0) ),
inference(definition_unfolding,[],[f157,f314]) ).
fof(f157,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
fof(f9581,plain,
spl0_535,
inference(avatar_split_clause,[],[f737,f9579]) ).
fof(f9579,plain,
( spl0_535
<=> ! [X0,X12,X3] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Otake(X3,c_List_Otl(X12,X0),X0),X0) = c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f737,plain,
! [X3,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Otake(X3,c_List_Otl(X12,X0),X0),X0) = c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ),
inference(definition_unfolding,[],[f410,f314]) ).
fof(f410,axiom,
! [X3,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otake(c_Suc(X3),X12,X0) = c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Otake(X3,c_List_Otl(X12,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc_0) ).
fof(f9577,plain,
spl0_534,
inference(avatar_split_clause,[],[f517,f9575]) ).
fof(f9575,plain,
( spl0_534
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f517,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
fof(f9573,plain,
spl0_533,
inference(avatar_split_clause,[],[f516,f9571]) ).
fof(f9571,plain,
( spl0_533
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f516,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
fof(f9569,plain,
spl0_532,
inference(avatar_split_clause,[],[f509,f9567]) ).
fof(f9567,plain,
( spl0_532
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f509,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
fof(f9565,plain,
( spl0_531
| ~ spl0_133
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1759,f1635,f1440,f9563]) ).
fof(f9563,plain,
( spl0_531
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f1759,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X1,X0),X0) )
| ~ spl0_133
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1758]) ).
fof(f1758,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X1,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_133
| ~ spl0_160 ),
inference(resolution,[],[f1636,f1441]) ).
fof(f9561,plain,
spl0_530,
inference(avatar_split_clause,[],[f508,f9559]) ).
fof(f9559,plain,
( spl0_530
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f508,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
fof(f9557,plain,
spl0_529,
inference(avatar_split_clause,[],[f387,f9555]) ).
fof(f9555,plain,
( spl0_529
<=> ! [X18,X0,X25] :
( ~ class_HOL_Oord(X0)
| ~ class_Int_Onumber(X0)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X25,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f387,axiom,
! [X0,X18,X25] :
( ~ class_HOL_Oord(X0)
| ~ class_Int_Onumber(X0)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X25,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__number__of_0) ).
fof(f9553,plain,
spl0_528,
inference(avatar_split_clause,[],[f309,f9551]) ).
fof(f9551,plain,
( spl0_528
<=> ! [X13,X0,X12,X3] : c_List_Odrop(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Odrop(X3,X12,X0),c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f309,axiom,
! [X3,X0,X12,X13] : c_List_Odrop(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Odrop(X3,X12,X0),c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__append_0) ).
fof(f9549,plain,
spl0_527,
inference(avatar_split_clause,[],[f269,f9547]) ).
fof(f9547,plain,
( spl0_527
<=> ! [X18,X0,X25] :
( ~ class_HOL_Oord(X0)
| ~ class_Int_Onumber(X0)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X18,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f269,axiom,
! [X0,X18,X25] :
( ~ class_HOL_Oord(X0)
| ~ class_Int_Onumber(X0)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X18,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__number__of_1) ).
fof(f9545,plain,
spl0_526,
inference(avatar_split_clause,[],[f251,f9543]) ).
fof(f9543,plain,
( spl0_526
<=> ! [X13,X0,X12,X3] : c_List_Otake(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f251,axiom,
! [X3,X0,X12,X13] : c_List_Otake(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__append_0) ).
fof(f9541,plain,
spl0_525,
inference(avatar_split_clause,[],[f60,f9539]) ).
fof(f9539,plain,
( spl0_525
<=> ! [X5,X13,X0,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X3,X5,X0) = c_List_Oappend(c_List_Olist__update(X12,X3,X5,X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f60,axiom,
! [X3,X0,X5,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X3,X5,X0) = c_List_Oappend(c_List_Olist__update(X12,X3,X5,X0),X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__append_0) ).
fof(f9286,plain,
spl0_524,
inference(avatar_split_clause,[],[f790,f9284]) ).
fof(f9284,plain,
( spl0_524
<=> ! [X3,X4,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f790,plain,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat),
inference(forward_demodulation,[],[f718,f355]) ).
fof(f718,plain,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f384,f314,f314]) ).
fof(f384,axiom,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X4),X3,tc_nat),c_Suc(X14),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
fof(f9280,plain,
spl0_523,
inference(avatar_split_clause,[],[f773,f9278]) ).
fof(f9278,plain,
( spl0_523
<=> ! [X0,X3] : c_List_Olist_ONil(X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_List_Olist_ONil(X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f773,plain,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_List_Olist_ONil(X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_List_Olist_ONil(X0),X0),X0),
inference(forward_demodulation,[],[f681,f293]) ).
fof(f293,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
fof(f681,plain,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)),tc_nat),c_List_Olist_ONil(X0),X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)),tc_nat),c_List_Olist_ONil(X0),X0),X0),
inference(definition_unfolding,[],[f563,f413]) ).
fof(f563,axiom,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Orotate(X3,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
fof(f9276,plain,
spl0_522,
inference(avatar_split_clause,[],[f714,f9274]) ).
fof(f9274,plain,
( spl0_522
<=> ! [X0,X12] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f714,plain,
! [X0,X12] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),tc_List_Olist(X0)),
inference(definition_unfolding,[],[f252,f282]) ).
fof(f252,axiom,
! [X0,X12] : c_Nat_Osize__class_Osize(c_List_Obutlast(X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__butlast_0) ).
fof(f9272,plain,
spl0_521,
inference(avatar_split_clause,[],[f430,f9270]) ).
fof(f9270,plain,
( spl0_521
<=> ! [X0,X12,X5,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otake(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f430,axiom,
! [X3,X0,X5,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otake(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).
fof(f9268,plain,
spl0_520,
inference(avatar_split_clause,[],[f386,f9266]) ).
fof(f9266,plain,
( spl0_520
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f386,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f9264,plain,
spl0_519,
inference(avatar_split_clause,[],[f380,f9262]) ).
fof(f9262,plain,
( spl0_519
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f380,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
fof(f9260,plain,
( spl0_518
| ~ spl0_129
| ~ spl0_511 ),
inference(avatar_split_clause,[],[f9097,f8657,f1424,f9258]) ).
fof(f9258,plain,
( spl0_518
<=> ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f8657,plain,
( spl0_511
<=> ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f9097,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_511 ),
inference(superposition,[],[f8658,f1425]) ).
fof(f8658,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_511 ),
inference(avatar_component_clause,[],[f8657]) ).
fof(f9256,plain,
spl0_517,
inference(avatar_split_clause,[],[f329,f9254]) ).
fof(f9254,plain,
( spl0_517
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f329,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
fof(f9252,plain,
spl0_516,
inference(avatar_split_clause,[],[f209,f9250]) ).
fof(f9250,plain,
( spl0_516
<=> ! [X5,X0,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f209,axiom,
! [X0,X8,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f9248,plain,
spl0_515,
inference(avatar_split_clause,[],[f208,f9246]) ).
fof(f9246,plain,
( spl0_515
<=> ! [X5,X0,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f208,axiom,
! [X0,X8,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f9173,plain,
spl0_514,
inference(avatar_split_clause,[],[f688,f9171]) ).
fof(f9171,plain,
( spl0_514
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f688,plain,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),
inference(definition_unfolding,[],[f587,f282]) ).
fof(f587,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
fof(f9169,plain,
spl0_513,
inference(avatar_split_clause,[],[f496,f9167]) ).
fof(f9167,plain,
( spl0_513
<=> ! [X5,X33,X0,X12,X6,X19] :
( X6 = X33
| c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X33,X19,X0) = c_List_Olist__update(c_List_Olist__update(X12,X33,X19,X0),X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f496,axiom,
! [X0,X6,X19,X5,X12,X33] :
( X6 = X33
| c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X33,X19,X0) = c_List_Olist__update(c_List_Olist__update(X12,X33,X19,X0),X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
fof(f9165,plain,
spl0_512,
inference(avatar_split_clause,[],[f423,f9163]) ).
fof(f9163,plain,
( spl0_512
<=> ! [X5,X13,X0,X12,X8] : c_List_Olist__update(c_List_Oappend(X12,c_List_Olist_OCons(X5,X13,X0),X0),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X8,X0) = c_List_Oappend(X12,c_List_Olist_OCons(X8,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f423,axiom,
! [X0,X8,X5,X12,X13] : c_List_Olist__update(c_List_Oappend(X12,c_List_Olist_OCons(X5,X13,X0),X0),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X8,X0) = c_List_Oappend(X12,c_List_Olist_OCons(X8,X13,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).
fof(f8659,plain,
( ~ spl0_20
| spl0_511
| ~ spl0_74
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1748,f1631,f1177,f8657,f922]) ).
fof(f1177,plain,
( spl0_74
<=> ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1748,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_74
| ~ spl0_159 ),
inference(resolution,[],[f1632,f1178]) ).
fof(f1178,plain,
( ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X6,tc_nat)
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1177]) ).
fof(f8655,plain,
spl0_510,
inference(avatar_split_clause,[],[f782,f8653]) ).
fof(f8653,plain,
( spl0_510
<=> ! [X4,X3] : c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Orderings_Oord__class_Omin(X4,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f782,plain,
! [X3,X4] : c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Orderings_Oord__class_Omin(X4,X3,tc_nat),tc_nat),
inference(forward_demodulation,[],[f701,f184]) ).
fof(f184,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f701,plain,
! [X3,X4] : c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(definition_unfolding,[],[f388,f314,f314,f314]) ).
fof(f388,axiom,
! [X3,X4] : c_Orderings_Oord__class_Omin(c_Suc(X4),c_Suc(X3),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X4,X3,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
fof(f8651,plain,
spl0_509,
inference(avatar_split_clause,[],[f747,f8649]) ).
fof(f8649,plain,
( spl0_509
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f747,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
inference(definition_unfolding,[],[f381,f314,f314]) ).
fof(f381,axiom,
! [X3,X4] :
( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
fof(f8647,plain,
spl0_508,
inference(avatar_split_clause,[],[f731,f8645]) ).
fof(f8645,plain,
( spl0_508
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f731,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f223,f314]) ).
fof(f223,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
fof(f8643,plain,
spl0_507,
inference(avatar_split_clause,[],[f720,f8641]) ).
fof(f8641,plain,
( spl0_507
<=> ! [X5,X0,X12,X6,X8] : c_List_Olist_OCons(X5,c_List_Olist__update(X12,X6,X8,X0),X0) = c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f720,plain,
! [X0,X8,X6,X5,X12] : c_List_Olist_OCons(X5,c_List_Olist__update(X12,X6,X8,X0),X0) = c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X8,X0),
inference(definition_unfolding,[],[f305,f314]) ).
fof(f305,axiom,
! [X0,X8,X6,X5,X12] : c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_Suc(X6),X8,X0) = c_List_Olist_OCons(X5,c_List_Olist__update(X12,X6,X8,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
fof(f8639,plain,
spl0_506,
inference(avatar_split_clause,[],[f498,f8637]) ).
fof(f8637,plain,
( spl0_506
<=> ! [X0,X12,X5,X3] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f498,axiom,
! [X3,X0,X5,X12] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
fof(f8635,plain,
spl0_505,
inference(avatar_split_clause,[],[f444,f8633]) ).
fof(f8633,plain,
( spl0_505
<=> ! [X5,X13,X0,X12,X8] : c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),c_List_Olist_OCons(X8,X13,X0),X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,c_List_Osplice(X12,X13,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f444,axiom,
! [X0,X8,X5,X12,X13] : c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),c_List_Olist_OCons(X8,X13,X0),X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,c_List_Osplice(X12,X13,X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
fof(f8631,plain,
spl0_504,
inference(avatar_split_clause,[],[f424,f8629]) ).
fof(f8629,plain,
( spl0_504
<=> ! [X0,X12,X28] :
( c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0) != X12
| c_List_Oappend(X12,c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0),X0) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f424,axiom,
! [X28,X0,X12] :
( c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0) != X12
| c_List_Oappend(X12,c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0),X0) = X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
fof(f8627,plain,
spl0_503,
inference(avatar_split_clause,[],[f408,f8625]) ).
fof(f8625,plain,
( spl0_503
<=> ! [X0,X8,X5,X28] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X8,X28,X0),X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f408,axiom,
! [X28,X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X8,X28,X0),X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
fof(f8623,plain,
spl0_502,
inference(avatar_split_clause,[],[f356,f8621]) ).
fof(f8621,plain,
( spl0_502
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f356,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f8619,plain,
spl0_501,
inference(avatar_split_clause,[],[f115,f8617]) ).
fof(f8617,plain,
( spl0_501
<=> ! [X4,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f115,axiom,
! [X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
fof(f8615,plain,
( spl0_500
| ~ spl0_129
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1625,f1533,f1424,f8613]) ).
fof(f8613,plain,
( spl0_500
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f1625,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_156 ),
inference(superposition,[],[f1534,f1425]) ).
fof(f8611,plain,
spl0_499,
inference(avatar_split_clause,[],[f112,f8609]) ).
fof(f8609,plain,
( spl0_499
<=> ! [X9,X0,X5,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X9,X5,X0),c_Power_Opower__class_Opower(X9,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f112,axiom,
! [X0,X8,X9,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X9,X5,X0),c_Power_Opower__class_Opower(X9,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
fof(f8607,plain,
spl0_498,
inference(avatar_split_clause,[],[f53,f8605]) ).
fof(f8605,plain,
( spl0_498
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f53,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f8504,plain,
( spl0_497
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f7675,f7671,f4986,f1424,f1318,f1197,f8502]) ).
fof(f8502,plain,
( spl0_497
<=> ! [X0,X13,X12,X5,X8] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X12 = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f7671,plain,
( spl0_491
<=> ! [X5,X13,X0,X12,X8] :
( X12 = X13
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f7675,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X12 = X13 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_491 ),
inference(forward_demodulation,[],[f7674,f5746]) ).
fof(f7674,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0)
| X12 = X13 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_491 ),
inference(forward_demodulation,[],[f7672,f5746]) ).
fof(f7672,plain,
( ! [X0,X8,X5,X12,X13] :
( X12 = X13
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f7671]) ).
fof(f8500,plain,
( spl0_496
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_490 ),
inference(avatar_split_clause,[],[f7669,f7665,f4986,f1424,f1318,f1197,f8498]) ).
fof(f8498,plain,
( spl0_496
<=> ! [X0,X13,X12,X5,X8] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X5 = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f7665,plain,
( spl0_490
<=> ! [X13,X0,X12,X5,X8] :
( X5 = X8
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f7669,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X5 = X8 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_490 ),
inference(forward_demodulation,[],[f7668,f5746]) ).
fof(f7668,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0)
| X5 = X8 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_490 ),
inference(forward_demodulation,[],[f7666,f5746]) ).
fof(f7666,plain,
( ! [X0,X8,X5,X12,X13] :
( X5 = X8
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_490 ),
inference(avatar_component_clause,[],[f7665]) ).
fof(f8496,plain,
( spl0_495
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f7663,f7660,f4986,f1424,f1318,f1197,f8494]) ).
fof(f8494,plain,
( spl0_495
<=> ! [X13,X0,X12,X8] :
( c_List_Oappend(c_List_Orev(X13,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f7660,plain,
( spl0_489
<=> ! [X13,X0,X12,X8] :
( c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0)
| c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f7663,plain,
( ! [X0,X8,X12,X13] :
( c_List_Oappend(c_List_Orev(X13,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0) )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_489 ),
inference(forward_demodulation,[],[f7661,f5746]) ).
fof(f7661,plain,
( ! [X0,X8,X12,X13] :
( c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0)
| c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) = X12 )
| ~ spl0_489 ),
inference(avatar_component_clause,[],[f7660]) ).
fof(f8492,plain,
( spl0_494
| ~ spl0_65
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1399,f1366,f1141,f8490]) ).
fof(f8490,plain,
( spl0_494
<=> ! [X0,X1] : c_List_Oremdups(X0,X1) = c_List_Oremdups(c_List_Oremdups(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1141,plain,
( spl0_65
<=> ! [X0,X12] : c_List_Odistinct(c_List_Oremdups(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1399,plain,
( ! [X0,X1] : c_List_Oremdups(X0,X1) = c_List_Oremdups(c_List_Oremdups(X0,X1),X1)
| ~ spl0_65
| ~ spl0_119 ),
inference(resolution,[],[f1367,f1142]) ).
fof(f1142,plain,
( ! [X0,X12] : c_List_Odistinct(c_List_Oremdups(X12,X0),X0)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f8488,plain,
( spl0_493
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_488 ),
inference(avatar_split_clause,[],[f7658,f7655,f4986,f1424,f1318,f1197,f8486]) ).
fof(f8486,plain,
( spl0_493
<=> ! [X0,X12] :
( c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Ohd(X12,X0),X0),X0)
| c_List_Olist_ONil(X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f7655,plain,
( spl0_488
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f7658,plain,
( ! [X0,X12] :
( c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Ohd(X12,X0),X0),X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_488 ),
inference(forward_demodulation,[],[f7656,f5746]) ).
fof(f7656,plain,
( ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_488 ),
inference(avatar_component_clause,[],[f7655]) ).
fof(f7688,plain,
spl0_492,
inference(avatar_split_clause,[],[f784,f7686]) ).
fof(f7686,plain,
( spl0_492
<=> ! [X4,X3] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X4,X3,tc_nat),tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f784,plain,
! [X3,X4] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Omod(X4,X3,tc_nat),tc_nat),X3,tc_nat),
inference(forward_demodulation,[],[f710,f184]) ).
fof(f710,plain,
! [X3,X4] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),
inference(definition_unfolding,[],[f260,f314,f314]) ).
fof(f260,axiom,
! [X3,X4] : c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
fof(f7673,plain,
spl0_491,
inference(avatar_split_clause,[],[f583,f7671]) ).
fof(f583,axiom,
! [X0,X8,X5,X12,X13] :
( X12 = X13
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
fof(f7667,plain,
spl0_490,
inference(avatar_split_clause,[],[f582,f7665]) ).
fof(f582,axiom,
! [X0,X8,X5,X12,X13] :
( X5 = X8
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
fof(f7662,plain,
spl0_489,
inference(avatar_split_clause,[],[f519,f7660]) ).
fof(f519,axiom,
! [X0,X8,X12,X13] :
( c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0)
| c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
fof(f7657,plain,
spl0_488,
inference(avatar_split_clause,[],[f434,f7655]) ).
fof(f434,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
fof(f7653,plain,
spl0_487,
inference(avatar_split_clause,[],[f431,f7651]) ).
fof(f7651,plain,
( spl0_487
<=> ! [X0,X12,X5,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Odrop(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f431,axiom,
! [X3,X0,X5,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Odrop(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).
fof(f7649,plain,
spl0_486,
inference(avatar_split_clause,[],[f415,f7647]) ).
fof(f7647,plain,
( spl0_486
<=> ! [X5,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f415,axiom,
! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__list__update_0) ).
fof(f7645,plain,
spl0_485,
inference(avatar_split_clause,[],[f379,f7643]) ).
fof(f7643,plain,
( spl0_485
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f379,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
fof(f7641,plain,
spl0_484,
inference(avatar_split_clause,[],[f350,f7639]) ).
fof(f7639,plain,
( spl0_484
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f350,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
fof(f7637,plain,
spl0_483,
inference(avatar_split_clause,[],[f344,f7635]) ).
fof(f7635,plain,
( spl0_483
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f344,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
fof(f7633,plain,
spl0_482,
inference(avatar_split_clause,[],[f343,f7631]) ).
fof(f7631,plain,
( spl0_482
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f343,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
fof(f7629,plain,
spl0_481,
inference(avatar_split_clause,[],[f342,f7627]) ).
fof(f7627,plain,
( spl0_481
<=> ! [X0,X8,X5,X25,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = X25
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) != c_HOL_Oplus__class_Oplus(X8,X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f342,axiom,
! [X0,X8,X7,X5,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = X25
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) != c_HOL_Oplus__class_Oplus(X8,X25,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f7625,plain,
spl0_480,
inference(avatar_split_clause,[],[f330,f7623]) ).
fof(f7623,plain,
( spl0_480
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f330,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f7621,plain,
spl0_479,
inference(avatar_split_clause,[],[f324,f7619]) ).
fof(f7619,plain,
( spl0_479
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(X10,X11,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f324,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(X10,X11,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f7617,plain,
spl0_478,
inference(avatar_split_clause,[],[f308,f7615]) ).
fof(f7615,plain,
( spl0_478
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ominus__class_Ominus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f308,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ominus__class_Ominus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
fof(f7613,plain,
spl0_477,
inference(avatar_split_clause,[],[f287,f7611]) ).
fof(f7611,plain,
( spl0_477
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f287,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f7609,plain,
spl0_476,
inference(avatar_split_clause,[],[f275,f7607]) ).
fof(f7607,plain,
( spl0_476
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f275,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
fof(f7605,plain,
spl0_475,
inference(avatar_split_clause,[],[f266,f7603]) ).
fof(f7603,plain,
( spl0_475
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f266,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f7601,plain,
spl0_474,
inference(avatar_split_clause,[],[f262,f7599]) ).
fof(f7599,plain,
( spl0_474
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f262,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f7597,plain,
spl0_473,
inference(avatar_split_clause,[],[f191,f7595]) ).
fof(f7595,plain,
( spl0_473
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f191,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f7593,plain,
spl0_472,
inference(avatar_split_clause,[],[f190,f7591]) ).
fof(f7591,plain,
( spl0_472
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f190,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f7588,plain,
spl0_471,
inference(avatar_split_clause,[],[f96,f7586]) ).
fof(f7586,plain,
( spl0_471
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f96,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f7584,plain,
spl0_470,
inference(avatar_split_clause,[],[f88,f7582]) ).
fof(f7582,plain,
( spl0_470
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f88,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f7580,plain,
spl0_469,
inference(avatar_split_clause,[],[f51,f7578]) ).
fof(f7578,plain,
( spl0_469
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f51,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f7576,plain,
spl0_468,
inference(avatar_split_clause,[],[f50,f7574]) ).
fof(f7574,plain,
( spl0_468
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f50,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f7572,plain,
spl0_467,
inference(avatar_split_clause,[],[f49,f7570]) ).
fof(f7570,plain,
( spl0_467
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f49,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f7568,plain,
spl0_466,
inference(avatar_split_clause,[],[f48,f7566]) ).
fof(f7566,plain,
( spl0_466
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f48,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f7564,plain,
spl0_465,
inference(avatar_split_clause,[],[f47,f7562]) ).
fof(f7562,plain,
( spl0_465
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f47,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f7560,plain,
spl0_464,
inference(avatar_split_clause,[],[f46,f7558]) ).
fof(f7558,plain,
( spl0_464
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f46,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f7556,plain,
spl0_463,
inference(avatar_split_clause,[],[f38,f7554]) ).
fof(f7554,plain,
( spl0_463
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f38,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f7552,plain,
spl0_462,
inference(avatar_split_clause,[],[f37,f7550]) ).
fof(f7550,plain,
( spl0_462
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f37,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f7539,plain,
spl0_461,
inference(avatar_split_clause,[],[f25,f7537]) ).
fof(f7537,plain,
( spl0_461
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f25,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f7535,plain,
spl0_460,
inference(avatar_split_clause,[],[f24,f7533]) ).
fof(f7533,plain,
( spl0_460
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f24,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
fof(f7311,plain,
( spl0_459
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f7067,f7064,f4986,f1424,f1318,f1197,f7309]) ).
fof(f7309,plain,
( spl0_459
<=> ! [X5,X0,X6] : c_List_Olist_OCons(X5,c_List_Oreplicate(X6,X5,X0),X0) = c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f7064,plain,
( spl0_454
<=> ! [X5,X0,X6] : c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X6,X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f7067,plain,
( ! [X0,X6,X5] : c_List_Olist_OCons(X5,c_List_Oreplicate(X6,X5,X0),X0) = c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_454 ),
inference(forward_demodulation,[],[f7065,f5746]) ).
fof(f7065,plain,
( ! [X0,X6,X5] : c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X6,X5,X0),X0)
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f7064]) ).
fof(f7083,plain,
spl0_458,
inference(avatar_split_clause,[],[f760,f7081]) ).
fof(f7081,plain,
( spl0_458
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f760,plain,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
inference(definition_unfolding,[],[f33,f314,f314]) ).
fof(f33,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Suc(X4) = X3
| c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f7079,plain,
spl0_457,
inference(avatar_split_clause,[],[f755,f7077]) ).
fof(f7077,plain,
( spl0_457
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f755,plain,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0),X0) ),
inference(definition_unfolding,[],[f54,f314]) ).
fof(f54,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
fof(f7075,plain,
spl0_456,
inference(avatar_split_clause,[],[f733,f7073]) ).
fof(f7073,plain,
( spl0_456
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f733,plain,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f271,f314]) ).
fof(f271,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Suc(c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I2_J_1) ).
fof(f7071,plain,
spl0_455,
inference(avatar_split_clause,[],[f716,f7069]) ).
fof(f7069,plain,
( spl0_455
<=> ! [X0,X12,X5,X3] : c_List_Olist_OCons(X5,c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f716,plain,
! [X3,X0,X5,X12] : c_List_Olist_OCons(X5,c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,X12,X0),X0),
inference(definition_unfolding,[],[f300,f314]) ).
fof(f300,axiom,
! [X3,X0,X5,X12] : c_List_Otake(c_Suc(X3),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(X3,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
fof(f7066,plain,
spl0_454,
inference(avatar_split_clause,[],[f522,f7064]) ).
fof(f522,axiom,
! [X0,X6,X5] : c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X6,X5,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
fof(f7062,plain,
spl0_453,
inference(avatar_split_clause,[],[f432,f7060]) ).
fof(f7060,plain,
( spl0_453
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otl(c_List_Oreplicate(X3,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f432,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otl(c_List_Oreplicate(X3,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__replicate_0) ).
fof(f7058,plain,
spl0_452,
inference(avatar_split_clause,[],[f281,f7056]) ).
fof(f7056,plain,
( spl0_452
<=> ! [X6,X0,X12] : c_List_Orev(c_List_Otake(X6,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f281,axiom,
! [X0,X6,X12] : c_List_Orev(c_List_Otake(X6,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__take_0) ).
fof(f7054,plain,
spl0_451,
inference(avatar_split_clause,[],[f280,f7052]) ).
fof(f7052,plain,
( spl0_451
<=> ! [X6,X0,X12] : c_List_Orev(c_List_Odrop(X6,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f280,axiom,
! [X0,X6,X12] : c_List_Orev(c_List_Odrop(X6,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__drop_0) ).
fof(f7050,plain,
spl0_450,
inference(avatar_split_clause,[],[f273,f7048]) ).
fof(f7048,plain,
( spl0_450
<=> ! [X19,X0,X5,X8,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X5,X0)
| c_lessequals(X20,X19,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f273,axiom,
! [X0,X8,X19,X5,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X5,X0)
| c_lessequals(X20,X19,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f7046,plain,
spl0_449,
inference(avatar_split_clause,[],[f250,f7044]) ).
fof(f7044,plain,
( spl0_449
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f250,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f7042,plain,
spl0_448,
inference(avatar_split_clause,[],[f139,f7040]) ).
fof(f7040,plain,
( spl0_448
<=> ! [X19,X20,X0,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X19,X20,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f139,axiom,
! [X0,X8,X19,X5,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X19,X20,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f7038,plain,
spl0_447,
inference(avatar_split_clause,[],[f106,f7036]) ).
fof(f7036,plain,
( spl0_447
<=> ! [X4,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X3 = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f106,axiom,
! [X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X3 = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X1,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f6992,plain,
( spl0_446
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f6434,f6431,f4986,f1424,f1318,f1197,f6990]) ).
fof(f6990,plain,
( spl0_446
<=> ! [X9,X1] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__CHAINED__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f6431,plain,
( spl0_443
<=> ! [X9,X1] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__CHAINED__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f6434,plain,
( ! [X1,X9] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__CHAINED__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_443 ),
inference(forward_demodulation,[],[f6432,f5746]) ).
fof(f6432,plain,
( ! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__CHAINED__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f6431]) ).
fof(f6988,plain,
( spl0_445
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f6429,f6426,f4986,f1424,f1318,f1197,f6986]) ).
fof(f6426,plain,
( spl0_442
<=> ! [X9,X1] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f6429,plain,
( ! [X1,X9] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 )
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_442 ),
inference(forward_demodulation,[],[f6427,f5746]) ).
fof(f6427,plain,
( ! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_442 ),
inference(avatar_component_clause,[],[f6426]) ).
fof(f6438,plain,
spl0_444,
inference(avatar_split_clause,[],[f792,f6436]) ).
fof(f6436,plain,
( spl0_444
<=> ! [X0,X14,X5,X3] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f792,plain,
! [X3,X0,X14,X5] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),X5,X0),
inference(forward_demodulation,[],[f485,f409]) ).
fof(f409,axiom,
! [X3,X0,X4,X5] : c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X5,X0) = c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X4,X5,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).
fof(f485,axiom,
! [X3,X0,X14,X5] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oappend(c_List_Oreplicate(X14,X5,X0),c_List_Oreplicate(X3,X5,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
fof(f6433,plain,
spl0_443,
inference(avatar_split_clause,[],[f607,f6431]) ).
fof(f607,axiom,
! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__CHAINED__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f6428,plain,
spl0_442,
inference(avatar_split_clause,[],[f596,f6426]) ).
fof(f596,axiom,
! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_third__alt_0) ).
fof(f6424,plain,
spl0_441,
inference(avatar_split_clause,[],[f482,f6422]) ).
fof(f6422,plain,
( spl0_441
<=> ! [X5,X13,X0,X12] : c_List_OremoveAll(X5,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_OremoveAll(X5,X12,X0),c_List_OremoveAll(X5,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f482,axiom,
! [X0,X5,X12,X13] : c_List_OremoveAll(X5,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_OremoveAll(X5,X12,X0),c_List_OremoveAll(X5,X13,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll__append_0) ).
fof(f6420,plain,
spl0_440,
inference(avatar_split_clause,[],[f443,f6418]) ).
fof(f6418,plain,
( spl0_440
<=> ! [X5,X0,X12,X8] :
( X5 = X8
| c_List_Oremove1(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_Oremove1(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f443,axiom,
! [X0,X8,X5,X12] :
( X5 = X8
| c_List_Oremove1(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_Oremove1(X5,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_1) ).
fof(f6416,plain,
spl0_439,
inference(avatar_split_clause,[],[f442,f6414]) ).
fof(f6414,plain,
( spl0_439
<=> ! [X5,X0,X12,X8] :
( X5 = X8
| c_List_OremoveAll(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_OremoveAll(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f442,axiom,
! [X0,X8,X5,X12] :
( X5 = X8
| c_List_OremoveAll(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_OremoveAll(X5,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_1) ).
fof(f6412,plain,
spl0_438,
inference(avatar_split_clause,[],[f412,f6410]) ).
fof(f6410,plain,
( spl0_438
<=> ! [X4,X0,X12,X3] : c_List_Odrop(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_List_Odrop(X3,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f412,axiom,
! [X3,X0,X4,X12] : c_List_Odrop(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_List_Odrop(X3,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__take_0) ).
fof(f6408,plain,
spl0_437,
inference(avatar_split_clause,[],[f411,f6406]) ).
fof(f411,axiom,
! [X3,X0,X4,X12] : c_List_Otake(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(X4,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__drop_0) ).
fof(f6404,plain,
spl0_436,
inference(avatar_split_clause,[],[f409,f6402]) ).
fof(f6402,plain,
( spl0_436
<=> ! [X4,X0,X5,X3] : c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X5,X0) = c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X4,X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f6400,plain,
spl0_435,
inference(avatar_split_clause,[],[f267,f6398]) ).
fof(f267,axiom,
! [X3,X6,X4] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X4,X6,tc_nat),c_HOL_Ominus__class_Ominus(X3,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X4,X3,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff_0) ).
fof(f6396,plain,
spl0_434,
inference(avatar_split_clause,[],[f238,f6394]) ).
fof(f6394,plain,
( spl0_434
<=> ! [X13,X0,X12] : c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f238,axiom,
! [X0,X12,X13] : c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__splice_0) ).
fof(f6368,plain,
( spl0_433
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f6364,f6361,f6366]) ).
fof(f6361,plain,
( spl0_432
<=> ! [X13,X0,X12] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f6364,plain,
( ! [X0,X12,X13] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0))
| ~ spl0_432 ),
inference(forward_demodulation,[],[f6362,f238]) ).
fof(f6362,plain,
( ! [X0,X12,X13] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat)
| ~ spl0_432 ),
inference(avatar_component_clause,[],[f6361]) ).
fof(f6363,plain,
spl0_432,
inference(avatar_split_clause,[],[f229,f6361]) ).
fof(f229,axiom,
! [X0,X12,X13] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__append_0) ).
fof(f6359,plain,
spl0_431,
inference(avatar_split_clause,[],[f111,f6357]) ).
fof(f6357,plain,
( spl0_431
<=> ! [X10,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f111,axiom,
! [X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f6355,plain,
spl0_430,
inference(avatar_split_clause,[],[f97,f6353]) ).
fof(f6353,plain,
( spl0_430
<=> ! [X15,X14,X6,X16] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f97,axiom,
! [X6,X16,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f6351,plain,
spl0_429,
inference(avatar_split_clause,[],[f69,f6349]) ).
fof(f6349,plain,
( spl0_429
<=> ! [X4,X16,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X16,X3,tc_nat),c_HOL_Ominus__class_Ominus(X16,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f69,axiom,
! [X3,X16,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X16,X3,tc_nat),c_HOL_Ominus__class_Ominus(X16,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f6347,plain,
spl0_428,
inference(avatar_split_clause,[],[f10,f6345]) ).
fof(f6345,plain,
( spl0_428
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f10,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f6288,plain,
( spl0_427
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f5990,f5987,f4986,f1424,f1318,f1197,f6286]) ).
fof(f6286,plain,
( spl0_427
<=> ! [X5,X0,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f5987,plain,
( spl0_421
<=> ! [X5,X0,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f5990,plain,
( ! [X0,X5,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| ~ spl0_79
| ~ spl0_107
| ~ spl0_129
| ~ spl0_391
| ~ spl0_421 ),
inference(forward_demodulation,[],[f5988,f5746]) ).
fof(f5988,plain,
( ! [X0,X5,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0)
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f5987]) ).
fof(f6233,plain,
( ~ spl0_425
| spl0_260
| ~ spl0_426
| ~ spl0_104
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3562,f3118,f1306,f6230,f2508,f6226]) ).
fof(f6226,plain,
( spl0_425
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2508,plain,
( spl0_260
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f6230,plain,
( spl0_426
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f1306,plain,
( spl0_104
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f3118,plain,
( spl0_311
<=> ! [X5,X0,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f3562,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_104
| ~ spl0_311 ),
inference(trivial_inequality_removal,[],[f3557]) ).
fof(f3557,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_104
| ~ spl0_311 ),
inference(superposition,[],[f3119,f1307]) ).
fof(f1307,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1306]) ).
fof(f3119,plain,
( ! [X0,X8,X5] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X8,X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f3118]) ).
fof(f6142,plain,
( spl0_424
| ~ spl0_189
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2542,f2326,f1869,f6140]) ).
fof(f6140,plain,
( spl0_424
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2542,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_189
| ~ spl0_256 ),
inference(resolution,[],[f2327,f1870]) ).
fof(f5998,plain,
spl0_423,
inference(avatar_split_clause,[],[f772,f5996]) ).
fof(f5996,plain,
( spl0_423
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f772,plain,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
inference(duplicate_literal_removal,[],[f328]) ).
fof(f328,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f5994,plain,
spl0_422,
inference(avatar_split_clause,[],[f712,f5992]) ).
fof(f5992,plain,
( spl0_422
<=> ! [X0,X12,X3] : c_List_Otake(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f712,plain,
! [X3,X0,X12] : c_List_Otake(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Otake(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0),
inference(definition_unfolding,[],[f418,f314]) ).
fof(f418,axiom,
! [X3,X0,X12] : c_List_Otake(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Otake(c_Suc(X3),X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__tl_0) ).
fof(f5989,plain,
spl0_421,
inference(avatar_split_clause,[],[f518,f5987]) ).
fof(f518,axiom,
! [X0,X5,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
fof(f5985,plain,
spl0_420,
inference(avatar_split_clause,[],[f481,f5983]) ).
fof(f5983,plain,
( spl0_420
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otl(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otl(X12,X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f481,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otl(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otl(X12,X0),X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).
fof(f5981,plain,
spl0_419,
inference(avatar_split_clause,[],[f428,f5979]) ).
fof(f428,axiom,
! [X3,X0,X12] : c_List_Otl(c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__take_0) ).
fof(f5977,plain,
( spl0_418
| ~ spl0_44
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1841,f1699,f1042,f5975]) ).
fof(f5975,plain,
( spl0_418
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f1042,plain,
( spl0_44
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1699,plain,
( spl0_176
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1841,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint)
| ~ spl0_44
| ~ spl0_176 ),
inference(resolution,[],[f1700,f1044]) ).
fof(f1044,plain,
( class_OrderedGroup_Omonoid__mult(tc_Int_Oint)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f1700,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X3,X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1699]) ).
fof(f5973,plain,
spl0_417,
inference(avatar_split_clause,[],[f352,f5971]) ).
fof(f5971,plain,
( spl0_417
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) = c_Orderings_Oord__class_Omin(X8,c_Orderings_Oord__class_Omin(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f352,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) = c_Orderings_Oord__class_Omin(X8,c_Orderings_Oord__class_Omin(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
fof(f5969,plain,
spl0_416,
inference(avatar_split_clause,[],[f351,f5967]) ).
fof(f5967,plain,
( spl0_416
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f351,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
fof(f5965,plain,
spl0_415,
inference(avatar_split_clause,[],[f340,f5963]) ).
fof(f5963,plain,
( spl0_415
<=> ! [X11,X0,X10,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X1,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f340,axiom,
! [X10,X0,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X1,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f5961,plain,
spl0_414,
inference(avatar_split_clause,[],[f339,f5959]) ).
fof(f5959,plain,
( spl0_414
<=> ! [X10,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f339,axiom,
! [X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f5957,plain,
spl0_413,
inference(avatar_split_clause,[],[f337,f5955]) ).
fof(f5955,plain,
( spl0_413
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f337,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f5953,plain,
spl0_412,
inference(avatar_split_clause,[],[f336,f5951]) ).
fof(f5951,plain,
( spl0_412
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f336,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f5949,plain,
spl0_411,
inference(avatar_split_clause,[],[f335,f5947]) ).
fof(f5947,plain,
( spl0_411
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f335,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f5945,plain,
spl0_410,
inference(avatar_split_clause,[],[f332,f5943]) ).
fof(f5943,plain,
( spl0_410
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f332,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f5941,plain,
spl0_409,
inference(avatar_split_clause,[],[f331,f5939]) ).
fof(f5939,plain,
( spl0_409
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f331,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f5937,plain,
spl0_408,
inference(avatar_split_clause,[],[f231,f5935]) ).
fof(f5935,plain,
( spl0_408
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f231,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f5933,plain,
( spl0_407
| ~ spl0_16
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1840,f1699,f902,f5931]) ).
fof(f5931,plain,
( spl0_407
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f902,plain,
( spl0_16
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1840,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_16
| ~ spl0_176 ),
inference(resolution,[],[f1700,f904]) ).
fof(f904,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f5929,plain,
spl0_406,
inference(avatar_split_clause,[],[f217,f5927]) ).
fof(f5927,plain,
( spl0_406
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X7,X0)
| c_lessequals(X8,X7,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f217,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X7,X0)
| c_lessequals(X8,X7,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
fof(f5925,plain,
spl0_405,
inference(avatar_split_clause,[],[f202,f5923]) ).
fof(f5923,plain,
( spl0_405
<=> ! [X9,X0,X5,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X1,X0)
| ~ c_lessequals(X5,X9,X0)
| c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f202,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X1,X0)
| ~ c_lessequals(X5,X9,X0)
| c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
fof(f5921,plain,
spl0_404,
inference(avatar_split_clause,[],[f138,f5919]) ).
fof(f5919,plain,
( spl0_404
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f138,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f5917,plain,
spl0_403,
inference(avatar_split_clause,[],[f76,f5915]) ).
fof(f5915,plain,
( spl0_403
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f76,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
fof(f5913,plain,
spl0_402,
inference(avatar_split_clause,[],[f68,f5911]) ).
fof(f5911,plain,
( spl0_402
<=> ! [X4,X14,X3,X16] :
( ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,X16,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f68,axiom,
! [X3,X16,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,X16,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f5909,plain,
spl0_401,
inference(avatar_split_clause,[],[f62,f5907]) ).
fof(f5907,plain,
( spl0_401
<=> ! [X0,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(c_List_Odrop(X3,X12,X0),X0) = c_List_Olast(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f62,axiom,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(c_List_Odrop(X3,X12,X0),X0) = c_List_Olast(X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__drop_0) ).
fof(f5905,plain,
spl0_400,
inference(avatar_split_clause,[],[f5,f5903]) ).
fof(f5903,plain,
( spl0_400
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f5,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
fof(f5825,plain,
( spl0_399
| ~ spl0_47
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1839,f1695,f1057,f5823]) ).
fof(f5823,plain,
( spl0_399
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f1695,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1839,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint)
| ~ spl0_47
| ~ spl0_175 ),
inference(resolution,[],[f1696,f1059]) ).
fof(f1696,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1695]) ).
fof(f5539,plain,
( spl0_398
| ~ spl0_18
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1838,f1695,f912,f5537]) ).
fof(f5537,plain,
( spl0_398
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f1838,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_18
| ~ spl0_175 ),
inference(resolution,[],[f1696,f914]) ).
fof(f5180,plain,
( spl0_397
| ~ spl0_55
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1835,f1687,f1097,f5178]) ).
fof(f5178,plain,
( spl0_397
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f1097,plain,
( spl0_55
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1687,plain,
( spl0_173
<=> ! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1835,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_55
| ~ spl0_173 ),
inference(resolution,[],[f1688,f1099]) ).
fof(f1099,plain,
( class_Power_Opower(tc_Int_Oint)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f1688,plain,
( ! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1687]) ).
fof(f5008,plain,
spl0_396,
inference(avatar_split_clause,[],[f796,f5006]) ).
fof(f5006,plain,
( spl0_396
<=> ! [X3] :
( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f796,plain,
! [X3] :
( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(forward_demodulation,[],[f742,f184]) ).
fof(f742,plain,
! [X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3 ),
inference(definition_unfolding,[],[f159,f314]) ).
fof(f159,axiom,
! [X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
fof(f5004,plain,
spl0_395,
inference(avatar_split_clause,[],[f759,f5002]) ).
fof(f5002,plain,
( spl0_395
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f759,plain,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X14,tc_nat) ),
inference(definition_unfolding,[],[f104,f314]) ).
fof(f104,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X6),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f5000,plain,
spl0_394,
inference(avatar_split_clause,[],[f754,f4998]) ).
fof(f4998,plain,
( spl0_394
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f754,plain,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0) ),
inference(definition_unfolding,[],[f198,f314]) ).
fof(f198,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X3),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f4996,plain,
spl0_393,
inference(avatar_split_clause,[],[f744,f4994]) ).
fof(f4994,plain,
( spl0_393
<=> ! [X6,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f744,plain,
! [X3,X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X6,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X3,tc_nat) ),
inference(definition_unfolding,[],[f55,f314]) ).
fof(f55,axiom,
! [X3,X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,c_Suc(X6),tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f4992,plain,
spl0_392,
inference(avatar_split_clause,[],[f741,f4990]) ).
fof(f4990,plain,
( spl0_392
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f741,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f40,f314,f314]) ).
fof(f40,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f4988,plain,
spl0_391,
inference(avatar_split_clause,[],[f706,f4986]) ).
fof(f706,plain,
! [X3,X0,X5] : c_List_Olist_OCons(X5,c_List_Oreplicate(X3,X5,X0),X0) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),
inference(definition_unfolding,[],[f306,f314]) ).
fof(f306,axiom,
! [X3,X0,X5] : c_List_Oreplicate(c_Suc(X3),X5,X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X3,X5,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
fof(f4984,plain,
( spl0_390
| ~ spl0_22
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1834,f1687,f932,f4982]) ).
fof(f4982,plain,
( spl0_390
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f932,plain,
( spl0_22
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1834,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_22
| ~ spl0_173 ),
inference(resolution,[],[f1688,f934]) ).
fof(f934,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f4980,plain,
spl0_389,
inference(avatar_split_clause,[],[f704,f4978]) ).
fof(f704,plain,
! [X0,X27,X5] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X27,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X27,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(definition_unfolding,[],[f320,f314]) ).
fof(f320,axiom,
! [X0,X27,X5] : c_Suc(c_Nat_Osize__class_Osize(X27,tc_List_Olist(X0))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X27,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
fof(f4976,plain,
spl0_388,
inference(avatar_split_clause,[],[f703,f4974]) ).
fof(f4974,plain,
( spl0_388
<=> ! [X0,X12,X5,X3] : c_List_Odrop(X3,X12,X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f703,plain,
! [X3,X0,X5,X12] : c_List_Odrop(X3,X12,X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Olist_OCons(X5,X12,X0),X0),
inference(definition_unfolding,[],[f301,f314]) ).
fof(f301,axiom,
! [X3,X0,X5,X12] : c_List_Odrop(X3,X12,X0) = c_List_Odrop(c_Suc(X3),c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
fof(f4972,plain,
spl0_387,
inference(avatar_split_clause,[],[f590,f4970]) ).
fof(f4970,plain,
( spl0_387
<=> ! [X5,X0,X12] :
( c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f590,axiom,
! [X0,X5,X12] :
( c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
fof(f4968,plain,
spl0_386,
inference(avatar_split_clause,[],[f452,f4966]) ).
fof(f4966,plain,
( spl0_386
<=> ! [X3,X4,X0,X5,X8] :
( X5 = X8
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f452,axiom,
! [X3,X0,X8,X4,X5] :
( X5 = X8
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
fof(f4964,plain,
spl0_385,
inference(avatar_split_clause,[],[f375,f4962]) ).
fof(f4962,plain,
( spl0_385
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X8,X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f375,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X8,X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f4960,plain,
spl0_384,
inference(avatar_split_clause,[],[f286,f4958]) ).
fof(f4958,plain,
( spl0_384
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f286,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f4956,plain,
spl0_383,
inference(avatar_split_clause,[],[f285,f4954]) ).
fof(f4954,plain,
( spl0_383
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f285,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f4952,plain,
spl0_382,
inference(avatar_split_clause,[],[f246,f4950]) ).
fof(f4950,plain,
( spl0_382
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f246,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f4948,plain,
spl0_381,
inference(avatar_split_clause,[],[f245,f4946]) ).
fof(f4946,plain,
( spl0_381
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f245,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f4944,plain,
spl0_380,
inference(avatar_split_clause,[],[f244,f4942]) ).
fof(f4942,plain,
( spl0_380
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f244,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f4940,plain,
( spl0_379
| ~ spl0_47
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1833,f1683,f1057,f4938]) ).
fof(f4938,plain,
( spl0_379
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f1683,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1833,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_47
| ~ spl0_172 ),
inference(resolution,[],[f1684,f1059]) ).
fof(f1684,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1683]) ).
fof(f4936,plain,
spl0_378,
inference(avatar_split_clause,[],[f243,f4934]) ).
fof(f243,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f4932,plain,
spl0_377,
inference(avatar_split_clause,[],[f242,f4930]) ).
fof(f242,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f4928,plain,
spl0_376,
inference(avatar_split_clause,[],[f241,f4926]) ).
fof(f4926,plain,
( spl0_376
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f241,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f4924,plain,
spl0_375,
inference(avatar_split_clause,[],[f193,f4922]) ).
fof(f4922,plain,
( spl0_375
<=> ! [X0,X12] :
( c_List_Oremdups(X12,X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) != c_Nat_Osize__class_Osize(c_List_Oremdups(X12,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f193,axiom,
! [X0,X12] :
( c_List_Oremdups(X12,X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) != c_Nat_Osize__class_Osize(c_List_Oremdups(X12,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__remdups__eq_0) ).
fof(f4920,plain,
spl0_374,
inference(avatar_split_clause,[],[f126,f4918]) ).
fof(f4918,plain,
( spl0_374
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f126,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f4916,plain,
spl0_373,
inference(avatar_split_clause,[],[f125,f4914]) ).
fof(f125,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f4912,plain,
spl0_372,
inference(avatar_split_clause,[],[f124,f4910]) ).
fof(f4910,plain,
( spl0_372
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f124,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f4908,plain,
spl0_371,
inference(avatar_split_clause,[],[f123,f4906]) ).
fof(f123,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f4904,plain,
spl0_370,
inference(avatar_split_clause,[],[f122,f4902]) ).
fof(f4902,plain,
( spl0_370
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f122,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f4900,plain,
spl0_369,
inference(avatar_split_clause,[],[f121,f4898]) ).
fof(f4898,plain,
( spl0_369
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f121,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f4896,plain,
( spl0_368
| ~ spl0_120
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1556,f1424,f1370,f4894]) ).
fof(f4894,plain,
( spl0_368
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f1556,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_120
| ~ spl0_129 ),
inference(superposition,[],[f1371,f1425]) ).
fof(f4892,plain,
spl0_367,
inference(avatar_split_clause,[],[f118,f4890]) ).
fof(f4890,plain,
( spl0_367
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f118,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).
fof(f4671,plain,
( spl0_366
| ~ spl0_121
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1555,f1424,f1374,f4669]) ).
fof(f4669,plain,
( spl0_366
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f1555,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat)
| ~ spl0_121
| ~ spl0_129 ),
inference(superposition,[],[f1375,f1425]) ).
fof(f3832,plain,
spl0_365,
inference(avatar_split_clause,[],[f822,f3830]) ).
fof(f3830,plain,
( spl0_365
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Oone__class_Oone(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f822,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Oone__class_Oone(tc_nat) = X4 ),
inference(forward_demodulation,[],[f821,f394]) ).
fof(f394,axiom,
! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f821,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f820,f394]) ).
fof(f820,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f767,f394]) ).
fof(f767,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f277,f314,f314,f314]) ).
fof(f277,axiom,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
fof(f3828,plain,
spl0_364,
inference(avatar_split_clause,[],[f815,f3826]) ).
fof(f3826,plain,
( spl0_364
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f815,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
inference(forward_demodulation,[],[f814,f394]) ).
fof(f814,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f764,f394]) ).
fof(f764,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f359,f314,f314]) ).
fof(f359,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
fof(f3824,plain,
spl0_363,
inference(avatar_split_clause,[],[f813,f3822]) ).
fof(f3822,plain,
( spl0_363
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f813,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
inference(forward_demodulation,[],[f812,f394]) ).
fof(f812,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f763,f394]) ).
fof(f763,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f360,f314,f314]) ).
fof(f360,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
fof(f3820,plain,
spl0_362,
inference(avatar_split_clause,[],[f810,f3818]) ).
fof(f3818,plain,
( spl0_362
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f810,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
inference(forward_demodulation,[],[f761,f394]) ).
fof(f761,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f278,f314]) ).
fof(f278,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
fof(f3816,plain,
spl0_361,
inference(avatar_split_clause,[],[f787,f3814]) ).
fof(f3814,plain,
( spl0_361
<=> ! [X13,X0,X8] : c_List_Olist_OCons(X8,X13,X0) = c_List_Orev(c_List_Orotate1(c_List_Olist_OCons(X8,c_List_Orev(X13,X0),X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f787,plain,
! [X0,X8,X13] : c_List_Olist_OCons(X8,X13,X0) = c_List_Orev(c_List_Orotate1(c_List_Olist_OCons(X8,c_List_Orev(X13,X0),X0),X0),X0),
inference(forward_demodulation,[],[f520,f521]) ).
fof(f520,axiom,
! [X0,X8,X13] : c_List_Olist_OCons(X8,X13,X0) = c_List_Orev(c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
fof(f3812,plain,
spl0_360,
inference(avatar_split_clause,[],[f785,f3810]) ).
fof(f3810,plain,
( spl0_360
<=> ! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X14,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f785,plain,
! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X14,X15,tc_nat),tc_nat),
inference(forward_demodulation,[],[f370,f355]) ).
fof(f370,axiom,
! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X14,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f3808,plain,
spl0_359,
inference(avatar_split_clause,[],[f756,f3806]) ).
fof(f3806,plain,
( spl0_359
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f756,plain,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f79,f314]) ).
fof(f79,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
fof(f3804,plain,
spl0_358,
inference(avatar_split_clause,[],[f700,f3802]) ).
fof(f700,plain,
! [X3,X0,X12] : c_List_Odrop(X3,c_List_Otl(X12,X0),X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),
inference(definition_unfolding,[],[f419,f314]) ).
fof(f419,axiom,
! [X3,X0,X12] : c_List_Odrop(c_Suc(X3),X12,X0) = c_List_Odrop(X3,c_List_Otl(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc_0) ).
fof(f3800,plain,
spl0_357,
inference(avatar_split_clause,[],[f521,f3798]) ).
fof(f3795,plain,
spl0_356,
inference(avatar_split_clause,[],[f503,f3793]) ).
fof(f3793,plain,
( spl0_356
<=> ! [X34,X0,X12,X32] : c_List_Oappend(X12,c_List_Oappend(X32,X34,X0),X0) = c_List_Oappend(c_List_Oappend(X12,X32,X0),X34,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f503,axiom,
! [X0,X34,X12,X32] : c_List_Oappend(X12,c_List_Oappend(X32,X34,X0),X0) = c_List_Oappend(c_List_Oappend(X12,X32,X0),X34,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
fof(f3791,plain,
spl0_355,
inference(avatar_split_clause,[],[f501,f3789]) ).
fof(f3789,plain,
( spl0_355
<=> ! [X5,X0,X12,X6,X8] : c_List_Olist__update(X12,X6,X8,X0) = c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X6,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f501,axiom,
! [X0,X8,X6,X5,X12] : c_List_Olist__update(X12,X6,X8,X0) = c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X6,X8,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
fof(f3787,plain,
spl0_354,
inference(avatar_split_clause,[],[f461,f3785]) ).
fof(f3785,plain,
( spl0_354
<=> ! [X0,X12,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Otake(X3,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f461,axiom,
! [X3,X0,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Otake(X3,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
fof(f3783,plain,
spl0_353,
inference(avatar_split_clause,[],[f451,f3781]) ).
fof(f3781,plain,
( spl0_353
<=> ! [X13,X0,X12] : c_List_Orev(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Orev(X13,X0),c_List_Orev(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f451,axiom,
! [X0,X12,X13] : c_List_Orev(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Orev(X13,X0),c_List_Orev(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
fof(f3779,plain,
spl0_352,
inference(avatar_split_clause,[],[f439,f3777]) ).
fof(f439,axiom,
! [X0,X5,X12,X13] : c_List_Oappend(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Oappend(X12,X13,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
fof(f3775,plain,
spl0_351,
inference(avatar_split_clause,[],[f417,f3773]) ).
fof(f3773,plain,
( spl0_351
<=> ! [X6,X0,X14,X5] : c_List_Odrop(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X14,X6,tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f417,axiom,
! [X0,X6,X14,X5] : c_List_Odrop(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X14,X6,tc_nat),X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
fof(f3771,plain,
spl0_350,
inference(avatar_split_clause,[],[f416,f3769]) ).
fof(f3769,plain,
( spl0_350
<=> ! [X6,X0,X14,X5] : c_List_Otake(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_Orderings_Oord__class_Omin(X6,X14,tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f416,axiom,
! [X0,X6,X14,X5] : c_List_Otake(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_Orderings_Oord__class_Omin(X6,X14,tc_nat),X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__replicate_0) ).
fof(f3767,plain,
spl0_349,
inference(avatar_split_clause,[],[f407,f3765]) ).
fof(f3765,plain,
( spl0_349
<=> ! [X0,X8,X5,X28] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f407,axiom,
! [X28,X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
fof(f3763,plain,
spl0_348,
inference(avatar_split_clause,[],[f365,f3761]) ).
fof(f3761,plain,
( spl0_348
<=> ! [X4,X3,X14] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f365,axiom,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f3759,plain,
spl0_347,
inference(avatar_split_clause,[],[f364,f3757]) ).
fof(f3757,plain,
( spl0_347
<=> ! [X3,X4,X14] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X14,tc_nat),c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f364,axiom,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X14,tc_nat),c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f3754,plain,
spl0_346,
inference(avatar_split_clause,[],[f355,f3752]) ).
fof(f3752,plain,
( spl0_346
<=> ! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f3750,plain,
spl0_345,
inference(avatar_split_clause,[],[f334,f3748]) ).
fof(f334,axiom,
! [X3,X14,X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f3746,plain,
spl0_344,
inference(avatar_split_clause,[],[f333,f3744]) ).
fof(f333,axiom,
! [X8,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f3742,plain,
spl0_343,
inference(avatar_split_clause,[],[f321,f3740]) ).
fof(f3740,plain,
( spl0_343
<=> ! [X4,X0,X12,X3] : c_List_Otake(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_Orderings_Oord__class_Omin(X3,X4,tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f321,axiom,
! [X3,X0,X4,X12] : c_List_Otake(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_Orderings_Oord__class_Omin(X3,X4,tc_nat),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__take_0) ).
fof(f3738,plain,
spl0_342,
inference(avatar_split_clause,[],[f317,f3736]) ).
fof(f3736,plain,
( spl0_342
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f317,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f3734,plain,
spl0_341,
inference(avatar_split_clause,[],[f316,f3732]) ).
fof(f3732,plain,
( spl0_341
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f316,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f3730,plain,
spl0_340,
inference(avatar_split_clause,[],[f307,f3728]) ).
fof(f3728,plain,
( spl0_340
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f307,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f3726,plain,
spl0_339,
inference(avatar_split_clause,[],[f270,f3724]) ).
fof(f3724,plain,
( spl0_339
<=> ! [X0,X12] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f270,axiom,
! [X0,X12] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__tl_0) ).
fof(f3722,plain,
spl0_338,
inference(avatar_split_clause,[],[f257,f3720]) ).
fof(f3720,plain,
( spl0_338
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f257,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f3718,plain,
spl0_337,
inference(avatar_split_clause,[],[f256,f3716]) ).
fof(f3716,plain,
( spl0_337
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f256,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f3714,plain,
spl0_336,
inference(avatar_split_clause,[],[f247,f3712]) ).
fof(f3712,plain,
( spl0_336
<=> ! [X4,X0,X12,X3] : c_List_Odrop(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f247,axiom,
! [X3,X0,X4,X12] : c_List_Odrop(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__drop_0) ).
fof(f3710,plain,
spl0_335,
inference(avatar_split_clause,[],[f230,f3708]) ).
fof(f230,axiom,
! [X3,X0,X12] : c_Nat_Osize__class_Osize(c_List_Odrop(X3,X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__drop_0) ).
fof(f3706,plain,
spl0_334,
inference(avatar_split_clause,[],[f224,f3704]) ).
fof(f3704,plain,
( spl0_334
<=> ! [X0,X12,X3] : c_Nat_Osize__class_Osize(c_List_Otake(X3,X12,X0),tc_List_Olist(X0)) = c_Orderings_Oord__class_Omin(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f224,axiom,
! [X3,X0,X12] : c_Nat_Osize__class_Osize(c_List_Otake(X3,X12,X0),tc_List_Olist(X0)) = c_Orderings_Oord__class_Omin(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__take_0) ).
fof(f3702,plain,
spl0_333,
inference(avatar_split_clause,[],[f199,f3700]) ).
fof(f3700,plain,
( spl0_333
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f199,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f3698,plain,
spl0_332,
inference(avatar_split_clause,[],[f75,f3696]) ).
fof(f3696,plain,
( spl0_332
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f75,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f3694,plain,
spl0_331,
inference(avatar_split_clause,[],[f74,f3692]) ).
fof(f3692,plain,
( spl0_331
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f74,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f3690,plain,
spl0_330,
inference(avatar_split_clause,[],[f73,f3688]) ).
fof(f3688,plain,
( spl0_330
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f73,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f3686,plain,
spl0_329,
inference(avatar_split_clause,[],[f72,f3684]) ).
fof(f3684,plain,
( spl0_329
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f3682,plain,
spl0_328,
inference(avatar_split_clause,[],[f71,f3680]) ).
fof(f3680,plain,
( spl0_328
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f71,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f3678,plain,
spl0_327,
inference(avatar_split_clause,[],[f45,f3676]) ).
fof(f3676,plain,
( spl0_327
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f45,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f3673,plain,
spl0_326,
inference(avatar_split_clause,[],[f44,f3671]) ).
fof(f3671,plain,
( spl0_326
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f44,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f3585,plain,
( spl0_325
| ~ spl0_60
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2053,f1881,f1121,f3583]) ).
fof(f1121,plain,
( spl0_60
<=> ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f2053,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_60
| ~ spl0_192 ),
inference(resolution,[],[f1882,f1122]) ).
fof(f1122,plain,
( ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f3379,plain,
( ~ spl0_323
| spl0_324
| ~ spl0_63
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3262,f3025,f1133,f3377,f3373]) ).
fof(f3373,plain,
( spl0_323
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3377,plain,
( spl0_324
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f1133,plain,
( spl0_63
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f3025,plain,
( spl0_289
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3262,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_63
| ~ spl0_289 ),
inference(resolution,[],[f3026,f1134]) ).
fof(f1134,plain,
( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1133]) ).
fof(f3026,plain,
( ! [X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3025]) ).
fof(f3165,plain,
spl0_322,
inference(avatar_split_clause,[],[f592,f3163]) ).
fof(f3163,plain,
( spl0_322
<=> ! [X5,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist_OCons(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f592,axiom,
! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist_OCons(X5,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
fof(f3161,plain,
spl0_321,
inference(avatar_split_clause,[],[f515,f3159]) ).
fof(f3159,plain,
( spl0_321
<=> ! [X5,X0,X12] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f515,axiom,
! [X0,X5,X12] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
fof(f3157,plain,
spl0_320,
inference(avatar_split_clause,[],[f514,f3155]) ).
fof(f514,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_OCons(c_List_Osko__List__Xneq__Nil__conv__1__1(X12,X0),c_List_Osko__List__Xneq__Nil__conv__1__2(X12,X0),X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_0) ).
fof(f3153,plain,
spl0_319,
inference(avatar_split_clause,[],[f512,f3151]) ).
fof(f512,axiom,
! [X0,X8] :
( c_List_Olist_ONil(X0) = X8
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X0),c_List_Osko__List__Xlist__Xexhaust__1__2(X8,X0),X0) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oexhaust_0) ).
fof(f3149,plain,
spl0_318,
inference(avatar_split_clause,[],[f507,f3147]) ).
fof(f507,axiom,
! [X0,X18] :
( c_List_Olist_ONil(X0) = X18
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xnchotomy__1__1(X18,X0),c_List_Osko__List__Xlist__Xnchotomy__1__2(X18,X0),X0) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Onchotomy_0) ).
fof(f3145,plain,
spl0_317,
inference(avatar_split_clause,[],[f484,f3143]) ).
fof(f3143,plain,
( spl0_317
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olast(c_List_Oappend(X12,X13,X0),X0) = c_List_Olast(X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f484,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olast(c_List_Oappend(X12,X13,X0),X0) = c_List_Olast(X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).
fof(f3141,plain,
spl0_316,
inference(avatar_split_clause,[],[f453,f3139]) ).
fof(f3139,plain,
( spl0_316
<=> ! [X0,X12,X5,X8] : c_List_Olist_OCons(X8,X12,X0) = c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_HOL_Ozero__class_Ozero(tc_nat),X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f453,axiom,
! [X0,X8,X5,X12] : c_List_Olist_OCons(X8,X12,X0) = c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_HOL_Ozero__class_Ozero(tc_nat),X8,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
fof(f3137,plain,
spl0_315,
inference(avatar_split_clause,[],[f450,f3135]) ).
fof(f3135,plain,
( spl0_315
<=> ! [X13,X0,X5,X8] :
( X5 = X8
| c_List_Omember(X5,X13,X0)
| ~ c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f450,axiom,
! [X0,X8,X5,X13] :
( X5 = X8
| c_List_Omember(X5,X13,X0)
| ~ c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_0) ).
fof(f3133,plain,
spl0_314,
inference(avatar_split_clause,[],[f378,f3131]) ).
fof(f3131,plain,
( spl0_314
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X10,X1,X0) != c_HOL_Oplus__class_Oplus(X9,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f378,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X10,X1,X0) != c_HOL_Oplus__class_Oplus(X9,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f3129,plain,
spl0_313,
inference(avatar_split_clause,[],[f377,f3127]) ).
fof(f3127,plain,
( spl0_313
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f377,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f3125,plain,
spl0_312,
inference(avatar_split_clause,[],[f376,f3123]) ).
fof(f3123,plain,
( spl0_312
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f376,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f3120,plain,
spl0_311,
inference(avatar_split_clause,[],[f367,f3118]) ).
fof(f367,axiom,
! [X0,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f3116,plain,
spl0_310,
inference(avatar_split_clause,[],[f362,f3114]) ).
fof(f3114,plain,
( spl0_310
<=> ! [X5,X0,X8] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_Int_Onumber__class_Onumber__of(X5,X0) != c_Int_Onumber__class_Onumber__of(X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f362,axiom,
! [X0,X8,X5] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_Int_Onumber__class_Onumber__of(X5,X0) != c_Int_Onumber__class_Onumber__of(X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f3112,plain,
spl0_309,
inference(avatar_split_clause,[],[f358,f3110]) ).
fof(f3110,plain,
( spl0_309
<=> ! [X20,X0,X5,X19] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X19 = X20
| c_HOL_Ominus__class_Ominus(X19,X20,X0) != c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f358,axiom,
! [X0,X19,X5,X20] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X19 = X20
| c_HOL_Ominus__class_Ominus(X19,X20,X0) != c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f3108,plain,
spl0_308,
inference(avatar_split_clause,[],[f318,f3106]) ).
fof(f3106,plain,
( spl0_308
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f318,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f3104,plain,
spl0_307,
inference(avatar_split_clause,[],[f312,f3102]) ).
fof(f3102,plain,
( spl0_307
<=> ! [X9,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X9,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f312,axiom,
! [X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X9,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f3100,plain,
spl0_306,
inference(avatar_split_clause,[],[f295,f3098]) ).
fof(f3098,plain,
( spl0_306
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(c_List_Oappend(X12,X13,X0),X0) = c_List_Ohd(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f295,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(c_List_Oappend(X12,X13,X0),X0) = c_List_Ohd(X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).
fof(f3096,plain,
spl0_305,
inference(avatar_split_clause,[],[f263,f3094]) ).
fof(f3094,plain,
( spl0_305
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X8,X7,X0)
| c_lessequals(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f263,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X8,X7,X0)
| c_lessequals(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3092,plain,
spl0_304,
inference(avatar_split_clause,[],[f261,f3090]) ).
fof(f3090,plain,
( spl0_304
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_lessequals(X7,X8,X0)
| c_lessequals(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f261,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_lessequals(X7,X8,X0)
| c_lessequals(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3088,plain,
spl0_303,
inference(avatar_split_clause,[],[f254,f3086]) ).
fof(f3086,plain,
( spl0_303
<=> ! [X9,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X9,X1,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f254,axiom,
! [X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X9,X1,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f3084,plain,
spl0_302,
inference(avatar_split_clause,[],[f253,f3082]) ).
fof(f253,axiom,
! [X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = c_Divides_Odiv__class_Omod(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f3077,plain,
spl0_301,
inference(avatar_split_clause,[],[f237,f3075]) ).
fof(f3075,plain,
( spl0_301
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f237,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f3073,plain,
spl0_300,
inference(avatar_split_clause,[],[f236,f3071]) ).
fof(f3071,plain,
( spl0_300
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f236,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f3069,plain,
spl0_299,
inference(avatar_split_clause,[],[f181,f3067]) ).
fof(f3067,plain,
( spl0_299
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,X0) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f181,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,X0) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f3065,plain,
spl0_298,
inference(avatar_split_clause,[],[f133,f3063]) ).
fof(f3063,plain,
( spl0_298
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f133,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f3061,plain,
spl0_297,
inference(avatar_split_clause,[],[f132,f3059]) ).
fof(f3059,plain,
( spl0_297
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f132,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3057,plain,
spl0_296,
inference(avatar_split_clause,[],[f131,f3055]) ).
fof(f3055,plain,
( spl0_296
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f131,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3053,plain,
spl0_295,
inference(avatar_split_clause,[],[f130,f3051]) ).
fof(f3051,plain,
( spl0_295
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f130,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3049,plain,
spl0_294,
inference(avatar_split_clause,[],[f129,f3047]) ).
fof(f129,axiom,
! [X3,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f3045,plain,
spl0_293,
inference(avatar_split_clause,[],[f128,f3043]) ).
fof(f128,axiom,
! [X3,X14,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f3041,plain,
spl0_292,
inference(avatar_split_clause,[],[f127,f3039]) ).
fof(f3039,plain,
( spl0_292
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f127,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f3035,plain,
spl0_291,
inference(avatar_split_clause,[],[f120,f3033]) ).
fof(f3033,plain,
( spl0_291
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f120,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f3031,plain,
spl0_290,
inference(avatar_split_clause,[],[f119,f3029]) ).
fof(f3029,plain,
( spl0_290
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f119,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f3027,plain,
spl0_289,
inference(avatar_split_clause,[],[f101,f3025]) ).
fof(f101,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f3023,plain,
spl0_288,
inference(avatar_split_clause,[],[f100,f3021]) ).
fof(f3021,plain,
( spl0_288
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f100,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f3019,plain,
spl0_287,
inference(avatar_split_clause,[],[f82,f3017]) ).
fof(f3017,plain,
( spl0_287
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f82,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3015,plain,
spl0_286,
inference(avatar_split_clause,[],[f9,f3013]) ).
fof(f3013,plain,
( spl0_286
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f9,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3011,plain,
spl0_285,
inference(avatar_split_clause,[],[f8,f3009]) ).
fof(f3009,plain,
( spl0_285
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f8,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f2884,plain,
( spl0_284
| ~ spl0_38
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1586,f1460,f1012,f2882]) ).
fof(f2882,plain,
( spl0_284
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f1012,plain,
( spl0_38
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1460,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1586,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_38
| ~ spl0_138 ),
inference(resolution,[],[f1461,f1014]) ).
fof(f1014,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1461,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1460]) ).
fof(f2666,plain,
spl0_283,
inference(avatar_split_clause,[],[f591,f2664]) ).
fof(f2664,plain,
( spl0_283
<=> ! [X5,X0] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f591,axiom,
! [X0,X5] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
fof(f2662,plain,
spl0_282,
inference(avatar_split_clause,[],[f581,f2659]) ).
fof(f581,axiom,
c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__1,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_alt3_0) ).
fof(f2657,plain,
spl0_281,
inference(avatar_split_clause,[],[f470,f2655]) ).
fof(f470,axiom,
! [X3,X0,X12] : c_List_Odrop(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Odrop(X3,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__tl_0) ).
fof(f2653,plain,
spl0_280,
inference(avatar_split_clause,[],[f427,f2651]) ).
fof(f2651,plain,
( spl0_280
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Ohd(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f427,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Ohd(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__rev_0) ).
fof(f2649,plain,
spl0_279,
inference(avatar_split_clause,[],[f426,f2647]) ).
fof(f2647,plain,
( spl0_279
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(X12,X0) = c_List_Olast(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f426,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(X12,X0) = c_List_Olast(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__rev_0) ).
fof(f2645,plain,
spl0_278,
inference(avatar_split_clause,[],[f389,f2643]) ).
fof(f2643,plain,
( spl0_278
<=> ! [X6,X0,X12,X5] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X12,X6,X5,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2641,plain,
spl0_277,
inference(avatar_split_clause,[],[f249,f2639]) ).
fof(f2639,plain,
( spl0_277
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f249,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f2637,plain,
spl0_276,
inference(avatar_split_clause,[],[f234,f2635]) ).
fof(f2635,plain,
( spl0_276
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Oorder(X0)
| X5 = X8
| ~ c_lessequals(X8,X5,X0)
| ~ c_lessequals(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f234,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Oorder(X0)
| X5 = X8
| ~ c_lessequals(X8,X5,X0)
| ~ c_lessequals(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f2633,plain,
spl0_275,
inference(avatar_split_clause,[],[f212,f2631]) ).
fof(f2631,plain,
( spl0_275
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f212,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f2629,plain,
spl0_274,
inference(avatar_split_clause,[],[f168,f2627]) ).
fof(f2627,plain,
( spl0_274
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f168,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
fof(f2625,plain,
spl0_273,
inference(avatar_split_clause,[],[f167,f2623]) ).
fof(f2623,plain,
( spl0_273
<=> ! [X5,X9,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X5,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f167,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X5,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
fof(f2621,plain,
( ~ spl0_272
| spl0_260
| ~ spl0_104
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2458,f2257,f1306,f2508,f2618]) ).
fof(f2618,plain,
( spl0_272
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2257,plain,
( spl0_239
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2458,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_104
| ~ spl0_239 ),
inference(trivial_inequality_removal,[],[f2455]) ).
fof(f2455,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_104
| ~ spl0_239 ),
inference(superposition,[],[f2258,f1307]) ).
fof(f2258,plain,
( ! [X0,X1,X9] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0)
| X1 = X9
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2257]) ).
fof(f2616,plain,
spl0_271,
inference(avatar_split_clause,[],[f165,f2614]) ).
fof(f165,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X9,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
fof(f2612,plain,
spl0_270,
inference(avatar_split_clause,[],[f164,f2610]) ).
fof(f164,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X1,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
fof(f2608,plain,
spl0_269,
inference(avatar_split_clause,[],[f149,f2606]) ).
fof(f2606,plain,
( spl0_269
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f149,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f2604,plain,
spl0_268,
inference(avatar_split_clause,[],[f147,f2602]) ).
fof(f2602,plain,
( spl0_268
<=> ! [X9,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X9
| ~ c_lessequals(X1,X9,X0)
| c_HOL_Oord__class_Oless(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f147,axiom,
! [X0,X1,X9] :
( ~ class_Orderings_Oorder(X0)
| X1 = X9
| ~ c_lessequals(X1,X9,X0)
| c_HOL_Oord__class_Oless(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
fof(f2600,plain,
spl0_267,
inference(avatar_split_clause,[],[f141,f2598]) ).
fof(f2598,plain,
( spl0_267
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f141,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f2596,plain,
spl0_266,
inference(avatar_split_clause,[],[f95,f2594]) ).
fof(f2594,plain,
( spl0_266
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f95,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f2592,plain,
spl0_265,
inference(avatar_split_clause,[],[f89,f2590]) ).
fof(f2590,plain,
( spl0_265
<=> ! [X5,X0,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f89,axiom,
! [X0,X8,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X8,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f2588,plain,
spl0_264,
inference(avatar_split_clause,[],[f32,f2586]) ).
fof(f2586,plain,
( spl0_264
<=> ! [X5,X0,X7,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f32,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
fof(f2584,plain,
spl0_263,
inference(avatar_split_clause,[],[f30,f2582]) ).
fof(f2582,plain,
( spl0_263
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f30,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f2580,plain,
spl0_262,
inference(avatar_split_clause,[],[f29,f2578]) ).
fof(f2578,plain,
( spl0_262
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f29,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f2576,plain,
spl0_261,
inference(avatar_split_clause,[],[f27,f2574]) ).
fof(f2574,plain,
( spl0_261
<=> ! [X9,X0,X5,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X5,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f27,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X5,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
fof(f2510,plain,
( ~ spl0_259
| spl0_260
| ~ spl0_104
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2450,f2253,f1306,f2508,f2504]) ).
fof(f2504,plain,
( spl0_259
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2253,plain,
( spl0_238
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2450,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_104
| ~ spl0_238 ),
inference(trivial_inequality_removal,[],[f2447]) ).
fof(f2447,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_104
| ~ spl0_238 ),
inference(superposition,[],[f2254,f1307]) ).
fof(f2254,plain,
( ! [X0,X1,X9] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0)
| X1 = X9
| ~ class_OrderedGroup_Ogroup__add(X0) )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2253]) ).
fof(f2404,plain,
( spl0_258
| ~ spl0_38
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1584,f1456,f1012,f2402]) ).
fof(f2402,plain,
( spl0_258
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1456,plain,
( spl0_137
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1584,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) = X0
| ~ spl0_38
| ~ spl0_137 ),
inference(resolution,[],[f1457,f1014]) ).
fof(f1457,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f2332,plain,
spl0_257,
inference(avatar_split_clause,[],[f740,f2330]) ).
fof(f740,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f36,f314]) ).
fof(f36,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f2328,plain,
spl0_256,
inference(avatar_split_clause,[],[f726,f2326]) ).
fof(f726,plain,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f35,f314]) ).
fof(f35,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f2324,plain,
( spl0_255
| ~ spl0_36
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1579,f1444,f1002,f2322]) ).
fof(f2322,plain,
( spl0_255
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1444,plain,
( spl0_134
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1579,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0
| ~ spl0_36
| ~ spl0_134 ),
inference(resolution,[],[f1445,f1004]) ).
fof(f1445,plain,
( ! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1444]) ).
fof(f2320,plain,
spl0_254,
inference(avatar_split_clause,[],[f598,f2318]) ).
fof(f2318,plain,
( spl0_254
<=> ! [X26,X38,X0,X1,X24] :
( X1 = X24
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f598,axiom,
! [X38,X0,X1,X26,X24] :
( X1 = X24
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
fof(f2316,plain,
spl0_253,
inference(avatar_split_clause,[],[f597,f2314]) ).
fof(f2314,plain,
( spl0_253
<=> ! [X1,X38,X0,X26,X24] :
( X26 = X38
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f597,axiom,
! [X38,X0,X1,X26,X24] :
( X26 = X38
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
fof(f2312,plain,
spl0_252,
inference(avatar_split_clause,[],[f566,f2310]) ).
fof(f2310,plain,
( spl0_252
<=> ! [X0,X14,X12,X5] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Olist__update(X12,X14,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f566,axiom,
! [X0,X14,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Olist__update(X12,X14,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
fof(f2308,plain,
( spl0_251
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2304,f2301,f2306]) ).
fof(f2306,plain,
( spl0_251
<=> ! [X12,X5,X0] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X5,X12,X0),X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2301,plain,
( spl0_250
<=> ! [X12,X5,X0] : c_List_Olast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2304,plain,
( ! [X0,X5,X12] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X5,X12,X0),X0),X0) = X5
| ~ spl0_250 ),
inference(forward_demodulation,[],[f2302,f521]) ).
fof(f2302,plain,
( ! [X0,X5,X12] : c_List_Olast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X5
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2301]) ).
fof(f2303,plain,
spl0_250,
inference(avatar_split_clause,[],[f510,f2301]) ).
fof(f510,axiom,
! [X0,X5,X12] : c_List_Olast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).
fof(f2299,plain,
spl0_249,
inference(avatar_split_clause,[],[f486,f2297]) ).
fof(f2297,plain,
( spl0_249
<=> ! [X5,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_OremoveAll(X5,X12,X0) = c_List_Oremove1(X5,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f486,axiom,
! [X0,X5,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_OremoveAll(X5,X12,X0) = c_List_Oremove1(X5,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1__removeAll_0) ).
fof(f2295,plain,
spl0_248,
inference(avatar_split_clause,[],[f473,f2293]) ).
fof(f473,axiom,
! [X28,X0,X12,X13] :
( X13 = X28
| c_List_Oappend(X12,X13,X0) != c_List_Oappend(X12,X28,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
fof(f2291,plain,
spl0_247,
inference(avatar_split_clause,[],[f472,f2289]) ).
fof(f472,axiom,
! [X28,X0,X12,X13] :
( X13 = X28
| c_List_Oappend(X13,X12,X0) != c_List_Oappend(X28,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
fof(f2287,plain,
spl0_246,
inference(avatar_split_clause,[],[f471,f2285]) ).
fof(f2285,plain,
( spl0_246
<=> ! [X5,X4,X0,X3,X8] :
( X3 = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f471,axiom,
! [X3,X0,X8,X4,X5] :
( X3 = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
fof(f2283,plain,
( spl0_245
| ~ spl0_10
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1578,f1444,f872,f2281]) ).
fof(f2281,plain,
( spl0_245
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f872,plain,
( spl0_10
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1578,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_10
| ~ spl0_134 ),
inference(resolution,[],[f1445,f874]) ).
fof(f874,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f872]) ).
fof(f2279,plain,
spl0_244,
inference(avatar_split_clause,[],[f459,f2277]) ).
fof(f459,axiom,
! [X3,X0,X12] : c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Odrop(X3,X12,X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
fof(f2275,plain,
spl0_243,
inference(avatar_split_clause,[],[f457,f2273]) ).
fof(f2273,plain,
( spl0_243
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olast(c_List_Oreplicate(X3,X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f457,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olast(c_List_Oreplicate(X3,X5,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__replicate_0) ).
fof(f2271,plain,
spl0_242,
inference(avatar_split_clause,[],[f448,f2269]) ).
fof(f2269,plain,
( spl0_242
<=> ! [X5,X0,X12] : c_List_OremoveAll(X5,X12,X0) = c_List_OremoveAll(X5,c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f448,axiom,
! [X0,X5,X12] : c_List_OremoveAll(X5,X12,X0) = c_List_OremoveAll(X5,c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I2_J_0) ).
fof(f2267,plain,
spl0_241,
inference(avatar_split_clause,[],[f373,f2265]) ).
fof(f373,axiom,
! [X3,X14,X4] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f2263,plain,
spl0_240,
inference(avatar_split_clause,[],[f372,f2261]) ).
fof(f372,axiom,
! [X8,X7,X5] :
( X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X8,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
fof(f2259,plain,
spl0_239,
inference(avatar_split_clause,[],[f369,f2257]) ).
fof(f369,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f2255,plain,
spl0_238,
inference(avatar_split_clause,[],[f368,f2253]) ).
fof(f368,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f2251,plain,
spl0_237,
inference(avatar_split_clause,[],[f348,f2249]) ).
fof(f348,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X8,X5,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2247,plain,
spl0_236,
inference(avatar_split_clause,[],[f347,f2245]) ).
fof(f347,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2243,plain,
spl0_235,
inference(avatar_split_clause,[],[f346,f2241]) ).
fof(f346,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2237,plain,
spl0_234,
inference(avatar_split_clause,[],[f304,f2235]) ).
fof(f2235,plain,
( spl0_234
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Ohd(c_List_Oreplicate(X3,X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f304,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Ohd(c_List_Oreplicate(X3,X5,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__replicate_0) ).
fof(f2233,plain,
spl0_233,
inference(avatar_split_clause,[],[f303,f2231]) ).
fof(f303,axiom,
! [X0,X12,X13] : c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
fof(f2229,plain,
spl0_232,
inference(avatar_split_clause,[],[f302,f2227]) ).
fof(f302,axiom,
! [X0,X12,X13] : c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
fof(f2225,plain,
spl0_231,
inference(avatar_split_clause,[],[f135,f2223]) ).
fof(f135,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2221,plain,
spl0_230,
inference(avatar_split_clause,[],[f134,f2219]) ).
fof(f134,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2217,plain,
spl0_229,
inference(avatar_split_clause,[],[f57,f2215]) ).
fof(f57,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
fof(f2213,plain,
spl0_228,
inference(avatar_split_clause,[],[f52,f2211]) ).
fof(f2211,plain,
( spl0_228
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f52,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f2209,plain,
spl0_227,
inference(avatar_split_clause,[],[f13,f2207]) ).
fof(f2207,plain,
( spl0_227
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f13,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f2182,plain,
( ~ spl0_20
| spl0_226
| ~ spl0_99
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1571,f1436,f1286,f2180,f922]) ).
fof(f2180,plain,
( spl0_226
<=> ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1571,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_99
| ~ spl0_132 ),
inference(superposition,[],[f1437,f1287]) ).
fof(f2137,plain,
( spl0_225
| ~ spl0_47
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1569,f1432,f1057,f2135]) ).
fof(f2135,plain,
( spl0_225
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1432,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1569,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_47
| ~ spl0_131 ),
inference(resolution,[],[f1433,f1059]) ).
fof(f1433,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1432]) ).
fof(f2120,plain,
( spl0_224
| ~ spl0_18
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1568,f1432,f912,f2118]) ).
fof(f2118,plain,
( spl0_224
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1568,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_18
| ~ spl0_131 ),
inference(resolution,[],[f1433,f914]) ).
fof(f2007,plain,
( spl0_223
| ~ spl0_47
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1567,f1428,f1057,f2005]) ).
fof(f2005,plain,
( spl0_223
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1428,plain,
( spl0_130
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1567,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X0,X0,tc_Int_Oint)
| ~ spl0_47
| ~ spl0_130 ),
inference(resolution,[],[f1429,f1059]) ).
fof(f1429,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f2003,plain,
spl0_222,
inference(avatar_split_clause,[],[f775,f2001]) ).
fof(f775,plain,
! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f684,f680]) ).
fof(f680,plain,
! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(definition_unfolding,[],[f313,f314]) ).
fof(f313,axiom,
! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
fof(f684,plain,
! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2,f314]) ).
fof(f2,axiom,
! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f1999,plain,
spl0_221,
inference(avatar_split_clause,[],[f774,f1997]) ).
fof(f774,plain,
! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X4,X6,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f683,f680]) ).
fof(f683,plain,
! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X6,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f3,f314]) ).
fof(f3,axiom,
! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Oplus__class_Oplus(X4,X6,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1995,plain,
spl0_220,
inference(avatar_split_clause,[],[f686,f1993]) ).
fof(f686,plain,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f7,f314]) ).
fof(f7,axiom,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_Suc(X4),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1991,plain,
spl0_219,
inference(avatar_split_clause,[],[f543,f1989]) ).
fof(f543,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
fof(f1987,plain,
spl0_218,
inference(avatar_split_clause,[],[f542,f1985]) ).
fof(f542,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
fof(f1983,plain,
spl0_217,
inference(avatar_split_clause,[],[f506,f1981]) ).
fof(f1981,plain,
( spl0_217
<=> ! [X0,X12,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X1,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f506,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X1,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remove1_0) ).
fof(f1979,plain,
spl0_216,
inference(avatar_split_clause,[],[f495,f1977]) ).
fof(f1977,plain,
( spl0_216
<=> ! [X13,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X13,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f495,axiom,
! [X0,X12,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X13,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_1) ).
fof(f1975,plain,
spl0_215,
inference(avatar_split_clause,[],[f494,f1973]) ).
fof(f1973,plain,
( spl0_215
<=> ! [X13,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f494,axiom,
! [X0,X12,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__append_0) ).
fof(f1971,plain,
spl0_214,
inference(avatar_split_clause,[],[f491,f1969]) ).
fof(f1969,plain,
( spl0_214
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f491,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X3,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
fof(f1967,plain,
spl0_213,
inference(avatar_split_clause,[],[f479,f1965]) ).
fof(f1965,plain,
( spl0_213
<=> ! [X5,X0,X3] : c_List_Oreplicate(X3,X5,X0) = c_List_Orev(c_List_Oreplicate(X3,X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f479,axiom,
! [X3,X0,X5] : c_List_Oreplicate(X3,X5,X0) = c_List_Orev(c_List_Oreplicate(X3,X5,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
fof(f1963,plain,
( spl0_212
| ~ spl0_18
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1566,f1428,f912,f1961]) ).
fof(f1961,plain,
( spl0_212
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1566,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_18
| ~ spl0_130 ),
inference(resolution,[],[f1429,f914]) ).
fof(f1959,plain,
spl0_211,
inference(avatar_split_clause,[],[f474,f1957]) ).
fof(f1957,plain,
( spl0_211
<=> ! [X0,X12,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Otake(X3,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f474,axiom,
! [X3,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Otake(X3,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__take_0) ).
fof(f1955,plain,
spl0_210,
inference(avatar_split_clause,[],[f469,f1953]) ).
fof(f1953,plain,
( spl0_210
<=> ! [X0,X12,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Odrop(X3,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f469,axiom,
! [X3,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Odrop(X3,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
fof(f1951,plain,
spl0_209,
inference(avatar_split_clause,[],[f445,f1949]) ).
fof(f1949,plain,
( spl0_209
<=> ! [X13,X0,X5,X8] :
( ~ c_List_Omember(X5,X13,X0)
| c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f445,axiom,
! [X0,X8,X5,X13] :
( ~ c_List_Omember(X5,X13,X0)
| c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_2) ).
fof(f1947,plain,
spl0_208,
inference(avatar_split_clause,[],[f435,f1945]) ).
fof(f1945,plain,
( spl0_208
<=> ! [X5,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f435,axiom,
! [X0,X5,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
fof(f1943,plain,
spl0_207,
inference(avatar_split_clause,[],[f404,f1941]) ).
fof(f404,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f1939,plain,
spl0_206,
inference(avatar_split_clause,[],[f396,f1937]) ).
fof(f1937,plain,
( spl0_206
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f396,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f1935,plain,
spl0_205,
inference(avatar_split_clause,[],[f366,f1933]) ).
fof(f366,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X8,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f1931,plain,
spl0_204,
inference(avatar_split_clause,[],[f326,f1929]) ).
fof(f1929,plain,
( spl0_204
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f326,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f1927,plain,
spl0_203,
inference(avatar_split_clause,[],[f319,f1925]) ).
fof(f319,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X9,X0),X9,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f1923,plain,
spl0_202,
inference(avatar_split_clause,[],[f294,f1921]) ).
fof(f294,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
fof(f1919,plain,
( spl0_201
| ~ spl0_94
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1557,f1424,f1257,f1917]) ).
fof(f1917,plain,
( spl0_201
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1257,plain,
( spl0_94
<=> ! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1557,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) != X0
| ~ spl0_94
| ~ spl0_129 ),
inference(superposition,[],[f1258,f1425]) ).
fof(f1258,plain,
( ! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X3
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1257]) ).
fof(f1915,plain,
spl0_200,
inference(avatar_split_clause,[],[f272,f1913]) ).
fof(f1913,plain,
( spl0_200
<=> ! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1911,plain,
spl0_199,
inference(avatar_split_clause,[],[f227,f1909]) ).
fof(f1909,plain,
( spl0_199
<=> ! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1907,plain,
spl0_198,
inference(avatar_split_clause,[],[f211,f1905]) ).
fof(f1905,plain,
( spl0_198
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f211,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1903,plain,
spl0_197,
inference(avatar_split_clause,[],[f210,f1901]) ).
fof(f1901,plain,
( spl0_197
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f210,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1899,plain,
spl0_196,
inference(avatar_split_clause,[],[f185,f1897]) ).
fof(f1897,plain,
( spl0_196
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f185,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1895,plain,
spl0_195,
inference(avatar_split_clause,[],[f183,f1893]) ).
fof(f183,axiom,
! [X0,X8,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f1891,plain,
spl0_194,
inference(avatar_split_clause,[],[f174,f1889]) ).
fof(f1889,plain,
( spl0_194
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f174,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f1887,plain,
spl0_193,
inference(avatar_split_clause,[],[f91,f1885]) ).
fof(f1885,plain,
( spl0_193
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f91,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f1883,plain,
spl0_192,
inference(avatar_split_clause,[],[f80,f1881]) ).
fof(f80,axiom,
! [X3,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X3,tc_nat),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f1879,plain,
spl0_191,
inference(avatar_split_clause,[],[f67,f1877]) ).
fof(f67,axiom,
! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X4,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f1875,plain,
( spl0_190
| ~ spl0_46
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1546,f1416,f1052,f1873]) ).
fof(f1873,plain,
( spl0_190
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1416,plain,
( spl0_127
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1546,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_46
| ~ spl0_127 ),
inference(resolution,[],[f1417,f1054]) ).
fof(f1417,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f1871,plain,
spl0_189,
inference(avatar_split_clause,[],[f66,f1869]) ).
fof(f66,axiom,
! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X15,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
fof(f1867,plain,
spl0_188,
inference(avatar_split_clause,[],[f65,f1865]) ).
fof(f65,axiom,
! [X6,X14,X15] :
( c_HOL_Oord__class_Oless(X6,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f1803,plain,
( spl0_187
| ~ spl0_67
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1751,f1631,f1149,f1801]) ).
fof(f1801,plain,
( spl0_187
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1149,plain,
( spl0_67
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1751,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_67
| ~ spl0_159 ),
inference(duplicate_literal_removal,[],[f1746]) ).
fof(f1746,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_67
| ~ spl0_159 ),
inference(resolution,[],[f1632,f1150]) ).
fof(f1150,plain,
( ! [X0,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1741,plain,
spl0_186,
inference(avatar_split_clause,[],[f557,f1739]) ).
fof(f1739,plain,
( spl0_186
<=> ! [X5,X0] :
( c_List_Olist_ONil(X0) = X5
| c_List_Olist_ONil(X0) != c_List_Oremdups(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f557,axiom,
! [X0,X5] :
( c_List_Olist_ONil(X0) = X5
| c_List_Olist_ONil(X0) != c_List_Oremdups(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_0) ).
fof(f1737,plain,
spl0_185,
inference(avatar_split_clause,[],[f552,f1735]) ).
fof(f1735,plain,
( spl0_185
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orotate1(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f552,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orotate1(X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
fof(f1733,plain,
( spl0_184
| ~ spl0_46
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1545,f1412,f1052,f1731]) ).
fof(f1731,plain,
( spl0_184
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1412,plain,
( spl0_126
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1545,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
| ~ spl0_46
| ~ spl0_126 ),
inference(resolution,[],[f1413,f1054]) ).
fof(f1413,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f1729,plain,
spl0_183,
inference(avatar_split_clause,[],[f538,f1727]) ).
fof(f538,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orev(X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
fof(f1725,plain,
spl0_182,
inference(avatar_split_clause,[],[f531,f1723]) ).
fof(f1723,plain,
( spl0_182
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Oappend(X12,X13,X0) != X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f531,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Oappend(X12,X13,X0) != X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
fof(f1721,plain,
spl0_181,
inference(avatar_split_clause,[],[f529,f1719]) ).
fof(f1719,plain,
( spl0_181
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(X12,X13,X0) != X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f529,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(X12,X13,X0) != X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
fof(f1717,plain,
spl0_180,
inference(avatar_split_clause,[],[f497,f1715]) ).
fof(f1715,plain,
( spl0_180
<=> ! [X0,X16] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X16,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f497,axiom,
! [X0,X16] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X16,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X16,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted__remdups_0) ).
fof(f1713,plain,
spl0_179,
inference(avatar_split_clause,[],[f488,f1711]) ).
fof(f488,axiom,
! [X0,X12,X13] :
( X12 = X13
| c_List_Orev(X12,X0) != c_List_Orev(X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
fof(f1709,plain,
spl0_178,
inference(avatar_split_clause,[],[f460,f1707]) ).
fof(f460,axiom,
! [X0,X5,X12] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
fof(f1705,plain,
spl0_177,
inference(avatar_split_clause,[],[f354,f1703]) ).
fof(f354,axiom,
! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f1701,plain,
spl0_176,
inference(avatar_split_clause,[],[f345,f1699]) ).
fof(f345,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1697,plain,
spl0_175,
inference(avatar_split_clause,[],[f315,f1695]) ).
fof(f315,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1693,plain,
spl0_174,
inference(avatar_split_clause,[],[f292,f1691]) ).
fof(f1691,plain,
( spl0_174
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f292,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f1689,plain,
spl0_173,
inference(avatar_split_clause,[],[f291,f1687]) ).
fof(f291,axiom,
! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f1685,plain,
spl0_172,
inference(avatar_split_clause,[],[f289,f1683]) ).
fof(f289,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f1681,plain,
spl0_171,
inference(avatar_split_clause,[],[f279,f1679]) ).
fof(f279,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1677,plain,
spl0_170,
inference(avatar_split_clause,[],[f179,f1675]) ).
fof(f179,axiom,
! [X1,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
fof(f1673,plain,
spl0_169,
inference(avatar_split_clause,[],[f153,f1671]) ).
fof(f153,axiom,
! [X0,X1,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f1669,plain,
spl0_168,
inference(avatar_split_clause,[],[f151,f1667]) ).
fof(f151,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1665,plain,
spl0_167,
inference(avatar_split_clause,[],[f150,f1663]) ).
fof(f150,axiom,
! [X0,X1,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1661,plain,
spl0_166,
inference(avatar_split_clause,[],[f105,f1659]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f1657,plain,
spl0_165,
inference(avatar_split_clause,[],[f99,f1655]) ).
fof(f99,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1653,plain,
spl0_164,
inference(avatar_split_clause,[],[f98,f1651]) ).
fof(f98,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1649,plain,
( ~ spl0_50
| spl0_163
| ~ spl0_124
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1573,f1436,f1403,f1647,f1072]) ).
fof(f1647,plain,
( spl0_163
<=> ! [X0] : c_lessequals(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1403,plain,
( spl0_124
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1573,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_Int_Oint)
| ~ class_Orderings_Olinorder(tc_Int_Oint) )
| ~ spl0_124
| ~ spl0_132 ),
inference(superposition,[],[f1437,f1404]) ).
fof(f1404,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_Int_Oint) = X0
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1403]) ).
fof(f1645,plain,
spl0_162,
inference(avatar_split_clause,[],[f81,f1643]) ).
fof(f81,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f1641,plain,
spl0_161,
inference(avatar_split_clause,[],[f21,f1639]) ).
fof(f1639,plain,
( spl0_161
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f21,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1637,plain,
spl0_160,
inference(avatar_split_clause,[],[f19,f1635]) ).
fof(f19,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1633,plain,
spl0_159,
inference(avatar_split_clause,[],[f18,f1631]) ).
fof(f18,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f1594,plain,
( ~ spl0_20
| spl0_158
| ~ spl0_123
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1572,f1436,f1384,f1592,f922]) ).
fof(f1592,plain,
( spl0_158
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1384,plain,
( spl0_123
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1572,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_123
| ~ spl0_132 ),
inference(superposition,[],[f1437,f1385]) ).
fof(f1385,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1384]) ).
fof(f1539,plain,
spl0_157,
inference(avatar_split_clause,[],[f795,f1537]) ).
fof(f795,plain,
! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
inference(forward_demodulation,[],[f794,f395]) ).
fof(f395,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f794,plain,
! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
inference(forward_demodulation,[],[f730,f184]) ).
fof(f730,plain,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f6,f314]) ).
fof(f6,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1535,plain,
spl0_156,
inference(avatar_split_clause,[],[f676,f1533]) ).
fof(f676,plain,
! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f22,f314]) ).
fof(f22,axiom,
! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X3),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
fof(f1531,plain,
spl0_155,
inference(avatar_split_clause,[],[f606,f1529]) ).
fof(f606,axiom,
! [X0,X5,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Olist_OCons(X5,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
fof(f1527,plain,
spl0_154,
inference(avatar_split_clause,[],[f595,f1525]) ).
fof(f1525,plain,
( spl0_154
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f595,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
fof(f1523,plain,
( spl0_153
| ~ spl0_78
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1406,f1374,f1193,f1520]) ).
fof(f1520,plain,
( spl0_153
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1406,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_78
| ~ spl0_121 ),
inference(superposition,[],[f1375,f1194]) ).
fof(f1518,plain,
spl0_152,
inference(avatar_split_clause,[],[f586,f1516]) ).
fof(f1516,plain,
( spl0_152
<=> ! [X5,X0] : c_List_Olast(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f586,axiom,
! [X0,X5] : c_List_Olast(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
fof(f1514,plain,
spl0_151,
inference(avatar_split_clause,[],[f580,f1512]) ).
fof(f1512,plain,
( spl0_151
<=> ! [X6,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Otake(X6,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f580,axiom,
! [X0,X6,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Otake(X6,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__take_0) ).
fof(f1510,plain,
spl0_150,
inference(avatar_split_clause,[],[f575,f1508]) ).
fof(f575,axiom,
! [X0,X6,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Odrop(X6,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
fof(f1506,plain,
spl0_149,
inference(avatar_split_clause,[],[f572,f1504]) ).
fof(f572,axiom,
! [X0,X12,X13] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_0) ).
fof(f1502,plain,
spl0_148,
inference(avatar_split_clause,[],[f571,f1500]) ).
fof(f1500,plain,
( spl0_148
<=> ! [X13,X0,X12] :
( c_List_Odistinct(X13,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f571,axiom,
! [X0,X12,X13] :
( c_List_Odistinct(X13,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__append_1) ).
fof(f1498,plain,
spl0_147,
inference(avatar_split_clause,[],[f570,f1496]) ).
fof(f1496,plain,
( spl0_147
<=> ! [X5,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Oremove1(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f570,axiom,
! [X0,X5,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Oremove1(X5,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remove1_0) ).
fof(f1494,plain,
spl0_146,
inference(avatar_split_clause,[],[f559,f1492]) ).
fof(f1492,plain,
( spl0_146
<=> ! [X6,X0,X8] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X6,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f559,axiom,
! [X0,X8,X6] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X6,X8,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
fof(f1490,plain,
spl0_145,
inference(avatar_split_clause,[],[f438,f1488]) ).
fof(f1488,plain,
( spl0_145
<=> ! [X5,X0,X12] : c_List_Oremove1(X5,c_List_Olist_OCons(X5,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f438,axiom,
! [X0,X5,X12] : c_List_Oremove1(X5,c_List_Olist_OCons(X5,X12,X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I2_J_0) ).
fof(f1486,plain,
spl0_144,
inference(avatar_split_clause,[],[f403,f1484]) ).
fof(f403,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X3,tc_nat) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1482,plain,
spl0_143,
inference(avatar_split_clause,[],[f402,f1480]) ).
fof(f402,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X3,tc_nat) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f1478,plain,
spl0_142,
inference(avatar_split_clause,[],[f401,f1476]) ).
fof(f1476,plain,
( spl0_142
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f401,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1474,plain,
spl0_141,
inference(avatar_split_clause,[],[f400,f1472]) ).
fof(f1472,plain,
( spl0_141
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f400,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1470,plain,
spl0_140,
inference(avatar_split_clause,[],[f399,f1468]) ).
fof(f1468,plain,
( spl0_140
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f399,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1466,plain,
spl0_139,
inference(avatar_split_clause,[],[f398,f1464]) ).
fof(f1464,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f398,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1462,plain,
spl0_138,
inference(avatar_split_clause,[],[f397,f1460]) ).
fof(f397,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1458,plain,
spl0_137,
inference(avatar_split_clause,[],[f392,f1456]) ).
fof(f392,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1454,plain,
spl0_136,
inference(avatar_split_clause,[],[f255,f1452]) ).
fof(f255,axiom,
! [X3,X0,X5] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X5,X0),tc_List_Olist(X0)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).
fof(f1450,plain,
spl0_135,
inference(avatar_split_clause,[],[f216,f1448]) ).
fof(f1448,plain,
( spl0_135
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f216,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
fof(f1446,plain,
spl0_134,
inference(avatar_split_clause,[],[f215,f1444]) ).
fof(f215,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1442,plain,
spl0_133,
inference(avatar_split_clause,[],[f201,f1440]) ).
fof(f201,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1438,plain,
spl0_132,
inference(avatar_split_clause,[],[f200,f1436]) ).
fof(f200,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1434,plain,
spl0_131,
inference(avatar_split_clause,[],[f188,f1432]) ).
fof(f188,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1430,plain,
spl0_130,
inference(avatar_split_clause,[],[f187,f1428]) ).
fof(f187,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1426,plain,
spl0_129,
inference(avatar_split_clause,[],[f184,f1424]) ).
fof(f1422,plain,
spl0_128,
inference(avatar_split_clause,[],[f178,f1420]) ).
fof(f1420,plain,
( spl0_128
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f178,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1418,plain,
spl0_127,
inference(avatar_split_clause,[],[f176,f1416]) ).
fof(f176,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1414,plain,
spl0_126,
inference(avatar_split_clause,[],[f175,f1412]) ).
fof(f175,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f1410,plain,
spl0_125,
inference(avatar_split_clause,[],[f109,f1408]) ).
fof(f109,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1405,plain,
( spl0_124
| ~ spl0_50
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1382,f1290,f1072,f1403]) ).
fof(f1290,plain,
( spl0_100
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1382,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_Int_Oint) = X0
| ~ spl0_50
| ~ spl0_100 ),
inference(resolution,[],[f1291,f1074]) ).
fof(f1291,plain,
( ! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f1386,plain,
( spl0_123
| ~ spl0_20
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1381,f1290,f922,f1384]) ).
fof(f1381,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_20
| ~ spl0_100 ),
inference(resolution,[],[f1291,f924]) ).
fof(f1380,plain,
spl0_122,
inference(avatar_split_clause,[],[f779,f1378]) ).
fof(f1378,plain,
( spl0_122
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f779,plain,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(forward_demodulation,[],[f778,f395]) ).
fof(f778,plain,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f687,f680]) ).
fof(f687,plain,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f222,f314]) ).
fof(f222,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1376,plain,
spl0_121,
inference(avatar_split_clause,[],[f673,f1374]) ).
fof(f673,plain,
! [X3] : c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f102,f314]) ).
fof(f102,axiom,
! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f1372,plain,
spl0_120,
inference(avatar_split_clause,[],[f669,f1370]) ).
fof(f669,plain,
! [X21] : c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(definition_unfolding,[],[f239,f314]) ).
fof(f239,axiom,
! [X21] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
fof(f1368,plain,
spl0_119,
inference(avatar_split_clause,[],[f579,f1366]) ).
fof(f579,axiom,
! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups__id_0) ).
fof(f1364,plain,
spl0_118,
inference(avatar_split_clause,[],[f578,f1362]) ).
fof(f1362,plain,
( spl0_118
<=> ! [X0,X12] :
( c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) != X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f578,axiom,
! [X0,X12] :
( c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) != X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__id__iff__distinct_0) ).
fof(f1360,plain,
spl0_117,
inference(avatar_split_clause,[],[f577,f1358]) ).
fof(f1358,plain,
( spl0_117
<=> ! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f577,axiom,
! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
fof(f1356,plain,
spl0_116,
inference(avatar_split_clause,[],[f576,f1354]) ).
fof(f576,axiom,
! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
fof(f1352,plain,
spl0_115,
inference(avatar_split_clause,[],[f574,f1350]) ).
fof(f1350,plain,
( spl0_115
<=> ! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f574,axiom,
! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_0) ).
fof(f1348,plain,
spl0_114,
inference(avatar_split_clause,[],[f573,f1346]) ).
fof(f573,axiom,
! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct1__rotate_1) ).
fof(f1344,plain,
spl0_113,
inference(avatar_split_clause,[],[f561,f1342]) ).
fof(f1342,plain,
( spl0_113
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_Oremove1(X5,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f561,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Oremove1(X5,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remove1_Osimps_I1_J_0) ).
fof(f1340,plain,
spl0_112,
inference(avatar_split_clause,[],[f553,f1338]) ).
fof(f1338,plain,
( spl0_112
<=> ! [X0,X3] : c_List_Olist_ONil(X0) = c_List_Otake(X3,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f553,axiom,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Otake(X3,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
fof(f1336,plain,
spl0_111,
inference(avatar_split_clause,[],[f546,f1334]) ).
fof(f1334,plain,
( spl0_111
<=> ! [X0,X37] : c_List_Olist_ONil(X0) = c_List_Olist__inter(c_List_Olist_ONil(X0),X37,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f546,axiom,
! [X0,X37] : c_List_Olist_ONil(X0) = c_List_Olist__inter(c_List_Olist_ONil(X0),X37,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__inter_Osimps_I1_J_0) ).
fof(f1332,plain,
spl0_110,
inference(avatar_split_clause,[],[f545,f1330]) ).
fof(f1330,plain,
( spl0_110
<=> ! [X0,X3] : c_List_Olist_ONil(X0) = c_List_Odrop(X3,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f545,axiom,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Odrop(X3,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
fof(f1328,plain,
spl0_109,
inference(avatar_split_clause,[],[f525,f1326]) ).
fof(f1326,plain,
( spl0_109
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_OremoveAll(X5,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f525,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_OremoveAll(X5,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_removeAll_Osimps_I1_J_0) ).
fof(f1324,plain,
spl0_108,
inference(avatar_split_clause,[],[f487,f1322]) ).
fof(f487,axiom,
! [X0,X12] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).
fof(f1320,plain,
spl0_107,
inference(avatar_split_clause,[],[f454,f1318]) ).
fof(f454,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
fof(f1316,plain,
spl0_106,
inference(avatar_split_clause,[],[f446,f1314]) ).
fof(f446,axiom,
! [X0,X5,X12] : c_List_Otl(c_List_Olist_OCons(X5,X12,X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
fof(f1312,plain,
spl0_105,
inference(avatar_split_clause,[],[f406,f1310]) ).
fof(f406,axiom,
! [X0,X5,X12] : c_List_Ohd(c_List_Olist_OCons(X5,X12,X0),X0) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
fof(f1308,plain,
spl0_104,
inference(avatar_split_clause,[],[f363,f1306]) ).
fof(f363,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1304,plain,
spl0_103,
inference(avatar_split_clause,[],[f293,f1302]) ).
fof(f1300,plain,
spl0_102,
inference(avatar_split_clause,[],[f290,f1298]) ).
fof(f1298,plain,
( spl0_102
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f290,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1296,plain,
spl0_101,
inference(avatar_split_clause,[],[f288,f1294]) ).
fof(f1294,plain,
( spl0_101
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f288,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1292,plain,
spl0_100,
inference(avatar_split_clause,[],[f228,f1290]) ).
fof(f228,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1288,plain,
spl0_99,
inference(avatar_split_clause,[],[f207,f1286]) ).
fof(f207,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0R_0) ).
fof(f1284,plain,
spl0_98,
inference(avatar_split_clause,[],[f163,f1282]) ).
fof(f163,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0L_0) ).
fof(f1280,plain,
spl0_97,
inference(avatar_split_clause,[],[f155,f1278]) ).
fof(f1278,plain,
( spl0_97
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f155,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1276,plain,
spl0_96,
inference(avatar_split_clause,[],[f154,f1274]) ).
fof(f1274,plain,
( spl0_96
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f154,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1272,plain,
( ~ spl0_95
| ~ spl0_78
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1267,f1257,f1193,f1269]) ).
fof(f1269,plain,
( spl0_95
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1267,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| ~ spl0_78
| ~ spl0_94 ),
inference(superposition,[],[f1258,f1194]) ).
fof(f1259,plain,
spl0_94,
inference(avatar_split_clause,[],[f667,f1257]) ).
fof(f667,plain,
! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) != X3,
inference(definition_unfolding,[],[f259,f314]) ).
fof(f259,axiom,
! [X3] : c_Suc(X3) != X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f1255,plain,
spl0_93,
inference(avatar_split_clause,[],[f600,f1253]) ).
fof(f600,axiom,
! [X38,X0,X24] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X24,X38,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
fof(f1251,plain,
spl0_92,
inference(avatar_split_clause,[],[f554,f1249]) ).
fof(f1249,plain,
( spl0_92
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orotate1(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f554,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orotate1(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
fof(f1247,plain,
spl0_91,
inference(avatar_split_clause,[],[f550,f1245]) ).
fof(f550,axiom,
! [X0,X5] : c_List_Oappend(c_List_Olist_ONil(X0),X5,X0) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
fof(f1243,plain,
spl0_90,
inference(avatar_split_clause,[],[f549,f1241]) ).
fof(f549,axiom,
! [X0,X12] : c_List_Oappend(X12,c_List_Olist_ONil(X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
fof(f1239,plain,
spl0_89,
inference(avatar_split_clause,[],[f536,f1237]) ).
fof(f1237,plain,
( spl0_89
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Otl(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f536,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Otl(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
fof(f1235,plain,
spl0_88,
inference(avatar_split_clause,[],[f535,f1233]) ).
fof(f1233,plain,
( spl0_88
<=> ! [X13,X0] : c_List_Osplice(c_List_Olist_ONil(X0),X13,X0) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f535,axiom,
! [X0,X13] : c_List_Osplice(c_List_Olist_ONil(X0),X13,X0) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
fof(f1231,plain,
spl0_87,
inference(avatar_split_clause,[],[f534,f1229]) ).
fof(f1229,plain,
( spl0_87
<=> ! [X0,X12] : c_List_Osplice(X12,c_List_Olist_ONil(X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f534,axiom,
! [X0,X12] : c_List_Osplice(X12,c_List_Olist_ONil(X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
fof(f1227,plain,
spl0_86,
inference(avatar_split_clause,[],[f528,f1225]) ).
fof(f1225,plain,
( spl0_86
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f528,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_remdups__eq__nil__right__iff_1) ).
fof(f1223,plain,
spl0_85,
inference(avatar_split_clause,[],[f526,f1221]) ).
fof(f1221,plain,
( spl0_85
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f526,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
fof(f1219,plain,
spl0_84,
inference(avatar_split_clause,[],[f524,f1217]) ).
fof(f1217,plain,
( spl0_84
<=> ! [X0,X12] :
( ~ c_List_Onull(X12,X0)
| c_List_Olist_ONil(X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f524,axiom,
! [X0,X12] :
( ~ c_List_Onull(X12,X0)
| c_List_Olist_ONil(X0) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_1) ).
fof(f1215,plain,
spl0_83,
inference(avatar_split_clause,[],[f477,f1213]) ).
fof(f477,axiom,
! [X0,X12] : c_List_Orev(c_List_Orev(X12,X0),X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
fof(f1211,plain,
spl0_82,
inference(avatar_split_clause,[],[f465,f1209]) ).
fof(f1209,plain,
( spl0_82
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f465,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f1207,plain,
spl0_81,
inference(avatar_split_clause,[],[f464,f1205]) ).
fof(f464,axiom,
! [X0,X12] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).
fof(f1203,plain,
spl0_80,
inference(avatar_split_clause,[],[f447,f1201]) ).
fof(f447,axiom,
! [X0,X5,X13] : c_List_Omember(X5,c_List_Olist_OCons(X5,X13,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I2_J_1) ).
fof(f1199,plain,
spl0_79,
inference(avatar_split_clause,[],[f395,f1197]) ).
fof(f1195,plain,
spl0_78,
inference(avatar_split_clause,[],[f394,f1193]) ).
fof(f1191,plain,
spl0_77,
inference(avatar_split_clause,[],[f173,f1189]) ).
fof(f173,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1187,plain,
spl0_76,
inference(avatar_split_clause,[],[f172,f1185]) ).
fof(f1185,plain,
( spl0_76
<=> ! [X4] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f172,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1183,plain,
spl0_75,
inference(avatar_split_clause,[],[f117,f1181]) ).
fof(f117,axiom,
! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X6,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1179,plain,
spl0_74,
inference(avatar_split_clause,[],[f116,f1177]) ).
fof(f116,axiom,
! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1175,plain,
spl0_73,
inference(avatar_split_clause,[],[f604,f1173]) ).
fof(f604,axiom,
! [X39,X0,X5] : c_List_Olist_OCons(X5,X39,X0) != X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f1171,plain,
spl0_72,
inference(avatar_split_clause,[],[f556,f1169]) ).
fof(f1169,plain,
( spl0_72
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f556,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
fof(f1167,plain,
spl0_71,
inference(avatar_split_clause,[],[f449,f1165]) ).
fof(f449,axiom,
! [X0,X5,X12] : ~ c_List_Onull(c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps_I2_J_0) ).
fof(f1163,plain,
spl0_70,
inference(avatar_split_clause,[],[f265,f1161]) ).
fof(f1161,plain,
( spl0_70
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f265,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1159,plain,
spl0_69,
inference(avatar_split_clause,[],[f264,f1157]) ).
fof(f1157,plain,
( spl0_69
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f264,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1155,plain,
spl0_68,
inference(avatar_split_clause,[],[f87,f1153]) ).
fof(f1153,plain,
( spl0_68
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f87,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1151,plain,
spl0_67,
inference(avatar_split_clause,[],[f86,f1149]) ).
fof(f86,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1147,plain,
spl0_66,
inference(avatar_split_clause,[],[f85,f1145]) ).
fof(f1145,plain,
( spl0_66
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f85,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1143,plain,
spl0_65,
inference(avatar_split_clause,[],[f567,f1141]) ).
fof(f567,axiom,
! [X0,X12] : c_List_Odistinct(c_List_Oremdups(X12,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct__remdups_0) ).
fof(f1139,plain,
spl0_64,
inference(avatar_split_clause,[],[f539,f1137]) ).
fof(f1137,plain,
( spl0_64
<=> ! [X5,X0] : ~ c_List_Omember(X5,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f539,axiom,
! [X0,X5] : ~ c_List_Omember(X5,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Omember_Osimps_I1_J_0) ).
fof(f1135,plain,
spl0_63,
inference(avatar_split_clause,[],[f11,f1133]) ).
fof(f11,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f1131,plain,
spl0_62,
inference(avatar_split_clause,[],[f599,f1129]) ).
fof(f1129,plain,
( spl0_62
<=> ! [X0] : c_List_Odistinct(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f599,axiom,
! [X0] : c_List_Odistinct(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
fof(f1127,plain,
spl0_61,
inference(avatar_split_clause,[],[f555,f1125]) ).
fof(f1125,plain,
( spl0_61
<=> ! [X0] : c_List_Onull(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f555,axiom,
! [X0] : c_List_Onull(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__null_0) ).
fof(f1123,plain,
spl0_60,
inference(avatar_split_clause,[],[f83,f1121]) ).
fof(f83,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1119,plain,
( spl0_59
| spl0_1 ),
inference(avatar_split_clause,[],[f610,f827,f1117]) ).
fof(f827,plain,
( spl0_1
<=> v_thesis____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f610,axiom,
! [X5] :
( v_thesis____
| ~ c_List_Odistinct(c_List_Olist_OCons(v_a____,c_List_Olist_OCons(v_b____,c_List_Olist_OCons(X5,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1115,plain,
~ spl0_58,
inference(avatar_split_clause,[],[f608,f1112]) ).
fof(f608,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f1110,plain,
spl0_57,
inference(avatar_split_clause,[],[f666,f1107]) ).
fof(f1107,plain,
( spl0_57
<=> class_HOL_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f666,axiom,
class_HOL_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__HOL_Oord) ).
fof(f1105,plain,
spl0_56,
inference(avatar_split_clause,[],[f665,f1102]) ).
fof(f1102,plain,
( spl0_56
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f665,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
fof(f1100,plain,
spl0_55,
inference(avatar_split_clause,[],[f664,f1097]) ).
fof(f664,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
fof(f1095,plain,
spl0_54,
inference(avatar_split_clause,[],[f663,f1092]) ).
fof(f1092,plain,
( spl0_54
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f663,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f1090,plain,
spl0_53,
inference(avatar_split_clause,[],[f662,f1087]) ).
fof(f1087,plain,
( spl0_53
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f662,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f1085,plain,
spl0_52,
inference(avatar_split_clause,[],[f661,f1082]) ).
fof(f1082,plain,
( spl0_52
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f661,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f1080,plain,
spl0_51,
inference(avatar_split_clause,[],[f660,f1077]) ).
fof(f1077,plain,
( spl0_51
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f660,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Oring__div) ).
fof(f1075,plain,
spl0_50,
inference(avatar_split_clause,[],[f659,f1072]) ).
fof(f659,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f1070,plain,
spl0_49,
inference(avatar_split_clause,[],[f658,f1067]) ).
fof(f1067,plain,
( spl0_49
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f658,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f1065,plain,
spl0_48,
inference(avatar_split_clause,[],[f657,f1062]) ).
fof(f1062,plain,
( spl0_48
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f657,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f1060,plain,
spl0_47,
inference(avatar_split_clause,[],[f656,f1057]) ).
fof(f656,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).
fof(f1055,plain,
spl0_46,
inference(avatar_split_clause,[],[f655,f1052]) ).
fof(f655,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f1050,plain,
spl0_45,
inference(avatar_split_clause,[],[f654,f1047]) ).
fof(f1047,plain,
( spl0_45
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f654,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f1045,plain,
spl0_44,
inference(avatar_split_clause,[],[f653,f1042]) ).
fof(f653,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f1040,plain,
spl0_43,
inference(avatar_split_clause,[],[f652,f1037]) ).
fof(f1037,plain,
( spl0_43
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f652,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f1035,plain,
spl0_42,
inference(avatar_split_clause,[],[f651,f1032]) ).
fof(f1032,plain,
( spl0_42
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f651,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f1030,plain,
spl0_41,
inference(avatar_split_clause,[],[f650,f1027]) ).
fof(f1027,plain,
( spl0_41
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f650,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(f1025,plain,
spl0_40,
inference(avatar_split_clause,[],[f649,f1022]) ).
fof(f1022,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f649,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f1020,plain,
spl0_39,
inference(avatar_split_clause,[],[f648,f1017]) ).
fof(f1017,plain,
( spl0_39
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f648,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f1015,plain,
spl0_38,
inference(avatar_split_clause,[],[f647,f1012]) ).
fof(f647,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f1010,plain,
spl0_37,
inference(avatar_split_clause,[],[f646,f1007]) ).
fof(f1007,plain,
( spl0_37
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f646,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f1005,plain,
spl0_36,
inference(avatar_split_clause,[],[f645,f1002]) ).
fof(f645,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1000,plain,
spl0_35,
inference(avatar_split_clause,[],[f644,f997]) ).
fof(f997,plain,
( spl0_35
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f644,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f995,plain,
spl0_34,
inference(avatar_split_clause,[],[f643,f992]) ).
fof(f992,plain,
( spl0_34
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f643,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f990,plain,
spl0_33,
inference(avatar_split_clause,[],[f642,f987]) ).
fof(f987,plain,
( spl0_33
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f642,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f985,plain,
spl0_32,
inference(avatar_split_clause,[],[f641,f982]) ).
fof(f982,plain,
( spl0_32
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f641,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f980,plain,
spl0_31,
inference(avatar_split_clause,[],[f640,f977]) ).
fof(f977,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f640,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f975,plain,
spl0_30,
inference(avatar_split_clause,[],[f639,f972]) ).
fof(f972,plain,
( spl0_30
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f639,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f970,plain,
spl0_29,
inference(avatar_split_clause,[],[f638,f967]) ).
fof(f967,plain,
( spl0_29
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f638,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f965,plain,
spl0_28,
inference(avatar_split_clause,[],[f637,f962]) ).
fof(f962,plain,
( spl0_28
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f637,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f960,plain,
spl0_27,
inference(avatar_split_clause,[],[f636,f957]) ).
fof(f957,plain,
( spl0_27
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f636,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f955,plain,
spl0_26,
inference(avatar_split_clause,[],[f635,f952]) ).
fof(f952,plain,
( spl0_26
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f635,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f950,plain,
spl0_25,
inference(avatar_split_clause,[],[f634,f947]) ).
fof(f947,plain,
( spl0_25
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f634,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f945,plain,
spl0_24,
inference(avatar_split_clause,[],[f633,f942]) ).
fof(f942,plain,
( spl0_24
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f633,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f940,plain,
spl0_23,
inference(avatar_split_clause,[],[f632,f937]) ).
fof(f937,plain,
( spl0_23
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f632,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
fof(f935,plain,
spl0_22,
inference(avatar_split_clause,[],[f631,f932]) ).
fof(f631,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f930,plain,
spl0_21,
inference(avatar_split_clause,[],[f630,f927]) ).
fof(f927,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f630,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f925,plain,
spl0_20,
inference(avatar_split_clause,[],[f629,f922]) ).
fof(f629,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f920,plain,
spl0_19,
inference(avatar_split_clause,[],[f628,f917]) ).
fof(f917,plain,
( spl0_19
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f628,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f915,plain,
spl0_18,
inference(avatar_split_clause,[],[f627,f912]) ).
fof(f627,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f910,plain,
spl0_17,
inference(avatar_split_clause,[],[f626,f907]) ).
fof(f907,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f626,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f905,plain,
spl0_16,
inference(avatar_split_clause,[],[f625,f902]) ).
fof(f625,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f900,plain,
spl0_15,
inference(avatar_split_clause,[],[f624,f897]) ).
fof(f897,plain,
( spl0_15
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f624,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f895,plain,
spl0_14,
inference(avatar_split_clause,[],[f623,f892]) ).
fof(f892,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f623,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f890,plain,
spl0_13,
inference(avatar_split_clause,[],[f622,f887]) ).
fof(f887,plain,
( spl0_13
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f622,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f885,plain,
spl0_12,
inference(avatar_split_clause,[],[f621,f882]) ).
fof(f882,plain,
( spl0_12
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f621,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f880,plain,
spl0_11,
inference(avatar_split_clause,[],[f620,f877]) ).
fof(f877,plain,
( spl0_11
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f620,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f875,plain,
spl0_10,
inference(avatar_split_clause,[],[f619,f872]) ).
fof(f619,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f870,plain,
spl0_9,
inference(avatar_split_clause,[],[f618,f867]) ).
fof(f867,plain,
( spl0_9
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f618,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f865,plain,
spl0_8,
inference(avatar_split_clause,[],[f617,f862]) ).
fof(f862,plain,
( spl0_8
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f617,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f860,plain,
spl0_7,
inference(avatar_split_clause,[],[f616,f857]) ).
fof(f857,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f616,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f855,plain,
spl0_6,
inference(avatar_split_clause,[],[f615,f852]) ).
fof(f852,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f615,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f850,plain,
spl0_5,
inference(avatar_split_clause,[],[f614,f847]) ).
fof(f847,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f614,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f845,plain,
spl0_4,
inference(avatar_split_clause,[],[f613,f842]) ).
fof(f842,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f613,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f840,plain,
spl0_3,
inference(avatar_split_clause,[],[f612,f837]) ).
fof(f837,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f612,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f835,plain,
spl0_2,
inference(avatar_split_clause,[],[f611,f832]) ).
fof(f832,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f611,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f830,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f609,f827]) ).
fof(f609,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT042-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 13:17:58 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (4862)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39 % (4869)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.39 % (4865)WARNING: value z3 for option sas not known
% 0.13/0.39 % (4863)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 % (4864)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39 % (4866)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39 % (4865)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.39 % (4867)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.39 % (4868)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.50 TRYING [1]
% 0.20/0.51 TRYING [2]
% 1.89/0.66 TRYING [1]
% 1.89/0.66 TRYING [3]
% 1.89/0.69 TRYING [2]
% 3.57/0.88 TRYING [1]
% 3.57/0.89 TRYING [2]
% 3.76/0.92 % (4867)First to succeed.
% 3.99/0.94 % (4867)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4862"
% 3.99/0.94 % (4867)Refutation found. Thanks to Tanya!
% 3.99/0.94 % SZS status Unsatisfiable for theBenchmark
% 3.99/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/0.95 % (4867)------------------------------
% 3.99/0.95 % (4867)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.99/0.95 % (4867)Termination reason: Refutation
% 3.99/0.95
% 3.99/0.95 % (4867)Memory used [KB]: 9555
% 3.99/0.95 % (4867)Time elapsed: 0.547 s
% 3.99/0.95 % (4867)Instructions burned: 1394 (million)
% 3.99/0.95 % (4862)Success in time 0.591 s
%------------------------------------------------------------------------------