TSTP Solution File: ALG387-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG387-1 : 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 : n028.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 04:30:14 EDT 2024
% Result : Unsatisfiable 4.48s 1.05s
% Output : Refutation 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1671
% Syntax : Number of formulae : 2810 ( 930 unt; 0 def)
% Number of atoms : 6722 ( 849 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 6913 (3001 ~;3019 |; 0 &)
% ( 893 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 962 ( 960 usr; 894 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 7 con; 0-3 aty)
% Number of variables : 4276 (4276 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17247,plain,
$false,
inference(avatar_sat_refutation,[],[f897,f902,f907,f912,f917,f922,f927,f932,f937,f942,f947,f952,f957,f962,f967,f972,f977,f982,f987,f992,f997,f1002,f1007,f1012,f1017,f1022,f1027,f1032,f1037,f1042,f1047,f1052,f1057,f1062,f1067,f1072,f1077,f1082,f1087,f1092,f1097,f1102,f1107,f1112,f1117,f1122,f1127,f1132,f1137,f1142,f1147,f1152,f1157,f1162,f1167,f1172,f1177,f1182,f1187,f1192,f1197,f1202,f1207,f1212,f1217,f1222,f1227,f1232,f1237,f1242,f1247,f1252,f1257,f1262,f1267,f1272,f1277,f1282,f1287,f1292,f1297,f1302,f1307,f1312,f1317,f1322,f1327,f1332,f1337,f1342,f1347,f1352,f1357,f1362,f1367,f1372,f1377,f1381,f1385,f1389,f1393,f1398,f1402,f1406,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,f1522,f1526,f1530,f1534,f1538,f1542,f1546,f1550,f1554,f1558,f1562,f1566,f1570,f1574,f1578,f1582,f1586,f1590,f1594,f1598,f1602,f1607,f1611,f1616,f1621,f1626,f1631,f1635,f1639,f1643,f1647,f1651,f1655,f1661,f1665,f1669,f1673,f1677,f1681,f1685,f1689,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1732,f1754,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1866,f1870,f1874,f1878,f1882,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f1918,f1922,f1971,f1994,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2060,f2064,f2068,f2072,f2076,f2080,f2084,f2088,f2092,f2096,f2100,f2104,f2108,f2112,f2116,f2120,f2124,f2128,f2132,f2136,f2140,f2144,f2148,f2152,f2156,f2160,f2164,f2168,f2172,f2176,f2189,f2226,f2266,f2372,f2394,f2398,f2402,f2406,f2410,f2414,f2418,f2422,f2432,f2436,f2440,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2472,f2476,f2480,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2518,f2522,f2526,f2530,f2534,f2538,f2542,f2546,f2550,f2554,f2558,f2562,f2566,f2570,f2574,f2578,f2603,f2731,f2820,f2824,f2828,f2832,f2836,f2840,f2844,f2848,f2852,f2856,f2860,f2864,f2868,f2872,f2876,f2880,f2884,f2888,f2892,f2896,f2900,f2904,f2908,f2912,f2916,f2920,f2924,f2928,f2932,f2936,f2940,f2944,f2948,f2952,f2956,f2960,f2964,f2968,f2972,f2976,f2980,f2984,f2988,f2992,f2996,f3000,f3004,f3008,f3012,f3075,f3139,f3457,f3624,f3628,f3632,f3636,f3640,f3644,f3648,f3652,f3656,f3660,f3664,f3668,f3672,f3697,f3701,f3705,f3709,f3713,f3717,f3721,f3725,f3729,f3733,f3737,f3741,f3745,f3749,f3753,f3757,f3761,f3765,f3769,f3773,f3777,f3796,f3800,f3804,f3808,f3812,f3816,f3820,f3824,f3828,f3832,f3836,f3840,f3844,f3848,f3852,f3856,f3860,f3864,f3868,f3872,f3876,f3880,f3884,f3888,f4162,f4780,f4911,f4915,f4919,f4923,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4967,f4975,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5121,f5125,f5129,f5133,f5137,f5141,f5145,f5149,f5153,f5157,f5178,f5182,f5186,f5190,f5194,f5198,f5202,f5441,f5578,f6280,f6552,f6556,f6560,f6564,f6568,f6572,f6576,f6580,f6584,f6588,f6592,f6596,f6600,f6630,f6634,f6638,f6642,f6646,f6650,f6654,f6658,f6662,f6666,f6695,f6699,f6703,f6707,f6711,f6715,f6719,f6723,f6727,f6731,f6735,f6739,f6743,f6747,f6751,f6940,f7053,f7162,f7166,f7170,f7174,f7178,f7182,f7186,f7190,f7194,f7198,f7227,f7231,f7235,f7239,f7243,f7247,f7251,f7255,f7259,f7263,f7267,f7271,f7275,f7279,f7283,f7287,f7291,f7295,f7300,f7354,f7529,f7901,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8006,f8010,f8014,f8018,f8022,f8026,f8030,f8034,f8038,f8042,f8046,f8050,f8054,f8058,f8062,f8070,f8074,f8078,f8082,f8086,f8090,f8094,f8098,f8102,f8106,f8110,f8114,f8118,f8122,f8126,f8131,f8136,f8140,f8144,f8148,f8152,f8184,f8188,f8586,f8723,f8727,f8731,f8735,f8739,f8743,f8747,f8751,f8755,f8759,f8763,f8767,f8771,f8775,f8779,f8783,f8787,f8791,f8795,f8799,f8803,f9326,f9461,f9465,f9469,f9473,f9477,f9481,f9489,f9493,f9497,f9501,f9505,f9509,f9513,f9517,f9521,f9525,f9529,f9533,f9537,f9541,f9545,f9730,f9753,f9757,f9761,f9765,f9769,f9773,f9777,f9781,f9785,f9789,f9793,f9797,f9801,f9805,f9809,f9813,f9817,f9825,f9829,f9833,f9837,f9841,f9845,f9849,f9853,f9857,f9861,f9865,f9869,f9873,f9877,f9881,f9885,f9889,f9893,f9897,f9901,f9905,f9909,f9913,f9917,f9921,f9925,f9929,f9933,f9937,f9941,f9945,f9949,f9953,f9957,f9961,f9965,f9969,f9973,f9977,f9981,f9985,f9989,f9993,f10022,f10026,f10030,f10034,f10038,f10042,f10046,f10050,f10054,f10058,f10087,f10091,f10095,f10099,f10103,f10107,f10111,f10115,f10119,f10123,f10156,f10160,f10714,f11223,f11382,f11612,f11620,f11624,f11628,f11632,f11636,f11640,f11644,f11648,f11652,f11656,f11660,f11664,f11668,f11672,f11676,f11680,f11684,f11688,f11692,f11696,f11700,f11729,f11733,f11737,f11741,f11745,f11749,f11753,f11757,f11761,f11765,f11807,f11811,f11815,f11819,f11823,f11827,f11831,f11835,f11843,f12393,f12638,f12794,f12798,f12802,f12810,f12814,f12818,f12912,f12916,f12920,f12924,f12928,f12932,f12963,f12980,f12994,f12998,f13002,f13048,f13052,f13056,f13060,f13064,f13068,f13072,f13076,f13080,f13084,f13261,f13265,f13269,f13274,f13278,f13282,f13485,f13489,f13567,f13590,f13594,f13598,f13602,f13606,f13610,f13614,f13619,f13623,f13627,f13961,f14010,f14014,f14018,f14022,f14026,f14030,f14034,f14038,f14043,f14047,f14397,f14407,f14769,f14914,f15672,f15677,f15681,f15685,f15689,f15693,f15697,f15701,f15709,f17045,f17049,f17053,f17057,f17092,f17108,f17112,f17116,f17120,f17124,f17128,f17132,f17137,f17141,f17145,f17149,f17153,f17157,f17161,f17165,f17169,f17173,f17177,f17209,f17213,f17217,f17221,f17225,f17229,f17233,f17237,f17241,f17245,f17246]) ).
fof(f17246,plain,
( spl0_821
| ~ spl0_264
| ~ spl0_873 ),
inference(avatar_split_clause,[],[f17179,f17134,f2162,f13271]) ).
fof(f13271,plain,
( spl0_821
<=> c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f2162,plain,
( spl0_264
<=> ! [X7,X3] :
( c_lessequals(X3,X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f17134,plain,
( spl0_873
<=> c_lessequals(c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f17179,plain,
( c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_264
| ~ spl0_873 ),
inference(resolution,[],[f17136,f2163]) ).
fof(f2163,plain,
( ! [X3,X7] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(X3,X7,tc_RealDef_Oreal) )
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2162]) ).
fof(f17136,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f17134]) ).
fof(f17245,plain,
( spl0_893
| ~ spl0_83
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f2723,f2536,f1304,f17243]) ).
fof(f17243,plain,
( spl0_893
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f1304,plain,
( spl0_83
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f2536,plain,
( spl0_306
<=> ! [X0,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2723,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
| ~ spl0_83
| ~ spl0_306 ),
inference(resolution,[],[f2537,f1306]) ).
fof(f1306,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f2537,plain,
( ! [X0,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X15 )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f2536]) ).
fof(f17241,plain,
( spl0_892
| ~ spl0_43
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f2722,f2536,f1104,f17239]) ).
fof(f17239,plain,
( spl0_892
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f1104,plain,
( spl0_43
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2722,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
| ~ spl0_43
| ~ spl0_306 ),
inference(resolution,[],[f2537,f1106]) ).
fof(f1106,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f17237,plain,
( spl0_891
| ~ spl0_83
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f2720,f2532,f1304,f17235]) ).
fof(f17235,plain,
( spl0_891
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2532,plain,
( spl0_305
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,tc_Polynomial_Opoly(X0)) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2720,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
| ~ spl0_83
| ~ spl0_305 ),
inference(resolution,[],[f2533,f1306]) ).
fof(f2533,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,tc_Polynomial_Opoly(X0)) = X5 )
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f2532]) ).
fof(f17233,plain,
( spl0_890
| ~ spl0_43
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f2719,f2532,f1104,f17231]) ).
fof(f17231,plain,
( spl0_890
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f2719,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
| ~ spl0_43
| ~ spl0_305 ),
inference(resolution,[],[f2533,f1106]) ).
fof(f17229,plain,
( spl0_889
| ~ spl0_74
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f2714,f2524,f1259,f17227]) ).
fof(f17227,plain,
( spl0_889
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1259,plain,
( spl0_74
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f2524,plain,
( spl0_303
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2714,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_74
| ~ spl0_303 ),
inference(resolution,[],[f2525,f1261]) ).
fof(f1261,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f2525,plain,
( ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X1,X0) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f2524]) ).
fof(f17225,plain,
( spl0_888
| ~ spl0_32
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f2713,f2524,f1049,f17223]) ).
fof(f17223,plain,
( spl0_888
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f1049,plain,
( spl0_32
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f2713,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal)
| ~ spl0_32
| ~ spl0_303 ),
inference(resolution,[],[f2525,f1051]) ).
fof(f1051,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f17221,plain,
( spl0_887
| ~ spl0_15
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f2690,f2516,f964,f17219]) ).
fof(f17219,plain,
( spl0_887
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f964,plain,
( spl0_15
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f2516,plain,
( spl0_301
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2690,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_15
| ~ spl0_301 ),
inference(resolution,[],[f2517,f966]) ).
fof(f966,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f2517,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f2516]) ).
fof(f17217,plain,
( spl0_886
| ~ spl0_15
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f2677,f2502,f964,f17215]) ).
fof(f17215,plain,
( spl0_886
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2502,plain,
( spl0_298
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2677,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_15
| ~ spl0_298 ),
inference(resolution,[],[f2503,f966]) ).
fof(f2503,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f2502]) ).
fof(f17213,plain,
( spl0_885
| ~ spl0_90
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f2655,f2486,f1339,f17211]) ).
fof(f17211,plain,
( spl0_885
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f1339,plain,
( spl0_90
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f2486,plain,
( spl0_294
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2655,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_90
| ~ spl0_294 ),
inference(resolution,[],[f2487,f1341]) ).
fof(f1341,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f2487,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f2486]) ).
fof(f17209,plain,
( spl0_884
| ~ spl0_85
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f2652,f2482,f1314,f17207]) ).
fof(f17207,plain,
( spl0_884
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f1314,plain,
( spl0_85
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f2482,plain,
( spl0_293
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2652,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_85
| ~ spl0_293 ),
inference(resolution,[],[f2483,f1316]) ).
fof(f1316,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f2483,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f2482]) ).
fof(f17177,plain,
( spl0_883
| ~ spl0_48
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f2651,f2482,f1129,f17175]) ).
fof(f17175,plain,
( spl0_883
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f1129,plain,
( spl0_48
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f2651,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_48
| ~ spl0_293 ),
inference(resolution,[],[f2483,f1131]) ).
fof(f1131,plain,
( class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f17173,plain,
( spl0_882
| ~ spl0_59
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2649,f2478,f1184,f17171]) ).
fof(f17171,plain,
( spl0_882
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f1184,plain,
( spl0_59
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f2478,plain,
( spl0_292
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X3,X0) = c_Orderings_Oord__class_Omin(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2649,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(X1,X0,tc_RealDef_Oreal)
| ~ spl0_59
| ~ spl0_292 ),
inference(resolution,[],[f2479,f1186]) ).
fof(f1186,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1184]) ).
fof(f2479,plain,
( ! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X3,X0) = c_Orderings_Oord__class_Omin(X3,X4,X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f2478]) ).
fof(f17169,plain,
( spl0_881
| ~ spl0_46
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f2647,f2466,f1119,f17167]) ).
fof(f17167,plain,
( spl0_881
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f1119,plain,
( spl0_46
<=> class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f2466,plain,
( spl0_289
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2647,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_RealDef_Oreal)
| ~ spl0_46
| ~ spl0_289 ),
inference(resolution,[],[f2467,f1121]) ).
fof(f1121,plain,
( class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f2467,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f2466]) ).
fof(f17165,plain,
( spl0_880
| ~ spl0_59
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f2645,f2462,f1184,f17163]) ).
fof(f17163,plain,
( spl0_880
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2462,plain,
( spl0_288
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2645,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_59
| ~ spl0_288 ),
inference(resolution,[],[f2463,f1186]) ).
fof(f2463,plain,
( ! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) = X3 )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f2462]) ).
fof(f17161,plain,
( spl0_879
| ~ spl0_74
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f2638,f2454,f1259,f17159]) ).
fof(f17159,plain,
( spl0_879
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2454,plain,
( spl0_286
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2638,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_74
| ~ spl0_286 ),
inference(resolution,[],[f2455,f1261]) ).
fof(f2455,plain,
( ! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(X4,X3,X0) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f2454]) ).
fof(f17157,plain,
( spl0_878
| ~ spl0_90
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f2623,f2442,f1339,f17155]) ).
fof(f17155,plain,
( spl0_878
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2442,plain,
( spl0_283
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2623,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
| ~ spl0_90
| ~ spl0_283 ),
inference(resolution,[],[f2443,f1341]) ).
fof(f2443,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2442]) ).
fof(f17153,plain,
( spl0_877
| ~ spl0_54
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f2622,f2442,f1159,f17151]) ).
fof(f17151,plain,
( spl0_877
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f1159,plain,
( spl0_54
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f2622,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0
| ~ spl0_54
| ~ spl0_283 ),
inference(resolution,[],[f2443,f1161]) ).
fof(f1161,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f17149,plain,
( spl0_876
| ~ spl0_92
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2612,f2430,f1349,f17147]) ).
fof(f17147,plain,
( spl0_876
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f1349,plain,
( spl0_92
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2430,plain,
( spl0_280
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2612,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex)
| ~ spl0_92
| ~ spl0_280 ),
inference(resolution,[],[f2431,f1351]) ).
fof(f1351,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f2431,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2430]) ).
fof(f17145,plain,
( spl0_875
| ~ spl0_57
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2611,f2430,f1174,f17143]) ).
fof(f17143,plain,
( spl0_875
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f1174,plain,
( spl0_57
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f2611,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal)
| ~ spl0_57
| ~ spl0_280 ),
inference(resolution,[],[f2431,f1176]) ).
fof(f1176,plain,
( class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1174]) ).
fof(f17141,plain,
( spl0_874
| ~ spl0_90
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f2609,f2420,f1339,f17139]) ).
fof(f17139,plain,
( spl0_874
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2420,plain,
( spl0_279
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2609,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_90
| ~ spl0_279 ),
inference(resolution,[],[f2421,f1341]) ).
fof(f2421,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f2420]) ).
fof(f17137,plain,
( spl0_873
| ~ spl0_183
| spl0_846 ),
inference(avatar_split_clause,[],[f14389,f14040,f1730,f17134]) ).
fof(f1730,plain,
( spl0_183
<=> ! [X29,X14] :
( c_lessequals(X14,X29,tc_RealDef_Oreal)
| c_lessequals(X29,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f14040,plain,
( spl0_846
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f14389,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_183
| spl0_846 ),
inference(resolution,[],[f14042,f1731]) ).
fof(f1731,plain,
( ! [X29,X14] :
( c_lessequals(X14,X29,tc_RealDef_Oreal)
| c_lessequals(X29,X14,tc_RealDef_Oreal) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1730]) ).
fof(f14042,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_846 ),
inference(avatar_component_clause,[],[f14040]) ).
fof(f17132,plain,
( spl0_872
| ~ spl0_54
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f2608,f2420,f1159,f17130]) ).
fof(f17130,plain,
( spl0_872
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2608,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_54
| ~ spl0_279 ),
inference(resolution,[],[f2421,f1161]) ).
fof(f17128,plain,
( spl0_871
| ~ spl0_59
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f2606,f2416,f1184,f17126]) ).
fof(f17126,plain,
( spl0_871
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2416,plain,
( spl0_278
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = c_Orderings_Oord__class_Omax(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2606,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(X1,X0,tc_RealDef_Oreal)
| ~ spl0_59
| ~ spl0_278 ),
inference(resolution,[],[f2417,f1186]) ).
fof(f2417,plain,
( ! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = c_Orderings_Oord__class_Omax(X4,X3,X0) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f17124,plain,
( spl0_870
| ~ spl0_59
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f2604,f2412,f1184,f17122]) ).
fof(f17122,plain,
( spl0_870
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2412,plain,
( spl0_277
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2604,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_59
| ~ spl0_277 ),
inference(resolution,[],[f2413,f1186]) ).
fof(f2413,plain,
( ! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) = X3 )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f2412]) ).
fof(f17120,plain,
( spl0_869
| ~ spl0_218
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2331,f2142,f1896,f17118]) ).
fof(f17118,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f1896,plain,
( spl0_218
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2142,plain,
( spl0_259
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2331,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_218
| ~ spl0_259 ),
inference(duplicate_literal_removal,[],[f2311]) ).
fof(f2311,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_218
| ~ spl0_259 ),
inference(resolution,[],[f2143,f1897]) ).
fof(f1897,plain,
( ! [X3,X0,X4] :
( c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f2143,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2142]) ).
fof(f17116,plain,
( spl0_868
| ~ spl0_219
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2330,f2142,f1900,f17114]) ).
fof(f17114,plain,
( spl0_868
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f1900,plain,
( spl0_219
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2330,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_219
| ~ spl0_259 ),
inference(duplicate_literal_removal,[],[f2312]) ).
fof(f2312,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_219
| ~ spl0_259 ),
inference(resolution,[],[f2143,f1901]) ).
fof(f1901,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,c_Orderings_Oord__class_Omax(X3,X4,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f17112,plain,
( spl0_867
| ~ spl0_220
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2329,f2142,f1904,f17110]) ).
fof(f17110,plain,
( spl0_867
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f1904,plain,
( spl0_220
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2329,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_220
| ~ spl0_259 ),
inference(duplicate_literal_removal,[],[f2325]) ).
fof(f2325,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_220
| ~ spl0_259 ),
inference(resolution,[],[f2143,f1905]) ).
fof(f1905,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f1904]) ).
fof(f17108,plain,
( spl0_866
| ~ spl0_221
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2328,f2142,f1908,f17106]) ).
fof(f17106,plain,
( spl0_866
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f1908,plain,
( spl0_221
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2328,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_221
| ~ spl0_259 ),
inference(duplicate_literal_removal,[],[f2326]) ).
fof(f2326,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_221
| ~ spl0_259 ),
inference(resolution,[],[f2143,f1909]) ).
fof(f1909,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f1908]) ).
fof(f17092,plain,
( ~ spl0_58
| spl0_865
| ~ spl0_172
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2299,f2134,f1683,f17090,f1179]) ).
fof(f1179,plain,
( spl0_58
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f17090,plain,
( spl0_865
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_Complex_ORe(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1683,plain,
( spl0_172
<=> ! [X3] : c_lessequals(c_Complex_ORe(X3),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f2134,plain,
( spl0_257
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2299,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_Complex_ORe(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_172
| ~ spl0_257 ),
inference(resolution,[],[f2135,f1684]) ).
fof(f1684,plain,
( ! [X3] : c_lessequals(c_Complex_ORe(X3),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1683]) ).
fof(f2135,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2134]) ).
fof(f17057,plain,
( ~ spl0_58
| spl0_864
| ~ spl0_170
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2258,f2122,f1675,f17055,f1179]) ).
fof(f17055,plain,
( spl0_864
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f1675,plain,
( spl0_170
<=> ! [X7,X15] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X15,X7),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f2122,plain,
( spl0_254
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2258,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_170
| ~ spl0_254 ),
inference(resolution,[],[f2123,f1676]) ).
fof(f1676,plain,
( ! [X7,X15] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X15,X7),tc_RealDef_Oreal)
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1675]) ).
fof(f2123,plain,
( ! [X3,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f17053,plain,
( spl0_863
| ~ spl0_100
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1979,f1864,f1387,f17051]) ).
fof(f17051,plain,
( spl0_863
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f1387,plain,
( spl0_100
<=> ! [X14] : c_Complex_Ocnj(c_Complex_Ocnj(X14)) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1864,plain,
( spl0_210
<=> ! [X14] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X14
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocnj(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1979,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(X0) )
| ~ spl0_100
| ~ spl0_210 ),
inference(superposition,[],[f1865,f1388]) ).
fof(f1388,plain,
( ! [X14] : c_Complex_Ocnj(c_Complex_Ocnj(X14)) = X14
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f1865,plain,
( ! [X14] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocnj(X14)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X14 )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f1864]) ).
fof(f17049,plain,
( spl0_862
| ~ spl0_148
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1736,f1698,f1580,f17047]) ).
fof(f17047,plain,
( spl0_862
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omin(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f1580,plain,
( spl0_148
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1698,plain,
( spl0_175
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1736,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omin(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_148
| ~ spl0_175 ),
inference(resolution,[],[f1699,f1581]) ).
fof(f1581,plain,
( ! [X36] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X36))
| ~ class_Ring__and__Field_Oordered__idom(X36) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1699,plain,
( ! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,X3,X0) = X3 )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1698]) ).
fof(f17045,plain,
( spl0_861
| ~ spl0_148
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1734,f1694,f1580,f17043]) ).
fof(f17043,plain,
( spl0_861
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f1694,plain,
( spl0_174
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1734,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_148
| ~ spl0_174 ),
inference(resolution,[],[f1695,f1581]) ).
fof(f1695,plain,
( ! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X3,X0) = X3 )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1694]) ).
fof(f15709,plain,
( spl0_860
| ~ spl0_181
| ~ spl0_850 ),
inference(avatar_split_clause,[],[f15631,f14766,f1722,f15706]) ).
fof(f15706,plain,
( spl0_860
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),v_r____,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1722,plain,
( spl0_181
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_lessequals(X3,X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f14766,plain,
( spl0_850
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),v_r____,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f15631,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),v_r____,tc_RealDef_Oreal)
| ~ spl0_181
| ~ spl0_850 ),
inference(resolution,[],[f14768,f1723]) ).
fof(f1723,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_lessequals(X3,X4,tc_RealDef_Oreal) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1722]) ).
fof(f14768,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),v_r____,tc_RealDef_Oreal)
| ~ spl0_850 ),
inference(avatar_component_clause,[],[f14766]) ).
fof(f15701,plain,
( spl0_859
| ~ spl0_236
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f3452,f2974,f2049,f15699]) ).
fof(f15699,plain,
( spl0_859
<=> ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f2049,plain,
( spl0_236
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2974,plain,
( spl0_358
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f3452,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_236
| ~ spl0_358 ),
inference(duplicate_literal_removal,[],[f3436]) ).
fof(f3436,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_236
| ~ spl0_358 ),
inference(resolution,[],[f2975,f2050]) ).
fof(f2050,plain,
( ! [X0] :
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f2975,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f2974]) ).
fof(f15697,plain,
( spl0_858
| ~ spl0_99
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3016,f2818,f1383,f15695]) ).
fof(f15695,plain,
( spl0_858
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1383,plain,
( spl0_99
<=> ! [X29] : c_lessequals(X29,X29,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2818,plain,
( spl0_319
<=> ! [X7,X3] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f3016,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_99
| ~ spl0_319 ),
inference(resolution,[],[f2819,f1384]) ).
fof(f1384,plain,
( ! [X29] : c_lessequals(X29,X29,tc_RealDef_Oreal)
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f2819,plain,
( ! [X3,X7] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f2818]) ).
fof(f15693,plain,
( spl0_857
| ~ spl0_74
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2228,f2082,f1259,f15691]) ).
fof(f15691,plain,
( spl0_857
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f2082,plain,
( spl0_244
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2228,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_74
| ~ spl0_244 ),
inference(resolution,[],[f2083,f1261]) ).
fof(f2083,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2082]) ).
fof(f15689,plain,
( spl0_856
| ~ spl0_32
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2227,f2082,f1049,f15687]) ).
fof(f15687,plain,
( spl0_856
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2227,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_32
| ~ spl0_244 ),
inference(resolution,[],[f2083,f1051]) ).
fof(f15685,plain,
( spl0_855
| ~ spl0_74
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2220,f2078,f1259,f15683]) ).
fof(f15683,plain,
( spl0_855
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2078,plain,
( spl0_243
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2220,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_74
| ~ spl0_243 ),
inference(resolution,[],[f2079,f1261]) ).
fof(f2079,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2078]) ).
fof(f15681,plain,
( spl0_854
| ~ spl0_32
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2219,f2078,f1049,f15679]) ).
fof(f15679,plain,
( spl0_854
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2219,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_32
| ~ spl0_243 ),
inference(resolution,[],[f2079,f1051]) ).
fof(f15677,plain,
( spl0_853
| ~ spl0_100
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1740,f1710,f1387,f15675]) ).
fof(f15675,plain,
( spl0_853
<=> ! [X0,X1] :
( c_Complex_Ocnj(X1) != X0
| c_Complex_Ocnj(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f1710,plain,
( spl0_178
<=> ! [X4,X3] :
( X3 = X4
| c_Complex_Ocnj(X3) != c_Complex_Ocnj(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1740,plain,
( ! [X0,X1] :
( c_Complex_Ocnj(X1) != X0
| c_Complex_Ocnj(X0) = X1 )
| ~ spl0_100
| ~ spl0_178 ),
inference(superposition,[],[f1711,f1388]) ).
fof(f1711,plain,
( ! [X3,X4] :
( c_Complex_Ocnj(X3) != c_Complex_Ocnj(X4)
| X3 = X4 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f15672,plain,
( spl0_852
| ~ spl0_158
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1690,f1683,f1623,f15669]) ).
fof(f15669,plain,
( spl0_852
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1623,plain,
( spl0_158
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1690,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_158
| ~ spl0_172 ),
inference(superposition,[],[f1684,f1625]) ).
fof(f1625,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1623]) ).
fof(f14914,plain,
( spl0_851
| ~ spl0_222
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2354,f2162,f1912,f14912]) ).
fof(f14912,plain,
( spl0_851
<=> ! [X0] : c_lessequals(c_Complex_OIm(X0),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1912,plain,
( spl0_222
<=> ! [X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(X3),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2354,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(X0),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_222
| ~ spl0_264 ),
inference(resolution,[],[f2163,f1913]) ).
fof(f1913,plain,
( ! [X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(X3),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f1912]) ).
fof(f14769,plain,
( ~ spl0_59
| spl0_850
| ~ spl0_258
| spl0_821 ),
inference(avatar_split_clause,[],[f13540,f13271,f2138,f14766,f1184]) ).
fof(f2138,plain,
( spl0_258
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f13540,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),v_r____,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ spl0_258
| spl0_821 ),
inference(resolution,[],[f13273,f2139]) ).
fof(f2139,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2138]) ).
fof(f13273,plain,
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_821 ),
inference(avatar_component_clause,[],[f13271]) ).
fof(f14407,plain,
( spl0_102
| spl0_849
| ~ spl0_153
| ~ spl0_816 ),
inference(avatar_split_clause,[],[f13203,f13078,f1600,f14405,f1395]) ).
fof(f1395,plain,
( spl0_102
<=> v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f14405,plain,
( spl0_849
<=> ! [X0] : ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(v_c____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_cs____),c_RealVector_Onorm__class_Onorm(hAPP(v_x,X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1600,plain,
( spl0_153
<=> ! [X25] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X25,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X25),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f13078,plain,
( spl0_816
<=> ! [X15,X14,X19,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X15
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X1,X19,X15),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X19,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X15,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f13203,plain,
( ! [X0] :
( ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(v_c____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_cs____),c_RealVector_Onorm__class_Onorm(hAPP(v_x,X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ spl0_153
| ~ spl0_816 ),
inference(resolution,[],[f13079,f1601]) ).
fof(f1601,plain,
( ! [X25] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X25,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X25),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1600]) ).
fof(f13079,plain,
( ! [X1,X19,X14,X15] :
( c_lessequals(X19,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X15,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X1,X19,X15),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X15 )
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f13078]) ).
fof(f14397,plain,
spl0_848,
inference(avatar_split_clause,[],[f279,f14395]) ).
fof(f14395,plain,
( spl0_848
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f279,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
fof(f14047,plain,
spl0_847,
inference(avatar_split_clause,[],[f533,f14045]) ).
fof(f14045,plain,
( spl0_847
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| X8 = X19
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f533,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| X8 = X19
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X19,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
fof(f14043,plain,
( ~ spl0_846
| ~ spl0_153
| ~ spl0_825 ),
inference(avatar_split_clause,[],[f13541,f13487,f1600,f14040]) ).
fof(f13487,plain,
( spl0_825
<=> ! [X29] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f13541,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_153
| ~ spl0_825 ),
inference(resolution,[],[f13488,f1601]) ).
fof(f13488,plain,
( ! [X29] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_825 ),
inference(avatar_component_clause,[],[f13487]) ).
fof(f14038,plain,
spl0_845,
inference(avatar_split_clause,[],[f425,f14036]) ).
fof(f14036,plain,
( spl0_845
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f425,axiom,
! [X2,X0,X1,X8,X18,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
fof(f14034,plain,
spl0_844,
inference(avatar_split_clause,[],[f424,f14032]) ).
fof(f14032,plain,
( spl0_844
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f424,axiom,
! [X2,X0,X1,X8,X18,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
fof(f14030,plain,
spl0_843,
inference(avatar_split_clause,[],[f423,f14028]) ).
fof(f14028,plain,
( spl0_843
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f423,axiom,
! [X2,X0,X1,X18,X8,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
fof(f14026,plain,
spl0_842,
inference(avatar_split_clause,[],[f422,f14024]) ).
fof(f14024,plain,
( spl0_842
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f422,axiom,
! [X2,X0,X1,X18,X8,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
fof(f14022,plain,
spl0_841,
inference(avatar_split_clause,[],[f110,f14020]) ).
fof(f14020,plain,
( spl0_841
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f110,axiom,
! [X2,X0,X1,X18,X8,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
fof(f14018,plain,
spl0_840,
inference(avatar_split_clause,[],[f109,f14016]) ).
fof(f14016,plain,
( spl0_840
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f109,axiom,
! [X2,X0,X1,X18,X8,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X19,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
fof(f14014,plain,
spl0_839,
inference(avatar_split_clause,[],[f108,f14012]) ).
fof(f14012,plain,
( spl0_839
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f108,axiom,
! [X2,X0,X1,X8,X18,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
fof(f14010,plain,
spl0_838,
inference(avatar_split_clause,[],[f107,f14008]) ).
fof(f14008,plain,
( spl0_838
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f107,axiom,
! [X2,X0,X1,X8,X18,X19] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X18,X0),X19,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
fof(f13961,plain,
( spl0_837
| ~ spl0_43
| ~ spl0_588
| ~ spl0_836 ),
inference(avatar_split_clause,[],[f13628,f13625,f8036,f1104,f13959]) ).
fof(f13959,plain,
( spl0_837
<=> ! [X17,X4,X16,X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X16,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f8036,plain,
( spl0_588
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f13625,plain,
( spl0_836
<=> ! [X17,X4,X16,X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X16,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f13628,plain,
( ! [X3,X16,X4,X17] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X16,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_43
| ~ spl0_588
| ~ spl0_836 ),
inference(forward_demodulation,[],[f13626,f8313]) ).
fof(f8313,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_43
| ~ spl0_588 ),
inference(resolution,[],[f8037,f1106]) ).
fof(f8037,plain,
( ! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) )
| ~ spl0_588 ),
inference(avatar_component_clause,[],[f8036]) ).
fof(f13626,plain,
( ! [X3,X16,X4,X17] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X16,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_836 ),
inference(avatar_component_clause,[],[f13625]) ).
fof(f13627,plain,
spl0_836,
inference(avatar_split_clause,[],[f890,f13625]) ).
fof(f890,plain,
! [X3,X16,X4,X17] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X16,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f889,f225]) ).
fof(f225,axiom,
! [X9,X7] : c_HOL_Ominus__class_Ominus(X7,X9,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ouminus__class_Ouminus(X9,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
fof(f889,plain,
! [X3,X16,X4,X17] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X16,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f888,f225]) ).
fof(f888,plain,
! [X3,X16,X4,X17] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f100,f225]) ).
fof(f100,axiom,
! [X3,X16,X4,X17] : c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X16,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X17,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__sum__triangle__ineq_0) ).
fof(f13623,plain,
spl0_835,
inference(avatar_split_clause,[],[f576,f13621]) ).
fof(f13621,plain,
( spl0_835
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f576,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f13619,plain,
( ~ spl0_834
| ~ spl0_153
| ~ spl0_823 ),
inference(avatar_split_clause,[],[f13459,f13280,f1600,f13616]) ).
fof(f13616,plain,
( spl0_834
<=> c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f13280,plain,
( spl0_823
<=> ! [X14] :
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f13459,plain,
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_153
| ~ spl0_823 ),
inference(resolution,[],[f13281,f1601]) ).
fof(f13281,plain,
( ! [X14] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f13280]) ).
fof(f13614,plain,
spl0_833,
inference(avatar_split_clause,[],[f575,f13612]) ).
fof(f13612,plain,
( spl0_833
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f575,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f13610,plain,
spl0_832,
inference(avatar_split_clause,[],[f574,f13608]) ).
fof(f13608,plain,
( spl0_832
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X19,X0),X0),X0),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X8,X0),X0),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X19,X0),X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f574,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X19,X0),X0),X0),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X8,X0),X0),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X19,X0),X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__diff__triangle__ineq_0) ).
fof(f13606,plain,
spl0_831,
inference(avatar_split_clause,[],[f381,f13604]) ).
fof(f13604,plain,
( spl0_831
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X19,X0),X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X8,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X19,X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f381,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X19,X0),X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X8,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X19,X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
fof(f13602,plain,
spl0_830,
inference(avatar_split_clause,[],[f208,f13600]) ).
fof(f13600,plain,
( spl0_830
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f208,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f13598,plain,
spl0_829,
inference(avatar_split_clause,[],[f207,f13596]) ).
fof(f13596,plain,
( spl0_829
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f207,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f13594,plain,
spl0_828,
inference(avatar_split_clause,[],[f153,f13592]) ).
fof(f13592,plain,
( spl0_828
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f153,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f13590,plain,
spl0_827,
inference(avatar_split_clause,[],[f120,f13588]) ).
fof(f13588,plain,
( spl0_827
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f120,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f13567,plain,
spl0_826,
inference(avatar_split_clause,[],[f403,f13565]) ).
fof(f13565,plain,
( spl0_826
<=> ! [X2,X18,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0) = X19
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f403,axiom,
! [X2,X0,X1,X18,X8,X19] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0) = X19
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
fof(f13489,plain,
spl0_825,
inference(avatar_split_clause,[],[f734,f13487]) ).
fof(f734,axiom,
! [X29] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f13485,plain,
spl0_824,
inference(avatar_split_clause,[],[f233,f13483]) ).
fof(f13483,plain,
( spl0_824
<=> ! [X2,X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X8,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f233,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X8,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
fof(f13282,plain,
spl0_823,
inference(avatar_split_clause,[],[f716,f13280]) ).
fof(f716,axiom,
! [X14] :
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r_0) ).
fof(f13278,plain,
spl0_822,
inference(avatar_split_clause,[],[f6,f13276]) ).
fof(f13276,plain,
( spl0_822
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
fof(f13274,plain,
( ~ spl0_821
| ~ spl0_153
| ~ spl0_817 ),
inference(avatar_split_clause,[],[f13235,f13082,f1600,f13271]) ).
fof(f13082,plain,
( spl0_817
<=> ! [X14] :
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f13235,plain,
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_153
| ~ spl0_817 ),
inference(resolution,[],[f13083,f1601]) ).
fof(f13083,plain,
( ! [X14] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f13082]) ).
fof(f13269,plain,
spl0_820,
inference(avatar_split_clause,[],[f5,f13267]) ).
fof(f13267,plain,
( spl0_820
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
fof(f13265,plain,
spl0_819,
inference(avatar_split_clause,[],[f4,f13263]) ).
fof(f13263,plain,
( spl0_819
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
fof(f13261,plain,
spl0_818,
inference(avatar_split_clause,[],[f3,f13259]) ).
fof(f13259,plain,
( spl0_818
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
fof(f13084,plain,
spl0_817,
inference(avatar_split_clause,[],[f715,f13082]) ).
fof(f715,axiom,
! [X14] :
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_v0_0) ).
fof(f13080,plain,
spl0_816,
inference(avatar_split_clause,[],[f711,f13078]) ).
fof(f711,axiom,
! [X1,X19,X14,X15] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X15
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X1,X19,X15),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X19,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X15,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__infinity_0) ).
fof(f13076,plain,
spl0_815,
inference(avatar_split_clause,[],[f558,f13074]) ).
fof(f13074,plain,
( spl0_815
<=> ! [X0,X1,X15] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f558,axiom,
! [X0,X1,X15] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_2) ).
fof(f13072,plain,
spl0_814,
inference(avatar_split_clause,[],[f398,f13070]) ).
fof(f13070,plain,
( spl0_814
<=> ! [X18,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f398,axiom,
! [X2,X0,X1,X18,X8] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X18,X0),X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
fof(f13068,plain,
spl0_813,
inference(avatar_split_clause,[],[f289,f13066]) ).
fof(f13066,plain,
( spl0_813
<=> ! [X18,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X18,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f289,axiom,
! [X2,X0,X1,X18,X8] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X18,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X18,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f13064,plain,
spl0_812,
inference(avatar_split_clause,[],[f167,f13062]) ).
fof(f13062,plain,
( spl0_812
<=> ! [X4,X0,X9,X3,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),X7,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(X7,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f167,axiom,
! [X3,X0,X9,X7,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),X7,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(X7,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__less_0) ).
fof(f13060,plain,
spl0_811,
inference(avatar_split_clause,[],[f145,f13058]) ).
fof(f13058,plain,
( spl0_811
<=> ! [X19,X0,X3,X8,X7] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X8 = X19
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X7,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f145,axiom,
! [X3,X0,X8,X19,X7] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X8 = X19
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X7,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f13056,plain,
spl0_810,
inference(avatar_split_clause,[],[f139,f13054]) ).
fof(f13054,plain,
( spl0_810
<=> ! [X5,X2,X0] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f139,axiom,
! [X2,X0,X5] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_2) ).
fof(f13052,plain,
( spl0_809
| ~ spl0_183
| ~ spl0_798 ),
inference(avatar_split_clause,[],[f12964,f12914,f1730,f13050]) ).
fof(f13050,plain,
( spl0_809
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f12914,plain,
( spl0_798
<=> ! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0)),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f12964,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_183
| ~ spl0_798 ),
inference(resolution,[],[f12915,f1731]) ).
fof(f12915,plain,
( ! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0)),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f12914]) ).
fof(f13048,plain,
spl0_808,
inference(avatar_split_clause,[],[f49,f13046]) ).
fof(f13046,plain,
( spl0_808
<=> ! [X4,X0,X9,X3,X7] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),X7,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0),c_HOL_Oplus__class_Oplus(X7,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f49,axiom,
! [X3,X0,X9,X7,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),X7,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0),c_HOL_Oplus__class_Oplus(X7,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__add__less_0) ).
fof(f13002,plain,
spl0_807,
inference(avatar_split_clause,[],[f468,f13000]) ).
fof(f13000,plain,
( spl0_807
<=> ! [X0,X3,X1,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X7,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X7,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f468,axiom,
! [X3,X0,X1,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X7,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X7,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
fof(f12998,plain,
spl0_806,
inference(avatar_split_clause,[],[f421,f12996]) ).
fof(f12996,plain,
( spl0_806
<=> ! [X15,X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f421,axiom,
! [X2,X0,X1,X15,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pCons_0) ).
fof(f12994,plain,
spl0_805,
inference(avatar_split_clause,[],[f127,f12992]) ).
fof(f12992,plain,
( spl0_805
<=> ! [X4,X0,X14,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X14,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f127,axiom,
! [X3,X0,X14,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X14,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f12980,plain,
spl0_804,
inference(avatar_split_clause,[],[f465,f12978]) ).
fof(f12978,plain,
( spl0_804
<=> ! [X0,X8,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Oplus__class_Oplus(X15,c_Polynomial_Osmult(X8,c_Polynomial_Osynthetic__div(X15,X8,X0),X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_Polynomial_Opoly(X15,X8,X0),c_Polynomial_Osynthetic__div(X15,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f465,axiom,
! [X0,X8,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Oplus__class_Oplus(X15,c_Polynomial_Osmult(X8,c_Polynomial_Osynthetic__div(X15,X8,X0),X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_Polynomial_Opoly(X15,X8,X0),c_Polynomial_Osynthetic__div(X15,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__correct_0) ).
fof(f12963,plain,
spl0_803,
inference(avatar_split_clause,[],[f111,f12961]) ).
fof(f12961,plain,
( spl0_803
<=> ! [X15,X0,X5,X2,X1] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(X15,X5,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f111,axiom,
! [X2,X0,X1,X15,X5] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(X15,X5,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_2) ).
fof(f12932,plain,
spl0_802,
inference(avatar_split_clause,[],[f305,f12930]) ).
fof(f12930,plain,
( spl0_802
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X8,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f305,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X8,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f12928,plain,
spl0_801,
inference(avatar_split_clause,[],[f222,f12926]) ).
fof(f12926,plain,
( spl0_801
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X19,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f222,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X19,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f12924,plain,
spl0_800,
inference(avatar_split_clause,[],[f82,f12922]) ).
fof(f12922,plain,
( spl0_800
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f82,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f12920,plain,
spl0_799,
inference(avatar_split_clause,[],[f81,f12918]) ).
fof(f12918,plain,
( spl0_799
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f81,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f12916,plain,
( spl0_798
| ~ spl0_153
| ~ spl0_796 ),
inference(avatar_split_clause,[],[f12886,f12816,f1600,f12914]) ).
fof(f12816,plain,
( spl0_796
<=> ! [X29,X7,X15] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),X7,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(X15,X7),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f12886,plain,
( ! [X0] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0)),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ spl0_153
| ~ spl0_796 ),
inference(resolution,[],[f12817,f1601]) ).
fof(f12817,plain,
( ! [X29,X7,X15] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(X15,X7),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),X7,tc_RealDef_Oreal) )
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f12816]) ).
fof(f12912,plain,
spl0_797,
inference(avatar_split_clause,[],[f53,f12910]) ).
fof(f12910,plain,
( spl0_797
<=> ! [X10,X11,X13,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X11,X0),c_HOL_Otimes__class_Otimes(X12,X13,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X12,X0),c_HOL_Otimes__class_Otimes(X11,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f53,axiom,
! [X10,X0,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X11,X0),c_HOL_Otimes__class_Otimes(X12,X13,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X12,X0),c_HOL_Otimes__class_Otimes(X11,X13,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f12818,plain,
spl0_796,
inference(avatar_split_clause,[],[f713,f12816]) ).
fof(f713,axiom,
! [X29,X7,X15] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),X7,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(X15,X7),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__minimum__modulus__disc_0) ).
fof(f12814,plain,
spl0_795,
inference(avatar_split_clause,[],[f611,f12812]) ).
fof(f12812,plain,
( spl0_795
<=> ! [X4,X0,X3,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f611,axiom,
! [X3,X0,X8,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).
fof(f12810,plain,
spl0_794,
inference(avatar_split_clause,[],[f212,f12808]) ).
fof(f12808,plain,
( spl0_794
<=> ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f212,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f12802,plain,
spl0_793,
inference(avatar_split_clause,[],[f210,f12800]) ).
fof(f12800,plain,
( spl0_793
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f210,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f12798,plain,
spl0_792,
inference(avatar_split_clause,[],[f106,f12796]) ).
fof(f12796,plain,
( spl0_792
<=> ! [X15,X0,X5,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X15,X0),c_Polynomial_Osmult(X1,X5,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f106,axiom,
! [X0,X1,X15,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X15,X0),c_Polynomial_Osmult(X1,X5,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__add__right_0) ).
fof(f12794,plain,
spl0_791,
inference(avatar_split_clause,[],[f80,f12792]) ).
fof(f12792,plain,
( spl0_791
<=> ! [X15,X0,X8,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X8,X15,X0),c_Polynomial_OpCons(X1,X15,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f80,axiom,
! [X0,X1,X8,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X8,X15,X0),c_Polynomial_OpCons(X1,X15,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).
fof(f12638,plain,
( ~ spl0_58
| spl0_790
| ~ spl0_257
| ~ spl0_497 ),
inference(avatar_split_clause,[],[f6606,f6278,f2134,f12636,f1179]) ).
fof(f12636,plain,
( spl0_790
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f6278,plain,
( spl0_497
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f6606,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_497 ),
inference(resolution,[],[f6279,f2135]) ).
fof(f6279,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_497 ),
inference(avatar_component_clause,[],[f6278]) ).
fof(f12393,plain,
( spl0_789
| ~ spl0_373
| ~ spl0_497 ),
inference(avatar_split_clause,[],[f6601,f6278,f3630,f12391]) ).
fof(f12391,plain,
( spl0_789
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f3630,plain,
( spl0_373
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f6601,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_497 ),
inference(resolution,[],[f6279,f3631]) ).
fof(f3631,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f3630]) ).
fof(f11843,plain,
( spl0_788
| ~ spl0_183
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3677,f3630,f1730,f11841]) ).
fof(f11841,plain,
( spl0_788
<=> ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f3677,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) )
| ~ spl0_183
| ~ spl0_373 ),
inference(resolution,[],[f3631,f1731]) ).
fof(f11835,plain,
spl0_787,
inference(avatar_split_clause,[],[f703,f11833]) ).
fof(f11833,plain,
( spl0_787
<=> ! [X15,X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(X15,X8,X0) = X7
| c_HOL_Oplus__class_Oplus(X15,c_Polynomial_Osmult(X8,X5,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f703,axiom,
! [X0,X8,X7,X15,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(X15,X8,X0) = X7
| c_HOL_Oplus__class_Oplus(X15,c_Polynomial_Osmult(X8,X5,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X7,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
fof(f11831,plain,
spl0_786,
inference(avatar_split_clause,[],[f620,f11829]) ).
fof(f11829,plain,
( spl0_786
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X0),c_Orderings_Oord__class_Omax(X3,X14,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f620,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X0),c_Orderings_Oord__class_Omax(X3,X14,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
fof(f11827,plain,
spl0_785,
inference(avatar_split_clause,[],[f617,f11825]) ).
fof(f11825,plain,
( spl0_785
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f617,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f11823,plain,
spl0_784,
inference(avatar_split_clause,[],[f616,f11821]) ).
fof(f11821,plain,
( spl0_784
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f616,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f11819,plain,
spl0_783,
inference(avatar_split_clause,[],[f615,f11817]) ).
fof(f11817,plain,
( spl0_783
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f615,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f11815,plain,
spl0_782,
inference(avatar_split_clause,[],[f614,f11813]) ).
fof(f11813,plain,
( spl0_782
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f614,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f11811,plain,
spl0_781,
inference(avatar_split_clause,[],[f598,f11809]) ).
fof(f11809,plain,
( spl0_781
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f598,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f11807,plain,
spl0_780,
inference(avatar_split_clause,[],[f586,f11805]) ).
fof(f11805,plain,
( spl0_780
<=> ! [X15,X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osynthetic__div(X15,X8,X0) = X5
| c_HOL_Oplus__class_Oplus(X15,c_Polynomial_Osmult(X8,X5,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f586,axiom,
! [X0,X8,X7,X15,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osynthetic__div(X15,X8,X0) = X5
| c_HOL_Oplus__class_Oplus(X15,c_Polynomial_Osmult(X8,X5,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X7,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__unique_1) ).
fof(f11765,plain,
spl0_779,
inference(avatar_split_clause,[],[f551,f11763]) ).
fof(f11763,plain,
( spl0_779
<=> ! [X0,X1,X15] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f551,axiom,
! [X0,X1,X15] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_1) ).
fof(f11761,plain,
spl0_778,
inference(avatar_split_clause,[],[f444,f11759]) ).
fof(f11759,plain,
( spl0_778
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f444,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f11757,plain,
spl0_777,
inference(avatar_split_clause,[],[f443,f11755]) ).
fof(f11755,plain,
( spl0_777
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f443,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
fof(f11753,plain,
spl0_776,
inference(avatar_split_clause,[],[f442,f11751]) ).
fof(f11751,plain,
( spl0_776
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f442,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f11749,plain,
spl0_775,
inference(avatar_split_clause,[],[f441,f11747]) ).
fof(f11747,plain,
( spl0_775
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f441,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
fof(f11745,plain,
spl0_774,
inference(avatar_split_clause,[],[f439,f11743]) ).
fof(f11743,plain,
( spl0_774
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f439,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f11741,plain,
spl0_773,
inference(avatar_split_clause,[],[f436,f11739]) ).
fof(f11739,plain,
( spl0_773
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f436,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
fof(f11737,plain,
spl0_772,
inference(avatar_split_clause,[],[f435,f11735]) ).
fof(f11735,plain,
( spl0_772
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f435,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f11733,plain,
spl0_771,
inference(avatar_split_clause,[],[f434,f11731]) ).
fof(f11731,plain,
( spl0_771
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f434,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f11729,plain,
spl0_770,
inference(avatar_split_clause,[],[f406,f11727]) ).
fof(f11727,plain,
( spl0_770
<=> ! [X15,X0,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X3,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X15,X3,X0),c_Polynomial_Opoly(X5,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f406,axiom,
! [X3,X0,X15,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X3,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X15,X3,X0),c_Polynomial_Opoly(X5,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__add_0) ).
fof(f11700,plain,
spl0_769,
inference(avatar_split_clause,[],[f332,f11698]) ).
fof(f11698,plain,
( spl0_769
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f332,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f11696,plain,
spl0_768,
inference(avatar_split_clause,[],[f274,f11694]) ).
fof(f11694,plain,
( spl0_768
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f274,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f11692,plain,
spl0_767,
inference(avatar_split_clause,[],[f273,f11690]) ).
fof(f11690,plain,
( spl0_767
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f273,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f11688,plain,
spl0_766,
inference(avatar_split_clause,[],[f272,f11686]) ).
fof(f11686,plain,
( spl0_766
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f272,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f11684,plain,
spl0_765,
inference(avatar_split_clause,[],[f271,f11682]) ).
fof(f11682,plain,
( spl0_765
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f271,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f11680,plain,
spl0_764,
inference(avatar_split_clause,[],[f270,f11678]) ).
fof(f11678,plain,
( spl0_764
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f270,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f11676,plain,
spl0_763,
inference(avatar_split_clause,[],[f269,f11674]) ).
fof(f11674,plain,
( spl0_763
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f269,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f11672,plain,
spl0_762,
inference(avatar_split_clause,[],[f262,f11670]) ).
fof(f11670,plain,
( spl0_762
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X6,X0),c_Power_Opower__class_Opower(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f262,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X6,X0),c_Power_Opower__class_Opower(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f11668,plain,
spl0_761,
inference(avatar_split_clause,[],[f217,f11666]) ).
fof(f11666,plain,
( spl0_761
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X0),c_Orderings_Oord__class_Omin(X3,X14,X0),X0),c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f217,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X0),c_Orderings_Oord__class_Omin(X3,X14,X0),X0),c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
fof(f11664,plain,
spl0_760,
inference(avatar_split_clause,[],[f144,f11662]) ).
fof(f11662,plain,
( spl0_760
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f144,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f11660,plain,
( spl0_759
| ~ spl0_183
| ~ spl0_618 ),
inference(avatar_split_clause,[],[f9998,f8584,f1730,f11658]) ).
fof(f11658,plain,
( spl0_759
<=> ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f8584,plain,
( spl0_618
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f9998,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),X0,tc_RealDef_Oreal) )
| ~ spl0_183
| ~ spl0_618 ),
inference(resolution,[],[f8585,f1731]) ).
fof(f8585,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_618 ),
inference(avatar_component_clause,[],[f8584]) ).
fof(f11656,plain,
spl0_758,
inference(avatar_split_clause,[],[f143,f11654]) ).
fof(f11654,plain,
( spl0_758
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f143,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f11652,plain,
spl0_757,
inference(avatar_split_clause,[],[f142,f11650]) ).
fof(f11650,plain,
( spl0_757
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f142,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f11648,plain,
spl0_756,
inference(avatar_split_clause,[],[f141,f11646]) ).
fof(f11646,plain,
( spl0_756
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f141,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f11644,plain,
spl0_755,
inference(avatar_split_clause,[],[f140,f11642]) ).
fof(f11642,plain,
( spl0_755
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f140,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f11640,plain,
spl0_754,
inference(avatar_split_clause,[],[f105,f11638]) ).
fof(f11638,plain,
( spl0_754
<=> ! [X15,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X0),X15,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X15,X0),c_Polynomial_Osmult(X2,X15,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f105,axiom,
! [X2,X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X0),X15,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X15,X0),c_Polynomial_Osmult(X2,X15,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__add__left_0) ).
fof(f11636,plain,
spl0_753,
inference(avatar_split_clause,[],[f97,f11634]) ).
fof(f11634,plain,
( spl0_753
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f97,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f11632,plain,
spl0_752,
inference(avatar_split_clause,[],[f96,f11630]) ).
fof(f11630,plain,
( spl0_752
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f96,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f11628,plain,
spl0_751,
inference(avatar_split_clause,[],[f95,f11626]) ).
fof(f11626,plain,
( spl0_751
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f95,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f11624,plain,
spl0_750,
inference(avatar_split_clause,[],[f94,f11622]) ).
fof(f11622,plain,
( spl0_750
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f94,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f11620,plain,
spl0_749,
inference(avatar_split_clause,[],[f67,f11618]) ).
fof(f11618,plain,
( spl0_749
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X6,X0),c_Power_Opower__class_Opower(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f67,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X6,X0),c_Power_Opower__class_Opower(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f11612,plain,
spl0_748,
inference(avatar_split_clause,[],[f15,f11610]) ).
fof(f11610,plain,
( spl0_748
<=> ! [X5,X2,X0] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f15,axiom,
! [X2,X0,X5] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_1) ).
fof(f11382,plain,
( ~ spl0_58
| spl0_747
| ~ spl0_257
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f6125,f5439,f2134,f11380,f1179]) ).
fof(f11380,plain,
( spl0_747
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f5439,plain,
( spl0_495
<=> ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f6125,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_495 ),
inference(resolution,[],[f5440,f2135]) ).
fof(f5440,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f5439]) ).
fof(f11223,plain,
( spl0_746
| ~ spl0_373
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f6121,f5439,f3630,f11221]) ).
fof(f11221,plain,
( spl0_746
<=> ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,hAPP(v_x,X0))),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f6121,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,hAPP(v_x,X0))),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_495 ),
inference(resolution,[],[f5440,f3631]) ).
fof(f10714,plain,
( spl0_745
| ~ spl0_618
| ~ spl0_701 ),
inference(avatar_split_clause,[],[f10539,f9907,f8584,f10712]) ).
fof(f10712,plain,
( spl0_745
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f9907,plain,
( spl0_701
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f10539,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_618
| ~ spl0_701 ),
inference(resolution,[],[f9908,f8585]) ).
fof(f9908,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f9907]) ).
fof(f10160,plain,
spl0_744,
inference(avatar_split_clause,[],[f710,f10158]) ).
fof(f10158,plain,
( spl0_744
<=> ! [X15,X0,X8,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_OpCons(c_Polynomial_Opoly(X15,X8,X0),c_Polynomial_Osynthetic__div(X15,X8,X0),X0) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X15,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f710,axiom,
! [X0,X1,X8,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_OpCons(c_Polynomial_Opoly(X15,X8,X0),c_Polynomial_Osynthetic__div(X15,X8,X0),X0) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X15,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__pCons_0) ).
fof(f10156,plain,
spl0_743,
inference(avatar_split_clause,[],[f702,f10154]) ).
fof(f10154,plain,
( spl0_743
<=> ! [X15,X0,X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X15,X0),X3,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X15,X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f702,axiom,
! [X3,X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X15,X0),X3,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X15,X3,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
fof(f10123,plain,
spl0_742,
inference(avatar_split_clause,[],[f698,f10121]) ).
fof(f10121,plain,
( spl0_742
<=> ! [X15,X0,X5,X2,X1] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X15,X5,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f698,axiom,
! [X2,X0,X1,X15,X5] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X15,X5,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_1) ).
fof(f10119,plain,
spl0_741,
inference(avatar_split_clause,[],[f609,f10117]) ).
fof(f10117,plain,
( spl0_741
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f609,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f10115,plain,
spl0_740,
inference(avatar_split_clause,[],[f563,f10113]) ).
fof(f10113,plain,
( spl0_740
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f563,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f10111,plain,
spl0_739,
inference(avatar_split_clause,[],[f557,f10109]) ).
fof(f10109,plain,
( spl0_739
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f557,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f10107,plain,
spl0_738,
inference(avatar_split_clause,[],[f552,f10105]) ).
fof(f10105,plain,
( spl0_738
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f552,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
fof(f10103,plain,
spl0_737,
inference(avatar_split_clause,[],[f508,f10101]) ).
fof(f10101,plain,
( spl0_737
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f508,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f10099,plain,
spl0_736,
inference(avatar_split_clause,[],[f483,f10097]) ).
fof(f10097,plain,
( spl0_736
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f483,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X19,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f10095,plain,
spl0_735,
inference(avatar_split_clause,[],[f476,f10093]) ).
fof(f10093,plain,
( spl0_735
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f476,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X8,X19,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f10091,plain,
spl0_734,
inference(avatar_split_clause,[],[f475,f10089]) ).
fof(f10089,plain,
( spl0_734
<=> ! [X19,X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f475,axiom,
! [X2,X0,X1,X8,X19] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X8,X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f10087,plain,
spl0_733,
inference(avatar_split_clause,[],[f385,f10085]) ).
fof(f10085,plain,
( spl0_733
<=> ! [X4,X0,X14,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X3,X14,X0),c_HOL_Ominus__class_Ominus(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f385,axiom,
! [X3,X0,X14,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X3,X14,X0),c_HOL_Ominus__class_Ominus(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
fof(f10058,plain,
spl0_732,
inference(avatar_split_clause,[],[f383,f10056]) ).
fof(f10056,plain,
( spl0_732
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f383,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f10054,plain,
spl0_731,
inference(avatar_split_clause,[],[f376,f10052]) ).
fof(f10052,plain,
( spl0_731
<=> ! [X4,X8,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,c_HOL_Oabs__class_Oabs(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f376,axiom,
! [X3,X8,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,c_HOL_Oabs__class_Oabs(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rabs__ratiotest__lemma_0) ).
fof(f10050,plain,
spl0_730,
inference(avatar_split_clause,[],[f374,f10048]) ).
fof(f10048,plain,
( spl0_730
<=> ! [X2,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),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f374,axiom,
! [X2,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),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f10046,plain,
spl0_729,
inference(avatar_split_clause,[],[f371,f10044]) ).
fof(f10044,plain,
( spl0_729
<=> ! [X4,X0,X14,X3,X30] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X14,X0) = X30
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) != c_HOL_Oplus__class_Oplus(X4,X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f371,axiom,
! [X3,X0,X14,X4,X30] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X14,X0) = X30
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) != c_HOL_Oplus__class_Oplus(X4,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f10042,plain,
spl0_728,
inference(avatar_split_clause,[],[f368,f10040]) ).
fof(f10040,plain,
( spl0_728
<=> ! [X4,X0,X14,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X3,X14,X0),c_HOL_Ominus__class_Ominus(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f368,axiom,
! [X3,X0,X14,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X3,X14,X0),c_HOL_Ominus__class_Ominus(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
fof(f10038,plain,
spl0_727,
inference(avatar_split_clause,[],[f365,f10036]) ).
fof(f10036,plain,
( spl0_727
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f365,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
fof(f10034,plain,
spl0_726,
inference(avatar_split_clause,[],[f364,f10032]) ).
fof(f10032,plain,
( spl0_726
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f364,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
fof(f10030,plain,
spl0_725,
inference(avatar_split_clause,[],[f363,f10028]) ).
fof(f10028,plain,
( spl0_725
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f363,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
fof(f10026,plain,
spl0_724,
inference(avatar_split_clause,[],[f362,f10024]) ).
fof(f10024,plain,
( spl0_724
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f362,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
fof(f10022,plain,
spl0_723,
inference(avatar_split_clause,[],[f353,f10020]) ).
fof(f10020,plain,
( spl0_723
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f353,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f9993,plain,
spl0_722,
inference(avatar_split_clause,[],[f352,f9991]) ).
fof(f9991,plain,
( spl0_722
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(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,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f352,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(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,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f9989,plain,
spl0_721,
inference(avatar_split_clause,[],[f350,f9987]) ).
fof(f9987,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f350,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
fof(f9985,plain,
spl0_720,
inference(avatar_split_clause,[],[f348,f9983]) ).
fof(f9983,plain,
( spl0_720
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f348,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
fof(f9981,plain,
spl0_719,
inference(avatar_split_clause,[],[f345,f9979]) ).
fof(f9979,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f345,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f9977,plain,
spl0_718,
inference(avatar_split_clause,[],[f344,f9975]) ).
fof(f9975,plain,
( spl0_718
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f344,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f9973,plain,
spl0_717,
inference(avatar_split_clause,[],[f319,f9971]) ).
fof(f9971,plain,
( spl0_717
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f319,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f9969,plain,
spl0_716,
inference(avatar_split_clause,[],[f318,f9967]) ).
fof(f9967,plain,
( spl0_716
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f318,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f9965,plain,
spl0_715,
inference(avatar_split_clause,[],[f304,f9963]) ).
fof(f9963,plain,
( spl0_715
<=> ! [X4,X0,X27,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Otimes__class_Otimes(X4,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f304,axiom,
! [X3,X0,X27,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Otimes__class_Otimes(X4,X27,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
fof(f9961,plain,
spl0_714,
inference(avatar_split_clause,[],[f301,f9959]) ).
fof(f9959,plain,
( spl0_714
<=> ! [X4,X0,X3,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X25,X3,X0),c_HOL_Otimes__class_Otimes(X25,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f301,axiom,
! [X3,X0,X4,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X25,X3,X0),c_HOL_Otimes__class_Otimes(X25,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
fof(f9957,plain,
spl0_713,
inference(avatar_split_clause,[],[f300,f9955]) ).
fof(f9955,plain,
( spl0_713
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f300,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f9953,plain,
( spl0_712
| ~ spl0_319
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f8395,f7976,f2818,f9951]) ).
fof(f9951,plain,
( spl0_712
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f7976,plain,
( spl0_573
<=> ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f8395,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ spl0_319
| ~ spl0_573 ),
inference(resolution,[],[f7977,f2819]) ).
fof(f7977,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_573 ),
inference(avatar_component_clause,[],[f7976]) ).
fof(f9949,plain,
spl0_711,
inference(avatar_split_clause,[],[f299,f9947]) ).
fof(f9947,plain,
( spl0_711
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f299,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f9945,plain,
spl0_710,
inference(avatar_split_clause,[],[f295,f9943]) ).
fof(f9943,plain,
( spl0_710
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f295,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f9941,plain,
spl0_709,
inference(avatar_split_clause,[],[f261,f9939]) ).
fof(f9939,plain,
( spl0_709
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f261,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f9937,plain,
spl0_708,
inference(avatar_split_clause,[],[f260,f9935]) ).
fof(f9935,plain,
( spl0_708
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f260,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__triangle__ineq3_0) ).
fof(f9933,plain,
spl0_707,
inference(avatar_split_clause,[],[f230,f9931]) ).
fof(f9931,plain,
( spl0_707
<=> ! [X4,X0,X14,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X3,X14,X0),c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f230,axiom,
! [X3,X0,X14,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X3,X14,X0),c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
fof(f9929,plain,
spl0_706,
inference(avatar_split_clause,[],[f213,f9927]) ).
fof(f9927,plain,
( spl0_706
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f213,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f9925,plain,
spl0_705,
inference(avatar_split_clause,[],[f211,f9923]) ).
fof(f9923,plain,
( spl0_705
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f211,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f9921,plain,
spl0_704,
inference(avatar_split_clause,[],[f209,f9919]) ).
fof(f9919,plain,
( spl0_704
<=> ! [X4,X0,X14,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X3,X14,X0),c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f209,axiom,
! [X3,X0,X14,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X3,X14,X0),c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
fof(f9917,plain,
spl0_703,
inference(avatar_split_clause,[],[f197,f9915]) ).
fof(f9915,plain,
( spl0_703
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f197,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f9913,plain,
spl0_702,
inference(avatar_split_clause,[],[f193,f9911]) ).
fof(f9911,plain,
( spl0_702
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f193,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f9909,plain,
( spl0_701
| ~ spl0_319
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f8319,f7352,f2818,f9907]) ).
fof(f7352,plain,
( spl0_567
<=> ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f8319,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ spl0_319
| ~ spl0_567 ),
inference(resolution,[],[f7353,f2819]) ).
fof(f7353,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_567 ),
inference(avatar_component_clause,[],[f7352]) ).
fof(f9905,plain,
spl0_700,
inference(avatar_split_clause,[],[f192,f9903]) ).
fof(f9903,plain,
( spl0_700
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f192,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f9901,plain,
spl0_699,
inference(avatar_split_clause,[],[f191,f9899]) ).
fof(f9899,plain,
( spl0_699
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f191,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f9897,plain,
spl0_698,
inference(avatar_split_clause,[],[f190,f9895]) ).
fof(f9895,plain,
( spl0_698
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f190,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f9893,plain,
spl0_697,
inference(avatar_split_clause,[],[f186,f9891]) ).
fof(f9891,plain,
( spl0_697
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f186,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f9889,plain,
spl0_696,
inference(avatar_split_clause,[],[f185,f9887]) ).
fof(f9887,plain,
( spl0_696
<=> ! [X4,X0,X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f185,axiom,
! [X3,X0,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X14,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f9885,plain,
spl0_695,
inference(avatar_split_clause,[],[f182,f9883]) ).
fof(f9883,plain,
( spl0_695
<=> ! [X4,X0,X27,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Otimes__class_Otimes(X4,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f182,axiom,
! [X3,X0,X27,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Otimes__class_Otimes(X4,X27,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
fof(f9881,plain,
spl0_694,
inference(avatar_split_clause,[],[f180,f9879]) ).
fof(f9879,plain,
( spl0_694
<=> ! [X4,X0,X3,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X3,X0),c_HOL_Otimes__class_Otimes(X25,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f180,axiom,
! [X3,X0,X4,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X3,X0),c_HOL_Otimes__class_Otimes(X25,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
fof(f9877,plain,
spl0_693,
inference(avatar_split_clause,[],[f179,f9875]) ).
fof(f9875,plain,
( spl0_693
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f179,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f9873,plain,
spl0_692,
inference(avatar_split_clause,[],[f166,f9871]) ).
fof(f9871,plain,
( spl0_692
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f166,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f9869,plain,
spl0_691,
inference(avatar_split_clause,[],[f165,f9867]) ).
fof(f9867,plain,
( spl0_691
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f165,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f9865,plain,
( spl0_690
| ~ spl0_183
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f8238,f7265,f1730,f9863]) ).
fof(f9863,plain,
( spl0_690
<=> ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f7265,plain,
( spl0_558
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f8238,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),X0,tc_RealDef_Oreal) )
| ~ spl0_183
| ~ spl0_558 ),
inference(resolution,[],[f7266,f1731]) ).
fof(f7266,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f7265]) ).
fof(f9861,plain,
spl0_689,
inference(avatar_split_clause,[],[f164,f9859]) ).
fof(f9859,plain,
( spl0_689
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f164,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f9857,plain,
spl0_688,
inference(avatar_split_clause,[],[f162,f9855]) ).
fof(f9855,plain,
( spl0_688
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f162,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
fof(f9853,plain,
spl0_687,
inference(avatar_split_clause,[],[f160,f9851]) ).
fof(f9851,plain,
( spl0_687
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f160,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f9849,plain,
spl0_686,
inference(avatar_split_clause,[],[f159,f9847]) ).
fof(f9847,plain,
( spl0_686
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X14,X0),X3,X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X3,X0),c_Orderings_Oord__class_Omax(X14,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f159,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X14,X0),X3,X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X3,X0),c_Orderings_Oord__class_Omax(X14,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
fof(f9845,plain,
spl0_685,
inference(avatar_split_clause,[],[f158,f9843]) ).
fof(f9843,plain,
( spl0_685
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X0),c_Orderings_Oord__class_Omax(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f158,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X0),c_Orderings_Oord__class_Omax(X3,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
fof(f9841,plain,
spl0_684,
inference(avatar_split_clause,[],[f157,f9839]) ).
fof(f9839,plain,
( spl0_684
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X6,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X6,X0),c_Power_Opower__class_Opower(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f157,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X6,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X6,X0),c_Power_Opower__class_Opower(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f9837,plain,
spl0_683,
inference(avatar_split_clause,[],[f156,f9835]) ).
fof(f9835,plain,
( spl0_683
<=> ! [X4,X0,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X3,X4,X0),X5,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X5,X0),c_Power_Opower__class_Opower(X4,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f156,axiom,
! [X3,X0,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X3,X4,X0),X5,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X5,X0),c_Power_Opower__class_Opower(X4,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f9833,plain,
spl0_682,
inference(avatar_split_clause,[],[f151,f9831]) ).
fof(f9831,plain,
( spl0_682
<=> ! [X15,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X15,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_Polynomial_Osmult(X1,X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f151,axiom,
! [X2,X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X15,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_Polynomial_Osmult(X1,X15,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
fof(f9829,plain,
spl0_681,
inference(avatar_split_clause,[],[f130,f9827]) ).
fof(f9827,plain,
( spl0_681
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f130,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
fof(f9825,plain,
spl0_680,
inference(avatar_split_clause,[],[f115,f9823]) ).
fof(f9823,plain,
( spl0_680
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X0),c_Orderings_Oord__class_Omin(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f115,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X0),c_Orderings_Oord__class_Omin(X3,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
fof(f9817,plain,
spl0_679,
inference(avatar_split_clause,[],[f114,f9815]) ).
fof(f9815,plain,
( spl0_679
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X14,X0),X3,X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X3,X0),c_Orderings_Oord__class_Omin(X14,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f114,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X14,X0),X3,X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X3,X0),c_Orderings_Oord__class_Omin(X14,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
fof(f9813,plain,
spl0_678,
inference(avatar_split_clause,[],[f113,f9811]) ).
fof(f9811,plain,
( spl0_678
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f113,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f9809,plain,
spl0_677,
inference(avatar_split_clause,[],[f112,f9807]) ).
fof(f9807,plain,
( spl0_677
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f112,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f9805,plain,
spl0_676,
inference(avatar_split_clause,[],[f71,f9803]) ).
fof(f9803,plain,
( spl0_676
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f71,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f9801,plain,
spl0_675,
inference(avatar_split_clause,[],[f70,f9799]) ).
fof(f9799,plain,
( spl0_675
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f70,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f9797,plain,
spl0_674,
inference(avatar_split_clause,[],[f69,f9795]) ).
fof(f9795,plain,
( spl0_674
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f69,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f9793,plain,
spl0_673,
inference(avatar_split_clause,[],[f68,f9791]) ).
fof(f9791,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f68,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f9789,plain,
spl0_672,
inference(avatar_split_clause,[],[f57,f9787]) ).
fof(f9787,plain,
( spl0_672
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f57,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f9785,plain,
spl0_671,
inference(avatar_split_clause,[],[f56,f9783]) ).
fof(f9783,plain,
( spl0_671
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f56,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f9781,plain,
spl0_670,
inference(avatar_split_clause,[],[f55,f9779]) ).
fof(f9779,plain,
( spl0_670
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f55,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f9777,plain,
( ~ spl0_58
| spl0_669
| ~ spl0_257
| ~ spl0_605 ),
inference(avatar_split_clause,[],[f8159,f8108,f2134,f9775,f1179]) ).
fof(f9775,plain,
( spl0_669
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f8108,plain,
( spl0_605
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f8159,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_605 ),
inference(resolution,[],[f8109,f2135]) ).
fof(f8109,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_605 ),
inference(avatar_component_clause,[],[f8108]) ).
fof(f9773,plain,
spl0_668,
inference(avatar_split_clause,[],[f27,f9771]) ).
fof(f9771,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f27,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f9769,plain,
spl0_667,
inference(avatar_split_clause,[],[f26,f9767]) ).
fof(f9767,plain,
( spl0_667
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
fof(f9765,plain,
spl0_666,
inference(avatar_split_clause,[],[f25,f9763]) ).
fof(f9763,plain,
( spl0_666
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f25,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f9761,plain,
spl0_665,
inference(avatar_split_clause,[],[f24,f9759]) ).
fof(f9759,plain,
( spl0_665
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f24,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f9757,plain,
spl0_664,
inference(avatar_split_clause,[],[f23,f9755]) ).
fof(f9755,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f9753,plain,
spl0_663,
inference(avatar_split_clause,[],[f22,f9751]) ).
fof(f9751,plain,
( spl0_663
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f9730,plain,
( spl0_662
| ~ spl0_373
| ~ spl0_605 ),
inference(avatar_split_clause,[],[f8154,f8108,f3630,f9728]) ).
fof(f9728,plain,
( spl0_662
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f8154,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_605 ),
inference(resolution,[],[f8109,f3631]) ).
fof(f9545,plain,
spl0_661,
inference(avatar_split_clause,[],[f613,f9543]) ).
fof(f9543,plain,
( spl0_661
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f613,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f9541,plain,
spl0_660,
inference(avatar_split_clause,[],[f550,f9539]) ).
fof(f9539,plain,
( spl0_660
<=> ! [X0,X1,X15] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f550,axiom,
! [X0,X1,X15] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_0) ).
fof(f9537,plain,
spl0_659,
inference(avatar_split_clause,[],[f530,f9535]) ).
fof(f9535,plain,
( spl0_659
<=> ! [X4,X20,X0,X3,X21] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X21,X20,X0)
| c_lessequals(X4,X3,X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ominus__class_Ominus(X20,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f530,axiom,
! [X21,X3,X0,X4,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X21,X20,X0)
| c_lessequals(X4,X3,X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ominus__class_Ominus(X20,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
fof(f9533,plain,
spl0_658,
inference(avatar_split_clause,[],[f447,f9531]) ).
fof(f9531,plain,
( spl0_658
<=> ! [X4,X3,X14] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f447,axiom,
! [X3,X14,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).
fof(f9529,plain,
( ~ spl0_58
| spl0_657
| ~ spl0_257
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f5251,f5057,f2134,f9527,f1179]) ).
fof(f9527,plain,
( spl0_657
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f5057,plain,
( spl0_467
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f5251,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_467 ),
inference(resolution,[],[f5058,f2135]) ).
fof(f5058,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f5057]) ).
fof(f9525,plain,
spl0_656,
inference(avatar_split_clause,[],[f446,f9523]) ).
fof(f9523,plain,
( spl0_656
<=> ! [X4,X3,X14] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f446,axiom,
! [X3,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
fof(f9521,plain,
spl0_655,
inference(avatar_split_clause,[],[f445,f9519]) ).
fof(f9519,plain,
( spl0_655
<=> ! [X4,X3,X14] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f445,axiom,
! [X3,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).
fof(f9517,plain,
spl0_654,
inference(avatar_split_clause,[],[f401,f9515]) ).
fof(f9515,plain,
( spl0_654
<=> ! [X15,X0,X5,X2,X1] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f401,axiom,
! [X2,X0,X1,X15,X5] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X15,X0),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_0) ).
fof(f9513,plain,
spl0_653,
inference(avatar_split_clause,[],[f369,f9511]) ).
fof(f9511,plain,
( spl0_653
<=> ! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osmult(X1,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f369,axiom,
! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osmult(X1,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
fof(f9509,plain,
spl0_652,
inference(avatar_split_clause,[],[f327,f9507]) ).
fof(f9507,plain,
( spl0_652
<=> ! [X4,X0,X3] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f327,axiom,
! [X3,X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__add_0) ).
fof(f9505,plain,
spl0_651,
inference(avatar_split_clause,[],[f278,f9503]) ).
fof(f9503,plain,
( spl0_651
<=> ! [X4,X3,X14] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f278,axiom,
! [X3,X14,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).
fof(f9501,plain,
spl0_650,
inference(avatar_split_clause,[],[f277,f9499]) ).
fof(f9499,plain,
( spl0_650
<=> ! [X4,X3,X14] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f277,axiom,
! [X3,X14,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).
fof(f9497,plain,
spl0_649,
inference(avatar_split_clause,[],[f276,f9495]) ).
fof(f9495,plain,
( spl0_649
<=> ! [X4,X3,X14] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f276,axiom,
! [X3,X14,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).
fof(f9493,plain,
spl0_648,
inference(avatar_split_clause,[],[f275,f9491]) ).
fof(f9491,plain,
( spl0_648
<=> ! [X4,X3,X14] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f275,axiom,
! [X3,X14,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).
fof(f9489,plain,
spl0_647,
inference(avatar_split_clause,[],[f268,f9487]) ).
fof(f9487,plain,
( spl0_647
<=> ! [X6,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f268,axiom,
! [X3,X0,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
fof(f9481,plain,
spl0_646,
inference(avatar_split_clause,[],[f155,f9479]) ).
fof(f9479,plain,
( spl0_646
<=> ! [X4,X0,X3,X21,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X20,X21,X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ominus__class_Ominus(X20,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f155,axiom,
! [X21,X3,X0,X4,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X20,X21,X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ominus__class_Ominus(X20,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f9477,plain,
spl0_645,
inference(avatar_split_clause,[],[f149,f9475]) ).
fof(f9475,plain,
( spl0_645
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f149,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f9473,plain,
spl0_644,
inference(avatar_split_clause,[],[f148,f9471]) ).
fof(f9471,plain,
( spl0_644
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f148,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f9469,plain,
spl0_643,
inference(avatar_split_clause,[],[f93,f9467]) ).
fof(f9467,plain,
( spl0_643
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f93,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f9465,plain,
spl0_642,
inference(avatar_split_clause,[],[f16,f9463]) ).
fof(f9463,plain,
( spl0_642
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f16,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f9461,plain,
spl0_641,
inference(avatar_split_clause,[],[f14,f9459]) ).
fof(f9459,plain,
( spl0_641
<=> ! [X5,X2,X0] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f14,axiom,
! [X2,X0,X5] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X5,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_0) ).
fof(f9326,plain,
( ~ spl0_58
| spl0_640
| ~ spl0_257
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f5161,f5013,f2134,f9324,f1179]) ).
fof(f9324,plain,
( spl0_640
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f5013,plain,
( spl0_456
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f5161,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_456 ),
inference(resolution,[],[f5014,f2135]) ).
fof(f5014,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ spl0_456 ),
inference(avatar_component_clause,[],[f5013]) ).
fof(f8803,plain,
spl0_639,
inference(avatar_split_clause,[],[f687,f8801]) ).
fof(f8801,plain,
( spl0_639
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f687,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).
fof(f8799,plain,
spl0_638,
inference(avatar_split_clause,[],[f685,f8797]) ).
fof(f8797,plain,
( spl0_638
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f685,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__triangle__ineq4_0) ).
fof(f8795,plain,
spl0_637,
inference(avatar_split_clause,[],[f684,f8793]) ).
fof(f8793,plain,
( spl0_637
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f684,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__diff__ineq_0) ).
fof(f8791,plain,
spl0_636,
inference(avatar_split_clause,[],[f683,f8789]) ).
fof(f8789,plain,
( spl0_636
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f683,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__triangle__ineq2_0) ).
fof(f8787,plain,
spl0_635,
inference(avatar_split_clause,[],[f682,f8785]) ).
fof(f8785,plain,
( spl0_635
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f682,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__triangle__ineq_0) ).
fof(f8783,plain,
( ~ spl0_58
| spl0_634
| ~ spl0_257
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f5104,f4778,f2134,f8781,f1179]) ).
fof(f8781,plain,
( spl0_634
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f4778,plain,
( spl0_430
<=> ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f5104,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_430 ),
inference(resolution,[],[f4779,f2135]) ).
fof(f4779,plain,
( ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f4778]) ).
fof(f8779,plain,
spl0_633,
inference(avatar_split_clause,[],[f618,f8777]) ).
fof(f8777,plain,
( spl0_633
<=> ! [X0,X3,X1,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X7,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f618,axiom,
! [X3,X0,X1,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X7,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
fof(f8775,plain,
spl0_632,
inference(avatar_split_clause,[],[f581,f8773]) ).
fof(f8773,plain,
( spl0_632
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f581,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
fof(f8771,plain,
spl0_631,
inference(avatar_split_clause,[],[f333,f8769]) ).
fof(f8769,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f333,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
fof(f8767,plain,
spl0_630,
inference(avatar_split_clause,[],[f321,f8765]) ).
fof(f8765,plain,
( spl0_630
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f321,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero_0) ).
fof(f8763,plain,
spl0_629,
inference(avatar_split_clause,[],[f320,f8761]) ).
fof(f8761,plain,
( spl0_629
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f320,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero2_0) ).
fof(f8759,plain,
spl0_628,
inference(avatar_split_clause,[],[f316,f8757]) ).
fof(f8757,plain,
( spl0_628
<=> ! [X0,X3,X1,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X7,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f316,axiom,
! [X3,X0,X1,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X7,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
fof(f8755,plain,
spl0_627,
inference(avatar_split_clause,[],[f259,f8753]) ).
fof(f8753,plain,
( spl0_627
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f259,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
fof(f8751,plain,
spl0_626,
inference(avatar_split_clause,[],[f184,f8749]) ).
fof(f8749,plain,
( spl0_626
<=> ! [X29,X22,X23] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X22,X23,tc_RealDef_Oreal),X29,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X29,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X23,X29,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f184,axiom,
! [X29,X22,X23] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X22,X23,tc_RealDef_Oreal),X29,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X29,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X23,X29,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__mult__distrib_0) ).
fof(f8747,plain,
spl0_625,
inference(avatar_split_clause,[],[f171,f8745]) ).
fof(f8745,plain,
( spl0_625
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f171,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
fof(f8743,plain,
spl0_624,
inference(avatar_split_clause,[],[f135,f8741]) ).
fof(f8741,plain,
( spl0_624
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f135,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f8739,plain,
( spl0_623
| ~ spl0_373
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f5100,f4778,f3630,f8737]) ).
fof(f8737,plain,
( spl0_623
<=> ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,hAPP(v_x,X0))),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f5100,plain,
( ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,hAPP(v_x,X0))),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_430 ),
inference(resolution,[],[f4779,f3631]) ).
fof(f8735,plain,
spl0_622,
inference(avatar_split_clause,[],[f119,f8733]) ).
fof(f8733,plain,
( spl0_622
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f119,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
fof(f8731,plain,
spl0_621,
inference(avatar_split_clause,[],[f72,f8729]) ).
fof(f8729,plain,
( spl0_621
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f72,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
fof(f8727,plain,
spl0_620,
inference(avatar_split_clause,[],[f45,f8725]) ).
fof(f8725,plain,
( spl0_620
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f45,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
fof(f8723,plain,
spl0_619,
inference(avatar_split_clause,[],[f21,f8721]) ).
fof(f8721,plain,
( spl0_619
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
fof(f8586,plain,
( spl0_618
| ~ spl0_365
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f4298,f4160,f3002,f8584]) ).
fof(f3002,plain,
( spl0_365
<=> ! [X34,X35,X33] :
( ~ c_lessequals(X34,X35,tc_RealDef_Oreal)
| ~ c_lessequals(X35,X33,tc_RealDef_Oreal)
| c_lessequals(X34,X33,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f4160,plain,
( spl0_429
<=> ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f4298,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_365
| ~ spl0_429 ),
inference(resolution,[],[f4161,f3003]) ).
fof(f3003,plain,
( ! [X34,X35,X33] :
( ~ c_lessequals(X35,X33,tc_RealDef_Oreal)
| ~ c_lessequals(X34,X35,tc_RealDef_Oreal)
| c_lessequals(X34,X33,tc_RealDef_Oreal) )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f3002]) ).
fof(f4161,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f4160]) ).
fof(f8188,plain,
spl0_617,
inference(avatar_split_clause,[],[f885,f8186]) ).
fof(f8186,plain,
( spl0_617
<=> ! [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_617])]) ).
fof(f885,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,[],[f239]) ).
fof(f239,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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f8184,plain,
spl0_616,
inference(avatar_split_clause,[],[f714,f8182]) ).
fof(f8182,plain,
( spl0_616
<=> ! [X7,X14,X15] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),X7,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X15,X7),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f714,axiom,
! [X7,X14,X15] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),X7,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X15,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X15,X7),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__bound__exists_1) ).
fof(f8152,plain,
spl0_615,
inference(avatar_split_clause,[],[f704,f8150]) ).
fof(f8150,plain,
( spl0_615
<=> ! [X15,X0,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X15,X5,X0),X3,X0) = c_Polynomial_Opoly(X15,c_Polynomial_Opoly(X5,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f704,axiom,
! [X3,X0,X15,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X15,X5,X0),X3,X0) = c_Polynomial_Opoly(X15,c_Polynomial_Opoly(X5,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pcompose_0) ).
fof(f8148,plain,
spl0_614,
inference(avatar_split_clause,[],[f653,f8146]) ).
fof(f8146,plain,
( spl0_614
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f653,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
fof(f8144,plain,
spl0_613,
inference(avatar_split_clause,[],[f647,f8142]) ).
fof(f8142,plain,
( spl0_613
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f647,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X3,X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
fof(f8140,plain,
spl0_612,
inference(avatar_split_clause,[],[f628,f8138]) ).
fof(f8138,plain,
( spl0_612
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f628,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f8136,plain,
spl0_611,
inference(avatar_split_clause,[],[f627,f8134]) ).
fof(f8134,plain,
( spl0_611
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f627,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f8131,plain,
spl0_610,
inference(avatar_split_clause,[],[f612,f8128]) ).
fof(f8128,plain,
( spl0_610
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f612,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__two__squares__add__zero__iff_2) ).
fof(f8126,plain,
spl0_609,
inference(avatar_split_clause,[],[f597,f8124]) ).
fof(f8124,plain,
( spl0_609
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f597,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f8122,plain,
spl0_608,
inference(avatar_split_clause,[],[f549,f8120]) ).
fof(f8120,plain,
( spl0_608
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X6,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f549,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X6,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
fof(f8118,plain,
spl0_607,
inference(avatar_split_clause,[],[f532,f8116]) ).
fof(f8116,plain,
( spl0_607
<=> ! [X4,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f532,axiom,
! [X3,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
fof(f8114,plain,
spl0_606,
inference(avatar_split_clause,[],[f507,f8112]) ).
fof(f8112,plain,
( spl0_606
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X3,X0)
| c_lessequals(X14,X4,X0)
| ~ c_lessequals(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f507,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X3,X0)
| c_lessequals(X14,X4,X0)
| ~ c_lessequals(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
fof(f8110,plain,
( spl0_605
| ~ spl0_15
| ~ spl0_426
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f5290,f4929,f3878,f964,f8108]) ).
fof(f3878,plain,
( spl0_426
<=> ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f4929,plain,
( spl0_436
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f5290,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_426
| ~ spl0_436 ),
inference(resolution,[],[f4930,f3879]) ).
fof(f3879,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f3878]) ).
fof(f4930,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
| ~ spl0_436 ),
inference(avatar_component_clause,[],[f4929]) ).
fof(f8106,plain,
spl0_604,
inference(avatar_split_clause,[],[f497,f8104]) ).
fof(f8104,plain,
( spl0_604
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X14,X0)
| c_lessequals(X4,X14,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f497,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X14,X0)
| c_lessequals(X4,X14,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
fof(f8102,plain,
spl0_603,
inference(avatar_split_clause,[],[f451,f8100]) ).
fof(f8100,plain,
( spl0_603
<=> ! [X15,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X15,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f451,axiom,
! [X2,X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X15,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__smult_0) ).
fof(f8098,plain,
spl0_602,
inference(avatar_split_clause,[],[f449,f8096]) ).
fof(f8096,plain,
( spl0_602
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f449,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
fof(f8094,plain,
spl0_601,
inference(avatar_split_clause,[],[f448,f8092]) ).
fof(f8092,plain,
( spl0_601
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0) = c_Orderings_Oord__class_Omax(X4,c_Orderings_Oord__class_Omax(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f448,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X14,X0),X0) = c_Orderings_Oord__class_Omax(X4,c_Orderings_Oord__class_Omax(X3,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
fof(f8090,plain,
spl0_600,
inference(avatar_split_clause,[],[f432,f8088]) ).
fof(f8088,plain,
( spl0_600
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X14,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f432,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X14,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
fof(f8086,plain,
spl0_599,
inference(avatar_split_clause,[],[f427,f8084]) ).
fof(f8084,plain,
( spl0_599
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f427,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
fof(f8082,plain,
spl0_598,
inference(avatar_split_clause,[],[f417,f8080]) ).
fof(f8080,plain,
( spl0_598
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X6,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f417,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X6,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f8078,plain,
spl0_597,
inference(avatar_split_clause,[],[f416,f8076]) ).
fof(f8076,plain,
( spl0_597
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f416,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult_0) ).
fof(f8074,plain,
spl0_596,
inference(avatar_split_clause,[],[f361,f8072]) ).
fof(f8072,plain,
( spl0_596
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) = c_Orderings_Oord__class_Omin(X4,c_Orderings_Oord__class_Omin(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f361,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) = c_Orderings_Oord__class_Omin(X4,c_Orderings_Oord__class_Omin(X3,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
fof(f8070,plain,
spl0_595,
inference(avatar_split_clause,[],[f360,f8068]) ).
fof(f8068,plain,
( spl0_595
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f360,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
fof(f8062,plain,
spl0_594,
inference(avatar_split_clause,[],[f322,f8060]) ).
fof(f8060,plain,
( spl0_594
<=> ! [X15,X0,X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X15,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X15,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f322,axiom,
! [X3,X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X15,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X15,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__smult_0) ).
fof(f8058,plain,
spl0_593,
inference(avatar_split_clause,[],[f255,f8056]) ).
fof(f8056,plain,
( spl0_593
<=> ! [X19,X0,X8,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X19,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f255,axiom,
! [X0,X1,X8,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X19,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f8054,plain,
spl0_592,
inference(avatar_split_clause,[],[f254,f8052]) ).
fof(f8052,plain,
( spl0_592
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f254,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f8050,plain,
spl0_591,
inference(avatar_split_clause,[],[f252,f8048]) ).
fof(f8048,plain,
( spl0_591
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f252,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f8046,plain,
spl0_590,
inference(avatar_split_clause,[],[f251,f8044]) ).
fof(f8044,plain,
( spl0_590
<=> ! [X4,X0,X14,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f251,axiom,
! [X3,X0,X14,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f8042,plain,
spl0_589,
inference(avatar_split_clause,[],[f250,f8040]) ).
fof(f8040,plain,
( spl0_589
<=> ! [X4,X0,X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f250,axiom,
! [X3,X0,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f8038,plain,
spl0_588,
inference(avatar_split_clause,[],[f249,f8036]) ).
fof(f249,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f8034,plain,
spl0_587,
inference(avatar_split_clause,[],[f248,f8032]) ).
fof(f8032,plain,
( spl0_587
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f248,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f8030,plain,
spl0_586,
inference(avatar_split_clause,[],[f176,f8028]) ).
fof(f8028,plain,
( spl0_586
<=> ! [X10,X13,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X12,X13,X0),X0) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X10,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f176,axiom,
! [X10,X0,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X12,X13,X0),X0) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Otimes__class_Otimes(X10,X13,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f8026,plain,
spl0_585,
inference(avatar_split_clause,[],[f175,f8024]) ).
fof(f8024,plain,
( spl0_585
<=> ! [X10,X13,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X12,X13,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X12,X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f175,axiom,
! [X10,X0,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X12,X13,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X12,X0),X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f8022,plain,
( ~ spl0_58
| spl0_584
| ~ spl0_257
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f4499,f3878,f2134,f8020,f1179]) ).
fof(f8020,plain,
( spl0_584
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f4499,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_426 ),
inference(resolution,[],[f3879,f2135]) ).
fof(f8018,plain,
spl0_583,
inference(avatar_split_clause,[],[f173,f8016]) ).
fof(f8016,plain,
( spl0_583
<=> ! [X10,X11,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X11,X0),X12,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X12,X0),X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f173,axiom,
! [X10,X0,X11,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X11,X0),X12,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X12,X0),X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f8014,plain,
spl0_582,
inference(avatar_split_clause,[],[f172,f8012]) ).
fof(f8012,plain,
( spl0_582
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f172,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f8010,plain,
spl0_581,
inference(avatar_split_clause,[],[f147,f8008]) ).
fof(f8008,plain,
( spl0_581
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f147,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel2_0) ).
fof(f8006,plain,
spl0_580,
inference(avatar_split_clause,[],[f146,f8004]) ).
fof(f8004,plain,
( spl0_580
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f146,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel_0) ).
fof(f8002,plain,
spl0_579,
inference(avatar_split_clause,[],[f126,f8000]) ).
fof(f8000,plain,
( spl0_579
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f126,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
fof(f7998,plain,
spl0_578,
inference(avatar_split_clause,[],[f121,f7996]) ).
fof(f7996,plain,
( spl0_578
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X14,X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f121,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X14,X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
fof(f7994,plain,
spl0_577,
inference(avatar_split_clause,[],[f79,f7992]) ).
fof(f7992,plain,
( spl0_577
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f79,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f7990,plain,
spl0_576,
inference(avatar_split_clause,[],[f77,f7988]) ).
fof(f7988,plain,
( spl0_576
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f77,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f7986,plain,
spl0_575,
inference(avatar_split_clause,[],[f64,f7984]) ).
fof(f7984,plain,
( spl0_575
<=> ! [X4,X0,X14,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f64,axiom,
! [X3,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f7982,plain,
spl0_574,
inference(avatar_split_clause,[],[f63,f7980]) ).
fof(f7980,plain,
( spl0_574
<=> ! [X4,X0,X14,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f63,axiom,
! [X3,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f7978,plain,
( spl0_573
| ~ spl0_373
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f4494,f3878,f3630,f7976]) ).
fof(f4494,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_426 ),
inference(resolution,[],[f3879,f3631]) ).
fof(f7974,plain,
spl0_572,
inference(avatar_split_clause,[],[f62,f7972]) ).
fof(f7972,plain,
( spl0_572
<=> ! [X4,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f62,axiom,
! [X3,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f7970,plain,
spl0_571,
inference(avatar_split_clause,[],[f61,f7968]) ).
fof(f7968,plain,
( spl0_571
<=> ! [X4,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f61,axiom,
! [X3,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f7966,plain,
spl0_570,
inference(avatar_split_clause,[],[f2,f7964]) ).
fof(f7964,plain,
( spl0_570
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f7901,plain,
( spl0_569
| ~ spl0_32
| ~ spl0_303
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f7296,f7293,f2524,f1049,f7899]) ).
fof(f7899,plain,
( spl0_569
<=> ! [X29,X14] : c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X29,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f7293,plain,
( spl0_565
<=> ! [X29,X14] : c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X29,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f7296,plain,
( ! [X29,X14] : c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X29,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_32
| ~ spl0_303
| ~ spl0_565 ),
inference(forward_demodulation,[],[f7294,f2713]) ).
fof(f7294,plain,
( ! [X29,X14] : c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X29,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_565 ),
inference(avatar_component_clause,[],[f7293]) ).
fof(f7529,plain,
( ~ spl0_58
| spl0_568
| ~ spl0_257
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f4051,f3834,f2134,f7527,f1179]) ).
fof(f7527,plain,
( spl0_568
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f3834,plain,
( spl0_415
<=> ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f4051,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_415 ),
inference(resolution,[],[f3835,f2135]) ).
fof(f3835,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_415 ),
inference(avatar_component_clause,[],[f3834]) ).
fof(f7354,plain,
( spl0_567
| ~ spl0_373
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f4046,f3834,f3630,f7352]) ).
fof(f4046,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_415 ),
inference(resolution,[],[f3835,f3631]) ).
fof(f7300,plain,
spl0_566,
inference(avatar_split_clause,[],[f696,f7298]) ).
fof(f7298,plain,
( spl0_566
<=> ! [X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f696,axiom,
! [X2,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__triangle__ineq2_0) ).
fof(f7295,plain,
spl0_565,
inference(avatar_split_clause,[],[f693,f7293]) ).
fof(f693,axiom,
! [X29,X14] : c_lessequals(c_RealVector_Onorm__class_Onorm(X29,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X29,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__triangle__sub_0) ).
fof(f7291,plain,
spl0_564,
inference(avatar_split_clause,[],[f686,f7289]) ).
fof(f7289,plain,
( spl0_564
<=> ! [X6,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(X3,X6,X0),X0),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(X3,X0),X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f686,axiom,
! [X3,X0,X6] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(X3,X6,X0),X0),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(X3,X0),X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__power__ineq_0) ).
fof(f7287,plain,
spl0_563,
inference(avatar_split_clause,[],[f643,f7285]) ).
fof(f7285,plain,
( spl0_563
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f643,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f7283,plain,
spl0_562,
inference(avatar_split_clause,[],[f642,f7281]) ).
fof(f7281,plain,
( spl0_562
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f642,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f7279,plain,
spl0_561,
inference(avatar_split_clause,[],[f641,f7277]) ).
fof(f7277,plain,
( spl0_561
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f641,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f7275,plain,
spl0_560,
inference(avatar_split_clause,[],[f640,f7273]) ).
fof(f7273,plain,
( spl0_560
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f640,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f7271,plain,
spl0_559,
inference(avatar_split_clause,[],[f639,f7269]) ).
fof(f7269,plain,
( spl0_559
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f639,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f7267,plain,
( spl0_558
| ~ spl0_365
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3779,f3735,f3002,f7265]) ).
fof(f3735,plain,
( spl0_394
<=> ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f3779,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_365
| ~ spl0_394 ),
inference(resolution,[],[f3736,f3003]) ).
fof(f3736,plain,
( ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_394 ),
inference(avatar_component_clause,[],[f3735]) ).
fof(f7263,plain,
spl0_557,
inference(avatar_split_clause,[],[f638,f7261]) ).
fof(f7261,plain,
( spl0_557
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f638,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f7259,plain,
spl0_556,
inference(avatar_split_clause,[],[f608,f7257]) ).
fof(f7257,plain,
( spl0_556
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f608,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f7255,plain,
spl0_555,
inference(avatar_split_clause,[],[f607,f7253]) ).
fof(f7253,plain,
( spl0_555
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f607,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f7251,plain,
spl0_554,
inference(avatar_split_clause,[],[f606,f7249]) ).
fof(f7249,plain,
( spl0_554
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f606,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f7247,plain,
spl0_553,
inference(avatar_split_clause,[],[f605,f7245]) ).
fof(f7245,plain,
( spl0_553
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f605,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f7243,plain,
spl0_552,
inference(avatar_split_clause,[],[f604,f7241]) ).
fof(f7241,plain,
( spl0_552
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f604,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f7239,plain,
spl0_551,
inference(avatar_split_clause,[],[f603,f7237]) ).
fof(f7237,plain,
( spl0_551
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f603,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f7235,plain,
spl0_550,
inference(avatar_split_clause,[],[f419,f7233]) ).
fof(f7233,plain,
( spl0_550
<=> ! [X2,X1,X8] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f419,axiom,
! [X2,X1,X8] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
fof(f7231,plain,
spl0_549,
inference(avatar_split_clause,[],[f418,f7229]) ).
fof(f7229,plain,
( spl0_549
<=> ! [X2,X1,X8] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f418,axiom,
! [X2,X1,X8] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
fof(f7227,plain,
spl0_548,
inference(avatar_split_clause,[],[f380,f7225]) ).
fof(f7225,plain,
( spl0_548
<=> ! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X15,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f380,axiom,
! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X15,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X15,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__pCons_1) ).
fof(f7198,plain,
spl0_547,
inference(avatar_split_clause,[],[f375,f7196]) ).
fof(f7196,plain,
( spl0_547
<=> ! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X15,X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f375,axiom,
! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X15,X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X15,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__pCons_0) ).
fof(f7194,plain,
spl0_546,
inference(avatar_split_clause,[],[f338,f7192]) ).
fof(f7192,plain,
( spl0_546
<=> ! [X4,X0,X14,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X14
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f338,axiom,
! [X3,X0,X14,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X14
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f7190,plain,
spl0_545,
inference(avatar_split_clause,[],[f326,f7188]) ).
fof(f7188,plain,
( spl0_545
<=> ! [X4,X0,X14,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X14,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f326,axiom,
! [X3,X0,X14,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X14,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f7186,plain,
spl0_544,
inference(avatar_split_clause,[],[f232,f7184]) ).
fof(f7184,plain,
( spl0_544
<=> ! [X7,X3] :
( ~ c_lessequals(X3,X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f232,axiom,
! [X3,X7] :
( ~ c_lessequals(X3,X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_2) ).
fof(f7182,plain,
spl0_543,
inference(avatar_split_clause,[],[f196,f7180]) ).
fof(f7180,plain,
( spl0_543
<=> ! [X0,X1,X8,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Polynomial_Osmult(X8,X15,X0) != c_Polynomial_OpCons(X1,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f196,axiom,
! [X0,X1,X8,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Polynomial_Osmult(X8,X15,X0) != c_Polynomial_OpCons(X1,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
fof(f7178,plain,
spl0_542,
inference(avatar_split_clause,[],[f103,f7176]) ).
fof(f7176,plain,
( spl0_542
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f103,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f7174,plain,
spl0_541,
inference(avatar_split_clause,[],[f91,f7172]) ).
fof(f7172,plain,
( spl0_541
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f91,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
fof(f7170,plain,
spl0_540,
inference(avatar_split_clause,[],[f60,f7168]) ).
fof(f7168,plain,
( spl0_540
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f60,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f7166,plain,
spl0_539,
inference(avatar_split_clause,[],[f12,f7164]) ).
fof(f7164,plain,
( spl0_539
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f7162,plain,
spl0_538,
inference(avatar_split_clause,[],[f11,f7160]) ).
fof(f7160,plain,
( spl0_538
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f7053,plain,
( ~ spl0_58
| spl0_537
| ~ spl0_257
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f6826,f6733,f2134,f7051,f1179]) ).
fof(f7051,plain,
( spl0_537
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_OIm(c_Complex_Ocnj(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex))),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f6733,plain,
( spl0_531
<=> ! [X0] : c_lessequals(c_Complex_OIm(c_Complex_Ocnj(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f6826,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_OIm(c_Complex_Ocnj(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex))),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_531 ),
inference(resolution,[],[f6734,f2135]) ).
fof(f6734,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(c_Complex_Ocnj(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_531 ),
inference(avatar_component_clause,[],[f6733]) ).
fof(f6940,plain,
( spl0_536
| ~ spl0_373
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f6822,f6733,f3630,f6938]) ).
fof(f6938,plain,
( spl0_536
<=> ! [X0] : c_lessequals(c_Complex_OIm(c_Complex_Ocnj(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f6822,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(c_Complex_Ocnj(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_531 ),
inference(resolution,[],[f6734,f3631]) ).
fof(f6751,plain,
spl0_535,
inference(avatar_split_clause,[],[f718,f6749]) ).
fof(f6749,plain,
( spl0_535
<=> ! [X29] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__Xhyps__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f718,axiom,
! [X29] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__Xhyps__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_Ohyps_0) ).
fof(f6747,plain,
spl0_534,
inference(avatar_split_clause,[],[f717,f6745]) ).
fof(f6745,plain,
( spl0_534
<=> ! [X29] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f717,axiom,
! [X29] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X29,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_0) ).
fof(f6743,plain,
spl0_533,
inference(avatar_split_clause,[],[f697,f6741]) ).
fof(f6741,plain,
( spl0_533
<=> ! [X0,X1,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f697,axiom,
! [X0,X1,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
fof(f6739,plain,
spl0_532,
inference(avatar_split_clause,[],[f692,f6737]) ).
fof(f6737,plain,
( spl0_532
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f692,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__commute_0) ).
fof(f6735,plain,
( ~ spl0_15
| spl0_531
| ~ spl0_180
| ~ spl0_415
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f5315,f4929,f3834,f1718,f6733,f964]) ).
fof(f1718,plain,
( spl0_180
<=> ! [X3] : c_Complex_OIm(c_Complex_Ocnj(X3)) = c_HOL_Ouminus__class_Ouminus(c_Complex_OIm(X3),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f5315,plain,
( ! [X0] :
( c_lessequals(c_Complex_OIm(c_Complex_Ocnj(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) )
| ~ spl0_180
| ~ spl0_415
| ~ spl0_436 ),
inference(forward_demodulation,[],[f5289,f1719]) ).
fof(f1719,plain,
( ! [X3] : c_Complex_OIm(c_Complex_Ocnj(X3)) = c_HOL_Ouminus__class_Ouminus(c_Complex_OIm(X3),tc_RealDef_Oreal)
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1718]) ).
fof(f5289,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_415
| ~ spl0_436 ),
inference(resolution,[],[f4930,f3835]) ).
fof(f6731,plain,
spl0_530,
inference(avatar_split_clause,[],[f610,f6729]) ).
fof(f6729,plain,
( spl0_530
<=> ! [X6,X0,X3] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(X3,X6,X0),X0) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(X3,X0),X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f610,axiom,
! [X3,X0,X6] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(X3,X6,X0),X0) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(X3,X0),X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__power_0) ).
fof(f6727,plain,
spl0_529,
inference(avatar_split_clause,[],[f592,f6725]) ).
fof(f6725,plain,
( spl0_529
<=> ! [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_529])]) ).
fof(f592,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f6723,plain,
spl0_528,
inference(avatar_split_clause,[],[f591,f6721]) ).
fof(f6721,plain,
( spl0_528
<=> ! [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_528])]) ).
fof(f591,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f6719,plain,
spl0_527,
inference(avatar_split_clause,[],[f580,f6717]) ).
fof(f6717,plain,
( spl0_527
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f580,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f6715,plain,
spl0_526,
inference(avatar_split_clause,[],[f536,f6713]) ).
fof(f6713,plain,
( spl0_526
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f536,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f6711,plain,
spl0_525,
inference(avatar_split_clause,[],[f426,f6709]) ).
fof(f6709,plain,
( spl0_525
<=> ! [X6,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,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f426,axiom,
! [X0,X1,X6] :
( ~ 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,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f6707,plain,
spl0_524,
inference(avatar_split_clause,[],[f389,f6705]) ).
fof(f6705,plain,
( spl0_524
<=> ! [X6,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,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f389,axiom,
! [X0,X1,X6] :
( ~ 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,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f6703,plain,
spl0_523,
inference(avatar_split_clause,[],[f388,f6701]) ).
fof(f6701,plain,
( spl0_523
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(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,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f388,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__idom(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,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
fof(f6699,plain,
spl0_522,
inference(avatar_split_clause,[],[f379,f6697]) ).
fof(f6697,plain,
( spl0_522
<=> ! [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_522])]) ).
fof(f379,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f6695,plain,
spl0_521,
inference(avatar_split_clause,[],[f378,f6693]) ).
fof(f6693,plain,
( spl0_521
<=> ! [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_521])]) ).
fof(f378,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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f6666,plain,
spl0_520,
inference(avatar_split_clause,[],[f377,f6664]) ).
fof(f6664,plain,
( spl0_520
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f377,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__0__imp__0_0) ).
fof(f6662,plain,
spl0_519,
inference(avatar_split_clause,[],[f324,f6660]) ).
fof(f6660,plain,
( spl0_519
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f324,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__pCons_3) ).
fof(f6658,plain,
spl0_518,
inference(avatar_split_clause,[],[f315,f6656]) ).
fof(f6656,plain,
( spl0_518
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X6,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f315,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X6,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
fof(f6654,plain,
spl0_517,
inference(avatar_split_clause,[],[f266,f6652]) ).
fof(f6652,plain,
( spl0_517
<=> ! [X6,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f266,axiom,
! [X3,X0,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
fof(f6650,plain,
spl0_516,
inference(avatar_split_clause,[],[f221,f6648]) ).
fof(f6648,plain,
( spl0_516
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f221,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
fof(f6646,plain,
spl0_515,
inference(avatar_split_clause,[],[f220,f6644]) ).
fof(f6644,plain,
( spl0_515
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f220,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).
fof(f6642,plain,
spl0_514,
inference(avatar_split_clause,[],[f215,f6640]) ).
fof(f6640,plain,
( spl0_514
<=> ! [X4,X3] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f215,axiom,
! [X3,X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__mult__self__sum__ge__zero_0) ).
fof(f6638,plain,
spl0_513,
inference(avatar_split_clause,[],[f206,f6636]) ).
fof(f6636,plain,
( spl0_513
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f206,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f6634,plain,
spl0_512,
inference(avatar_split_clause,[],[f205,f6632]) ).
fof(f6632,plain,
( spl0_512
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(X2,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f205,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(X2,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f6630,plain,
spl0_511,
inference(avatar_split_clause,[],[f203,f6628]) ).
fof(f6628,plain,
( spl0_511
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f203,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f6600,plain,
spl0_510,
inference(avatar_split_clause,[],[f201,f6598]) ).
fof(f6598,plain,
( spl0_510
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f201,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
fof(f6596,plain,
spl0_509,
inference(avatar_split_clause,[],[f189,f6594]) ).
fof(f6594,plain,
( spl0_509
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f189,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
fof(f6592,plain,
spl0_508,
inference(avatar_split_clause,[],[f188,f6590]) ).
fof(f6590,plain,
( spl0_508
<=> ! [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_508])]) ).
fof(f188,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f6588,plain,
spl0_507,
inference(avatar_split_clause,[],[f187,f6586]) ).
fof(f6586,plain,
( spl0_507
<=> ! [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_507])]) ).
fof(f187,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f6584,plain,
spl0_506,
inference(avatar_split_clause,[],[f177,f6582]) ).
fof(f6582,plain,
( spl0_506
<=> ! [X22,X24,X23] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,tc_RealDef_Oreal),X24,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X23,X24,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f177,axiom,
! [X24,X22,X23] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,tc_RealDef_Oreal),X24,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X23,X24,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
fof(f6580,plain,
spl0_505,
inference(avatar_split_clause,[],[f150,f6578]) ).
fof(f6578,plain,
( spl0_505
<=> ! [X5,X0,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X15,X0)
| ~ c_Polynomial_Opos__poly(X5,X0)
| c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f150,axiom,
! [X0,X15,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X15,X0)
| ~ c_Polynomial_Opos__poly(X5,X0)
| c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(X15,X5,tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__add_0) ).
fof(f6576,plain,
spl0_504,
inference(avatar_split_clause,[],[f76,f6574]) ).
fof(f6574,plain,
( spl0_504
<=> ! [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_504])]) ).
fof(f76,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/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f6572,plain,
spl0_503,
inference(avatar_split_clause,[],[f75,f6570]) ).
fof(f6570,plain,
( spl0_503
<=> ! [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_503])]) ).
fof(f75,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/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f6568,plain,
spl0_502,
inference(avatar_split_clause,[],[f74,f6566]) ).
fof(f6566,plain,
( spl0_502
<=> ! [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_502])]) ).
fof(f74,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f6564,plain,
spl0_501,
inference(avatar_split_clause,[],[f73,f6562]) ).
fof(f6562,plain,
( spl0_501
<=> ! [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_501])]) ).
fof(f73,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f6560,plain,
( spl0_500
| ~ spl0_290
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3690,f3630,f2470,f6558]) ).
fof(f6558,plain,
( spl0_500
<=> ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2470,plain,
( spl0_290
<=> ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f3690,plain,
( ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_290
| ~ spl0_373 ),
inference(resolution,[],[f3631,f2471]) ).
fof(f2471,plain,
( ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f2470]) ).
fof(f6556,plain,
spl0_499,
inference(avatar_split_clause,[],[f8,f6554]) ).
fof(f6554,plain,
( spl0_499
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f6552,plain,
spl0_498,
inference(avatar_split_clause,[],[f7,f6550]) ).
fof(f6550,plain,
( spl0_498
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f6280,plain,
( spl0_497
| ~ spl0_266
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3689,f3630,f2170,f6278]) ).
fof(f2170,plain,
( spl0_266
<=> ! [X3] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3689,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_266
| ~ spl0_373 ),
inference(resolution,[],[f3631,f2171]) ).
fof(f2171,plain,
( ! [X3] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f2170]) ).
fof(f5578,plain,
( ~ spl0_58
| spl0_496
| ~ spl0_257
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f4301,f4160,f2134,f5576,f1179]) ).
fof(f5576,plain,
( spl0_496
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f4301,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_429 ),
inference(resolution,[],[f4161,f2135]) ).
fof(f5441,plain,
( spl0_495
| ~ spl0_373
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f4297,f4160,f3630,f5439]) ).
fof(f4297,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_429 ),
inference(resolution,[],[f4161,f3631]) ).
fof(f5202,plain,
spl0_494,
inference(avatar_split_clause,[],[f728,f5200]) ).
fof(f5200,plain,
( spl0_494
<=> ! [X15,X2,X0,X5,X1] :
( ~ class_HOL_Ozero(X0)
| X5 = X15
| c_Polynomial_OpCons(X2,X5,X0) != c_Polynomial_OpCons(X1,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f728,axiom,
! [X2,X0,X1,X15,X5] :
( ~ class_HOL_Ozero(X0)
| X5 = X15
| c_Polynomial_OpCons(X2,X5,X0) != c_Polynomial_OpCons(X1,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
fof(f5198,plain,
spl0_493,
inference(avatar_split_clause,[],[f727,f5196]) ).
fof(f5196,plain,
( spl0_493
<=> ! [X15,X0,X5,X2,X1] :
( ~ class_HOL_Ozero(X0)
| X1 = X2
| c_Polynomial_OpCons(X2,X5,X0) != c_Polynomial_OpCons(X1,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f727,axiom,
! [X2,X0,X1,X15,X5] :
( ~ class_HOL_Ozero(X0)
| X1 = X2
| c_Polynomial_OpCons(X2,X5,X0) != c_Polynomial_OpCons(X1,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
fof(f5194,plain,
spl0_492,
inference(avatar_split_clause,[],[f722,f5192]) ).
fof(f5192,plain,
( spl0_492
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X14,X0)
| c_lessequals(X3,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f722,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X14,X0)
| c_lessequals(X3,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f5190,plain,
spl0_491,
inference(avatar_split_clause,[],[f721,f5188]) ).
fof(f5188,plain,
( spl0_491
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X14,X4,X0)
| c_lessequals(X14,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f721,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X14,X4,X0)
| c_lessequals(X14,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f5186,plain,
spl0_490,
inference(avatar_split_clause,[],[f677,f5184]) ).
fof(f5184,plain,
( spl0_490
<=> ! [X4,X3,X14] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X14,X3,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f677,axiom,
! [X3,X14,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X14,X3,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X14,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
fof(f5182,plain,
spl0_489,
inference(avatar_split_clause,[],[f671,f5180]) ).
fof(f5180,plain,
( spl0_489
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f671,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
fof(f5178,plain,
spl0_488,
inference(avatar_split_clause,[],[f670,f5176]) ).
fof(f5176,plain,
( spl0_488
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f670,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
fof(f5157,plain,
spl0_487,
inference(avatar_split_clause,[],[f651,f5155]) ).
fof(f5155,plain,
( spl0_487
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f651,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f5153,plain,
spl0_486,
inference(avatar_split_clause,[],[f650,f5151]) ).
fof(f5151,plain,
( spl0_486
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f650,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f5149,plain,
spl0_485,
inference(avatar_split_clause,[],[f622,f5147]) ).
fof(f5147,plain,
( spl0_485
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f622,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f5145,plain,
spl0_484,
inference(avatar_split_clause,[],[f621,f5143]) ).
fof(f5143,plain,
( spl0_484
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f621,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f5141,plain,
spl0_483,
inference(avatar_split_clause,[],[f595,f5139]) ).
fof(f5139,plain,
( spl0_483
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f595,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f5137,plain,
spl0_482,
inference(avatar_split_clause,[],[f585,f5135]) ).
fof(f5135,plain,
( spl0_482
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f585,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f5133,plain,
spl0_481,
inference(avatar_split_clause,[],[f584,f5131]) ).
fof(f5131,plain,
( spl0_481
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f584,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f5129,plain,
spl0_480,
inference(avatar_split_clause,[],[f570,f5127]) ).
fof(f5127,plain,
( spl0_480
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f570,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f5125,plain,
spl0_479,
inference(avatar_split_clause,[],[f569,f5123]) ).
fof(f5123,plain,
( spl0_479
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f569,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f5121,plain,
spl0_478,
inference(avatar_split_clause,[],[f562,f5119]) ).
fof(f5119,plain,
( spl0_478
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f562,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f5099,plain,
spl0_477,
inference(avatar_split_clause,[],[f561,f5097]) ).
fof(f5097,plain,
( spl0_477
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f561,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f5095,plain,
spl0_476,
inference(avatar_split_clause,[],[f488,f5093]) ).
fof(f5093,plain,
( spl0_476
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f488,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f5091,plain,
spl0_475,
inference(avatar_split_clause,[],[f485,f5089]) ).
fof(f5089,plain,
( spl0_475
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f485,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f5087,plain,
spl0_474,
inference(avatar_split_clause,[],[f484,f5085]) ).
fof(f5085,plain,
( spl0_474
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X14,X0)
| c_HOL_Oord__class_Oless(X3,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f484,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X14,X0)
| c_HOL_Oord__class_Oless(X3,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f5083,plain,
spl0_473,
inference(avatar_split_clause,[],[f482,f5081]) ).
fof(f5081,plain,
( spl0_473
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| ~ c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X14,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f482,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| ~ c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X14,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f5079,plain,
spl0_472,
inference(avatar_split_clause,[],[f481,f5077]) ).
fof(f5077,plain,
( spl0_472
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_lessequals(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f481,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_lessequals(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f5075,plain,
spl0_471,
inference(avatar_split_clause,[],[f479,f5073]) ).
fof(f5073,plain,
( spl0_471
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f479,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
fof(f5071,plain,
spl0_470,
inference(avatar_split_clause,[],[f477,f5069]) ).
fof(f5069,plain,
( spl0_470
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f477,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
fof(f5067,plain,
spl0_469,
inference(avatar_split_clause,[],[f453,f5065]) ).
fof(f5065,plain,
( spl0_469
<=> ! [X4,X3] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f453,axiom,
! [X3,X4] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__add__iff_1) ).
fof(f5063,plain,
spl0_468,
inference(avatar_split_clause,[],[f452,f5061]) ).
fof(f5061,plain,
( spl0_468
<=> ! [X4,X3] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f452,axiom,
! [X3,X4] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__add__iff_0) ).
fof(f5059,plain,
( spl0_467
| ~ spl0_319
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f4492,f3878,f2818,f5057]) ).
fof(f4492,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ spl0_319
| ~ spl0_426 ),
inference(resolution,[],[f3879,f2819]) ).
fof(f5055,plain,
spl0_466,
inference(avatar_split_clause,[],[f430,f5053]) ).
fof(f5053,plain,
( spl0_466
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f430,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f5051,plain,
spl0_465,
inference(avatar_split_clause,[],[f429,f5049]) ).
fof(f5049,plain,
( spl0_465
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f429,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f5047,plain,
spl0_464,
inference(avatar_split_clause,[],[f415,f5045]) ).
fof(f5045,plain,
( spl0_464
<=> ! [X0,X1,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f415,axiom,
! [X0,X1,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
fof(f5043,plain,
spl0_463,
inference(avatar_split_clause,[],[f400,f5041]) ).
fof(f5041,plain,
( spl0_463
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f400,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__less__0__iff_1) ).
fof(f5039,plain,
spl0_462,
inference(avatar_split_clause,[],[f399,f5037]) ).
fof(f5037,plain,
( spl0_462
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f399,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__less__0__iff_0) ).
fof(f5035,plain,
spl0_461,
inference(avatar_split_clause,[],[f367,f5033]) ).
fof(f5033,plain,
( spl0_461
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f367,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f5031,plain,
spl0_460,
inference(avatar_split_clause,[],[f366,f5029]) ).
fof(f5029,plain,
( spl0_460
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f366,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f5027,plain,
spl0_459,
inference(avatar_split_clause,[],[f341,f5025]) ).
fof(f5025,plain,
( spl0_459
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X8,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f341,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X8,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f5023,plain,
spl0_458,
inference(avatar_split_clause,[],[f340,f5021]) ).
fof(f5021,plain,
( spl0_458
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f340,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f5019,plain,
spl0_457,
inference(avatar_split_clause,[],[f339,f5017]) ).
fof(f5017,plain,
( spl0_457
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f339,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f5015,plain,
( spl0_456
| ~ spl0_319
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f4044,f3834,f2818,f5013]) ).
fof(f4044,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ spl0_319
| ~ spl0_415 ),
inference(resolution,[],[f3835,f2819]) ).
fof(f5011,plain,
spl0_455,
inference(avatar_split_clause,[],[f331,f5009]) ).
fof(f5009,plain,
( spl0_455
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f331,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f5007,plain,
spl0_454,
inference(avatar_split_clause,[],[f325,f5005]) ).
fof(f5005,plain,
( spl0_454
<=> ! [X4,X3] : c_lessequals(X3,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f325,axiom,
! [X3,X4] : c_lessequals(X3,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__real__sqrt__sumsq_0) ).
fof(f5003,plain,
spl0_453,
inference(avatar_split_clause,[],[f298,f5001]) ).
fof(f5001,plain,
( spl0_453
<=> ! [X4,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f298,axiom,
! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f4999,plain,
spl0_452,
inference(avatar_split_clause,[],[f264,f4997]) ).
fof(f4997,plain,
( spl0_452
<=> ! [X4,X0,X3,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X4 = X25
| c_HOL_Ominus__class_Ominus(X3,X3,X0) != c_HOL_Ominus__class_Ominus(X25,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f264,axiom,
! [X3,X0,X4,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X4 = X25
| c_HOL_Ominus__class_Ominus(X3,X3,X0) != c_HOL_Ominus__class_Ominus(X25,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
fof(f4995,plain,
spl0_451,
inference(avatar_split_clause,[],[f245,f4993]) ).
fof(f4993,plain,
( spl0_451
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| c_HOL_Oord__class_Oless(X3,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f245,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| c_HOL_Oord__class_Oless(X3,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f4991,plain,
spl0_450,
inference(avatar_split_clause,[],[f244,f4989]) ).
fof(f4989,plain,
( spl0_450
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f244,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f4987,plain,
spl0_449,
inference(avatar_split_clause,[],[f194,f4985]) ).
fof(f4985,plain,
( spl0_449
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f194,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f4983,plain,
spl0_448,
inference(avatar_split_clause,[],[f169,f4981]) ).
fof(f4981,plain,
( spl0_448
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f169,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
fof(f4979,plain,
spl0_447,
inference(avatar_split_clause,[],[f168,f4977]) ).
fof(f4977,plain,
( spl0_447
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f168,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__less__add__iff_0) ).
fof(f4975,plain,
spl0_446,
inference(avatar_split_clause,[],[f131,f4973]) ).
fof(f4973,plain,
( spl0_446
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f131,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f4967,plain,
spl0_445,
inference(avatar_split_clause,[],[f125,f4965]) ).
fof(f4965,plain,
( spl0_445
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f4963,plain,
spl0_444,
inference(avatar_split_clause,[],[f124,f4961]) ).
fof(f4961,plain,
( spl0_444
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f124,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f4959,plain,
spl0_443,
inference(avatar_split_clause,[],[f104,f4957]) ).
fof(f4957,plain,
( spl0_443
<=> ! [X4,X3] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f104,axiom,
! [X3,X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__self__sum__ge__zero_0) ).
fof(f4955,plain,
spl0_442,
inference(avatar_split_clause,[],[f98,f4953]) ).
fof(f4953,plain,
( spl0_442
<=> ! [X0,X1,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X3,X1,X0) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f98,axiom,
! [X3,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X3,X1,X0) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f4951,plain,
spl0_441,
inference(avatar_split_clause,[],[f90,f4949]) ).
fof(f4949,plain,
( spl0_441
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f90,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f4947,plain,
spl0_440,
inference(avatar_split_clause,[],[f89,f4945]) ).
fof(f4945,plain,
( spl0_440
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f89,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f4943,plain,
spl0_439,
inference(avatar_split_clause,[],[f66,f4941]) ).
fof(f4941,plain,
( spl0_439
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f66,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f4939,plain,
spl0_438,
inference(avatar_split_clause,[],[f59,f4937]) ).
fof(f4937,plain,
( spl0_438
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f59,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f4935,plain,
spl0_437,
inference(avatar_split_clause,[],[f58,f4933]) ).
fof(f4933,plain,
( spl0_437
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f58,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f4931,plain,
spl0_436,
inference(avatar_split_clause,[],[f30,f4929]) ).
fof(f30,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f4927,plain,
( ~ spl0_58
| spl0_435
| ~ spl0_257
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3782,f3735,f2134,f4925,f1179]) ).
fof(f4925,plain,
( spl0_435
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f3782,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_257
| ~ spl0_394 ),
inference(resolution,[],[f3736,f2135]) ).
fof(f4923,plain,
spl0_434,
inference(avatar_split_clause,[],[f19,f4921]) ).
fof(f4921,plain,
( spl0_434
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f19,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f4919,plain,
spl0_433,
inference(avatar_split_clause,[],[f18,f4917]) ).
fof(f4917,plain,
( spl0_433
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f18,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f4915,plain,
spl0_432,
inference(avatar_split_clause,[],[f10,f4913]) ).
fof(f4913,plain,
( spl0_432
<=> ! [X4,X3] :
( c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f10,axiom,
! [X3,X4] :
( c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__le__0__iff_0) ).
fof(f4911,plain,
spl0_431,
inference(avatar_split_clause,[],[f9,f4909]) ).
fof(f4909,plain,
( spl0_431
<=> ! [X4,X3] :
( ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f9,axiom,
! [X3,X4] :
( ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__le__0__iff_1) ).
fof(f4780,plain,
( spl0_430
| ~ spl0_373
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3778,f3735,f3630,f4778]) ).
fof(f3778,plain,
( ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,hAPP(v_x,X0)),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_373
| ~ spl0_394 ),
inference(resolution,[],[f3736,f3631]) ).
fof(f4162,plain,
( spl0_429
| ~ spl0_264
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f4045,f3834,f2162,f4160]) ).
fof(f4045,plain,
( ! [X0] : c_lessequals(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_264
| ~ spl0_415 ),
inference(resolution,[],[f3835,f2163]) ).
fof(f3888,plain,
spl0_428,
inference(avatar_split_clause,[],[f887,f3886]) ).
fof(f3886,plain,
( spl0_428
<=> ! [X4,X3] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f887,plain,
! [X3,X4] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f886,f225]) ).
fof(f886,plain,
! [X3,X4] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f123,f225]) ).
fof(f123,axiom,
! [X3,X4] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__add__cancel_0) ).
fof(f3884,plain,
spl0_427,
inference(avatar_split_clause,[],[f730,f3882]) ).
fof(f3882,plain,
( spl0_427
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f730,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f3880,plain,
( spl0_426
| ~ spl0_223
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3687,f3630,f1916,f3878]) ).
fof(f1916,plain,
( spl0_223
<=> ! [X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X3),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f3687,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_223
| ~ spl0_373 ),
inference(resolution,[],[f3631,f1917]) ).
fof(f1917,plain,
( ! [X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X3),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f1916]) ).
fof(f3876,plain,
spl0_425,
inference(avatar_split_clause,[],[f689,f3874]) ).
fof(f3874,plain,
( spl0_425
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f689,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
fof(f3872,plain,
spl0_424,
inference(avatar_split_clause,[],[f625,f3870]) ).
fof(f3870,plain,
( spl0_424
<=> ! [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(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f625,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(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f3868,plain,
spl0_423,
inference(avatar_split_clause,[],[f624,f3866]) ).
fof(f3866,plain,
( spl0_423
<=> ! [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(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f624,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(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f3864,plain,
spl0_422,
inference(avatar_split_clause,[],[f566,f3862]) ).
fof(f3862,plain,
( spl0_422
<=> ! [X4,X3] :
( X3 = X4
| c_Complex_OIm(X3) != c_Complex_OIm(X4)
| c_Complex_ORe(X3) != c_Complex_ORe(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f566,axiom,
! [X3,X4] :
( X3 = X4
| c_Complex_OIm(X3) != c_Complex_OIm(X4)
| c_Complex_ORe(X3) != c_Complex_ORe(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__equality_0) ).
fof(f3860,plain,
spl0_421,
inference(avatar_split_clause,[],[f565,f3858]) ).
fof(f3858,plain,
( spl0_421
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f565,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f3856,plain,
spl0_420,
inference(avatar_split_clause,[],[f564,f3854]) ).
fof(f3854,plain,
( spl0_420
<=> ! [X4,X0,X14] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X14,X0),c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f564,axiom,
! [X0,X14,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X14,X0),c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f3852,plain,
spl0_419,
inference(avatar_split_clause,[],[f528,f3850]) ).
fof(f3850,plain,
( spl0_419
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f528,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
fof(f3848,plain,
spl0_418,
inference(avatar_split_clause,[],[f523,f3846]) ).
fof(f3846,plain,
( spl0_418
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f523,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f3844,plain,
spl0_417,
inference(avatar_split_clause,[],[f518,f3842]) ).
fof(f3842,plain,
( spl0_417
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f518,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f3840,plain,
spl0_416,
inference(avatar_split_clause,[],[f517,f3838]) ).
fof(f3838,plain,
( spl0_416
<=> ! [X2,X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f517,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f3836,plain,
( spl0_415
| ~ spl0_222
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3686,f3630,f1912,f3834]) ).
fof(f3686,plain,
( ! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_222
| ~ spl0_373 ),
inference(resolution,[],[f3631,f1913]) ).
fof(f3832,plain,
spl0_414,
inference(avatar_split_clause,[],[f516,f3830]) ).
fof(f3830,plain,
( spl0_414
<=> ! [X4,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f516,axiom,
! [X3,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f3828,plain,
spl0_413,
inference(avatar_split_clause,[],[f515,f3826]) ).
fof(f3826,plain,
( spl0_413
<=> ! [X4,X0,X14,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f515,axiom,
! [X3,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
fof(f3824,plain,
spl0_412,
inference(avatar_split_clause,[],[f506,f3822]) ).
fof(f3822,plain,
( spl0_412
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f506,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
fof(f3820,plain,
spl0_411,
inference(avatar_split_clause,[],[f502,f3818]) ).
fof(f3818,plain,
( spl0_411
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f502,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X14,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
fof(f3816,plain,
spl0_410,
inference(avatar_split_clause,[],[f501,f3814]) ).
fof(f3814,plain,
( spl0_410
<=> ! [X4,X0,X3,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X14,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f501,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X14,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
fof(f3812,plain,
spl0_409,
inference(avatar_split_clause,[],[f499,f3810]) ).
fof(f3810,plain,
( spl0_409
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f499,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X14,X0)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
fof(f3808,plain,
spl0_408,
inference(avatar_split_clause,[],[f496,f3806]) ).
fof(f3806,plain,
( spl0_408
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f496,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
fof(f3804,plain,
spl0_407,
inference(avatar_split_clause,[],[f495,f3802]) ).
fof(f3802,plain,
( spl0_407
<=> ! [X2,X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f495,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
fof(f3800,plain,
spl0_406,
inference(avatar_split_clause,[],[f494,f3798]) ).
fof(f3798,plain,
( spl0_406
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f494,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
fof(f3796,plain,
spl0_405,
inference(avatar_split_clause,[],[f493,f3794]) ).
fof(f3794,plain,
( spl0_405
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f493,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
fof(f3777,plain,
spl0_404,
inference(avatar_split_clause,[],[f474,f3775]) ).
fof(f3775,plain,
( spl0_404
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f474,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f3773,plain,
spl0_403,
inference(avatar_split_clause,[],[f450,f3771]) ).
fof(f3771,plain,
( spl0_403
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f450,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f3769,plain,
spl0_402,
inference(avatar_split_clause,[],[f405,f3767]) ).
fof(f3767,plain,
( spl0_402
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f405,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f3765,plain,
spl0_401,
inference(avatar_split_clause,[],[f397,f3763]) ).
fof(f3763,plain,
( spl0_401
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f397,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f3761,plain,
spl0_400,
inference(avatar_split_clause,[],[f396,f3759]) ).
fof(f3759,plain,
( spl0_400
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f396,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f3757,plain,
spl0_399,
inference(avatar_split_clause,[],[f395,f3755]) ).
fof(f3755,plain,
( spl0_399
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f395,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f3753,plain,
spl0_398,
inference(avatar_split_clause,[],[f394,f3751]) ).
fof(f3751,plain,
( spl0_398
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f394,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f3749,plain,
spl0_397,
inference(avatar_split_clause,[],[f393,f3747]) ).
fof(f3747,plain,
( spl0_397
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f393,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f3745,plain,
spl0_396,
inference(avatar_split_clause,[],[f392,f3743]) ).
fof(f3743,plain,
( spl0_396
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f392,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f3741,plain,
spl0_395,
inference(avatar_split_clause,[],[f391,f3739]) ).
fof(f3739,plain,
( spl0_395
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f391,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f3737,plain,
( spl0_394
| ~ spl0_172
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3693,f3630,f1683,f3735]) ).
fof(f3693,plain,
( ! [X0] : c_lessequals(c_Complex_ORe(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex)),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_172
| ~ spl0_373 ),
inference(resolution,[],[f3631,f1684]) ).
fof(f3733,plain,
spl0_393,
inference(avatar_split_clause,[],[f390,f3731]) ).
fof(f3731,plain,
( spl0_393
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f390,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f3729,plain,
spl0_392,
inference(avatar_split_clause,[],[f356,f3727]) ).
fof(f3727,plain,
( spl0_392
<=> ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f356,axiom,
! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
fof(f3725,plain,
spl0_391,
inference(avatar_split_clause,[],[f309,f3723]) ).
fof(f3723,plain,
( spl0_391
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X3,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f309,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X3,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f3721,plain,
spl0_390,
inference(avatar_split_clause,[],[f308,f3719]) ).
fof(f3719,plain,
( spl0_390
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f308,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f3717,plain,
spl0_389,
inference(avatar_split_clause,[],[f307,f3715]) ).
fof(f3715,plain,
( spl0_389
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X14,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f307,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X14,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
fof(f3713,plain,
spl0_388,
inference(avatar_split_clause,[],[f306,f3711]) ).
fof(f3711,plain,
( spl0_388
<=> ! [X4,X0,X3,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f306,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X14,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
fof(f3709,plain,
spl0_387,
inference(avatar_split_clause,[],[f283,f3707]) ).
fof(f3707,plain,
( spl0_387
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f283,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X3,X0)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
fof(f3705,plain,
spl0_386,
inference(avatar_split_clause,[],[f282,f3703]) ).
fof(f3703,plain,
( spl0_386
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f282,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X4,X0)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
fof(f3701,plain,
spl0_385,
inference(avatar_split_clause,[],[f281,f3699]) ).
fof(f3699,plain,
( spl0_385
<=> ! [X4,X0,X14,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f281,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f3697,plain,
spl0_384,
inference(avatar_split_clause,[],[f280,f3695]) ).
fof(f3695,plain,
( spl0_384
<=> ! [X4,X0,X3,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X4,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f280,axiom,
! [X3,X0,X14,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X4,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f3672,plain,
spl0_383,
inference(avatar_split_clause,[],[f229,f3670]) ).
fof(f3670,plain,
( spl0_383
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f229,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
fof(f3668,plain,
spl0_382,
inference(avatar_split_clause,[],[f228,f3666]) ).
fof(f3666,plain,
( spl0_382
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f228,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f3664,plain,
spl0_381,
inference(avatar_split_clause,[],[f227,f3662]) ).
fof(f3662,plain,
( spl0_381
<=> ! [X4,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f227,axiom,
! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f3660,plain,
spl0_380,
inference(avatar_split_clause,[],[f83,f3658]) ).
fof(f3658,plain,
( spl0_380
<=> ! [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_380])]) ).
fof(f83,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/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f3656,plain,
spl0_379,
inference(avatar_split_clause,[],[f48,f3654]) ).
fof(f3654,plain,
( spl0_379
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f48,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f3652,plain,
spl0_378,
inference(avatar_split_clause,[],[f38,f3650]) ).
fof(f3650,plain,
( spl0_378
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f38,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f3648,plain,
spl0_377,
inference(avatar_split_clause,[],[f37,f3646]) ).
fof(f3646,plain,
( spl0_377
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f37,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f3644,plain,
spl0_376,
inference(avatar_split_clause,[],[f33,f3642]) ).
fof(f3642,plain,
( spl0_376
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f33,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f3640,plain,
spl0_375,
inference(avatar_split_clause,[],[f31,f3638]) ).
fof(f3638,plain,
( spl0_375
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f31,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f3636,plain,
spl0_374,
inference(avatar_split_clause,[],[f20,f3634]) ).
fof(f3634,plain,
( spl0_374
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f20,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
fof(f3632,plain,
( spl0_373
| ~ spl0_290
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f3603,f3002,f2470,f3630]) ).
fof(f3603,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_290
| ~ spl0_365 ),
inference(resolution,[],[f3003,f2471]) ).
fof(f3628,plain,
spl0_372,
inference(avatar_split_clause,[],[f17,f3626]) ).
fof(f3626,plain,
( spl0_372
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f17,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f3624,plain,
spl0_371,
inference(avatar_split_clause,[],[f1,f3622]) ).
fof(f3622,plain,
( spl0_371
<=> ! [X2,X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f3457,plain,
( spl0_370
| ~ spl0_90
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1977,f1860,f1339,f3454]) ).
fof(f3454,plain,
( spl0_370
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f1860,plain,
( spl0_209
<=> ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1977,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_90
| ~ spl0_209 ),
inference(resolution,[],[f1861,f1341]) ).
fof(f1861,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1860]) ).
fof(f3139,plain,
( spl0_369
| ~ spl0_90
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1964,f1844,f1339,f3137]) ).
fof(f3137,plain,
( spl0_369
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f1844,plain,
( spl0_205
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1964,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_90
| ~ spl0_205 ),
inference(resolution,[],[f1845,f1341]) ).
fof(f1845,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1844]) ).
fof(f3075,plain,
( spl0_368
| ~ spl0_54
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1963,f1844,f1159,f3073]) ).
fof(f3073,plain,
( spl0_368
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f1963,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_54
| ~ spl0_205 ),
inference(resolution,[],[f1845,f1161]) ).
fof(f3012,plain,
spl0_367,
inference(avatar_split_clause,[],[f892,f3010]) ).
fof(f3010,plain,
( spl0_367
<=> ! [X32,X31] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X31,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X32,X31,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f892,plain,
! [X31,X32] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X31,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X32,X31,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f337,f225]) ).
fof(f337,axiom,
! [X31,X32] :
( c_HOL_Oord__class_Oless(X32,X31,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X31,c_HOL_Ouminus__class_Ouminus(X32,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__gt__zero__less_0) ).
fof(f3008,plain,
spl0_366,
inference(avatar_split_clause,[],[f891,f3006]) ).
fof(f3006,plain,
( spl0_366
<=> ! [X32,X31] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X31,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X32,X31,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f891,plain,
! [X31,X32] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X31,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X32,X31,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f336,f225]) ).
fof(f336,axiom,
! [X31,X32] :
( ~ c_HOL_Oord__class_Oless(X32,X31,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X31,c_HOL_Ouminus__class_Ouminus(X32,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__sum__gt__zero_0) ).
fof(f3004,plain,
spl0_365,
inference(avatar_split_clause,[],[f724,f3002]) ).
fof(f724,axiom,
! [X34,X35,X33] :
( ~ c_lessequals(X34,X35,tc_RealDef_Oreal)
| ~ c_lessequals(X35,X33,tc_RealDef_Oreal)
| c_lessequals(X34,X33,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f3000,plain,
( spl0_364
| ~ spl0_89
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1949,f1820,f1334,f2998]) ).
fof(f2998,plain,
( spl0_364
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f1334,plain,
( spl0_89
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1820,plain,
( spl0_199
<=> ! [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_199])]) ).
fof(f1949,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_89
| ~ spl0_199 ),
inference(resolution,[],[f1821,f1336]) ).
fof(f1336,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f1821,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1820]) ).
fof(f2996,plain,
spl0_363,
inference(avatar_split_clause,[],[f679,f2994]) ).
fof(f2994,plain,
( spl0_363
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f679,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__le__cancel__iff_0) ).
fof(f2992,plain,
spl0_362,
inference(avatar_split_clause,[],[f678,f2990]) ).
fof(f2990,plain,
( spl0_362
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f678,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__le__cancel__iff_1) ).
fof(f2988,plain,
spl0_361,
inference(avatar_split_clause,[],[f668,f2986]) ).
fof(f2986,plain,
( spl0_361
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f668,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f2984,plain,
spl0_360,
inference(avatar_split_clause,[],[f667,f2982]) ).
fof(f2982,plain,
( spl0_360
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f667,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f2980,plain,
spl0_359,
inference(avatar_split_clause,[],[f666,f2978]) ).
fof(f2978,plain,
( spl0_359
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f666,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f2976,plain,
spl0_358,
inference(avatar_split_clause,[],[f652,f2974]) ).
fof(f652,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f2972,plain,
spl0_357,
inference(avatar_split_clause,[],[f619,f2970]) ).
fof(f2970,plain,
( spl0_357
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f619,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
fof(f2968,plain,
spl0_356,
inference(avatar_split_clause,[],[f602,f2966]) ).
fof(f2966,plain,
( spl0_356
<=> ! [X4,X3] : c_Complex_ORe(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_ORe(X3),c_Complex_ORe(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f602,axiom,
! [X3,X4] : c_Complex_ORe(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_ORe(X3),c_Complex_ORe(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Oadd_0) ).
fof(f2964,plain,
spl0_355,
inference(avatar_split_clause,[],[f599,f2962]) ).
fof(f2962,plain,
( spl0_355
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f599,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f2960,plain,
spl0_354,
inference(avatar_split_clause,[],[f596,f2958]) ).
fof(f2958,plain,
( spl0_354
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f596,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f2956,plain,
( spl0_353
| ~ spl0_53
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1948,f1820,f1154,f2954]) ).
fof(f2954,plain,
( spl0_353
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f1154,plain,
( spl0_53
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1948,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_53
| ~ spl0_199 ),
inference(resolution,[],[f1821,f1156]) ).
fof(f1156,plain,
( class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f2952,plain,
spl0_352,
inference(avatar_split_clause,[],[f589,f2950]) ).
fof(f2950,plain,
( spl0_352
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f589,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
fof(f2948,plain,
spl0_351,
inference(avatar_split_clause,[],[f587,f2946]) ).
fof(f2946,plain,
( spl0_351
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f587,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
fof(f2944,plain,
spl0_350,
inference(avatar_split_clause,[],[f579,f2942]) ).
fof(f2942,plain,
( spl0_350
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f579,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__0_0) ).
fof(f2940,plain,
spl0_349,
inference(avatar_split_clause,[],[f567,f2938]) ).
fof(f2938,plain,
( spl0_349
<=> ! [X5,X0,X15] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| X5 = X15
| ~ c_HOL_Oeq__class_Oeq(X15,X5,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f567,axiom,
! [X0,X15,X5] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| X5 = X15
| ~ c_HOL_Oeq__class_Oeq(X15,X5,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__def_0) ).
fof(f2936,plain,
spl0_348,
inference(avatar_split_clause,[],[f560,f2934]) ).
fof(f2934,plain,
( spl0_348
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f560,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__eq__diff_0) ).
fof(f2932,plain,
spl0_347,
inference(avatar_split_clause,[],[f559,f2930]) ).
fof(f2930,plain,
( spl0_347
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f559,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__eq__diff_1) ).
fof(f2928,plain,
spl0_346,
inference(avatar_split_clause,[],[f514,f2926]) ).
fof(f2926,plain,
( spl0_346
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f514,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2924,plain,
spl0_345,
inference(avatar_split_clause,[],[f513,f2922]) ).
fof(f2922,plain,
( spl0_345
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f513,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2920,plain,
spl0_344,
inference(avatar_split_clause,[],[f512,f2918]) ).
fof(f2918,plain,
( spl0_344
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f512,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Orderings_Oord__class_Omin(X3,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2916,plain,
spl0_343,
inference(avatar_split_clause,[],[f511,f2914]) ).
fof(f2914,plain,
( spl0_343
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f511,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2912,plain,
( spl0_342
| ~ spl0_89
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1946,f1816,f1334,f2910]) ).
fof(f2910,plain,
( spl0_342
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f1816,plain,
( spl0_198
<=> ! [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_198])]) ).
fof(f1946,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_89
| ~ spl0_198 ),
inference(resolution,[],[f1817,f1336]) ).
fof(f1817,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f2908,plain,
spl0_341,
inference(avatar_split_clause,[],[f510,f2906]) ).
fof(f2906,plain,
( spl0_341
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f510,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2904,plain,
spl0_340,
inference(avatar_split_clause,[],[f509,f2902]) ).
fof(f2902,plain,
( spl0_340
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f509,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2900,plain,
spl0_339,
inference(avatar_split_clause,[],[f431,f2898]) ).
fof(f2898,plain,
( spl0_339
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f431,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2896,plain,
spl0_338,
inference(avatar_split_clause,[],[f428,f2894]) ).
fof(f2894,plain,
( spl0_338
<=> ! [X4,X3] :
( c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f428,axiom,
! [X3,X4] :
( c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_0) ).
fof(f2892,plain,
spl0_337,
inference(avatar_split_clause,[],[f373,f2890]) ).
fof(f2890,plain,
( spl0_337
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f373,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
fof(f2888,plain,
spl0_336,
inference(avatar_split_clause,[],[f355,f2886]) ).
fof(f2886,plain,
( spl0_336
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f355,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__less__cancel_0) ).
fof(f2884,plain,
spl0_335,
inference(avatar_split_clause,[],[f354,f2882]) ).
fof(f2882,plain,
( spl0_335
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f354,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__less__mono_0) ).
fof(f2880,plain,
spl0_334,
inference(avatar_split_clause,[],[f323,f2878]) ).
fof(f2878,plain,
( spl0_334
<=> ! [X30,X3] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X30,X30,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f323,axiom,
! [X3,X30] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X30,X30,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).
fof(f2876,plain,
spl0_333,
inference(avatar_split_clause,[],[f317,f2874]) ).
fof(f2874,plain,
( spl0_333
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f317,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f2872,plain,
spl0_332,
inference(avatar_split_clause,[],[f312,f2870]) ).
fof(f2870,plain,
( spl0_332
<=> ! [X4,X3] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f312,axiom,
! [X3,X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
fof(f2868,plain,
( spl0_331
| ~ spl0_53
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1945,f1816,f1154,f2866]) ).
fof(f2866,plain,
( spl0_331
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f1945,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_53
| ~ spl0_198 ),
inference(resolution,[],[f1817,f1156]) ).
fof(f2864,plain,
spl0_330,
inference(avatar_split_clause,[],[f297,f2862]) ).
fof(f2862,plain,
( spl0_330
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f297,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f2860,plain,
spl0_329,
inference(avatar_split_clause,[],[f296,f2858]) ).
fof(f2858,plain,
( spl0_329
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f296,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f2856,plain,
spl0_328,
inference(avatar_split_clause,[],[f235,f2854]) ).
fof(f2854,plain,
( spl0_328
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f235,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pcompose__0_0) ).
fof(f2852,plain,
spl0_327,
inference(avatar_split_clause,[],[f170,f2850]) ).
fof(f2850,plain,
( spl0_327
<=> ! [X4,X3] : c_Complex_OIm(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_OIm(X3),c_Complex_OIm(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f170,axiom,
! [X3,X4] : c_Complex_OIm(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_OIm(X3),c_Complex_OIm(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Oadd_0) ).
fof(f2848,plain,
spl0_326,
inference(avatar_split_clause,[],[f136,f2846]) ).
fof(f2846,plain,
( spl0_326
<=> ! [X4,X3] : c_Complex_Ocnj(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_Ocnj(X3),c_Complex_Ocnj(X4),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f136,axiom,
! [X3,X4] : c_Complex_Ocnj(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_Ocnj(X3),c_Complex_Ocnj(X4),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Oadd_0) ).
fof(f2844,plain,
spl0_325,
inference(avatar_split_clause,[],[f116,f2842]) ).
fof(f2842,plain,
( spl0_325
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f116,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f2840,plain,
spl0_324,
inference(avatar_split_clause,[],[f99,f2838]) ).
fof(f2838,plain,
( spl0_324
<=> ! [X1,X3] :
( X1 = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f99,axiom,
! [X3,X1] :
( X1 = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__minus__iff_0) ).
fof(f2836,plain,
spl0_323,
inference(avatar_split_clause,[],[f92,f2834]) ).
fof(f2834,plain,
( spl0_323
<=> ! [X7] :
( ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(X7,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X7,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f92,axiom,
! [X7] :
( ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(X7,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X7,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__abs__def_0) ).
fof(f2832,plain,
spl0_322,
inference(avatar_split_clause,[],[f54,f2830]) ).
fof(f2830,plain,
( spl0_322
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f54,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
fof(f2828,plain,
spl0_321,
inference(avatar_split_clause,[],[f43,f2826]) ).
fof(f2826,plain,
( spl0_321
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f43,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2824,plain,
spl0_320,
inference(avatar_split_clause,[],[f34,f2822]) ).
fof(f2822,plain,
( spl0_320
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f34,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f2820,plain,
spl0_319,
inference(avatar_split_clause,[],[f29,f2818]) ).
fof(f29,axiom,
! [X3,X7] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).
fof(f2731,plain,
( spl0_318
| ~ spl0_61
| ~ spl0_256
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2424,f2370,f2130,f1194,f2729]) ).
fof(f2729,plain,
( spl0_318
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1194,plain,
( spl0_61
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f2130,plain,
( spl0_256
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2370,plain,
( spl0_271
<=> ! [X0] : c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2424,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_256
| ~ spl0_271 ),
inference(resolution,[],[f2371,f2131]) ).
fof(f2131,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2130]) ).
fof(f2371,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2370]) ).
fof(f2603,plain,
( spl0_317
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f2388,f2174,f2601]) ).
fof(f2601,plain,
( spl0_317
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2174,plain,
( spl0_267
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2388,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_267 ),
inference(factoring,[],[f2175]) ).
fof(f2175,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,X3,X0)
| c_lessequals(X3,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f2174]) ).
fof(f2578,plain,
spl0_316,
inference(avatar_split_clause,[],[f732,f2576]) ).
fof(f2576,plain,
( spl0_316
<=> ! [X29,X14] :
( X14 = X29
| ~ c_lessequals(X14,X29,tc_RealDef_Oreal)
| ~ c_lessequals(X29,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f732,axiom,
! [X29,X14] :
( X14 = X29
| ~ c_lessequals(X14,X29,tc_RealDef_Oreal)
| ~ c_lessequals(X29,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f2574,plain,
spl0_315,
inference(avatar_split_clause,[],[f699,f2572]) ).
fof(f2572,plain,
( spl0_315
<=> ! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X15,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f699,axiom,
! [X0,X1,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X15,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X15,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__pCons_2) ).
fof(f2570,plain,
spl0_314,
inference(avatar_split_clause,[],[f691,f2568]) ).
fof(f2568,plain,
( spl0_314
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X1,X0) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f691,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X1,X0) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
fof(f2566,plain,
spl0_313,
inference(avatar_split_clause,[],[f690,f2564]) ).
fof(f2564,plain,
( spl0_313
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X3,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f690,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X3,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f2562,plain,
spl0_312,
inference(avatar_split_clause,[],[f676,f2560]) ).
fof(f2560,plain,
( spl0_312
<=> ! [X4,X3] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f676,axiom,
! [X3,X4] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f2558,plain,
( spl0_311
| ~ spl0_99
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2357,f2162,f1383,f2556]) ).
fof(f2556,plain,
( spl0_311
<=> ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2357,plain,
( ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_99
| ~ spl0_264 ),
inference(resolution,[],[f2163,f1384]) ).
fof(f2554,plain,
spl0_310,
inference(avatar_split_clause,[],[f590,f2552]) ).
fof(f2552,plain,
( spl0_310
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f590,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
fof(f2550,plain,
spl0_309,
inference(avatar_split_clause,[],[f588,f2548]) ).
fof(f2548,plain,
( spl0_309
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f588,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
fof(f2546,plain,
spl0_308,
inference(avatar_split_clause,[],[f467,f2544]) ).
fof(f2544,plain,
( spl0_308
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f467,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2542,plain,
spl0_307,
inference(avatar_split_clause,[],[f460,f2540]) ).
fof(f2540,plain,
( spl0_307
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f460,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2538,plain,
spl0_306,
inference(avatar_split_clause,[],[f456,f2536]) ).
fof(f456,axiom,
! [X0,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
fof(f2534,plain,
spl0_305,
inference(avatar_split_clause,[],[f455,f2532]) ).
fof(f455,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,tc_Polynomial_Opoly(X0)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).
fof(f2530,plain,
spl0_304,
inference(avatar_split_clause,[],[f413,f2528]) ).
fof(f2528,plain,
( spl0_304
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f413,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2526,plain,
spl0_303,
inference(avatar_split_clause,[],[f411,f2524]) ).
fof(f411,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2522,plain,
spl0_302,
inference(avatar_split_clause,[],[f408,f2520]) ).
fof(f2520,plain,
( spl0_302
<=> ! [X3,X33] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(X3,X33,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(X3),X33,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f408,axiom,
! [X3,X33] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(X3,X33,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(X3),X33,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__power_0) ).
fof(f2518,plain,
spl0_301,
inference(avatar_split_clause,[],[f402,f2516]) ).
fof(f402,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f2512,plain,
spl0_300,
inference(avatar_split_clause,[],[f358,f2510]) ).
fof(f2510,plain,
( spl0_300
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f358,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
fof(f2508,plain,
spl0_299,
inference(avatar_split_clause,[],[f357,f2506]) ).
fof(f2506,plain,
( spl0_299
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f357,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_1) ).
fof(f2504,plain,
spl0_298,
inference(avatar_split_clause,[],[f335,f2502]) ).
fof(f335,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f2500,plain,
spl0_297,
inference(avatar_split_clause,[],[f314,f2498]) ).
fof(f2498,plain,
( spl0_297
<=> ! [X3] :
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f314,axiom,
! [X3] :
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
fof(f2496,plain,
spl0_296,
inference(avatar_split_clause,[],[f313,f2494]) ).
fof(f2494,plain,
( spl0_296
<=> ! [X3] :
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f313,axiom,
! [X3] :
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
fof(f2492,plain,
spl0_295,
inference(avatar_split_clause,[],[f293,f2490]) ).
fof(f2490,plain,
( spl0_295
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f293,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f2488,plain,
spl0_294,
inference(avatar_split_clause,[],[f292,f2486]) ).
fof(f292,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2484,plain,
spl0_293,
inference(avatar_split_clause,[],[f291,f2482]) ).
fof(f291,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2480,plain,
spl0_292,
inference(avatar_split_clause,[],[f288,f2478]) ).
fof(f288,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X3,X0) = c_Orderings_Oord__class_Omin(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f2476,plain,
spl0_291,
inference(avatar_split_clause,[],[f287,f2474]) ).
fof(f2474,plain,
( spl0_291
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f287,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f2472,plain,
( spl0_290
| ~ spl0_181
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2423,f2370,f1722,f2470]) ).
fof(f2423,plain,
( ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_181
| ~ spl0_271 ),
inference(resolution,[],[f2371,f1723]) ).
fof(f2468,plain,
spl0_289,
inference(avatar_split_clause,[],[f286,f2466]) ).
fof(f286,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f2464,plain,
spl0_288,
inference(avatar_split_clause,[],[f265,f2462]) ).
fof(f265,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f2460,plain,
spl0_287,
inference(avatar_split_clause,[],[f241,f2458]) ).
fof(f2458,plain,
( spl0_287
<=> ! [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_287])]) ).
fof(f241,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/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2456,plain,
spl0_286,
inference(avatar_split_clause,[],[f240,f2454]) ).
fof(f240,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f2452,plain,
spl0_285,
inference(avatar_split_clause,[],[f238,f2450]) ).
fof(f2450,plain,
( spl0_285
<=> ! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f238,axiom,
! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
fof(f2448,plain,
spl0_284,
inference(avatar_split_clause,[],[f237,f2446]) ).
fof(f2446,plain,
( spl0_284
<=> ! [X3] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f237,axiom,
! [X3] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
fof(f2444,plain,
spl0_283,
inference(avatar_split_clause,[],[f234,f2442]) ).
fof(f234,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2440,plain,
spl0_282,
inference(avatar_split_clause,[],[f225,f2438]) ).
fof(f2438,plain,
( spl0_282
<=> ! [X9,X7] : c_HOL_Ominus__class_Ominus(X7,X9,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Ouminus__class_Ouminus(X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2436,plain,
spl0_281,
inference(avatar_split_clause,[],[f224,f2434]) ).
fof(f2434,plain,
( spl0_281
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f224,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__0_0) ).
fof(f2432,plain,
spl0_280,
inference(avatar_split_clause,[],[f223,f2430]) ).
fof(f223,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__root_1) ).
fof(f2422,plain,
spl0_279,
inference(avatar_split_clause,[],[f219,f2420]) ).
fof(f219,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2418,plain,
spl0_278,
inference(avatar_split_clause,[],[f218,f2416]) ).
fof(f218,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X4,X0) = c_Orderings_Oord__class_Omax(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f2414,plain,
spl0_277,
inference(avatar_split_clause,[],[f214,f2412]) ).
fof(f214,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f2410,plain,
spl0_276,
inference(avatar_split_clause,[],[f195,f2408]) ).
fof(f2408,plain,
( spl0_276
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f195,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2406,plain,
spl0_275,
inference(avatar_split_clause,[],[f134,f2404]) ).
fof(f2404,plain,
( spl0_275
<=> ! [X3] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f134,axiom,
! [X3] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__zero_0) ).
fof(f2402,plain,
spl0_274,
inference(avatar_split_clause,[],[f133,f2400]) ).
fof(f2400,plain,
( spl0_274
<=> ! [X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f133,axiom,
! [X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
fof(f2398,plain,
spl0_273,
inference(avatar_split_clause,[],[f117,f2396]) ).
fof(f2396,plain,
( spl0_273
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f2394,plain,
spl0_272,
inference(avatar_split_clause,[],[f88,f2392]) ).
fof(f2392,plain,
( spl0_272
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f88,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2372,plain,
( ~ spl0_59
| spl0_271
| ~ spl0_153
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f2301,f2138,f1600,f2370,f1184]) ).
fof(f2301,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
| ~ spl0_153
| ~ spl0_258 ),
inference(resolution,[],[f2139,f1601]) ).
fof(f2266,plain,
( spl0_270
| ~ spl0_78
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1944,f1812,f1279,f2263]) ).
fof(f2263,plain,
( spl0_270
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1279,plain,
( spl0_78
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1812,plain,
( spl0_197
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1944,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_78
| ~ spl0_197 ),
inference(resolution,[],[f1813,f1281]) ).
fof(f1281,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f1813,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1812]) ).
fof(f2226,plain,
( spl0_269
| ~ spl0_36
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1943,f1812,f1069,f2223]) ).
fof(f2223,plain,
( spl0_269
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1069,plain,
( spl0_36
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1943,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_36
| ~ spl0_197 ),
inference(resolution,[],[f1813,f1071]) ).
fof(f1071,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f2189,plain,
( spl0_268
| ~ spl0_15
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1935,f1792,f964,f2186]) ).
fof(f2186,plain,
( spl0_268
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1792,plain,
( spl0_192
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1935,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_15
| ~ spl0_192 ),
inference(resolution,[],[f1793,f966]) ).
fof(f1793,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f2176,plain,
spl0_267,
inference(avatar_split_clause,[],[f720,f2174]) ).
fof(f720,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2172,plain,
spl0_266,
inference(avatar_split_clause,[],[f707,f2170]) ).
fof(f707,axiom,
! [X3] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).
fof(f2168,plain,
spl0_265,
inference(avatar_split_clause,[],[f688,f2166]) ).
fof(f2166,plain,
( spl0_265
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f688,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f2164,plain,
spl0_264,
inference(avatar_split_clause,[],[f681,f2162]) ).
fof(f681,axiom,
! [X3,X7] :
( c_lessequals(X3,X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
fof(f2160,plain,
spl0_263,
inference(avatar_split_clause,[],[f680,f2158]) ).
fof(f2158,plain,
( spl0_263
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oarctan(X3),c_Transcendental_Oarctan(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f680,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oarctan(X3),c_Transcendental_Oarctan(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__monotone_H_0) ).
fof(f2156,plain,
( spl0_262
| ~ spl0_90
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1930,f1772,f1339,f2154]) ).
fof(f2154,plain,
( spl0_262
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1772,plain,
( spl0_187
<=> ! [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_187])]) ).
fof(f1930,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_90
| ~ spl0_187 ),
inference(resolution,[],[f1773,f1341]) ).
fof(f1773,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f2152,plain,
spl0_261,
inference(avatar_split_clause,[],[f675,f2150]) ).
fof(f2150,plain,
( spl0_261
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f675,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
fof(f2148,plain,
spl0_260,
inference(avatar_split_clause,[],[f674,f2146]) ).
fof(f2146,plain,
( spl0_260
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f674,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
fof(f2144,plain,
spl0_259,
inference(avatar_split_clause,[],[f662,f2142]) ).
fof(f662,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f2140,plain,
spl0_258,
inference(avatar_split_clause,[],[f659,f2138]) ).
fof(f659,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f2136,plain,
spl0_257,
inference(avatar_split_clause,[],[f658,f2134]) ).
fof(f658,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2132,plain,
spl0_256,
inference(avatar_split_clause,[],[f632,f2130]) ).
fof(f632,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2128,plain,
spl0_255,
inference(avatar_split_clause,[],[f631,f2126]) ).
fof(f2126,plain,
( spl0_255
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f631,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2124,plain,
spl0_254,
inference(avatar_split_clause,[],[f630,f2122]) ).
fof(f630,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f2120,plain,
spl0_253,
inference(avatar_split_clause,[],[f601,f2118]) ).
fof(f2118,plain,
( spl0_253
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f601,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f2116,plain,
spl0_252,
inference(avatar_split_clause,[],[f594,f2114]) ).
fof(f2114,plain,
( spl0_252
<=> ! [X7] :
( c_HOL_Oabs__class_Oabs(X7,tc_RealDef_Oreal) = X7
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f594,axiom,
! [X7] :
( c_HOL_Oabs__class_Oabs(X7,tc_RealDef_Oreal) = X7
| c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
fof(f2112,plain,
( spl0_251
| ~ spl0_54
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1929,f1772,f1159,f2110]) ).
fof(f2110,plain,
( spl0_251
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1929,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_54
| ~ spl0_187 ),
inference(resolution,[],[f1773,f1161]) ).
fof(f2108,plain,
spl0_250,
inference(avatar_split_clause,[],[f548,f2106]) ).
fof(f2106,plain,
( spl0_250
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f548,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f2104,plain,
spl0_249,
inference(avatar_split_clause,[],[f547,f2102]) ).
fof(f2102,plain,
( spl0_249
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f547,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f2100,plain,
spl0_248,
inference(avatar_split_clause,[],[f546,f2098]) ).
fof(f2098,plain,
( spl0_248
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f546,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2096,plain,
spl0_247,
inference(avatar_split_clause,[],[f545,f2094]) ).
fof(f2094,plain,
( spl0_247
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f545,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2092,plain,
spl0_246,
inference(avatar_split_clause,[],[f543,f2090]) ).
fof(f2090,plain,
( spl0_246
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f543,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f2088,plain,
spl0_245,
inference(avatar_split_clause,[],[f541,f2086]) ).
fof(f2086,plain,
( spl0_245
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f541,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f2084,plain,
spl0_244,
inference(avatar_split_clause,[],[f539,f2082]) ).
fof(f539,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2080,plain,
spl0_243,
inference(avatar_split_clause,[],[f538,f2078]) ).
fof(f538,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f2076,plain,
spl0_242,
inference(avatar_split_clause,[],[f487,f2074]) ).
fof(f2074,plain,
( spl0_242
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f487,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2072,plain,
spl0_241,
inference(avatar_split_clause,[],[f486,f2070]) ).
fof(f2070,plain,
( spl0_241
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f486,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2068,plain,
( spl0_240
| ~ spl0_85
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1924,f1764,f1314,f2066]) ).
fof(f2066,plain,
( spl0_240
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1764,plain,
( spl0_185
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1924,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_85
| ~ spl0_185 ),
inference(resolution,[],[f1765,f1316]) ).
fof(f1765,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f2064,plain,
spl0_239,
inference(avatar_split_clause,[],[f420,f2062]) ).
fof(f2062,plain,
( spl0_239
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f420,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f2060,plain,
~ spl0_238,
inference(avatar_split_clause,[],[f410,f2057]) ).
fof(f2057,plain,
( spl0_238
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f410,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f2055,plain,
spl0_237,
inference(avatar_split_clause,[],[f384,f2053]) ).
fof(f2053,plain,
( spl0_237
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X3),c_Transcendental_Oarctan(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f384,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X3),c_Transcendental_Oarctan(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__monotone_0) ).
fof(f2051,plain,
spl0_236,
inference(avatar_split_clause,[],[f351,f2049]) ).
fof(f351,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f2047,plain,
spl0_235,
inference(avatar_split_clause,[],[f343,f2045]) ).
fof(f2045,plain,
( spl0_235
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f343,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f2043,plain,
spl0_234,
inference(avatar_split_clause,[],[f330,f2041]) ).
fof(f2041,plain,
( spl0_234
<=> ! [X0,X3] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f330,axiom,
! [X3,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
fof(f2039,plain,
spl0_233,
inference(avatar_split_clause,[],[f329,f2037]) ).
fof(f2037,plain,
( spl0_233
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f329,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
fof(f2035,plain,
spl0_232,
inference(avatar_split_clause,[],[f328,f2033]) ).
fof(f2033,plain,
( spl0_232
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f328,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
fof(f2031,plain,
spl0_231,
inference(avatar_split_clause,[],[f163,f2029]) ).
fof(f2029,plain,
( spl0_231
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f163,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f2027,plain,
spl0_230,
inference(avatar_split_clause,[],[f138,f2025]) ).
fof(f2025,plain,
( spl0_230
<=> ! [X4,X3] :
( X3 = X4
| c_Transcendental_Oexp(X3,tc_RealDef_Oreal) != c_Transcendental_Oexp(X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f138,axiom,
! [X3,X4] :
( X3 = X4
| c_Transcendental_Oexp(X3,tc_RealDef_Oreal) != c_Transcendental_Oexp(X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__inj__iff_0) ).
fof(f2023,plain,
( spl0_229
| ~ spl0_48
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1923,f1764,f1129,f2021]) ).
fof(f2021,plain,
( spl0_229
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1923,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal)
| ~ spl0_48
| ~ spl0_185 ),
inference(resolution,[],[f1765,f1131]) ).
fof(f2019,plain,
spl0_228,
inference(avatar_split_clause,[],[f50,f2017]) ).
fof(f2017,plain,
( spl0_228
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f50,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
fof(f2015,plain,
spl0_227,
inference(avatar_split_clause,[],[f44,f2013]) ).
fof(f2013,plain,
( spl0_227
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f44,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f1994,plain,
( spl0_226
| ~ spl0_170
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1749,f1722,f1675,f1992]) ).
fof(f1992,plain,
( spl0_226
<=> ! [X0,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1749,plain,
( ! [X0,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal)
| ~ spl0_170
| ~ spl0_181 ),
inference(resolution,[],[f1723,f1676]) ).
fof(f1971,plain,
( spl0_225
| ~ spl0_157
| ~ spl0_159
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1748,f1718,f1628,f1618,f1968]) ).
fof(f1968,plain,
( spl0_225
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1618,plain,
( spl0_157
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1628,plain,
( spl0_159
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_OIm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1748,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_157
| ~ spl0_159
| ~ spl0_180 ),
inference(forward_demodulation,[],[f1747,f1630]) ).
fof(f1630,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_OIm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1628]) ).
fof(f1747,plain,
( c_Complex_OIm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_157
| ~ spl0_159
| ~ spl0_180 ),
inference(forward_demodulation,[],[f1746,f1620]) ).
fof(f1620,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1618]) ).
fof(f1746,plain,
( c_Complex_OIm(c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_159
| ~ spl0_180 ),
inference(superposition,[],[f1719,f1630]) ).
fof(f1922,plain,
spl0_224,
inference(avatar_split_clause,[],[f706,f1920]) ).
fof(f1920,plain,
( spl0_224
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f706,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f1918,plain,
spl0_223,
inference(avatar_split_clause,[],[f695,f1916]) ).
fof(f695,axiom,
! [X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X3),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__Re__le__cmod_0) ).
fof(f1914,plain,
spl0_222,
inference(avatar_split_clause,[],[f694,f1912]) ).
fof(f694,axiom,
! [X3] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_OIm(X3),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__Im__le__cmod_0) ).
fof(f1910,plain,
spl0_221,
inference(avatar_split_clause,[],[f657,f1908]) ).
fof(f657,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1906,plain,
spl0_220,
inference(avatar_split_clause,[],[f656,f1904]) ).
fof(f656,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1902,plain,
spl0_219,
inference(avatar_split_clause,[],[f649,f1900]) ).
fof(f649,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1898,plain,
spl0_218,
inference(avatar_split_clause,[],[f648,f1896]) ).
fof(f648,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1894,plain,
spl0_217,
inference(avatar_split_clause,[],[f637,f1892]) ).
fof(f1892,plain,
( spl0_217
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f637,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1890,plain,
spl0_216,
inference(avatar_split_clause,[],[f636,f1888]) ).
fof(f1888,plain,
( spl0_216
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f636,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1886,plain,
spl0_215,
inference(avatar_split_clause,[],[f635,f1884]) ).
fof(f1884,plain,
( spl0_215
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f635,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1882,plain,
spl0_214,
inference(avatar_split_clause,[],[f634,f1880]) ).
fof(f1880,plain,
( spl0_214
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f634,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1878,plain,
spl0_213,
inference(avatar_split_clause,[],[f626,f1876]) ).
fof(f1876,plain,
( spl0_213
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f626,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1874,plain,
spl0_212,
inference(avatar_split_clause,[],[f593,f1872]) ).
fof(f1872,plain,
( spl0_212
<=> ! [X3] : c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f593,axiom,
! [X3] : c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).
fof(f1870,plain,
spl0_211,
inference(avatar_split_clause,[],[f583,f1868]) ).
fof(f1868,plain,
( spl0_211
<=> ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f583,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1866,plain,
spl0_210,
inference(avatar_split_clause,[],[f577,f1864]) ).
fof(f577,axiom,
! [X14] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X14
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocnj(X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
fof(f1862,plain,
spl0_209,
inference(avatar_split_clause,[],[f573,f1860]) ).
fof(f573,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
fof(f1858,plain,
spl0_208,
inference(avatar_split_clause,[],[f571,f1856]) ).
fof(f1856,plain,
( spl0_208
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f571,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1854,plain,
spl0_207,
inference(avatar_split_clause,[],[f568,f1852]) ).
fof(f1852,plain,
( spl0_207
<=> ! [X4,X0,X3] :
( ~ class_HOL_Oeq(X0)
| X3 = X4
| ~ c_HOL_Oeq__class_Oeq(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f568,axiom,
! [X3,X0,X4] :
( ~ class_HOL_Oeq(X0)
| X3 = X4
| ~ c_HOL_Oeq__class_Oeq(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equals_0) ).
fof(f1850,plain,
spl0_206,
inference(avatar_split_clause,[],[f535,f1848]) ).
fof(f1848,plain,
( spl0_206
<=> ! [X3] : c_Transcendental_Oexp(X3,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f535,axiom,
! [X3] : c_Transcendental_Oexp(X3,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__exp__cancel_0) ).
fof(f1846,plain,
spl0_205,
inference(avatar_split_clause,[],[f473,f1844]) ).
fof(f473,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f1842,plain,
( spl0_204
| ~ spl0_46
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1745,f1714,f1119,f1840]) ).
fof(f1840,plain,
( spl0_204
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1714,plain,
( spl0_179
<=> ! [X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1745,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0
| ~ spl0_46
| ~ spl0_179 ),
inference(resolution,[],[f1715,f1121]) ).
fof(f1715,plain,
( ! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1714]) ).
fof(f1838,plain,
spl0_203,
inference(avatar_split_clause,[],[f463,f1836]) ).
fof(f1836,plain,
( spl0_203
<=> ! [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_203])]) ).
fof(f463,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1834,plain,
spl0_202,
inference(avatar_split_clause,[],[f462,f1832]) ).
fof(f1832,plain,
( spl0_202
<=> ! [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_202])]) ).
fof(f462,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1830,plain,
spl0_201,
inference(avatar_split_clause,[],[f461,f1828]) ).
fof(f1828,plain,
( spl0_201
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f461,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f1826,plain,
spl0_200,
inference(avatar_split_clause,[],[f459,f1824]) ).
fof(f1824,plain,
( spl0_200
<=> ! [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_200])]) ).
fof(f459,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1822,plain,
spl0_199,
inference(avatar_split_clause,[],[f458,f1820]) ).
fof(f458,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/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1818,plain,
spl0_198,
inference(avatar_split_clause,[],[f457,f1816]) ).
fof(f457,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/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1814,plain,
spl0_197,
inference(avatar_split_clause,[],[f414,f1812]) ).
fof(f414,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f1810,plain,
spl0_196,
inference(avatar_split_clause,[],[f409,f1808]) ).
fof(f1808,plain,
( spl0_196
<=> ! [X3] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X3),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f409,axiom,
! [X3] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X3),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__minus_0) ).
fof(f1806,plain,
spl0_195,
inference(avatar_split_clause,[],[f382,f1804]) ).
fof(f1804,plain,
( spl0_195
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f382,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
fof(f1802,plain,
spl0_194,
inference(avatar_split_clause,[],[f294,f1800]) ).
fof(f1800,plain,
( spl0_194
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f294,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_1) ).
fof(f1798,plain,
( spl0_193
| ~ spl0_59
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1735,f1698,f1184,f1796]) ).
fof(f1796,plain,
( spl0_193
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1735,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_RealDef_Oreal) = X0
| ~ spl0_59
| ~ spl0_175 ),
inference(resolution,[],[f1699,f1186]) ).
fof(f1794,plain,
spl0_192,
inference(avatar_split_clause,[],[f246,f1792]) ).
fof(f246,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1790,plain,
spl0_191,
inference(avatar_split_clause,[],[f242,f1788]) ).
fof(f1788,plain,
( spl0_191
<=> ! [X29,X14] : c_HOL_Otimes__class_Otimes(X14,X29,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X29,X14,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f242,axiom,
! [X29,X14] : c_HOL_Otimes__class_Otimes(X14,X29,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X29,X14,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f1786,plain,
spl0_190,
inference(avatar_split_clause,[],[f198,f1784]) ).
fof(f1784,plain,
( spl0_190
<=> ! [X0,X3] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f198,axiom,
! [X3,X0] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__def_1) ).
fof(f1782,plain,
spl0_189,
inference(avatar_split_clause,[],[f129,f1780]) ).
fof(f1780,plain,
( spl0_189
<=> ! [X3] : c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(X3),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f129,axiom,
! [X3] : c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(X3),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__minus_0) ).
fof(f1778,plain,
spl0_188,
inference(avatar_split_clause,[],[f122,f1776]) ).
fof(f1776,plain,
( spl0_188
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f122,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f1774,plain,
spl0_187,
inference(avatar_split_clause,[],[f86,f1772]) ).
fof(f86,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/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1770,plain,
spl0_186,
inference(avatar_split_clause,[],[f85,f1768]) ).
fof(f1768,plain,
( spl0_186
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f85,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f1766,plain,
spl0_185,
inference(avatar_split_clause,[],[f84,f1764]) ).
fof(f84,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1754,plain,
( spl0_184
| ~ spl0_59
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1733,f1694,f1184,f1752]) ).
fof(f1752,plain,
( spl0_184
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1733,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_RealDef_Oreal) = X0
| ~ spl0_59
| ~ spl0_174 ),
inference(resolution,[],[f1695,f1186]) ).
fof(f1732,plain,
spl0_183,
inference(avatar_split_clause,[],[f719,f1730]) ).
fof(f719,axiom,
! [X29,X14] :
( c_lessequals(X14,X29,tc_RealDef_Oreal)
| c_lessequals(X29,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1728,plain,
spl0_182,
inference(avatar_split_clause,[],[f701,f1726]) ).
fof(f1726,plain,
( spl0_182
<=> ! [X14] : c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(X14),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f701,axiom,
! [X14] : c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(X14),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__cnj_0) ).
fof(f1724,plain,
spl0_181,
inference(avatar_split_clause,[],[f673,f1722]) ).
fof(f673,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_lessequals(X3,X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f1720,plain,
spl0_180,
inference(avatar_split_clause,[],[f623,f1718]) ).
fof(f623,axiom,
! [X3] : c_Complex_OIm(c_Complex_Ocnj(X3)) = c_HOL_Ouminus__class_Ouminus(c_Complex_OIm(X3),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Im__cnj_0) ).
fof(f1716,plain,
spl0_179,
inference(avatar_split_clause,[],[f600,f1714]) ).
fof(f600,axiom,
! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1712,plain,
spl0_178,
inference(avatar_split_clause,[],[f578,f1710]) ).
fof(f578,axiom,
! [X3,X4] :
( X3 = X4
| c_Complex_Ocnj(X3) != c_Complex_Ocnj(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
fof(f1708,plain,
spl0_177,
inference(avatar_split_clause,[],[f498,f1706]) ).
fof(f1706,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f498,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1704,plain,
spl0_176,
inference(avatar_split_clause,[],[f137,f1702]) ).
fof(f1702,plain,
( spl0_176
<=> ! [X4,X3] :
( X3 = X4
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f137,axiom,
! [X3,X4] :
( X3 = X4
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
fof(f1700,plain,
spl0_175,
inference(avatar_split_clause,[],[f46,f1698]) ).
fof(f46,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1696,plain,
spl0_174,
inference(avatar_split_clause,[],[f35,f1694]) ).
fof(f35,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1689,plain,
spl0_173,
inference(avatar_split_clause,[],[f884,f1687]) ).
fof(f1687,plain,
( spl0_173
<=> ! [X36] :
( ~ class_HOL_Oeq(X36)
| ~ class_HOL_Ozero(X36)
| class_HOL_Oeq(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f884,axiom,
! [X36] :
( ~ class_HOL_Oeq(X36)
| ~ class_HOL_Ozero(X36)
| class_HOL_Oeq(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Oeq) ).
fof(f1685,plain,
spl0_172,
inference(avatar_split_clause,[],[f708,f1683]) ).
fof(f708,axiom,
! [X3] : c_lessequals(c_Complex_ORe(X3),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_0) ).
fof(f1681,plain,
spl0_171,
inference(avatar_split_clause,[],[f454,f1679]) ).
fof(f1679,plain,
( spl0_171
<=> ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f454,axiom,
! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__gt__zero_0) ).
fof(f1677,plain,
spl0_170,
inference(avatar_split_clause,[],[f342,f1675]) ).
fof(f342,axiom,
! [X7,X15] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X15,X7),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).
fof(f1673,plain,
spl0_169,
inference(avatar_split_clause,[],[f247,f1671]) ).
fof(f1671,plain,
( spl0_169
<=> ! [X3] : ~ c_lessequals(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f247,axiom,
! [X3] : ~ c_lessequals(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__exp__le__zero_0) ).
fof(f1669,plain,
spl0_168,
inference(avatar_split_clause,[],[f132,f1667]) ).
fof(f1667,plain,
( spl0_168
<=> ! [X3] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f132,axiom,
! [X3] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__ge__zero_0) ).
fof(f1665,plain,
spl0_167,
inference(avatar_split_clause,[],[f65,f1663]) ).
fof(f1663,plain,
( spl0_167
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f65,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__pos__poly__0_0) ).
fof(f1661,plain,
spl0_166,
inference(avatar_split_clause,[],[f47,f1659]) ).
fof(f1659,plain,
( spl0_166
<=> ! [X3] : ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f47,axiom,
! [X3] : ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X3,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__exp__less__zero_0) ).
fof(f1655,plain,
spl0_165,
inference(avatar_split_clause,[],[f726,f1653]) ).
fof(f1653,plain,
( spl0_165
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f726,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1651,plain,
spl0_164,
inference(avatar_split_clause,[],[f725,f1649]) ).
fof(f1649,plain,
( spl0_164
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f725,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1647,plain,
spl0_163,
inference(avatar_split_clause,[],[f572,f1645]) ).
fof(f1645,plain,
( spl0_163
<=> ! [X3] : c_Complex_ORe(X3) = c_Complex_ORe(c_Complex_Ocnj(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f572,axiom,
! [X3] : c_Complex_ORe(X3) = c_Complex_ORe(c_Complex_Ocnj(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__cnj_0) ).
fof(f1643,plain,
spl0_162,
inference(avatar_split_clause,[],[f556,f1641]) ).
fof(f1641,plain,
( spl0_162
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f556,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1639,plain,
spl0_161,
inference(avatar_split_clause,[],[f554,f1637]) ).
fof(f1637,plain,
( spl0_161
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f554,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1635,plain,
spl0_160,
inference(avatar_split_clause,[],[f553,f1633]) ).
fof(f1633,plain,
( spl0_160
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f553,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1631,plain,
spl0_159,
inference(avatar_split_clause,[],[f537,f1628]) ).
fof(f537,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_OIm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Ozero_0) ).
fof(f1626,plain,
spl0_158,
inference(avatar_split_clause,[],[f258,f1623]) ).
fof(f258,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ozero_0) ).
fof(f1621,plain,
spl0_157,
inference(avatar_split_clause,[],[f236,f1618]) ).
fof(f236,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
fof(f1616,plain,
spl0_156,
inference(avatar_split_clause,[],[f216,f1613]) ).
fof(f1613,plain,
( spl0_156
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f216,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
fof(f1611,plain,
spl0_155,
inference(avatar_split_clause,[],[f199,f1609]) ).
fof(f1609,plain,
( spl0_155
<=> ! [X0,X3] :
( ~ class_HOL_Oeq(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f199,axiom,
! [X3,X0] :
( ~ class_HOL_Oeq(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__class_Oeq__refl_0) ).
fof(f1607,plain,
spl0_154,
inference(avatar_split_clause,[],[f36,f1604]) ).
fof(f1604,plain,
( spl0_154
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f36,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__zero__zero_0) ).
fof(f1602,plain,
spl0_153,
inference(avatar_split_clause,[],[f736,f1600]) ).
fof(f736,axiom,
! [X25] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X25,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,X25),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1598,plain,
spl0_152,
inference(avatar_split_clause,[],[f883,f1596]) ).
fof(f1596,plain,
( spl0_152
<=> ! [X36] :
( ~ class_HOL_Ozero(X36)
| class_HOL_Ozero(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f883,axiom,
! [X36] :
( ~ class_HOL_Ozero(X36)
| class_HOL_Ozero(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(f1594,plain,
spl0_151,
inference(avatar_split_clause,[],[f882,f1592]) ).
fof(f1592,plain,
( spl0_151
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_Power_Opower(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f882,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_Power_Opower(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(f1590,plain,
spl0_150,
inference(avatar_split_clause,[],[f881,f1588]) ).
fof(f1588,plain,
( spl0_150
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f881,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f1586,plain,
spl0_149,
inference(avatar_split_clause,[],[f880,f1584]) ).
fof(f1584,plain,
( spl0_149
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f880,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f1582,plain,
spl0_148,
inference(avatar_split_clause,[],[f879,f1580]) ).
fof(f879,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f1578,plain,
spl0_147,
inference(avatar_split_clause,[],[f878,f1576]) ).
fof(f1576,plain,
( spl0_147
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f878,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f1574,plain,
spl0_146,
inference(avatar_split_clause,[],[f877,f1572]) ).
fof(f1572,plain,
( spl0_146
<=> ! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f877,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(f1570,plain,
spl0_145,
inference(avatar_split_clause,[],[f876,f1568]) ).
fof(f1568,plain,
( spl0_145
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring(X36)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f876,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring(X36)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(f1566,plain,
spl0_144,
inference(avatar_split_clause,[],[f875,f1564]) ).
fof(f1564,plain,
( spl0_144
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f875,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
fof(f1562,plain,
spl0_143,
inference(avatar_split_clause,[],[f874,f1560]) ).
fof(f1560,plain,
( spl0_143
<=> ! [X36] :
( ~ class_OrderedGroup_Oab__group__add(X36)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f874,axiom,
! [X36] :
( ~ class_OrderedGroup_Oab__group__add(X36)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(f1558,plain,
spl0_142,
inference(avatar_split_clause,[],[f873,f1556]) ).
fof(f1556,plain,
( spl0_142
<=> ! [X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f873,axiom,
! [X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(f1554,plain,
spl0_141,
inference(avatar_split_clause,[],[f872,f1552]) ).
fof(f1552,plain,
( spl0_141
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f872,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(f1550,plain,
spl0_140,
inference(avatar_split_clause,[],[f871,f1548]) ).
fof(f1548,plain,
( spl0_140
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f871,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(f1546,plain,
spl0_139,
inference(avatar_split_clause,[],[f870,f1544]) ).
fof(f1544,plain,
( spl0_139
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f870,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(f1542,plain,
spl0_138,
inference(avatar_split_clause,[],[f869,f1540]) ).
fof(f1540,plain,
( spl0_138
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f869,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(f1538,plain,
spl0_137,
inference(avatar_split_clause,[],[f868,f1536]) ).
fof(f1536,plain,
( spl0_137
<=> ! [X36] :
( ~ class_OrderedGroup_Oab__group__add(X36)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f868,axiom,
! [X36] :
( ~ class_OrderedGroup_Oab__group__add(X36)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(f1534,plain,
spl0_136,
inference(avatar_split_clause,[],[f867,f1532]) ).
fof(f1532,plain,
( spl0_136
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f867,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(f1530,plain,
spl0_135,
inference(avatar_split_clause,[],[f866,f1528]) ).
fof(f1528,plain,
( spl0_135
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f866,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(f1526,plain,
spl0_134,
inference(avatar_split_clause,[],[f865,f1524]) ).
fof(f1524,plain,
( spl0_134
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f865,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(f1522,plain,
spl0_133,
inference(avatar_split_clause,[],[f864,f1520]) ).
fof(f1520,plain,
( spl0_133
<=> ! [X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f864,axiom,
! [X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(f1518,plain,
spl0_132,
inference(avatar_split_clause,[],[f863,f1516]) ).
fof(f1516,plain,
( spl0_132
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f863,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(f1514,plain,
spl0_131,
inference(avatar_split_clause,[],[f862,f1512]) ).
fof(f1512,plain,
( spl0_131
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f862,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(f1510,plain,
spl0_130,
inference(avatar_split_clause,[],[f861,f1508]) ).
fof(f1508,plain,
( spl0_130
<=> ! [X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f861,axiom,
! [X36] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(f1506,plain,
spl0_129,
inference(avatar_split_clause,[],[f860,f1504]) ).
fof(f1504,plain,
( spl0_129
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f860,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1502,plain,
spl0_128,
inference(avatar_split_clause,[],[f859,f1500]) ).
fof(f1500,plain,
( spl0_128
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f859,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(f1498,plain,
spl0_127,
inference(avatar_split_clause,[],[f858,f1496]) ).
fof(f1496,plain,
( spl0_127
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f858,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1494,plain,
spl0_126,
inference(avatar_split_clause,[],[f857,f1492]) ).
fof(f1492,plain,
( spl0_126
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f857,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1490,plain,
spl0_125,
inference(avatar_split_clause,[],[f856,f1488]) ).
fof(f1488,plain,
( spl0_125
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f856,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(f1486,plain,
spl0_124,
inference(avatar_split_clause,[],[f855,f1484]) ).
fof(f1484,plain,
( spl0_124
<=> ! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f855,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(f1482,plain,
spl0_123,
inference(avatar_split_clause,[],[f854,f1480]) ).
fof(f1480,plain,
( spl0_123
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f854,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(f1478,plain,
spl0_122,
inference(avatar_split_clause,[],[f853,f1476]) ).
fof(f1476,plain,
( spl0_122
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f853,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
fof(f1474,plain,
spl0_121,
inference(avatar_split_clause,[],[f852,f1472]) ).
fof(f1472,plain,
( spl0_121
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f852,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(f1470,plain,
spl0_120,
inference(avatar_split_clause,[],[f851,f1468]) ).
fof(f1468,plain,
( spl0_120
<=> ! [X36] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f851,axiom,
! [X36] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1466,plain,
spl0_119,
inference(avatar_split_clause,[],[f850,f1464]) ).
fof(f1464,plain,
( spl0_119
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f850,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(f1462,plain,
spl0_118,
inference(avatar_split_clause,[],[f849,f1460]) ).
fof(f1460,plain,
( spl0_118
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f849,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(f1458,plain,
spl0_117,
inference(avatar_split_clause,[],[f848,f1456]) ).
fof(f1456,plain,
( spl0_117
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f848,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(f1454,plain,
spl0_116,
inference(avatar_split_clause,[],[f847,f1452]) ).
fof(f1452,plain,
( spl0_116
<=> ! [X36] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f847,axiom,
! [X36] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1450,plain,
spl0_115,
inference(avatar_split_clause,[],[f846,f1448]) ).
fof(f1448,plain,
( spl0_115
<=> ! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f846,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1446,plain,
spl0_114,
inference(avatar_split_clause,[],[f845,f1444]) ).
fof(f1444,plain,
( spl0_114
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f845,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1442,plain,
spl0_113,
inference(avatar_split_clause,[],[f844,f1440]) ).
fof(f1440,plain,
( spl0_113
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f844,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1438,plain,
spl0_112,
inference(avatar_split_clause,[],[f843,f1436]) ).
fof(f1436,plain,
( spl0_112
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f843,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1434,plain,
spl0_111,
inference(avatar_split_clause,[],[f842,f1432]) ).
fof(f1432,plain,
( spl0_111
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f842,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1430,plain,
spl0_110,
inference(avatar_split_clause,[],[f841,f1428]) ).
fof(f1428,plain,
( spl0_110
<=> ! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f841,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oidom(X36)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1426,plain,
spl0_109,
inference(avatar_split_clause,[],[f840,f1424]) ).
fof(f1424,plain,
( spl0_109
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f840,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1422,plain,
spl0_108,
inference(avatar_split_clause,[],[f839,f1420]) ).
fof(f1420,plain,
( spl0_108
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f839,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1418,plain,
spl0_107,
inference(avatar_split_clause,[],[f838,f1416]) ).
fof(f1416,plain,
( spl0_107
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f838,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1414,plain,
spl0_106,
inference(avatar_split_clause,[],[f837,f1412]) ).
fof(f1412,plain,
( spl0_106
<=> ! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f837,axiom,
! [X36] :
( ~ class_Ring__and__Field_Oordered__idom(X36)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1410,plain,
spl0_105,
inference(avatar_split_clause,[],[f739,f1408]) ).
fof(f1408,plain,
( spl0_105
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f739,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(f1406,plain,
spl0_104,
inference(avatar_split_clause,[],[f738,f1404]) ).
fof(f1404,plain,
( spl0_104
<=> ! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring(X36)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f738,axiom,
! [X36] :
( ~ class_Ring__and__Field_Ocomm__ring(X36)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(f1402,plain,
spl0_103,
inference(avatar_split_clause,[],[f737,f1400]) ).
fof(f1400,plain,
( spl0_103
<=> ! [X36] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f737,axiom,
! [X36] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1398,plain,
~ spl0_102,
inference(avatar_split_clause,[],[f705,f1395]) ).
fof(f705,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cs0_0) ).
fof(f1393,plain,
spl0_101,
inference(avatar_split_clause,[],[f466,f1391]) ).
fof(f1391,plain,
( spl0_101
<=> ! [X0,X3] : c_Fun_Oid(X3,X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f466,axiom,
! [X3,X0] : c_Fun_Oid(X3,X0) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
fof(f1389,plain,
spl0_100,
inference(avatar_split_clause,[],[f407,f1387]) ).
fof(f407,axiom,
! [X14] : c_Complex_Ocnj(c_Complex_Ocnj(X14)) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
fof(f1385,plain,
spl0_99,
inference(avatar_split_clause,[],[f723,f1383]) ).
fof(f723,axiom,
! [X29] : c_lessequals(X29,X29,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1381,plain,
spl0_98,
inference(avatar_split_clause,[],[f555,f1379]) ).
fof(f1379,plain,
( spl0_98
<=> ! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f555,axiom,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f1377,plain,
spl0_97,
inference(avatar_split_clause,[],[f836,f1374]) ).
fof(f1374,plain,
( spl0_97
<=> class_HOL_Oeq(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f836,axiom,
class_HOL_Oeq(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Oeq) ).
fof(f1372,plain,
spl0_96,
inference(avatar_split_clause,[],[f835,f1369]) ).
fof(f1369,plain,
( spl0_96
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f835,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f1367,plain,
spl0_95,
inference(avatar_split_clause,[],[f834,f1364]) ).
fof(f1364,plain,
( spl0_95
<=> class_SEQ_Obanach(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f834,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
fof(f1362,plain,
spl0_94,
inference(avatar_split_clause,[],[f833,f1359]) ).
fof(f1359,plain,
( spl0_94
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f833,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f1357,plain,
spl0_93,
inference(avatar_split_clause,[],[f832,f1354]) ).
fof(f1354,plain,
( spl0_93
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f832,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1352,plain,
spl0_92,
inference(avatar_split_clause,[],[f831,f1349]) ).
fof(f831,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1347,plain,
spl0_91,
inference(avatar_split_clause,[],[f830,f1344]) ).
fof(f1344,plain,
( spl0_91
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f830,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1342,plain,
spl0_90,
inference(avatar_split_clause,[],[f829,f1339]) ).
fof(f829,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1337,plain,
spl0_89,
inference(avatar_split_clause,[],[f828,f1334]) ).
fof(f828,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1332,plain,
spl0_88,
inference(avatar_split_clause,[],[f827,f1329]) ).
fof(f1329,plain,
( spl0_88
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f827,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1327,plain,
spl0_87,
inference(avatar_split_clause,[],[f826,f1324]) ).
fof(f1324,plain,
( spl0_87
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f826,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1322,plain,
spl0_86,
inference(avatar_split_clause,[],[f825,f1319]) ).
fof(f1319,plain,
( spl0_86
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f825,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f1317,plain,
spl0_85,
inference(avatar_split_clause,[],[f824,f1314]) ).
fof(f824,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1312,plain,
spl0_84,
inference(avatar_split_clause,[],[f823,f1309]) ).
fof(f1309,plain,
( spl0_84
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f823,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1307,plain,
spl0_83,
inference(avatar_split_clause,[],[f822,f1304]) ).
fof(f822,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1302,plain,
spl0_82,
inference(avatar_split_clause,[],[f821,f1299]) ).
fof(f1299,plain,
( spl0_82
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f821,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1297,plain,
spl0_81,
inference(avatar_split_clause,[],[f820,f1294]) ).
fof(f1294,plain,
( spl0_81
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f820,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f1292,plain,
spl0_80,
inference(avatar_split_clause,[],[f819,f1289]) ).
fof(f1289,plain,
( spl0_80
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f819,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1287,plain,
spl0_79,
inference(avatar_split_clause,[],[f818,f1284]) ).
fof(f1284,plain,
( spl0_79
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f818,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1282,plain,
spl0_78,
inference(avatar_split_clause,[],[f817,f1279]) ).
fof(f817,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1277,plain,
spl0_77,
inference(avatar_split_clause,[],[f816,f1274]) ).
fof(f1274,plain,
( spl0_77
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f816,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1272,plain,
spl0_76,
inference(avatar_split_clause,[],[f815,f1269]) ).
fof(f1269,plain,
( spl0_76
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f815,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1267,plain,
spl0_75,
inference(avatar_split_clause,[],[f814,f1264]) ).
fof(f1264,plain,
( spl0_75
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f814,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1262,plain,
spl0_74,
inference(avatar_split_clause,[],[f813,f1259]) ).
fof(f813,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1257,plain,
spl0_73,
inference(avatar_split_clause,[],[f812,f1254]) ).
fof(f1254,plain,
( spl0_73
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f812,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f1252,plain,
spl0_72,
inference(avatar_split_clause,[],[f811,f1249]) ).
fof(f1249,plain,
( spl0_72
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f811,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f1247,plain,
spl0_71,
inference(avatar_split_clause,[],[f810,f1244]) ).
fof(f1244,plain,
( spl0_71
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f810,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1242,plain,
spl0_70,
inference(avatar_split_clause,[],[f809,f1239]) ).
fof(f1239,plain,
( spl0_70
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f809,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f1237,plain,
spl0_69,
inference(avatar_split_clause,[],[f808,f1234]) ).
fof(f1234,plain,
( spl0_69
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f808,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1232,plain,
spl0_68,
inference(avatar_split_clause,[],[f807,f1229]) ).
fof(f1229,plain,
( spl0_68
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f807,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1227,plain,
spl0_67,
inference(avatar_split_clause,[],[f806,f1224]) ).
fof(f1224,plain,
( spl0_67
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f806,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1222,plain,
spl0_66,
inference(avatar_split_clause,[],[f805,f1219]) ).
fof(f1219,plain,
( spl0_66
<=> class_HOL_Oeq(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f805,axiom,
class_HOL_Oeq(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Oeq) ).
fof(f1217,plain,
spl0_65,
inference(avatar_split_clause,[],[f804,f1214]) ).
fof(f1214,plain,
( spl0_65
<=> class_HOL_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f804,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
fof(f1212,plain,
spl0_64,
inference(avatar_split_clause,[],[f803,f1209]) ).
fof(f1209,plain,
( spl0_64
<=> class_SEQ_Obanach(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f803,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
fof(f1207,plain,
spl0_63,
inference(avatar_split_clause,[],[f802,f1204]) ).
fof(f1204,plain,
( spl0_63
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f802,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
fof(f1202,plain,
spl0_62,
inference(avatar_split_clause,[],[f801,f1199]) ).
fof(f1199,plain,
( spl0_62
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f801,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1197,plain,
spl0_61,
inference(avatar_split_clause,[],[f800,f1194]) ).
fof(f800,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1192,plain,
spl0_60,
inference(avatar_split_clause,[],[f799,f1189]) ).
fof(f1189,plain,
( spl0_60
<=> class_Lattices_Olattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f799,axiom,
class_Lattices_Olattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olattice) ).
fof(f1187,plain,
spl0_59,
inference(avatar_split_clause,[],[f798,f1184]) ).
fof(f798,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1182,plain,
spl0_58,
inference(avatar_split_clause,[],[f797,f1179]) ).
fof(f797,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1177,plain,
spl0_57,
inference(avatar_split_clause,[],[f796,f1174]) ).
fof(f796,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1172,plain,
spl0_56,
inference(avatar_split_clause,[],[f795,f1169]) ).
fof(f1169,plain,
( spl0_56
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f795,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1167,plain,
spl0_55,
inference(avatar_split_clause,[],[f794,f1164]) ).
fof(f1164,plain,
( spl0_55
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f794,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
fof(f1162,plain,
spl0_54,
inference(avatar_split_clause,[],[f793,f1159]) ).
fof(f793,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1157,plain,
spl0_53,
inference(avatar_split_clause,[],[f792,f1154]) ).
fof(f792,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f1152,plain,
spl0_52,
inference(avatar_split_clause,[],[f791,f1149]) ).
fof(f1149,plain,
( spl0_52
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f791,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f1147,plain,
spl0_51,
inference(avatar_split_clause,[],[f790,f1144]) ).
fof(f1144,plain,
( spl0_51
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f790,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f1142,plain,
spl0_50,
inference(avatar_split_clause,[],[f789,f1139]) ).
fof(f1139,plain,
( spl0_50
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f789,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
fof(f1137,plain,
spl0_49,
inference(avatar_split_clause,[],[f788,f1134]) ).
fof(f1134,plain,
( spl0_49
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f788,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
fof(f1132,plain,
spl0_48,
inference(avatar_split_clause,[],[f787,f1129]) ).
fof(f787,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1127,plain,
spl0_47,
inference(avatar_split_clause,[],[f786,f1124]) ).
fof(f1124,plain,
( spl0_47
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f786,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
fof(f1122,plain,
spl0_46,
inference(avatar_split_clause,[],[f785,f1119]) ).
fof(f785,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
fof(f1117,plain,
spl0_45,
inference(avatar_split_clause,[],[f784,f1114]) ).
fof(f1114,plain,
( spl0_45
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f784,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f1112,plain,
spl0_44,
inference(avatar_split_clause,[],[f783,f1109]) ).
fof(f1109,plain,
( spl0_44
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f783,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f1107,plain,
spl0_43,
inference(avatar_split_clause,[],[f782,f1104]) ).
fof(f782,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1102,plain,
spl0_42,
inference(avatar_split_clause,[],[f781,f1099]) ).
fof(f1099,plain,
( spl0_42
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f781,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f1097,plain,
spl0_41,
inference(avatar_split_clause,[],[f780,f1094]) ).
fof(f1094,plain,
( spl0_41
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f780,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f1092,plain,
spl0_40,
inference(avatar_split_clause,[],[f779,f1089]) ).
fof(f1089,plain,
( spl0_40
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f779,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
fof(f1087,plain,
spl0_39,
inference(avatar_split_clause,[],[f778,f1084]) ).
fof(f1084,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f778,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
fof(f1082,plain,
spl0_38,
inference(avatar_split_clause,[],[f777,f1079]) ).
fof(f1079,plain,
( spl0_38
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f777,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f1077,plain,
spl0_37,
inference(avatar_split_clause,[],[f776,f1074]) ).
fof(f1074,plain,
( spl0_37
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f776,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1072,plain,
spl0_36,
inference(avatar_split_clause,[],[f775,f1069]) ).
fof(f775,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1067,plain,
spl0_35,
inference(avatar_split_clause,[],[f774,f1064]) ).
fof(f1064,plain,
( spl0_35
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f774,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f1062,plain,
spl0_34,
inference(avatar_split_clause,[],[f773,f1059]) ).
fof(f1059,plain,
( spl0_34
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f773,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f1057,plain,
spl0_33,
inference(avatar_split_clause,[],[f772,f1054]) ).
fof(f1054,plain,
( spl0_33
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f772,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1052,plain,
spl0_32,
inference(avatar_split_clause,[],[f771,f1049]) ).
fof(f771,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1047,plain,
spl0_31,
inference(avatar_split_clause,[],[f770,f1044]) ).
fof(f1044,plain,
( spl0_31
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f770,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1042,plain,
spl0_30,
inference(avatar_split_clause,[],[f769,f1039]) ).
fof(f1039,plain,
( spl0_30
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f769,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
fof(f1037,plain,
spl0_29,
inference(avatar_split_clause,[],[f768,f1034]) ).
fof(f1034,plain,
( spl0_29
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f768,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
fof(f1032,plain,
spl0_28,
inference(avatar_split_clause,[],[f767,f1029]) ).
fof(f1029,plain,
( spl0_28
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f767,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f1027,plain,
spl0_27,
inference(avatar_split_clause,[],[f766,f1024]) ).
fof(f1024,plain,
( spl0_27
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f766,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
fof(f1022,plain,
spl0_26,
inference(avatar_split_clause,[],[f765,f1019]) ).
fof(f1019,plain,
( spl0_26
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f765,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
fof(f1017,plain,
spl0_25,
inference(avatar_split_clause,[],[f764,f1014]) ).
fof(f1014,plain,
( spl0_25
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f764,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1012,plain,
spl0_24,
inference(avatar_split_clause,[],[f763,f1009]) ).
fof(f1009,plain,
( spl0_24
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f763,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f1007,plain,
spl0_23,
inference(avatar_split_clause,[],[f762,f1004]) ).
fof(f1004,plain,
( spl0_23
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f762,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f1002,plain,
spl0_22,
inference(avatar_split_clause,[],[f761,f999]) ).
fof(f999,plain,
( spl0_22
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f761,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f997,plain,
spl0_21,
inference(avatar_split_clause,[],[f760,f994]) ).
fof(f994,plain,
( spl0_21
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f760,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f992,plain,
spl0_20,
inference(avatar_split_clause,[],[f759,f989]) ).
fof(f989,plain,
( spl0_20
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f759,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
fof(f987,plain,
spl0_19,
inference(avatar_split_clause,[],[f758,f984]) ).
fof(f984,plain,
( spl0_19
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f758,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f982,plain,
spl0_18,
inference(avatar_split_clause,[],[f757,f979]) ).
fof(f979,plain,
( spl0_18
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f757,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f977,plain,
spl0_17,
inference(avatar_split_clause,[],[f756,f974]) ).
fof(f974,plain,
( spl0_17
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f756,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f972,plain,
spl0_16,
inference(avatar_split_clause,[],[f755,f969]) ).
fof(f969,plain,
( spl0_16
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f755,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f967,plain,
spl0_15,
inference(avatar_split_clause,[],[f754,f964]) ).
fof(f754,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f962,plain,
spl0_14,
inference(avatar_split_clause,[],[f753,f959]) ).
fof(f959,plain,
( spl0_14
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f753,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f957,plain,
spl0_13,
inference(avatar_split_clause,[],[f752,f954]) ).
fof(f954,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f752,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f952,plain,
spl0_12,
inference(avatar_split_clause,[],[f751,f949]) ).
fof(f949,plain,
( spl0_12
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f751,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f947,plain,
spl0_11,
inference(avatar_split_clause,[],[f750,f944]) ).
fof(f944,plain,
( spl0_11
<=> class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f750,axiom,
class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) ).
fof(f942,plain,
spl0_10,
inference(avatar_split_clause,[],[f749,f939]) ).
fof(f939,plain,
( spl0_10
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f749,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f937,plain,
spl0_9,
inference(avatar_split_clause,[],[f748,f934]) ).
fof(f934,plain,
( spl0_9
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f748,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f932,plain,
spl0_8,
inference(avatar_split_clause,[],[f747,f929]) ).
fof(f929,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f747,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f927,plain,
spl0_7,
inference(avatar_split_clause,[],[f746,f924]) ).
fof(f924,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f746,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f922,plain,
spl0_6,
inference(avatar_split_clause,[],[f745,f919]) ).
fof(f919,plain,
( spl0_6
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f745,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
fof(f917,plain,
spl0_5,
inference(avatar_split_clause,[],[f744,f914]) ).
fof(f914,plain,
( spl0_5
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f744,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
fof(f912,plain,
spl0_4,
inference(avatar_split_clause,[],[f743,f909]) ).
fof(f909,plain,
( spl0_4
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f743,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f907,plain,
spl0_3,
inference(avatar_split_clause,[],[f742,f904]) ).
fof(f904,plain,
( spl0_3
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f742,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f902,plain,
spl0_2,
inference(avatar_split_clause,[],[f741,f899]) ).
fof(f899,plain,
( spl0_2
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f741,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f897,plain,
spl0_1,
inference(avatar_split_clause,[],[f740,f894]) ).
fof(f894,plain,
( spl0_1
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f740,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ALG387-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 19:58:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (11355)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.40 % (11358)WARNING: value z3 for option sas not known
% 0.14/0.40 % (11357)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (11359)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (11356)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (11358)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.40 % (11360)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.40 % (11361)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.41 % (11362)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)
% 0.20/0.49 TRYING [1]
% 0.20/0.50 TRYING [2]
% 2.37/0.72 TRYING [3]
% 2.79/0.77 TRYING [1]
% 2.79/0.81 TRYING [2]
% 4.48/1.03 % (11360)First to succeed.
% 4.48/1.05 % (11360)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11355"
% 4.48/1.05 % (11360)Refutation found. Thanks to Tanya!
% 4.48/1.05 % SZS status Unsatisfiable for theBenchmark
% 4.48/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 4.48/1.07 % (11360)------------------------------
% 4.48/1.07 % (11360)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.48/1.07 % (11360)Termination reason: Refutation
% 4.48/1.07
% 4.48/1.07 % (11360)Memory used [KB]: 10406
% 4.48/1.07 % (11360)Time elapsed: 0.639 s
% 4.48/1.07 % (11360)Instructions burned: 1625 (million)
% 4.48/1.07 % (11355)Success in time 0.7 s
%------------------------------------------------------------------------------