TSTP Solution File: ALG424-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG424-1 : 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 : n019.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 04:30:22 EDT 2024
% Result : Unsatisfiable 2.30s 0.73s
% Output : Refutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1404
% Syntax : Number of formulae : 2258 ( 764 unt; 0 def)
% Number of atoms : 5475 ( 862 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 5598 (2381 ~;2488 |; 0 &)
% ( 729 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 795 ( 793 usr; 730 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 6 con; 0-3 aty)
% Number of variables : 3487 (3487 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11035,plain,
$false,
inference(avatar_sat_refutation,[],[f1041,f1046,f1051,f1056,f1061,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1101,f1106,f1111,f1116,f1121,f1126,f1131,f1136,f1141,f1146,f1151,f1156,f1161,f1166,f1171,f1176,f1181,f1186,f1191,f1196,f1201,f1206,f1211,f1216,f1221,f1226,f1231,f1236,f1241,f1246,f1251,f1256,f1261,f1266,f1271,f1276,f1281,f1286,f1291,f1296,f1301,f1306,f1311,f1316,f1321,f1326,f1331,f1336,f1341,f1346,f1351,f1356,f1361,f1366,f1371,f1376,f1381,f1386,f1391,f1396,f1401,f1405,f1409,f1414,f1418,f1422,f1427,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1492,f1496,f1500,f1504,f1508,f1512,f1516,f1520,f1524,f1528,f1532,f1536,f1540,f1544,f1548,f1552,f1556,f1560,f1564,f1568,f1572,f1576,f1580,f1584,f1588,f1592,f1596,f1600,f1604,f1608,f1612,f1616,f1620,f1624,f1628,f1632,f1636,f1640,f1644,f1648,f1652,f1656,f1660,f1664,f1668,f1672,f1676,f1680,f1684,f1688,f1692,f1696,f1700,f1705,f1711,f1715,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1753,f1757,f1761,f1765,f1769,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1829,f1833,f1837,f1841,f1845,f1849,f1853,f1857,f1861,f1865,f1869,f1873,f1877,f1881,f1885,f1889,f1893,f1906,f1969,f1998,f2020,f2024,f2028,f2032,f2036,f2040,f2044,f2048,f2052,f2056,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,f2176,f2218,f2263,f2317,f2321,f2325,f2329,f2333,f2337,f2341,f2345,f2349,f2353,f2357,f2361,f2365,f2369,f2373,f2377,f2381,f2385,f2389,f2393,f2397,f2401,f2405,f2409,f2413,f2417,f2421,f2425,f2429,f2433,f2437,f2441,f2445,f2449,f2518,f2550,f2575,f2609,f2613,f2617,f2621,f2625,f2629,f2633,f2637,f2641,f2645,f2649,f2653,f2657,f2661,f2665,f2669,f2673,f2677,f2681,f2685,f2689,f2693,f2697,f2701,f2705,f2709,f2713,f2717,f2721,f2725,f2729,f2733,f2800,f2858,f2896,f2900,f2904,f2908,f2912,f2917,f2921,f2925,f2929,f2933,f2937,f2941,f2945,f2949,f2953,f2957,f2961,f2965,f2969,f2973,f2977,f2981,f2985,f2989,f2993,f2997,f3001,f3005,f3009,f3013,f3017,f3021,f3025,f3029,f3033,f3037,f3041,f3045,f3049,f3053,f3057,f3201,f3314,f3424,f3428,f3432,f3436,f3440,f3444,f3448,f3452,f3456,f3460,f3464,f3468,f3472,f3476,f3480,f3484,f3488,f3492,f3496,f3500,f3514,f3518,f3522,f3526,f3530,f3534,f3538,f3542,f3546,f3550,f3556,f3560,f3564,f3568,f3572,f3576,f3580,f3584,f3588,f3592,f3598,f3602,f3606,f3610,f3614,f3618,f3622,f3626,f3630,f3634,f3647,f3651,f3655,f3659,f3663,f3667,f3671,f3675,f3679,f3683,f3687,f4279,f4464,f4468,f4472,f4476,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4605,f4609,f4613,f4617,f4621,f4625,f4629,f4633,f4637,f4641,f4657,f4970,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5163,f5167,f5171,f5175,f5179,f5183,f5187,f5191,f5195,f5199,f5204,f5208,f5212,f5216,f5220,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5252,f5257,f5820,f5824,f5828,f5832,f5836,f5840,f5844,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5890,f5894,f5898,f5903,f5907,f5911,f5915,f5919,f5923,f5927,f5931,f5935,f5939,f5943,f5947,f5951,f5955,f5959,f5963,f5967,f5971,f5975,f5979,f5983,f5987,f5991,f5995,f5999,f6003,f6007,f6011,f6070,f6117,f6164,f6253,f6257,f6261,f6265,f6269,f6273,f6277,f6281,f6285,f6289,f6293,f6297,f6301,f6305,f6309,f6313,f6317,f6321,f6429,f6593,f6600,f6604,f6608,f6612,f6616,f6620,f6624,f6628,f6632,f6636,f6640,f6644,f6648,f6652,f6656,f6660,f6664,f6668,f6672,f6676,f6680,f6684,f6688,f6692,f6696,f6700,f6704,f6708,f6733,f6942,f7085,f7097,f7101,f7105,f7109,f7113,f7117,f7121,f7125,f7129,f7133,f7137,f7141,f7145,f7149,f7153,f7157,f7161,f7165,f7169,f7173,f7177,f7181,f7185,f7189,f7193,f7197,f7201,f7205,f7209,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7268,f7272,f7299,f7303,f7307,f7311,f7315,f7319,f7323,f7327,f7331,f7335,f7339,f7343,f7347,f7351,f7355,f7359,f7363,f7367,f7371,f7375,f7379,f7383,f7387,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7423,f7427,f7431,f7435,f7439,f7443,f7447,f7451,f7455,f7459,f7510,f7514,f7518,f7522,f7526,f7530,f7534,f7803,f9245,f9249,f9253,f9257,f9261,f9265,f9269,f9273,f9277,f9281,f9307,f9311,f9315,f9319,f9323,f9327,f9331,f9335,f9339,f9343,f9351,f9355,f9359,f9363,f9367,f9371,f9375,f9379,f9383,f9387,f9391,f9395,f9399,f9403,f9407,f9411,f9415,f9419,f9423,f9427,f9431,f9435,f9439,f9443,f9733,f10013,f11013,f11017,f11021,f11025,f11029,f11033,f11034]) ).
fof(f11034,plain,
( ~ spl0_68
| spl0_80
| ~ spl0_148
| ~ spl0_489
| ~ spl0_720 ),
inference(avatar_split_clause,[],[f11009,f9441,f5254,f1702,f1429,f1373]) ).
fof(f1373,plain,
( spl0_68
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1429,plain,
( spl0_80
<=> v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1702,plain,
( spl0_148
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f5254,plain,
( spl0_489
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f9441,plain,
( spl0_720
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X5,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Polynomial_Opoly(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f11009,plain,
( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_489
| ~ spl0_720 ),
inference(trivial_inequality_removal,[],[f11008]) ).
fof(f11008,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_489
| ~ spl0_720 ),
inference(forward_demodulation,[],[f11007,f1704]) ).
fof(f1704,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex)
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1702]) ).
fof(f11007,plain,
( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex)
| ~ spl0_489
| ~ spl0_720 ),
inference(trivial_inequality_removal,[],[f11006]) ).
fof(f11006,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex)
| ~ spl0_489
| ~ spl0_720 ),
inference(superposition,[],[f9442,f5256]) ).
fof(f5256,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex)
| ~ spl0_489 ),
inference(avatar_component_clause,[],[f5254]) ).
fof(f9442,plain,
( ! [X0,X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X5,X6,X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X6
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Polynomial_Opoly(X6,X5,X0) )
| ~ spl0_720 ),
inference(avatar_component_clause,[],[f9441]) ).
fof(f11033,plain,
spl0_729,
inference(avatar_split_clause,[],[f882,f11031]) ).
fof(f11031,plain,
( spl0_729
<=> ! [X0,X14,X5,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X14,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f882,axiom,
! [X0,X7,X14,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X14,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
fof(f11029,plain,
spl0_728,
inference(avatar_split_clause,[],[f534,f11027]) ).
fof(f11027,plain,
( spl0_728
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X5,X0),X14,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X14,X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f534,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X5,X0),X14,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X14,X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
fof(f11025,plain,
spl0_727,
inference(avatar_split_clause,[],[f212,f11023]) ).
fof(f11023,plain,
( spl0_727
<=> ! [X5,X0,X8,X7] :
( ~ 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(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f212,axiom,
! [X0,X8,X7,X5] :
( ~ 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(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f11021,plain,
spl0_726,
inference(avatar_split_clause,[],[f210,f11019]) ).
fof(f11019,plain,
( spl0_726
<=> ! [X0,X5,X8,X7] :
( ~ 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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f210,axiom,
! [X0,X8,X7,X5] :
( ~ 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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f11017,plain,
spl0_725,
inference(avatar_split_clause,[],[f181,f11015]) ).
fof(f11015,plain,
( spl0_725
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X7,X0),c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f181,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X7,X0),c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
fof(f11013,plain,
spl0_724,
inference(avatar_split_clause,[],[f180,f11011]) ).
fof(f11011,plain,
( spl0_724
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X7,X5,X0),X7,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X7,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f180,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X7,X5,X0),X7,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X5,X7,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
fof(f10013,plain,
( ~ spl0_722
| ~ spl0_723
| ~ spl0_205
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f3635,f2216,f2050,f10010,f10006]) ).
fof(f10006,plain,
( spl0_722
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f10010,plain,
( spl0_723
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2050,plain,
( spl0_205
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2216,plain,
( spl0_236
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f3635,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_Complex_Ocomplex)
| ~ spl0_205
| ~ spl0_236 ),
inference(superposition,[],[f2051,f2217]) ).
fof(f2217,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2216]) ).
fof(f2051,plain,
( ! [X0,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2050]) ).
fof(f9733,plain,
( spl0_721
| ~ spl0_299
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f3510,f3458,f2703,f9731]) ).
fof(f9731,plain,
( spl0_721
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2703,plain,
( spl0_299
<=> ! [X13,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oabs__class_Oabs(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f3458,plain,
( spl0_361
<=> ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f3510,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X0),X1,X0) )
| ~ spl0_299
| ~ spl0_361 ),
inference(duplicate_literal_removal,[],[f3501]) ).
fof(f3501,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_299
| ~ spl0_361 ),
inference(resolution,[],[f3459,f2704]) ).
fof(f2704,plain,
( ! [X10,X0,X13] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oabs__class_Oabs(X10,X0),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f2703]) ).
fof(f3459,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f3458]) ).
fof(f9443,plain,
spl0_720,
inference(avatar_split_clause,[],[f903,f9441]) ).
fof(f903,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X5,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Polynomial_Opoly(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f9439,plain,
spl0_719,
inference(avatar_split_clause,[],[f808,f9437]) ).
fof(f9437,plain,
( spl0_719
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f808,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f9435,plain,
( spl0_718
| ~ spl0_302
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f3509,f3458,f2715,f9433]) ).
fof(f9433,plain,
( spl0_718
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f2715,plain,
( spl0_302
<=> ! [X13,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X13,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3509,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) )
| ~ spl0_302
| ~ spl0_361 ),
inference(duplicate_literal_removal,[],[f3508]) ).
fof(f3508,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_302
| ~ spl0_361 ),
inference(resolution,[],[f3459,f2716]) ).
fof(f2716,plain,
( ! [X10,X0,X13] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X13,X0),X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f2715]) ).
fof(f9431,plain,
spl0_717,
inference(avatar_split_clause,[],[f807,f9429]) ).
fof(f9429,plain,
( spl0_717
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f807,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f9427,plain,
spl0_716,
inference(avatar_split_clause,[],[f806,f9425]) ).
fof(f9425,plain,
( spl0_716
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f806,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f9423,plain,
spl0_715,
inference(avatar_split_clause,[],[f805,f9421]) ).
fof(f9421,plain,
( spl0_715
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X7,X5,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f805,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X7,X5,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f9419,plain,
spl0_714,
inference(avatar_split_clause,[],[f768,f9417]) ).
fof(f9417,plain,
( spl0_714
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f768,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f9415,plain,
spl0_713,
inference(avatar_split_clause,[],[f764,f9413]) ).
fof(f9413,plain,
( spl0_713
<=> ! [X0,X7,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f764,axiom,
! [X2,X0,X1,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
fof(f9411,plain,
spl0_712,
inference(avatar_split_clause,[],[f763,f9409]) ).
fof(f9409,plain,
( spl0_712
<=> ! [X0,X7,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f763,axiom,
! [X2,X0,X1,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
fof(f9407,plain,
spl0_711,
inference(avatar_split_clause,[],[f683,f9405]) ).
fof(f9405,plain,
( spl0_711
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X7,X5,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f683,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X7,X5,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f9403,plain,
spl0_710,
inference(avatar_split_clause,[],[f682,f9401]) ).
fof(f9401,plain,
( spl0_710
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f682,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
fof(f9399,plain,
spl0_709,
inference(avatar_split_clause,[],[f681,f9397]) ).
fof(f9397,plain,
( spl0_709
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f681,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f9395,plain,
spl0_708,
inference(avatar_split_clause,[],[f680,f9393]) ).
fof(f9393,plain,
( spl0_708
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f680,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
fof(f9391,plain,
spl0_707,
inference(avatar_split_clause,[],[f678,f9389]) ).
fof(f9389,plain,
( spl0_707
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f678,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f9387,plain,
spl0_706,
inference(avatar_split_clause,[],[f674,f9385]) ).
fof(f9385,plain,
( spl0_706
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f674,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f9383,plain,
spl0_705,
inference(avatar_split_clause,[],[f673,f9381]) ).
fof(f9381,plain,
( spl0_705
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f673,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f9379,plain,
spl0_704,
inference(avatar_split_clause,[],[f672,f9377]) ).
fof(f9377,plain,
( spl0_704
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f672,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
fof(f9375,plain,
spl0_703,
inference(avatar_split_clause,[],[f671,f9373]) ).
fof(f9373,plain,
( spl0_703
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f671,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,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,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f9371,plain,
spl0_702,
inference(avatar_split_clause,[],[f641,f9369]) ).
fof(f9369,plain,
( spl0_702
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X5,X0),X8,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X8,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f641,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X5,X0),X8,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X8,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
fof(f9367,plain,
spl0_701,
inference(avatar_split_clause,[],[f505,f9365]) ).
fof(f9365,plain,
( spl0_701
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f505,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f9363,plain,
spl0_700,
inference(avatar_split_clause,[],[f504,f9361]) ).
fof(f9361,plain,
( spl0_700
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f504,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f9359,plain,
spl0_699,
inference(avatar_split_clause,[],[f503,f9357]) ).
fof(f9357,plain,
( spl0_699
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f503,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f9355,plain,
spl0_698,
inference(avatar_split_clause,[],[f502,f9353]) ).
fof(f9353,plain,
( spl0_698
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f502,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f9351,plain,
( ~ spl0_696
| spl0_697
| ~ spl0_204
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f2877,f2723,f2046,f9349,f9345]) ).
fof(f9345,plain,
( spl0_696
<=> class_Ring__and__Field_Ocomm__ring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f9349,plain,
( spl0_697
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f2046,plain,
( spl0_204
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2723,plain,
( spl0_304
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2877,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(tc_nat) )
| ~ spl0_204
| ~ spl0_304 ),
inference(resolution,[],[f2724,f2047]) ).
fof(f2047,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat)
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2046]) ).
fof(f2724,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_304 ),
inference(avatar_component_clause,[],[f2723]) ).
fof(f9343,plain,
spl0_695,
inference(avatar_split_clause,[],[f501,f9341]) ).
fof(f9341,plain,
( spl0_695
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f501,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f9339,plain,
spl0_694,
inference(avatar_split_clause,[],[f500,f9337]) ).
fof(f9337,plain,
( spl0_694
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f500,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f9335,plain,
spl0_693,
inference(avatar_split_clause,[],[f491,f9333]) ).
fof(f9333,plain,
( spl0_693
<=> ! [X0,X14,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f491,axiom,
! [X0,X7,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f9331,plain,
spl0_692,
inference(avatar_split_clause,[],[f455,f9329]) ).
fof(f9329,plain,
( spl0_692
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f455,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
fof(f9327,plain,
spl0_691,
inference(avatar_split_clause,[],[f434,f9325]) ).
fof(f9325,plain,
( spl0_691
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X5,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f434,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X5,X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
fof(f9323,plain,
spl0_690,
inference(avatar_split_clause,[],[f374,f9321]) ).
fof(f9321,plain,
( spl0_690
<=> ! [X0,X14,X5,X32] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X14,X32,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_lessequals(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X5,X32,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f374,axiom,
! [X0,X14,X5,X32] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X14,X32,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_lessequals(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X5,X32,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
fof(f9319,plain,
spl0_689,
inference(avatar_split_clause,[],[f291,f9317]) ).
fof(f9317,plain,
( spl0_689
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f291,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f9315,plain,
spl0_688,
inference(avatar_split_clause,[],[f290,f9313]) ).
fof(f9313,plain,
( spl0_688
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f290,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f9311,plain,
spl0_687,
inference(avatar_split_clause,[],[f289,f9309]) ).
fof(f9309,plain,
( spl0_687
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f289,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f9307,plain,
spl0_686,
inference(avatar_split_clause,[],[f288,f9305]) ).
fof(f9305,plain,
( spl0_686
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f288,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f9281,plain,
spl0_685,
inference(avatar_split_clause,[],[f258,f9279]) ).
fof(f9279,plain,
( spl0_685
<=> ! [X0,X14,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f258,axiom,
! [X0,X7,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f9277,plain,
spl0_684,
inference(avatar_split_clause,[],[f200,f9275]) ).
fof(f9275,plain,
( spl0_684
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X5,X7,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f200,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X5,X7,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
fof(f9273,plain,
spl0_683,
inference(avatar_split_clause,[],[f199,f9271]) ).
fof(f9271,plain,
( spl0_683
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X5,X7,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f199,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X5,X7,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
fof(f9269,plain,
spl0_682,
inference(avatar_split_clause,[],[f168,f9267]) ).
fof(f9267,plain,
( spl0_682
<=> ! [X0,X7,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| c_lessequals(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f168,axiom,
! [X2,X0,X1,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| c_lessequals(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
fof(f9265,plain,
spl0_681,
inference(avatar_split_clause,[],[f167,f9263]) ).
fof(f9263,plain,
( spl0_681
<=> ! [X0,X7,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f167,axiom,
! [X2,X0,X1,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X7,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X7,X1,X0),c_Power_Opower__class_Opower(X7,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
fof(f9261,plain,
spl0_680,
inference(avatar_split_clause,[],[f62,f9259]) ).
fof(f9259,plain,
( spl0_680
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f62,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f9257,plain,
spl0_679,
inference(avatar_split_clause,[],[f61,f9255]) ).
fof(f9255,plain,
( spl0_679
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f61,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f9253,plain,
spl0_678,
inference(avatar_split_clause,[],[f60,f9251]) ).
fof(f9251,plain,
( spl0_678
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f60,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f9249,plain,
spl0_677,
inference(avatar_split_clause,[],[f59,f9247]) ).
fof(f9247,plain,
( spl0_677
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f59,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f9245,plain,
spl0_676,
inference(avatar_split_clause,[],[f58,f9243]) ).
fof(f9243,plain,
( spl0_676
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f58,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f7803,plain,
( ~ spl0_69
| spl0_675
| ~ spl0_193
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f7607,f6591,f1891,f7801,f1378]) ).
fof(f1378,plain,
( spl0_69
<=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f7801,plain,
( spl0_675
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1891,plain,
( spl0_193
<=> ! [X0,X7,X10] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X7,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f6591,plain,
( spl0_557
<=> ! [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_557])]) ).
fof(f7607,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
| ~ spl0_193
| ~ spl0_557 ),
inference(superposition,[],[f1892,f6592]) ).
fof(f6592,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_557 ),
inference(avatar_component_clause,[],[f6591]) ).
fof(f1892,plain,
( ! [X10,X0,X7] :
( c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X7,X10,X0),X0)
| ~ class_Ring__and__Field_Odvd(X0) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1891]) ).
fof(f7534,plain,
spl0_674,
inference(avatar_split_clause,[],[f872,f7532]) ).
fof(f7532,plain,
( spl0_674
<=> ! [X0,X29,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X29,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X29,X0),c_Power_Opower__class_Opower(X2,X29,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f872,axiom,
! [X2,X0,X29,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X29,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X29,X0),c_Power_Opower__class_Opower(X2,X29,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f7530,plain,
spl0_673,
inference(avatar_split_clause,[],[f871,f7528]) ).
fof(f7528,plain,
( spl0_673
<=> ! [X0,X14,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X5,X7,X0),X14,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f871,axiom,
! [X0,X7,X14,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X5,X7,X0),X14,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X14,X0),c_Power_Opower__class_Opower(X7,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f7526,plain,
spl0_672,
inference(avatar_split_clause,[],[f842,f7524]) ).
fof(f7524,plain,
( spl0_672
<=> ! [X13,X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X14,X13,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X14,X0),c_Power_Opower__class_Opower(X2,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f842,axiom,
! [X2,X0,X1,X14,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X14,X13,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X14,X0),c_Power_Opower__class_Opower(X2,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).
fof(f7522,plain,
spl0_671,
inference(avatar_split_clause,[],[f839,f7520]) ).
fof(f7520,plain,
( spl0_671
<=> ! [X0,X10,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X1,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X2,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f839,axiom,
! [X2,X10,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X1,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X2,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_2) ).
fof(f7518,plain,
spl0_670,
inference(avatar_split_clause,[],[f836,f7516]) ).
fof(f7516,plain,
( spl0_670
<=> ! [X9,X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f836,axiom,
! [X0,X8,X9,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
fof(f7514,plain,
spl0_669,
inference(avatar_split_clause,[],[f834,f7512]) ).
fof(f7512,plain,
( spl0_669
<=> ! [X13,X0,X14,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X13,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X14,X0),X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X13,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f834,axiom,
! [X0,X7,X14,X5,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X13,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X14,X0),X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X13,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).
fof(f7510,plain,
spl0_668,
inference(avatar_split_clause,[],[f816,f7508]) ).
fof(f7508,plain,
( spl0_668
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f816,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
fof(f7459,plain,
spl0_667,
inference(avatar_split_clause,[],[f815,f7457]) ).
fof(f7457,plain,
( spl0_667
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f815,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
fof(f7455,plain,
spl0_666,
inference(avatar_split_clause,[],[f794,f7453]) ).
fof(f7453,plain,
( spl0_666
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f794,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f7451,plain,
spl0_665,
inference(avatar_split_clause,[],[f792,f7449]) ).
fof(f7449,plain,
( spl0_665
<=> ! [X5,X0,X9,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X9,X0)
| ~ c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f792,axiom,
! [X0,X8,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X9,X0)
| ~ c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f7447,plain,
spl0_664,
inference(avatar_split_clause,[],[f723,f7445]) ).
fof(f7445,plain,
( spl0_664
<=> ! [X9,X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f723,axiom,
! [X0,X8,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f7443,plain,
spl0_663,
inference(avatar_split_clause,[],[f722,f7441]) ).
fof(f7441,plain,
( spl0_663
<=> ! [X5,X0,X9,X8,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X8,X9,X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f722,axiom,
! [X0,X8,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X8,X9,X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f7439,plain,
spl0_662,
inference(avatar_split_clause,[],[f714,f7437]) ).
fof(f7437,plain,
( spl0_662
<=> ! [X13,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X14,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f714,axiom,
! [X0,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X13,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X14,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f7435,plain,
spl0_661,
inference(avatar_split_clause,[],[f712,f7433]) ).
fof(f7433,plain,
( spl0_661
<=> ! [X0,X27,X2,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X27,X0),c_HOL_Oinverse__class_Odivide(X2,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f712,axiom,
! [X2,X0,X1,X27] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X27,X0),c_HOL_Oinverse__class_Odivide(X2,X27,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f7431,plain,
spl0_660,
inference(avatar_split_clause,[],[f711,f7429]) ).
fof(f7429,plain,
( spl0_660
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X8,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f711,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X8,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f7427,plain,
spl0_659,
inference(avatar_split_clause,[],[f695,f7425]) ).
fof(f7425,plain,
( spl0_659
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f695,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
fof(f7423,plain,
spl0_658,
inference(avatar_split_clause,[],[f694,f7421]) ).
fof(f7421,plain,
( spl0_658
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f694,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
fof(f7415,plain,
spl0_657,
inference(avatar_split_clause,[],[f654,f7413]) ).
fof(f7413,plain,
( spl0_657
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f654,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f7411,plain,
spl0_656,
inference(avatar_split_clause,[],[f653,f7409]) ).
fof(f7409,plain,
( spl0_656
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f653,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f7407,plain,
spl0_655,
inference(avatar_split_clause,[],[f652,f7405]) ).
fof(f7405,plain,
( spl0_655
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X8,X0),X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f652,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X8,X0),X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
fof(f7403,plain,
spl0_654,
inference(avatar_split_clause,[],[f651,f7401]) ).
fof(f7401,plain,
( spl0_654
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Omod(X7,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f651,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Omod(X7,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
fof(f7399,plain,
spl0_653,
inference(avatar_split_clause,[],[f615,f7397]) ).
fof(f7397,plain,
( spl0_653
<=> ! [X9,X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f615,axiom,
! [X0,X8,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f7395,plain,
spl0_652,
inference(avatar_split_clause,[],[f607,f7393]) ).
fof(f7393,plain,
( spl0_652
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f607,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f7391,plain,
spl0_651,
inference(avatar_split_clause,[],[f599,f7389]) ).
fof(f7389,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X0),X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f599,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X0),X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
fof(f7387,plain,
spl0_650,
inference(avatar_split_clause,[],[f565,f7385]) ).
fof(f7385,plain,
( spl0_650
<=> ! [X29,X0,X6] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X29
| c_lessequals(c_Polynomial_Odegree(X6,X0),c_Polynomial_Odegree(X29,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f565,axiom,
! [X0,X29,X6] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X29
| c_lessequals(c_Polynomial_Odegree(X6,X0),c_Polynomial_Odegree(X29,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__degree__le_0) ).
fof(f7383,plain,
spl0_649,
inference(avatar_split_clause,[],[f531,f7381]) ).
fof(f7381,plain,
( spl0_649
<=> ! [X0,X5,X28,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X28,X0),X7,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X28,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f531,axiom,
! [X28,X0,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X28,X0),X7,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X28,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
fof(f7379,plain,
spl0_648,
inference(avatar_split_clause,[],[f530,f7377]) ).
fof(f7377,plain,
( spl0_648
<=> ! [X0,X5,X26,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ominus__class_Ominus(X7,X26,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X5,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f530,axiom,
! [X0,X26,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ominus__class_Ominus(X7,X26,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X5,X26,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
fof(f7375,plain,
spl0_647,
inference(avatar_split_clause,[],[f528,f7373]) ).
fof(f7373,plain,
( spl0_647
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f528,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f7371,plain,
spl0_646,
inference(avatar_split_clause,[],[f527,f7369]) ).
fof(f7369,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f527,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f7367,plain,
spl0_645,
inference(avatar_split_clause,[],[f522,f7365]) ).
fof(f7365,plain,
( spl0_645
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f522,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f7363,plain,
spl0_644,
inference(avatar_split_clause,[],[f514,f7361]) ).
fof(f7361,plain,
( spl0_644
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f514,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
fof(f7359,plain,
spl0_643,
inference(avatar_split_clause,[],[f490,f7357]) ).
fof(f7357,plain,
( spl0_643
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f490,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f7355,plain,
spl0_642,
inference(avatar_split_clause,[],[f483,f7353]) ).
fof(f7353,plain,
( spl0_642
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X5,X8,X0),X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f483,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X5,X8,X0),X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
fof(f7351,plain,
spl0_641,
inference(avatar_split_clause,[],[f441,f7349]) ).
fof(f7349,plain,
( spl0_641
<=> ! [X5,X0,X7] :
( ~ 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(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f441,axiom,
! [X0,X7,X5] :
( ~ 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(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
fof(f7347,plain,
spl0_640,
inference(avatar_split_clause,[],[f404,f7345]) ).
fof(f7345,plain,
( spl0_640
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f404,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f7343,plain,
spl0_639,
inference(avatar_split_clause,[],[f392,f7341]) ).
fof(f7341,plain,
( spl0_639
<=> ! [X9,X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(X8,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f392,axiom,
! [X0,X8,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(X8,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f7339,plain,
spl0_638,
inference(avatar_split_clause,[],[f391,f7337]) ).
fof(f7337,plain,
( spl0_638
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f391,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f7335,plain,
spl0_637,
inference(avatar_split_clause,[],[f383,f7333]) ).
fof(f7333,plain,
( spl0_637
<=> ! [X2,X17,X0,X33,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X17,X0) = X33
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) != c_HOL_Oplus__class_Oplus(X2,X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f383,axiom,
! [X2,X0,X1,X17,X33] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X17,X0) = X33
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) != c_HOL_Oplus__class_Oplus(X2,X33,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f7331,plain,
spl0_636,
inference(avatar_split_clause,[],[f381,f7329]) ).
fof(f7329,plain,
( spl0_636
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,c_Divides_Odiv__class_Omod(X7,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f381,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,c_Divides_Odiv__class_Omod(X7,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
fof(f7327,plain,
spl0_635,
inference(avatar_split_clause,[],[f380,f7325]) ).
fof(f7325,plain,
( spl0_635
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X5,X8,X0),X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f380,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X7,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X5,X8,X0),X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
fof(f7323,plain,
spl0_634,
inference(avatar_split_clause,[],[f365,f7321]) ).
fof(f7321,plain,
( spl0_634
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f365,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f7319,plain,
spl0_633,
inference(avatar_split_clause,[],[f364,f7317]) ).
fof(f7317,plain,
( spl0_633
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f364,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f7315,plain,
spl0_632,
inference(avatar_split_clause,[],[f357,f7313]) ).
fof(f7313,plain,
( spl0_632
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f357,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
fof(f7311,plain,
spl0_631,
inference(avatar_split_clause,[],[f356,f7309]) ).
fof(f7309,plain,
( spl0_631
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f356,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f7307,plain,
spl0_630,
inference(avatar_split_clause,[],[f355,f7305]) ).
fof(f7305,plain,
( spl0_630
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f355,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f7303,plain,
spl0_629,
inference(avatar_split_clause,[],[f354,f7301]) ).
fof(f7301,plain,
( spl0_629
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f354,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f7299,plain,
spl0_628,
inference(avatar_split_clause,[],[f311,f7297]) ).
fof(f7297,plain,
( spl0_628
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f311,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f7272,plain,
spl0_627,
inference(avatar_split_clause,[],[f310,f7270]) ).
fof(f7270,plain,
( spl0_627
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f310,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X7,X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f7268,plain,
spl0_626,
inference(avatar_split_clause,[],[f273,f7266]) ).
fof(f7266,plain,
( spl0_626
<=> ! [X0,X27,X2,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X27,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X27,X0),c_HOL_Oinverse__class_Odivide(X2,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f273,axiom,
! [X2,X0,X1,X27] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X27,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X27,X0),c_HOL_Oinverse__class_Odivide(X2,X27,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
fof(f7264,plain,
spl0_625,
inference(avatar_split_clause,[],[f272,f7262]) ).
fof(f7262,plain,
( spl0_625
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X7,X0),X8,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X8,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f272,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X7,X0),X8,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X8,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f7260,plain,
spl0_624,
inference(avatar_split_clause,[],[f262,f7258]) ).
fof(f7258,plain,
( spl0_624
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f262,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f7256,plain,
spl0_623,
inference(avatar_split_clause,[],[f261,f7254]) ).
fof(f7254,plain,
( spl0_623
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f261,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f7252,plain,
spl0_622,
inference(avatar_split_clause,[],[f260,f7250]) ).
fof(f7250,plain,
( spl0_622
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f260,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f7248,plain,
spl0_621,
inference(avatar_split_clause,[],[f259,f7246]) ).
fof(f7246,plain,
( spl0_621
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X7,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f259,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X7,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f7244,plain,
spl0_620,
inference(avatar_split_clause,[],[f247,f7242]) ).
fof(f7242,plain,
( spl0_620
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f247,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f7240,plain,
spl0_619,
inference(avatar_split_clause,[],[f246,f7238]) ).
fof(f7238,plain,
( spl0_619
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f246,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f7236,plain,
spl0_618,
inference(avatar_split_clause,[],[f243,f7234]) ).
fof(f7234,plain,
( spl0_618
<=> ! [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_618])]) ).
fof(f243,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/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f7209,plain,
spl0_617,
inference(avatar_split_clause,[],[f213,f7207]) ).
fof(f7207,plain,
( spl0_617
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f213,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f7205,plain,
spl0_616,
inference(avatar_split_clause,[],[f211,f7203]) ).
fof(f7203,plain,
( spl0_616
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f211,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f7201,plain,
spl0_615,
inference(avatar_split_clause,[],[f178,f7199]) ).
fof(f7199,plain,
( spl0_615
<=> ! [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_615])]) ).
fof(f178,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/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f7197,plain,
spl0_614,
inference(avatar_split_clause,[],[f175,f7195]) ).
fof(f7195,plain,
( spl0_614
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f175,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f7193,plain,
spl0_613,
inference(avatar_split_clause,[],[f174,f7191]) ).
fof(f7191,plain,
( spl0_613
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f174,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f7189,plain,
spl0_612,
inference(avatar_split_clause,[],[f173,f7187]) ).
fof(f7187,plain,
( spl0_612
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f173,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f7185,plain,
spl0_611,
inference(avatar_split_clause,[],[f172,f7183]) ).
fof(f7183,plain,
( spl0_611
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f172,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f7181,plain,
spl0_610,
inference(avatar_split_clause,[],[f153,f7179]) ).
fof(f7179,plain,
( spl0_610
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f153,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f7177,plain,
spl0_609,
inference(avatar_split_clause,[],[f152,f7175]) ).
fof(f7175,plain,
( spl0_609
<=> ! [X17,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X17,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f152,axiom,
! [X2,X0,X1,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X17,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f7173,plain,
spl0_608,
inference(avatar_split_clause,[],[f150,f7171]) ).
fof(f7171,plain,
( spl0_608
<=> ! [X0,X27,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X27,X0),c_HOL_Otimes__class_Otimes(X2,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f150,axiom,
! [X2,X0,X1,X27] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X27,X0),c_HOL_Otimes__class_Otimes(X2,X27,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
fof(f7169,plain,
( spl0_607
| ~ spl0_206
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2774,f2627,f2054,f7167]) ).
fof(f7167,plain,
( spl0_607
<=> ! [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_607])]) ).
fof(f2054,plain,
( spl0_206
<=> ! [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_206])]) ).
fof(f2627,plain,
( spl0_280
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2774,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_206
| ~ spl0_280 ),
inference(duplicate_literal_removal,[],[f2769]) ).
fof(f2769,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_206
| ~ spl0_280 ),
inference(resolution,[],[f2628,f2055]) ).
fof(f2055,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_206 ),
inference(avatar_component_clause,[],[f2054]) ).
fof(f2628,plain,
( ! [X0,X7,X5] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0)
| c_lessequals(X5,X7,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2627]) ).
fof(f7165,plain,
spl0_606,
inference(avatar_split_clause,[],[f149,f7163]) ).
fof(f7163,plain,
( spl0_606
<=> ! [X0,X5,X26,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X7,X26,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X5,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f149,axiom,
! [X0,X26,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X7,X26,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X5,X26,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
fof(f7161,plain,
spl0_605,
inference(avatar_split_clause,[],[f147,f7159]) ).
fof(f7159,plain,
( spl0_605
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f147,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f7157,plain,
spl0_604,
inference(avatar_split_clause,[],[f134,f7155]) ).
fof(f7155,plain,
( spl0_604
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f134,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f7153,plain,
spl0_603,
inference(avatar_split_clause,[],[f133,f7151]) ).
fof(f7151,plain,
( spl0_603
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f133,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f7149,plain,
spl0_602,
inference(avatar_split_clause,[],[f132,f7147]) ).
fof(f7147,plain,
( spl0_602
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f132,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f7145,plain,
spl0_601,
inference(avatar_split_clause,[],[f84,f7143]) ).
fof(f7143,plain,
( spl0_601
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f84,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f7141,plain,
spl0_600,
inference(avatar_split_clause,[],[f78,f7139]) ).
fof(f7139,plain,
( spl0_600
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f78,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f7137,plain,
spl0_599,
inference(avatar_split_clause,[],[f77,f7135]) ).
fof(f7135,plain,
( spl0_599
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f77,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f7133,plain,
spl0_598,
inference(avatar_split_clause,[],[f76,f7131]) ).
fof(f7131,plain,
( spl0_598
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f76,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f7129,plain,
spl0_597,
inference(avatar_split_clause,[],[f75,f7127]) ).
fof(f7127,plain,
( spl0_597
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f75,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f7125,plain,
( spl0_596
| ~ spl0_60
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2312,f2166,f1333,f7123]) ).
fof(f7123,plain,
( spl0_596
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1333,plain,
( spl0_60
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f2166,plain,
( spl0_234
<=> ! [X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2312,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_60
| ~ spl0_234 ),
inference(resolution,[],[f2167,f1335]) ).
fof(f1335,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1333]) ).
fof(f2167,plain,
( ! [X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X14,X0) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2166]) ).
fof(f7121,plain,
spl0_595,
inference(avatar_split_clause,[],[f73,f7119]) ).
fof(f7119,plain,
( spl0_595
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f73,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f7117,plain,
spl0_594,
inference(avatar_split_clause,[],[f72,f7115]) ).
fof(f7115,plain,
( spl0_594
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f72,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
fof(f7113,plain,
spl0_593,
inference(avatar_split_clause,[],[f64,f7111]) ).
fof(f7111,plain,
( spl0_593
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X14,X0),c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X14,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f64,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X5,X14,X0),c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X14,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
fof(f7109,plain,
spl0_592,
inference(avatar_split_clause,[],[f34,f7107]) ).
fof(f7107,plain,
( spl0_592
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Oinverse(X5,X0) != c_HOL_Oinverse__class_Oinverse(X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f34,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Oinverse(X5,X0) != c_HOL_Oinverse__class_Oinverse(X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(f7105,plain,
spl0_591,
inference(avatar_split_clause,[],[f30,f7103]) ).
fof(f7103,plain,
( spl0_591
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f30,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
fof(f7101,plain,
spl0_590,
inference(avatar_split_clause,[],[f28,f7099]) ).
fof(f7099,plain,
( spl0_590
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f28,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f7097,plain,
spl0_589,
inference(avatar_split_clause,[],[f6,f7095]) ).
fof(f7095,plain,
( spl0_589
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,c_Divides_Odiv__class_Omod(X7,X8,X0),X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f6,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,c_Divides_Odiv__class_Omod(X7,X8,X0),X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
fof(f7085,plain,
( spl0_588
| ~ spl0_28
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2311,f2166,f1173,f7083]) ).
fof(f7083,plain,
( spl0_588
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1173,plain,
( spl0_28
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f2311,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_28
| ~ spl0_234 ),
inference(resolution,[],[f2167,f1175]) ).
fof(f1175,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f6942,plain,
( spl0_587
| ~ spl0_72
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2279,f2134,f1393,f6939]) ).
fof(f6939,plain,
( spl0_587
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1393,plain,
( spl0_72
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f2134,plain,
( spl0_226
<=> ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2279,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_72
| ~ spl0_226 ),
inference(resolution,[],[f2135,f1395]) ).
fof(f1395,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f2135,plain,
( ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2134]) ).
fof(f6733,plain,
( spl0_586
| ~ spl0_37
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2278,f2134,f1218,f6730]) ).
fof(f6730,plain,
( spl0_586
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1218,plain,
( spl0_37
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f2278,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat)
| ~ spl0_37
| ~ spl0_226 ),
inference(resolution,[],[f2135,f1220]) ).
fof(f1220,plain,
( class_HOL_Ozero(tc_nat)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f6708,plain,
spl0_585,
inference(avatar_split_clause,[],[f879,f6706]) ).
fof(f6706,plain,
( spl0_585
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f879,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f6704,plain,
spl0_584,
inference(avatar_split_clause,[],[f804,f6702]) ).
fof(f6702,plain,
( spl0_584
<=> ! [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_584])]) ).
fof(f804,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/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f6700,plain,
spl0_583,
inference(avatar_split_clause,[],[f741,f6698]) ).
fof(f6698,plain,
( spl0_583
<=> ! [X13,X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X13 = X14
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_Power_Opower__class_Opower(X5,X14,X0) != c_Power_Opower__class_Opower(X5,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f741,axiom,
! [X0,X14,X5,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X13 = X14
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_Power_Opower__class_Opower(X5,X14,X0) != c_Power_Opower__class_Opower(X5,X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f6696,plain,
spl0_582,
inference(avatar_split_clause,[],[f687,f6694]) ).
fof(f6694,plain,
( spl0_582
<=> ! [X16,X10,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X15,tc_nat),c_HOL_Otimes__class_Otimes(X10,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f687,axiom,
! [X10,X16,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X15,tc_nat),c_HOL_Otimes__class_Otimes(X10,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
fof(f6692,plain,
spl0_581,
inference(avatar_split_clause,[],[f686,f6690]) ).
fof(f6690,plain,
( spl0_581
<=> ! [X16,X10,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X10,tc_nat),c_HOL_Otimes__class_Otimes(X16,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f686,axiom,
! [X10,X16,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X15,X10,tc_nat),c_HOL_Otimes__class_Otimes(X16,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
fof(f6688,plain,
spl0_580,
inference(avatar_split_clause,[],[f666,f6686]) ).
fof(f6686,plain,
( spl0_580
<=> ! [X17,X0,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X17,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X17,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f666,axiom,
! [X2,X0,X1,X17] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X17,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X17,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
fof(f6684,plain,
spl0_579,
inference(avatar_split_clause,[],[f574,f6682]) ).
fof(f6682,plain,
( spl0_579
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X5,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f574,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X5,X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
fof(f6680,plain,
( spl0_578
| ~ spl0_66
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2276,f2122,f1363,f6678]) ).
fof(f6678,plain,
( spl0_578
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1363,plain,
( spl0_66
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f2122,plain,
( spl0_223
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2276,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_66
| ~ spl0_223 ),
inference(resolution,[],[f2123,f1365]) ).
fof(f1365,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1363]) ).
fof(f2123,plain,
( ! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X5,X0) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f6676,plain,
spl0_577,
inference(avatar_split_clause,[],[f509,f6674]) ).
fof(f6674,plain,
( spl0_577
<=> ! [X13,X14,X10] :
( c_lessequals(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f509,axiom,
! [X10,X14,X13] :
( c_lessequals(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
fof(f6672,plain,
spl0_576,
inference(avatar_split_clause,[],[f508,f6670]) ).
fof(f6670,plain,
( spl0_576
<=> ! [X13,X14,X10] :
( c_lessequals(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f508,axiom,
! [X10,X14,X13] :
( c_lessequals(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
fof(f6668,plain,
spl0_575,
inference(avatar_split_clause,[],[f499,f6666]) ).
fof(f6666,plain,
( spl0_575
<=> ! [X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X14,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f499,axiom,
! [X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X14,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
fof(f6664,plain,
spl0_574,
inference(avatar_split_clause,[],[f435,f6662]) ).
fof(f6662,plain,
( spl0_574
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f435,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f6660,plain,
spl0_573,
inference(avatar_split_clause,[],[f382,f6658]) ).
fof(f6658,plain,
( spl0_573
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X6
| c_Polynomial_Osmult(X5,X6,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f382,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X6
| c_Polynomial_Osmult(X5,X6,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
fof(f6656,plain,
spl0_572,
inference(avatar_split_clause,[],[f361,f6654]) ).
fof(f6654,plain,
( spl0_572
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X0),c_HOL_Oinverse__class_Oinverse(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f361,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X0),c_HOL_Oinverse__class_Oinverse(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
fof(f6652,plain,
spl0_571,
inference(avatar_split_clause,[],[f336,f6650]) ).
fof(f6650,plain,
( spl0_571
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f336,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f6648,plain,
spl0_570,
inference(avatar_split_clause,[],[f287,f6646]) ).
fof(f6646,plain,
( spl0_570
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| X5 = X7
| c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
| c_HOL_Otimes__class_Otimes(X5,X5,X0) != c_HOL_Otimes__class_Otimes(X7,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f287,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| X5 = X7
| c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
| c_HOL_Otimes__class_Otimes(X5,X5,X0) != c_HOL_Otimes__class_Otimes(X7,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f6644,plain,
spl0_569,
inference(avatar_split_clause,[],[f161,f6642]) ).
fof(f6642,plain,
( spl0_569
<=> ! [X6,X0,X5,X29] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),X29,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f161,axiom,
! [X0,X29,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),X29,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd_0) ).
fof(f6640,plain,
spl0_568,
inference(avatar_split_clause,[],[f160,f6638]) ).
fof(f6638,plain,
( spl0_568
<=> ! [X6,X0,X5,X29] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_Polynomial_Osmult(X5,X29,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f160,axiom,
! [X0,X29,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_Polynomial_Osmult(X5,X29,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_0) ).
fof(f6636,plain,
( spl0_567
| ~ spl0_31
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2266,f2110,f1188,f6634]) ).
fof(f6634,plain,
( spl0_567
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f1188,plain,
( spl0_31
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2110,plain,
( spl0_220
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2266,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_31
| ~ spl0_220 ),
inference(resolution,[],[f2111,f1190]) ).
fof(f1190,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1188]) ).
fof(f2111,plain,
( ! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2110]) ).
fof(f6632,plain,
spl0_566,
inference(avatar_split_clause,[],[f159,f6630]) ).
fof(f6630,plain,
( spl0_566
<=> ! [X6,X0,X5,X29] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_Polynomial_Osmult(X5,X29,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f159,axiom,
! [X0,X29,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_Polynomial_Osmult(X5,X29,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_1) ).
fof(f6628,plain,
spl0_565,
inference(avatar_split_clause,[],[f158,f6626]) ).
fof(f6626,plain,
( spl0_565
<=> ! [X6,X0,X5,X29] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),X29,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f158,axiom,
! [X0,X29,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),X29,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_1) ).
fof(f6624,plain,
spl0_564,
inference(avatar_split_clause,[],[f139,f6622]) ).
fof(f6622,plain,
( spl0_564
<=> ! [X2,X0,X1] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
fof(f6620,plain,
spl0_563,
inference(avatar_split_clause,[],[f138,f6618]) ).
fof(f6618,plain,
( spl0_563
<=> ! [X2,X0,X1] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
fof(f6616,plain,
spl0_562,
inference(avatar_split_clause,[],[f56,f6614]) ).
fof(f6614,plain,
( spl0_562
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f56,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f6612,plain,
spl0_561,
inference(avatar_split_clause,[],[f55,f6610]) ).
fof(f6610,plain,
( spl0_561
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f55,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f6608,plain,
spl0_560,
inference(avatar_split_clause,[],[f27,f6606]) ).
fof(f6606,plain,
( spl0_560
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f27,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_4) ).
fof(f6604,plain,
spl0_559,
inference(avatar_split_clause,[],[f3,f6602]) ).
fof(f6602,plain,
( spl0_559
<=> ! [X2,X4,X0,X3,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
fof(f6600,plain,
spl0_558,
inference(avatar_split_clause,[],[f1,f6598]) ).
fof(f6598,plain,
( spl0_558
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
fof(f6593,plain,
( spl0_557
| ~ spl0_44
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2248,f2082,f1253,f6591]) ).
fof(f1253,plain,
( spl0_44
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2082,plain,
( spl0_213
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2248,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_44
| ~ spl0_213 ),
inference(resolution,[],[f2083,f1255]) ).
fof(f1255,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f2083,plain,
( ! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2082]) ).
fof(f6429,plain,
( spl0_556
| ~ spl0_44
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2245,f2078,f1253,f6427]) ).
fof(f6427,plain,
( spl0_556
<=> ! [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_556])]) ).
fof(f2078,plain,
( spl0_212
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2245,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_44
| ~ spl0_212 ),
inference(resolution,[],[f2079,f1255]) ).
fof(f2079,plain,
( ! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2078]) ).
fof(f6321,plain,
spl0_555,
inference(avatar_split_clause,[],[f897,f6319]) ).
fof(f6319,plain,
( spl0_555
<=> ! [X0,X14,X6,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Opoly(c_Power_Opower__class_Opower(X6,X14,tc_Polynomial_Opoly(X0)),X1,X0) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X6,X1,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f897,axiom,
! [X0,X1,X6,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Opoly(c_Power_Opower__class_Opower(X6,X14,tc_Polynomial_Opoly(X0)),X1,X0) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(X6,X1,X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__power_0) ).
fof(f6317,plain,
spl0_554,
inference(avatar_split_clause,[],[f837,f6315]) ).
fof(f6315,plain,
( spl0_554
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X0)
| c_Divides_Odiv__class_Omod(X5,X8,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f837,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X7,X0)
| c_Divides_Odiv__class_Omod(X5,X8,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
fof(f6313,plain,
spl0_553,
inference(avatar_split_clause,[],[f809,f6311]) ).
fof(f6311,plain,
( spl0_553
<=> ! [X18,X0,X5,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X5,X18,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X5,X0),X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f809,axiom,
! [X0,X1,X18,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X5,X18,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X5,X0),X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
fof(f6309,plain,
spl0_552,
inference(avatar_split_clause,[],[f746,f6307]) ).
fof(f6307,plain,
( spl0_552
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f746,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
fof(f6305,plain,
spl0_551,
inference(avatar_split_clause,[],[f644,f6303]) ).
fof(f6303,plain,
( spl0_551
<=> ! [X18,X0,X5,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X18,X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X5,X0),X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f644,axiom,
! [X0,X18,X1,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X18,X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X5,X0),X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
fof(f6301,plain,
( spl0_550
| ~ spl0_31
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2199,f2058,f1188,f6299]) ).
fof(f6299,plain,
( spl0_550
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2058,plain,
( spl0_207
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2199,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_31
| ~ spl0_207 ),
inference(resolution,[],[f2059,f1190]) ).
fof(f2059,plain,
( ! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X5,X0) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2058]) ).
fof(f6297,plain,
spl0_549,
inference(avatar_split_clause,[],[f597,f6295]) ).
fof(f6295,plain,
( spl0_549
<=> ! [X13,X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X13,X0) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Otimes__class_Otimes(X5,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f597,axiom,
! [X0,X5,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X13,X0) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Otimes__class_Otimes(X5,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f6293,plain,
spl0_548,
inference(avatar_split_clause,[],[f596,f6291]) ).
fof(f6291,plain,
( spl0_548
<=> ! [X13,X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),X13,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f596,axiom,
! [X0,X5,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),X13,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f6289,plain,
spl0_547,
inference(avatar_split_clause,[],[f470,f6287]) ).
fof(f6287,plain,
( spl0_547
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X5,X7,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f470,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X5,X7,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
fof(f6285,plain,
spl0_546,
inference(avatar_split_clause,[],[f347,f6283]) ).
fof(f6283,plain,
( spl0_546
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f347,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
fof(f6281,plain,
spl0_545,
inference(avatar_split_clause,[],[f263,f6279]) ).
fof(f6279,plain,
( spl0_545
<=> ! [X13,X14] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f263,axiom,
! [X14,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
fof(f6277,plain,
spl0_544,
inference(avatar_split_clause,[],[f214,f6275]) ).
fof(f6275,plain,
( spl0_544
<=> ! [X5,X0,X7] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X5,X7,X0),X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f214,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X5,X7,X0),X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
fof(f6273,plain,
spl0_543,
inference(avatar_split_clause,[],[f195,f6271]) ).
fof(f6271,plain,
( spl0_543
<=> ! [X15,X10,X16,X30] :
( ~ c_lessequals(X15,X16,tc_nat)
| ~ c_lessequals(X10,X30,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X15,X10,tc_nat),c_HOL_Otimes__class_Otimes(X16,X30,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f195,axiom,
! [X10,X16,X15,X30] :
( ~ c_lessequals(X15,X16,tc_nat)
| ~ c_lessequals(X10,X30,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X15,X10,tc_nat),c_HOL_Otimes__class_Otimes(X16,X30,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
fof(f6269,plain,
spl0_542,
inference(avatar_split_clause,[],[f137,f6267]) ).
fof(f6267,plain,
( spl0_542
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f137,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
fof(f6265,plain,
spl0_541,
inference(avatar_split_clause,[],[f126,f6263]) ).
fof(f6263,plain,
( spl0_541
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X14,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f126,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X14,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
fof(f6261,plain,
spl0_540,
inference(avatar_split_clause,[],[f81,f6259]) ).
fof(f6259,plain,
( spl0_540
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f81,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
fof(f6257,plain,
( spl0_539
| ~ spl0_31
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2192,f2042,f1188,f6255]) ).
fof(f6255,plain,
( spl0_539
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2042,plain,
( spl0_203
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2192,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_31
| ~ spl0_203 ),
inference(resolution,[],[f2043,f1190]) ).
fof(f2043,plain,
( ! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X5,X0) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2042]) ).
fof(f6253,plain,
spl0_538,
inference(avatar_split_clause,[],[f69,f6251]) ).
fof(f6251,plain,
( spl0_538
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f69,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f6164,plain,
( spl0_537
| ~ spl0_31
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2190,f2038,f1188,f6162]) ).
fof(f6162,plain,
( spl0_537
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2038,plain,
( spl0_202
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2190,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_31
| ~ spl0_202 ),
inference(resolution,[],[f2039,f1190]) ).
fof(f2039,plain,
( ! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2038]) ).
fof(f6117,plain,
( spl0_536
| ~ spl0_44
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2178,f2022,f1253,f6115]) ).
fof(f6115,plain,
( spl0_536
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2022,plain,
( spl0_198
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2178,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)
| ~ spl0_44
| ~ spl0_198 ),
inference(resolution,[],[f2023,f1255]) ).
fof(f2023,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2022]) ).
fof(f6070,plain,
( spl0_535
| ~ spl0_16
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2177,f2022,f1113,f6068]) ).
fof(f6068,plain,
( spl0_535
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f1113,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f2177,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_16
| ~ spl0_198 ),
inference(resolution,[],[f2023,f1115]) ).
fof(f1115,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1113]) ).
fof(f6011,plain,
spl0_534,
inference(avatar_split_clause,[],[f1034,f6009]) ).
fof(f6009,plain,
( spl0_534
<=> ! [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_534])]) ).
fof(f1034,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,[],[f449]) ).
fof(f449,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f6007,plain,
spl0_533,
inference(avatar_split_clause,[],[f896,f6005]) ).
fof(f6005,plain,
( spl0_533
<=> ! [X6,X0,X29,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X6,X0),X29,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X6,X29,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f896,axiom,
! [X0,X29,X1,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X6,X0),X29,X0) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X6,X29,tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
fof(f6003,plain,
spl0_532,
inference(avatar_split_clause,[],[f888,f6001]) ).
fof(f6001,plain,
( spl0_532
<=> ! [X13,X0,X14,X10] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X14,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X13,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f888,axiom,
! [X10,X0,X14,X13] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X14,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X13,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X13,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
fof(f5999,plain,
spl0_531,
inference(avatar_split_clause,[],[f887,f5997]) ).
fof(f5997,plain,
( spl0_531
<=> ! [X13,X0,X14,X10] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X14,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X13,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f887,axiom,
! [X10,X0,X14,X13] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X14,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X13,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_Divides_Odiv__class_Omod(X13,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
fof(f5995,plain,
spl0_530,
inference(avatar_split_clause,[],[f884,f5993]) ).
fof(f5993,plain,
( spl0_530
<=> ! [X17,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X17,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X17,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f884,axiom,
! [X2,X0,X1,X17] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X17,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X17,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
fof(f5991,plain,
spl0_529,
inference(avatar_split_clause,[],[f870,f5989]) ).
fof(f5989,plain,
( spl0_529
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X5,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f870,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X5,X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).
fof(f5987,plain,
( ~ spl0_69
| spl0_528
| ~ spl0_193
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f3939,f2335,f1891,f5985,f1378]) ).
fof(f5985,plain,
( spl0_528
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2335,plain,
( spl0_243
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f3939,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
| ~ spl0_193
| ~ spl0_243 ),
inference(superposition,[],[f1892,f2336]) ).
fof(f2336,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2335]) ).
fof(f5983,plain,
spl0_527,
inference(avatar_split_clause,[],[f866,f5981]) ).
fof(f5981,plain,
( spl0_527
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f866,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
fof(f5979,plain,
spl0_526,
inference(avatar_split_clause,[],[f851,f5977]) ).
fof(f5977,plain,
( spl0_526
<=> ! [X5,X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X14,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f851,axiom,
! [X0,X14,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X5,c_Power_Opower__class_Opower(X5,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X5,X14,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f5975,plain,
spl0_525,
inference(avatar_split_clause,[],[f833,f5973]) ).
fof(f5973,plain,
( spl0_525
<=> ! [X13,X0,X14,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),X0) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X5,X13,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f833,axiom,
! [X0,X14,X5,X13] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),X0) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X5,X13,X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
fof(f5971,plain,
spl0_524,
inference(avatar_split_clause,[],[f824,f5969]) ).
fof(f5969,plain,
( spl0_524
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f824,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f5967,plain,
spl0_523,
inference(avatar_split_clause,[],[f823,f5965]) ).
fof(f5965,plain,
( spl0_523
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f823,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f5963,plain,
spl0_522,
inference(avatar_split_clause,[],[f803,f5961]) ).
fof(f5961,plain,
( spl0_522
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X5,X7,X0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X7,X0),X7,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f803,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X5,X7,X0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X7,X0),X7,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(f5959,plain,
spl0_521,
inference(avatar_split_clause,[],[f799,f5957]) ).
fof(f5957,plain,
( spl0_521
<=> ! [X6,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X6,X14,tc_Polynomial_Opoly(X0)),X0),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X6,X0),X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f799,axiom,
! [X0,X6,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_lessequals(c_Polynomial_Odegree(c_Power_Opower__class_Opower(X6,X14,tc_Polynomial_Opoly(X0)),X0),c_HOL_Otimes__class_Otimes(c_Polynomial_Odegree(X6,X0),X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__power__le_0) ).
fof(f5955,plain,
spl0_520,
inference(avatar_split_clause,[],[f765,f5953]) ).
fof(f5953,plain,
( spl0_520
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f765,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f5951,plain,
spl0_519,
inference(avatar_split_clause,[],[f693,f5949]) ).
fof(f5949,plain,
( spl0_519
<=> ! [X5,X0,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X7,X6,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X5,X7,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f693,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X7,X6,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X5,X7,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).
fof(f5947,plain,
spl0_518,
inference(avatar_split_clause,[],[f692,f5945]) ).
fof(f5945,plain,
( spl0_518
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X8,X7,X0),X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f692,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X8,X7,X0),X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
fof(f5943,plain,
spl0_517,
inference(avatar_split_clause,[],[f691,f5941]) ).
fof(f5941,plain,
( spl0_517
<=> ! [X0,X5,X8,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f691,axiom,
! [X0,X8,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
fof(f5939,plain,
spl0_516,
inference(avatar_split_clause,[],[f656,f5937]) ).
fof(f5937,plain,
( spl0_516
<=> ! [X5,X0,X6,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X5,X6,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X5,c_Polynomial_Opoly(X6,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f656,axiom,
! [X0,X1,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X5,X6,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X5,c_Polynomial_Opoly(X6,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
fof(f5935,plain,
spl0_515,
inference(avatar_split_clause,[],[f595,f5933]) ).
fof(f5933,plain,
( spl0_515
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X5,X0),X14,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f595,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X5,X0),X14,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
fof(f5931,plain,
spl0_514,
inference(avatar_split_clause,[],[f580,f5929]) ).
fof(f5929,plain,
( spl0_514
<=> ! [X0,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X7,X8,X0),X8,X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f580,axiom,
! [X0,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X7,X8,X0),X8,X0) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
fof(f5927,plain,
spl0_513,
inference(avatar_split_clause,[],[f575,f5925]) ).
fof(f5925,plain,
( spl0_513
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f575,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
fof(f5923,plain,
spl0_512,
inference(avatar_split_clause,[],[f510,f5921]) ).
fof(f5921,plain,
( spl0_512
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f510,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f5919,plain,
spl0_511,
inference(avatar_split_clause,[],[f494,f5917]) ).
fof(f5917,plain,
( spl0_511
<=> ! [X13,X14,X10] :
( X13 = X14
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Otimes__class_Otimes(X10,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X10,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f494,axiom,
! [X10,X14,X13] :
( X13 = X14
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Otimes__class_Otimes(X10,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X10,X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
fof(f5915,plain,
spl0_510,
inference(avatar_split_clause,[],[f467,f5913]) ).
fof(f5913,plain,
( spl0_510
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f467,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(f5911,plain,
spl0_509,
inference(avatar_split_clause,[],[f466,f5909]) ).
fof(f5909,plain,
( spl0_509
<=> ! [X9,X0,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f466,axiom,
! [X0,X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f5907,plain,
spl0_508,
inference(avatar_split_clause,[],[f465,f5905]) ).
fof(f5905,plain,
( spl0_508
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f465,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f5903,plain,
( spl0_507
| ~ spl0_148
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f4460,f3681,f1702,f5900]) ).
fof(f5900,plain,
( spl0_507
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_qa____,v_a____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f3681,plain,
( spl0_411
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_pa____,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_qa____,X1,tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f4460,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_qa____,v_a____,tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_411 ),
inference(trivial_inequality_removal,[],[f4459]) ).
fof(f4459,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_qa____,v_a____,tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_411 ),
inference(superposition,[],[f3682,f1704]) ).
fof(f3682,plain,
( ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_pa____,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_qa____,X1,tc_Complex_Ocomplex) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f3681]) ).
fof(f5898,plain,
spl0_506,
inference(avatar_split_clause,[],[f463,f5896]) ).
fof(f5896,plain,
( spl0_506
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f463,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f5894,plain,
spl0_505,
inference(avatar_split_clause,[],[f462,f5892]) ).
fof(f5892,plain,
( spl0_505
<=> ! [X17,X0,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X17,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f462,axiom,
! [X2,X0,X1,X17] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X17,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f5890,plain,
spl0_504,
inference(avatar_split_clause,[],[f460,f5888]) ).
fof(f5888,plain,
( spl0_504
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f460,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f5886,plain,
spl0_503,
inference(avatar_split_clause,[],[f459,f5884]) ).
fof(f5884,plain,
( spl0_503
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f459,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X5,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f5882,plain,
spl0_502,
inference(avatar_split_clause,[],[f443,f5880]) ).
fof(f5880,plain,
( spl0_502
<=> ! [X17,X0,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X17,X0),X0) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X0),X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f443,axiom,
! [X2,X0,X1,X17] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X17,X0),X0) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X0),X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__assoc_0) ).
fof(f5878,plain,
spl0_501,
inference(avatar_split_clause,[],[f442,f5876]) ).
fof(f5876,plain,
( spl0_501
<=> ! [X17,X0,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X17,X0),X0) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X17,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f442,axiom,
! [X2,X0,X1,X17] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X17,X0),X0) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X17,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__left__commute_0) ).
fof(f5874,plain,
spl0_500,
inference(avatar_split_clause,[],[f269,f5872]) ).
fof(f5872,plain,
( spl0_500
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f269,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
fof(f5870,plain,
spl0_499,
inference(avatar_split_clause,[],[f268,f5868]) ).
fof(f5868,plain,
( spl0_499
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f268,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f5866,plain,
spl0_498,
inference(avatar_split_clause,[],[f164,f5864]) ).
fof(f5864,plain,
( spl0_498
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f164,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f5862,plain,
spl0_497,
inference(avatar_split_clause,[],[f146,f5860]) ).
fof(f5860,plain,
( spl0_497
<=> ! [X17,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X17,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f146,axiom,
! [X2,X0,X1,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X17,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
fof(f5844,plain,
spl0_496,
inference(avatar_split_clause,[],[f144,f5842]) ).
fof(f5842,plain,
( spl0_496
<=> ! [X24,X0,X23,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X21,c_HOL_Otimes__class_Otimes(X23,X24,X0),X0) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X21,X24,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f144,axiom,
! [X21,X0,X24,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X21,c_HOL_Otimes__class_Otimes(X23,X24,X0),X0) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X21,X24,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f5840,plain,
spl0_495,
inference(avatar_split_clause,[],[f141,f5838]) ).
fof(f5838,plain,
( spl0_495
<=> ! [X0,X21,X23,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X21,X22,X0),X23,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X21,X23,X0),X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f141,axiom,
! [X21,X0,X22,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X21,X22,X0),X23,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X21,X23,X0),X22,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f5836,plain,
spl0_494,
inference(avatar_split_clause,[],[f140,f5834]) ).
fof(f5834,plain,
( spl0_494
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f140,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f5832,plain,
spl0_493,
inference(avatar_split_clause,[],[f104,f5830]) ).
fof(f5830,plain,
( spl0_493
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f104,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f5828,plain,
spl0_492,
inference(avatar_split_clause,[],[f82,f5826]) ).
fof(f5826,plain,
( spl0_492
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f82,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
fof(f5824,plain,
spl0_491,
inference(avatar_split_clause,[],[f12,f5822]) ).
fof(f5822,plain,
( spl0_491
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Odiv(X5,X7,X0),X0),c_Divides_Odiv__class_Omod(X5,X7,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f12,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Odiv(X5,X7,X0),X0),c_Divides_Odiv__class_Omod(X5,X7,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
fof(f5820,plain,
spl0_490,
inference(avatar_split_clause,[],[f11,f5818]) ).
fof(f5818,plain,
( spl0_490
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X7,X0),X7,X0),c_Divides_Odiv__class_Omod(X5,X7,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f11,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X5,X7,X0),X7,X0),c_Divides_Odiv__class_Omod(X5,X7,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
fof(f5257,plain,
( spl0_73
| spl0_489 ),
inference(avatar_split_clause,[],[f905,f5254,f1398]) ).
fof(f1398,plain,
( spl0_73
<=> c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f905,axiom,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).
fof(f5252,plain,
spl0_488,
inference(avatar_split_clause,[],[f901,f5250]) ).
fof(f5250,plain,
( spl0_488
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X5,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f901,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X5,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_2) ).
fof(f5248,plain,
spl0_487,
inference(avatar_split_clause,[],[f899,f5246]) ).
fof(f5246,plain,
( spl0_487
<=> ! [X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X14,X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f899,axiom,
! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X1,X14,X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
fof(f5244,plain,
spl0_486,
inference(avatar_split_clause,[],[f856,f5242]) ).
fof(f5242,plain,
( spl0_486
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f856,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X5,X0),c_HOL_Otimes__class_Otimes(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
fof(f5240,plain,
spl0_485,
inference(avatar_split_clause,[],[f855,f5238]) ).
fof(f5238,plain,
( spl0_485
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f855,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X8,X0),c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
fof(f5236,plain,
spl0_484,
inference(avatar_split_clause,[],[f852,f5234]) ).
fof(f5234,plain,
( spl0_484
<=> ! [X13,X0,X14,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X13,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X13,X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f852,axiom,
! [X0,X14,X5,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X13,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X5,X13,X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).
fof(f5232,plain,
spl0_483,
inference(avatar_split_clause,[],[f784,f5230]) ).
fof(f5230,plain,
( spl0_483
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f784,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f5228,plain,
spl0_482,
inference(avatar_split_clause,[],[f783,f5226]) ).
fof(f5226,plain,
( spl0_482
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f783,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f5224,plain,
spl0_481,
inference(avatar_split_clause,[],[f782,f5222]) ).
fof(f5222,plain,
( spl0_481
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f782,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f5220,plain,
spl0_480,
inference(avatar_split_clause,[],[f781,f5218]) ).
fof(f5218,plain,
( spl0_480
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f781,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f5216,plain,
spl0_479,
inference(avatar_split_clause,[],[f780,f5214]) ).
fof(f5214,plain,
( spl0_479
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f780,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f5212,plain,
spl0_478,
inference(avatar_split_clause,[],[f779,f5210]) ).
fof(f5210,plain,
( spl0_478
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f779,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f5208,plain,
spl0_477,
inference(avatar_split_clause,[],[f736,f5206]) ).
fof(f5206,plain,
( spl0_477
<=> ! [X29,X0,X6] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X29
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0),X29,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f736,axiom,
! [X0,X29,X6] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X29
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0),X29,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_0) ).
fof(f5204,plain,
( ~ spl0_476
| spl0_457
| ~ spl0_77
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f2804,f2675,f1416,f4964,f5201]) ).
fof(f5201,plain,
( spl0_476
<=> class_Ring__and__Field_Oabs__if(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f4964,plain,
( spl0_457
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f1416,plain,
( spl0_77
<=> ! [X13] : ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f2675,plain,
( spl0_292
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2804,plain,
( ! [X0] :
( c_HOL_Oabs__class_Oabs(X0,tc_nat) = X0
| ~ class_Ring__and__Field_Oabs__if(tc_nat) )
| ~ spl0_77
| ~ spl0_292 ),
inference(resolution,[],[f2676,f1417]) ).
fof(f1417,plain,
( ! [X13] : ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f2676,plain,
( ! [X0,X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f2675]) ).
fof(f5199,plain,
spl0_475,
inference(avatar_split_clause,[],[f662,f5197]) ).
fof(f5197,plain,
( spl0_475
<=> ! [X17,X0,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X17,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f662,axiom,
! [X2,X0,X1,X17] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X17,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f5195,plain,
spl0_474,
inference(avatar_split_clause,[],[f556,f5193]) ).
fof(f5193,plain,
( spl0_474
<=> ! [X13,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X13,X13,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f556,axiom,
! [X0,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X13,X13,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f5191,plain,
spl0_473,
inference(avatar_split_clause,[],[f543,f5189]) ).
fof(f5189,plain,
( spl0_473
<=> ! [X13,X14,X10] :
( X13 = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X10
| c_HOL_Otimes__class_Otimes(X10,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X10,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f543,axiom,
! [X10,X14,X13] :
( X13 = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X10
| c_HOL_Otimes__class_Otimes(X10,X13,tc_nat) != c_HOL_Otimes__class_Otimes(X10,X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
fof(f5187,plain,
spl0_472,
inference(avatar_split_clause,[],[f542,f5185]) ).
fof(f5185,plain,
( spl0_472
<=> ! [X13,X14,X10] :
( X13 = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X10
| c_HOL_Otimes__class_Otimes(X13,X10,tc_nat) != c_HOL_Otimes__class_Otimes(X14,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f542,axiom,
! [X10,X14,X13] :
( X13 = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X10
| c_HOL_Otimes__class_Otimes(X13,X10,tc_nat) != c_HOL_Otimes__class_Otimes(X14,X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
fof(f5183,plain,
spl0_471,
inference(avatar_split_clause,[],[f469,f5181]) ).
fof(f5181,plain,
( spl0_471
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f469,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f5179,plain,
spl0_470,
inference(avatar_split_clause,[],[f349,f5177]) ).
fof(f5177,plain,
( spl0_470
<=> ! [X17,X0,X2,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X17
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f349,axiom,
! [X2,X0,X1,X17] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X17
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f5175,plain,
spl0_469,
inference(avatar_split_clause,[],[f300,f5173]) ).
fof(f5173,plain,
( spl0_469
<=> ! [X2,X0,X1] :
( ~ 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(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f300,axiom,
! [X2,X0,X1] :
( ~ 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(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f5171,plain,
spl0_468,
inference(avatar_split_clause,[],[f254,f5169]) ).
fof(f5169,plain,
( spl0_468
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f254,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f5167,plain,
spl0_467,
inference(avatar_split_clause,[],[f135,f5165]) ).
fof(f5165,plain,
( spl0_467
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f135,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f5163,plain,
spl0_466,
inference(avatar_split_clause,[],[f111,f5161]) ).
fof(f5161,plain,
( spl0_466
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f111,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f5123,plain,
spl0_465,
inference(avatar_split_clause,[],[f110,f5121]) ).
fof(f5121,plain,
( spl0_465
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f110,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f5119,plain,
spl0_464,
inference(avatar_split_clause,[],[f109,f5117]) ).
fof(f5117,plain,
( spl0_464
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f109,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f5115,plain,
spl0_463,
inference(avatar_split_clause,[],[f108,f5113]) ).
fof(f5113,plain,
( spl0_463
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f108,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X5,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f5111,plain,
spl0_462,
inference(avatar_split_clause,[],[f107,f5109]) ).
fof(f5109,plain,
( spl0_462
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f107,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f5107,plain,
spl0_461,
inference(avatar_split_clause,[],[f106,f5105]) ).
fof(f5105,plain,
( spl0_461
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f106,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X8,X0),c_HOL_Oplus__class_Oplus(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f5103,plain,
spl0_460,
inference(avatar_split_clause,[],[f83,f5101]) ).
fof(f5101,plain,
( spl0_460
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f83,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f5099,plain,
spl0_459,
inference(avatar_split_clause,[],[f5,f5097]) ).
fof(f5097,plain,
( spl0_459
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Polynomial_Odegree(c_Polynomial_Osmult(X5,X6,X0),X0) = c_Polynomial_Odegree(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f5,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Polynomial_Odegree(c_Polynomial_Osmult(X5,X6,X0),X0) = c_Polynomial_Odegree(X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_1) ).
fof(f4970,plain,
( spl0_457
| ~ spl0_458
| ~ spl0_78
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2734,f2607,f1420,f4967,f4964]) ).
fof(f4967,plain,
( spl0_458
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f1420,plain,
( spl0_78
<=> ! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f2607,plain,
( spl0_275
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2734,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat)
| c_HOL_Oabs__class_Oabs(X0,tc_nat) = X0 )
| ~ spl0_78
| ~ spl0_275 ),
inference(resolution,[],[f2608,f1421]) ).
fof(f1421,plain,
( ! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1420]) ).
fof(f2608,plain,
( ! [X0,X5] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5 )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2607]) ).
fof(f4657,plain,
spl0_456,
inference(avatar_split_clause,[],[f898,f4655]) ).
fof(f4655,plain,
( spl0_456
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X5,X0),X14,X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f898,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X5,X0),X14,X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).
fof(f4641,plain,
spl0_455,
inference(avatar_split_clause,[],[f895,f4639]) ).
fof(f4639,plain,
( spl0_455
<=> ! [X5,X6,X0,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_Polynomial_Osmult(X5,X29,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f895,axiom,
! [X0,X29,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_Polynomial_Osmult(X5,X29,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult_0) ).
fof(f4637,plain,
spl0_454,
inference(avatar_split_clause,[],[f894,f4635]) ).
fof(f4635,plain,
( spl0_454
<=> ! [X29,X0,X5,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),X29,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f894,axiom,
! [X0,X29,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X29,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X6,X0),X29,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__cancel_0) ).
fof(f4633,plain,
spl0_453,
inference(avatar_split_clause,[],[f854,f4631]) ).
fof(f4631,plain,
( spl0_453
<=> ! [X0,X10,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X1,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f854,axiom,
! [X2,X10,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X1,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).
fof(f4629,plain,
spl0_452,
inference(avatar_split_clause,[],[f853,f4627]) ).
fof(f4627,plain,
( spl0_452
<=> ! [X0,X10,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X2,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f853,axiom,
! [X2,X10,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,X2,tc_Polynomial_Opoly(X0))
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).
fof(f4625,plain,
spl0_451,
inference(avatar_split_clause,[],[f744,f4623]) ).
fof(f4623,plain,
( spl0_451
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f744,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f4621,plain,
spl0_450,
inference(avatar_split_clause,[],[f669,f4619]) ).
fof(f4619,plain,
( spl0_450
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X5,X0),X5,X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f669,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X5,X0),X5,X0) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
fof(f4617,plain,
spl0_449,
inference(avatar_split_clause,[],[f668,f4615]) ).
fof(f4615,plain,
( spl0_449
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Odiv(X7,X5,X0),X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f668,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Odiv(X7,X5,X0),X0) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
fof(f4613,plain,
spl0_448,
inference(avatar_split_clause,[],[f573,f4611]) ).
fof(f4611,plain,
( spl0_448
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X5,X5,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f573,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X5,X5,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f4609,plain,
spl0_447,
inference(avatar_split_clause,[],[f566,f4607]) ).
fof(f4607,plain,
( spl0_447
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f566,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f4605,plain,
spl0_446,
inference(avatar_split_clause,[],[f563,f4603]) ).
fof(f4603,plain,
( spl0_446
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X8,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f563,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X8,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
fof(f4590,plain,
spl0_445,
inference(avatar_split_clause,[],[f511,f4588]) ).
fof(f4588,plain,
( spl0_445
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f511,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f4586,plain,
spl0_444,
inference(avatar_split_clause,[],[f498,f4584]) ).
fof(f4584,plain,
( spl0_444
<=> ! [X0,X1,X14] :
( ~ 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_Power_Opower__class_Opower(X1,X14,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f498,axiom,
! [X0,X1,X14] :
( ~ 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_Power_Opower__class_Opower(X1,X14,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
fof(f4582,plain,
spl0_443,
inference(avatar_split_clause,[],[f496,f4580]) ).
fof(f4580,plain,
( spl0_443
<=> ! [X13,X14,X10] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f496,axiom,
! [X10,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
fof(f4578,plain,
spl0_442,
inference(avatar_split_clause,[],[f495,f4576]) ).
fof(f4576,plain,
( spl0_442
<=> ! [X13,X14,X10] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f495,axiom,
! [X10,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
fof(f4574,plain,
spl0_441,
inference(avatar_split_clause,[],[f448,f4572]) ).
fof(f4572,plain,
( spl0_441
<=> ! [X13,X14,X10] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f448,axiom,
! [X10,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
fof(f4570,plain,
spl0_440,
inference(avatar_split_clause,[],[f447,f4568]) ).
fof(f4568,plain,
( spl0_440
<=> ! [X13,X14,X10] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f447,axiom,
! [X10,X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
fof(f4566,plain,
spl0_439,
inference(avatar_split_clause,[],[f416,f4564]) ).
fof(f4564,plain,
( spl0_439
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f416,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f4562,plain,
spl0_438,
inference(avatar_split_clause,[],[f406,f4560]) ).
fof(f4560,plain,
( spl0_438
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f406,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f4558,plain,
spl0_437,
inference(avatar_split_clause,[],[f405,f4556]) ).
fof(f4556,plain,
( spl0_437
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f405,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X5,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
fof(f4554,plain,
spl0_436,
inference(avatar_split_clause,[],[f271,f4552]) ).
fof(f4552,plain,
( spl0_436
<=> ! [X13,X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X13
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f271,axiom,
! [X14,X13] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X13
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
fof(f4546,plain,
spl0_435,
inference(avatar_split_clause,[],[f267,f4544]) ).
fof(f4544,plain,
( spl0_435
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f267,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f4542,plain,
spl0_434,
inference(avatar_split_clause,[],[f266,f4540]) ).
fof(f4540,plain,
( spl0_434
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f266,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f4538,plain,
spl0_433,
inference(avatar_split_clause,[],[f245,f4536]) ).
fof(f4536,plain,
( spl0_433
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f245,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
fof(f4534,plain,
spl0_432,
inference(avatar_split_clause,[],[f244,f4532]) ).
fof(f4532,plain,
( spl0_432
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f244,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
fof(f4530,plain,
spl0_431,
inference(avatar_split_clause,[],[f194,f4528]) ).
fof(f4528,plain,
( spl0_431
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f194,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).
fof(f4526,plain,
spl0_430,
inference(avatar_split_clause,[],[f193,f4524]) ).
fof(f4524,plain,
( spl0_430
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f193,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).
fof(f4522,plain,
spl0_429,
inference(avatar_split_clause,[],[f192,f4520]) ).
fof(f4520,plain,
( spl0_429
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f192,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
fof(f4518,plain,
spl0_428,
inference(avatar_split_clause,[],[f191,f4516]) ).
fof(f4516,plain,
( spl0_428
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X5,X7,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f191,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X5,X7,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f4514,plain,
spl0_427,
inference(avatar_split_clause,[],[f190,f4512]) ).
fof(f4512,plain,
( spl0_427
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = c_HOL_Otimes__class_Otimes(X7,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f190,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = c_HOL_Otimes__class_Otimes(X7,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f4510,plain,
spl0_426,
inference(avatar_split_clause,[],[f188,f4508]) ).
fof(f4508,plain,
( spl0_426
<=> ! [X5,X0,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f188,axiom,
! [X0,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f4504,plain,
spl0_425,
inference(avatar_split_clause,[],[f186,f4502]) ).
fof(f4502,plain,
( spl0_425
<=> ! [X5,X0,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f186,axiom,
! [X0,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
fof(f4500,plain,
spl0_424,
inference(avatar_split_clause,[],[f171,f4498]) ).
fof(f4498,plain,
( spl0_424
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f171,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_1) ).
fof(f4496,plain,
spl0_423,
inference(avatar_split_clause,[],[f170,f4494]) ).
fof(f4494,plain,
( spl0_423
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f170,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_0) ).
fof(f4492,plain,
spl0_422,
inference(avatar_split_clause,[],[f165,f4490]) ).
fof(f4490,plain,
( spl0_422
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f165,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f4488,plain,
spl0_421,
inference(avatar_split_clause,[],[f163,f4486]) ).
fof(f4486,plain,
( spl0_421
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f163,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
fof(f4484,plain,
spl0_420,
inference(avatar_split_clause,[],[f145,f4482]) ).
fof(f4482,plain,
( spl0_420
<=> ! [X13,X14,X10] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),X10,tc_nat) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f145,axiom,
! [X10,X14,X13] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),X10,tc_nat) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
fof(f4480,plain,
spl0_419,
inference(avatar_split_clause,[],[f131,f4478]) ).
fof(f4478,plain,
( spl0_419
<=> ! [X5,X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X8,X0),X8,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f131,axiom,
! [X0,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X8,X0),X8,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
fof(f4476,plain,
spl0_418,
inference(avatar_split_clause,[],[f98,f4474]) ).
fof(f4474,plain,
( spl0_418
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f98,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f4472,plain,
spl0_417,
inference(avatar_split_clause,[],[f97,f4470]) ).
fof(f4470,plain,
( spl0_417
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f97,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f4468,plain,
spl0_416,
inference(avatar_split_clause,[],[f63,f4466]) ).
fof(f4466,plain,
( spl0_416
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f63,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X5,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
fof(f4464,plain,
spl0_415,
inference(avatar_split_clause,[],[f26,f4462]) ).
fof(f4462,plain,
( spl0_415
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f26,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
fof(f4279,plain,
( ~ spl0_413
| spl0_414
| ~ spl0_77
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f4113,f3600,f1416,f4277,f4273]) ).
fof(f4273,plain,
( spl0_413
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f4277,plain,
( spl0_414
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f3600,plain,
( spl0_393
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f4113,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_77
| ~ spl0_393 ),
inference(resolution,[],[f3601,f1417]) ).
fof(f3601,plain,
( ! [X0,X7,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f3600]) ).
fof(f3687,plain,
( ~ spl0_69
| spl0_412
| ~ spl0_193
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f3639,f2216,f1891,f3685,f1378]) ).
fof(f3685,plain,
( spl0_412
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f3639,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
| ~ spl0_193
| ~ spl0_236 ),
inference(superposition,[],[f1892,f2217]) ).
fof(f3683,plain,
spl0_411,
inference(avatar_split_clause,[],[f890,f3681]) ).
fof(f890,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_pa____,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_qa____,X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pq0_0) ).
fof(f3679,plain,
spl0_410,
inference(avatar_split_clause,[],[f880,f3677]) ).
fof(f3677,plain,
( spl0_410
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f880,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
fof(f3675,plain,
spl0_409,
inference(avatar_split_clause,[],[f835,f3673]) ).
fof(f3673,plain,
( spl0_409
<=> ! [X0,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f835,axiom,
! [X0,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_0) ).
fof(f3671,plain,
spl0_408,
inference(avatar_split_clause,[],[f812,f3669]) ).
fof(f3669,plain,
( spl0_408
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f812,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f3667,plain,
spl0_407,
inference(avatar_split_clause,[],[f811,f3665]) ).
fof(f3665,plain,
( spl0_407
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f811,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f3663,plain,
spl0_406,
inference(avatar_split_clause,[],[f797,f3661]) ).
fof(f3661,plain,
( spl0_406
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X17,X2,X0)
| c_lessequals(X17,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f797,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X17,X2,X0)
| c_lessequals(X17,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3659,plain,
spl0_405,
inference(avatar_split_clause,[],[f796,f3657]) ).
fof(f3657,plain,
( spl0_405
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X17,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X17,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f796,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X17,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X17,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3655,plain,
spl0_404,
inference(avatar_split_clause,[],[f795,f3653]) ).
fof(f3653,plain,
( spl0_404
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X17,X2,X0)
| c_HOL_Oord__class_Oless(X17,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f795,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X17,X2,X0)
| c_HOL_Oord__class_Oless(X17,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3651,plain,
spl0_403,
inference(avatar_split_clause,[],[f793,f3649]) ).
fof(f3649,plain,
( spl0_403
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X17,X0)
| c_lessequals(X1,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f793,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X17,X0)
| c_lessequals(X1,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3647,plain,
spl0_402,
inference(avatar_split_clause,[],[f791,f3645]) ).
fof(f3645,plain,
( spl0_402
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X17,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f791,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X17,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f3634,plain,
spl0_401,
inference(avatar_split_clause,[],[f790,f3632]) ).
fof(f3632,plain,
( spl0_401
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X17,X0)
| c_HOL_Oord__class_Oless(X1,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f790,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X17,X0)
| c_HOL_Oord__class_Oless(X1,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3630,plain,
spl0_400,
inference(avatar_split_clause,[],[f731,f3628]) ).
fof(f3628,plain,
( spl0_400
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0)
| c_lessequals(X7,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f731,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0)
| c_lessequals(X7,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
fof(f3626,plain,
spl0_399,
inference(avatar_split_clause,[],[f728,f3624]) ).
fof(f3624,plain,
( spl0_399
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,X0),X5,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f728,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,X0),X5,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
fof(f3622,plain,
spl0_398,
inference(avatar_split_clause,[],[f726,f3620]) ).
fof(f3620,plain,
( spl0_398
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ouminus__class_Ouminus(X5,X0),X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f726,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ouminus__class_Ouminus(X5,X0),X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
fof(f3618,plain,
spl0_397,
inference(avatar_split_clause,[],[f724,f3616]) ).
fof(f3616,plain,
( spl0_397
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X7,X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f724,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X7,X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
fof(f3614,plain,
spl0_396,
inference(avatar_split_clause,[],[f670,f3612]) ).
fof(f3612,plain,
( spl0_396
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oabs__class_Oabs(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f670,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oabs__class_Oabs(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f3610,plain,
spl0_395,
inference(avatar_split_clause,[],[f642,f3608]) ).
fof(f3608,plain,
( spl0_395
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X1
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f642,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X1
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
fof(f3606,plain,
spl0_394,
inference(avatar_split_clause,[],[f629,f3604]) ).
fof(f3604,plain,
( spl0_394
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f629,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f3602,plain,
spl0_393,
inference(avatar_split_clause,[],[f628,f3600]) ).
fof(f628,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f3598,plain,
spl0_392,
inference(avatar_split_clause,[],[f614,f3596]) ).
fof(f3596,plain,
( spl0_392
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f614,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f3592,plain,
spl0_391,
inference(avatar_split_clause,[],[f613,f3590]) ).
fof(f3590,plain,
( spl0_391
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f613,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f3588,plain,
spl0_390,
inference(avatar_split_clause,[],[f606,f3586]) ).
fof(f3586,plain,
( spl0_390
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f606,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3584,plain,
spl0_389,
inference(avatar_split_clause,[],[f576,f3582]) ).
fof(f3582,plain,
( spl0_389
<=> ! [X13,X14] :
( c_HOL_Oone__class_Oone(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X13
| c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) != X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f576,axiom,
! [X14,X13] :
( c_HOL_Oone__class_Oone(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X13
| c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) != X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
fof(f3580,plain,
spl0_388,
inference(avatar_split_clause,[],[f568,f3578]) ).
fof(f3578,plain,
( spl0_388
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f568,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f3576,plain,
spl0_387,
inference(avatar_split_clause,[],[f567,f3574]) ).
fof(f3574,plain,
( spl0_387
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f567,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f3572,plain,
spl0_386,
inference(avatar_split_clause,[],[f526,f3570]) ).
fof(f3570,plain,
( spl0_386
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f526,axiom,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f3568,plain,
spl0_385,
inference(avatar_split_clause,[],[f493,f3566]) ).
fof(f3566,plain,
( spl0_385
<=> ! [X2,X0,X25,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X2 = X25
| c_HOL_Ominus__class_Ominus(X1,X1,X0) != c_HOL_Ominus__class_Ominus(X25,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f493,axiom,
! [X2,X0,X1,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X2 = X25
| c_HOL_Ominus__class_Ominus(X1,X1,X0) != c_HOL_Ominus__class_Ominus(X25,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
fof(f3564,plain,
spl0_384,
inference(avatar_split_clause,[],[f457,f3562]) ).
fof(f3562,plain,
( spl0_384
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X17,X0)
| c_HOL_Oord__class_Oless(X1,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f457,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X17,X0)
| c_HOL_Oord__class_Oless(X1,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f3560,plain,
spl0_383,
inference(avatar_split_clause,[],[f456,f3558]) ).
fof(f3558,plain,
( spl0_383
<=> ! [X17,X0,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X17,X2,X0)
| c_HOL_Oord__class_Oless(X17,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f456,axiom,
! [X2,X0,X1,X17] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X17,X2,X0)
| c_HOL_Oord__class_Oless(X17,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3556,plain,
spl0_382,
inference(avatar_split_clause,[],[f437,f3554]) ).
fof(f3554,plain,
( spl0_382
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f437,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f3550,plain,
spl0_381,
inference(avatar_split_clause,[],[f436,f3548]) ).
fof(f3548,plain,
( spl0_381
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f436,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f3546,plain,
spl0_380,
inference(avatar_split_clause,[],[f401,f3544]) ).
fof(f3544,plain,
( spl0_380
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f401,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f3542,plain,
spl0_379,
inference(avatar_split_clause,[],[f376,f3540]) ).
fof(f3540,plain,
( spl0_379
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f376,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f3538,plain,
spl0_378,
inference(avatar_split_clause,[],[f375,f3536]) ).
fof(f3536,plain,
( spl0_378
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f375,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f3534,plain,
spl0_377,
inference(avatar_split_clause,[],[f352,f3532]) ).
fof(f3532,plain,
( spl0_377
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X7,X5,X0) != c_HOL_Oplus__class_Oplus(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f352,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X7,X5,X0) != c_HOL_Oplus__class_Oplus(X8,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f3530,plain,
spl0_376,
inference(avatar_split_clause,[],[f351,f3528]) ).
fof(f3528,plain,
( spl0_376
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f351,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f3526,plain,
spl0_375,
inference(avatar_split_clause,[],[f350,f3524]) ).
fof(f3524,plain,
( spl0_375
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f350,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f3522,plain,
spl0_374,
inference(avatar_split_clause,[],[f316,f3520]) ).
fof(f3520,plain,
( spl0_374
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f316,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f3518,plain,
spl0_373,
inference(avatar_split_clause,[],[f315,f3516]) ).
fof(f3516,plain,
( spl0_373
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f315,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f3514,plain,
spl0_372,
inference(avatar_split_clause,[],[f298,f3512]) ).
fof(f3512,plain,
( spl0_372
<=> ! [X5,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oplus__class_Oplus(X1,X5,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f298,axiom,
! [X0,X1,X5] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oplus__class_Oplus(X1,X5,X0) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f3500,plain,
spl0_371,
inference(avatar_split_clause,[],[f285,f3498]) ).
fof(f3498,plain,
( spl0_371
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oabs__class_Oabs(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f285,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oabs__class_Oabs(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f3496,plain,
spl0_370,
inference(avatar_split_clause,[],[f284,f3494]) ).
fof(f3494,plain,
( spl0_370
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oabs__class_Oabs(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f284,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oabs__class_Oabs(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f3492,plain,
spl0_369,
inference(avatar_split_clause,[],[f256,f3490]) ).
fof(f3490,plain,
( spl0_369
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f256,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f3488,plain,
spl0_368,
inference(avatar_split_clause,[],[f249,f3486]) ).
fof(f3486,plain,
( spl0_368
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f249,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f3484,plain,
spl0_367,
inference(avatar_split_clause,[],[f248,f3482]) ).
fof(f3482,plain,
( spl0_367
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f248,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f3480,plain,
spl0_366,
inference(avatar_split_clause,[],[f113,f3478]) ).
fof(f3478,plain,
( spl0_366
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f113,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
fof(f3476,plain,
spl0_365,
inference(avatar_split_clause,[],[f112,f3474]) ).
fof(f3474,plain,
( spl0_365
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f112,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
fof(f3472,plain,
spl0_364,
inference(avatar_split_clause,[],[f105,f3470]) ).
fof(f3470,plain,
( spl0_364
<=> ! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f105,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__0__0_0) ).
fof(f3468,plain,
spl0_363,
inference(avatar_split_clause,[],[f96,f3466]) ).
fof(f3466,plain,
( spl0_363
<=> ! [X13,X14,X10] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f96,axiom,
! [X10,X14,X13] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X13,X10,tc_nat),c_HOL_Otimes__class_Otimes(X14,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
fof(f3464,plain,
spl0_362,
inference(avatar_split_clause,[],[f95,f3462]) ).
fof(f3462,plain,
( spl0_362
<=> ! [X13,X14,X10] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f95,axiom,
! [X10,X14,X13] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,X13,tc_nat),c_HOL_Otimes__class_Otimes(X10,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
fof(f3460,plain,
( spl0_361
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f3348,f3035,f3458]) ).
fof(f3035,plain,
( spl0_344
<=> ! [X0,X30,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,X10,X0)
| c_HOL_Oabs__class_Oabs(X30,X0) != c_HOL_Oabs__class_Oabs(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f3348,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_344 ),
inference(equality_resolution,[],[f3036]) ).
fof(f3036,plain,
( ! [X10,X0,X30] :
( c_HOL_Oabs__class_Oabs(X30,X0) != c_HOL_Oabs__class_Oabs(X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,X10,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f3035]) ).
fof(f3456,plain,
spl0_360,
inference(avatar_split_clause,[],[f88,f3454]) ).
fof(f3454,plain,
( spl0_360
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f88,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f3452,plain,
spl0_359,
inference(avatar_split_clause,[],[f87,f3450]) ).
fof(f3450,plain,
( spl0_359
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f87,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f3448,plain,
spl0_358,
inference(avatar_split_clause,[],[f80,f3446]) ).
fof(f3446,plain,
( spl0_358
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f80,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f3444,plain,
spl0_357,
inference(avatar_split_clause,[],[f79,f3442]) ).
fof(f3442,plain,
( spl0_357
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f79,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f3440,plain,
spl0_356,
inference(avatar_split_clause,[],[f71,f3438]) ).
fof(f3438,plain,
( spl0_356
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f71,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f3436,plain,
spl0_355,
inference(avatar_split_clause,[],[f54,f3434]) ).
fof(f3434,plain,
( spl0_355
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X5,X0) = X7
| c_HOL_Otimes__class_Otimes(X5,X7,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f54,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X5,X0) = X7
| c_HOL_Otimes__class_Otimes(X5,X7,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
fof(f3432,plain,
spl0_354,
inference(avatar_split_clause,[],[f37,f3430]) ).
fof(f3430,plain,
( spl0_354
<=> ! [X16,X10,X15] :
( ~ c_lessequals(X15,X16,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X15,tc_nat),c_HOL_Otimes__class_Otimes(X10,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f37,axiom,
! [X10,X16,X15] :
( ~ c_lessequals(X15,X16,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X15,tc_nat),c_HOL_Otimes__class_Otimes(X10,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
fof(f3428,plain,
spl0_353,
inference(avatar_split_clause,[],[f36,f3426]) ).
fof(f3426,plain,
( spl0_353
<=> ! [X16,X10,X15] :
( ~ c_lessequals(X15,X16,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X15,X10,tc_nat),c_HOL_Otimes__class_Otimes(X16,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f36,axiom,
! [X10,X16,X15] :
( ~ c_lessequals(X15,X16,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X15,X10,tc_nat),c_HOL_Otimes__class_Otimes(X16,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
fof(f3424,plain,
spl0_352,
inference(avatar_split_clause,[],[f35,f3422]) ).
fof(f3422,plain,
( spl0_352
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X5 = X7
| c_HOL_Oinverse__class_Oinverse(X5,X0) != c_HOL_Oinverse__class_Oinverse(X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f35,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X5 = X7
| c_HOL_Oinverse__class_Oinverse(X5,X0) != c_HOL_Oinverse__class_Oinverse(X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
fof(f3314,plain,
( ~ spl0_32
| spl0_351
| ~ spl0_152
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2013,f1891,f1721,f3312,f1193]) ).
fof(f1193,plain,
( spl0_32
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f3312,plain,
( spl0_351
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f1721,plain,
( spl0_152
<=> ! [X13] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f2013,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_152
| ~ spl0_193 ),
inference(superposition,[],[f1892,f1722]) ).
fof(f1722,plain,
( ! [X13] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1721]) ).
fof(f3201,plain,
( ~ spl0_32
| spl0_350
| ~ spl0_142
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2011,f1891,f1678,f3199,f1193]) ).
fof(f3199,plain,
( spl0_350
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f1678,plain,
( spl0_142
<=> ! [X14] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X14,tc_nat) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f2011,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_142
| ~ spl0_193 ),
inference(superposition,[],[f1892,f1679]) ).
fof(f1679,plain,
( ! [X14] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X14,tc_nat) = X14
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1678]) ).
fof(f3057,plain,
spl0_349,
inference(avatar_split_clause,[],[f878,f3055]) ).
fof(f3055,plain,
( spl0_349
<=> ! [X5,X0,X14] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f878,axiom,
! [X0,X14,X5] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f3053,plain,
spl0_348,
inference(avatar_split_clause,[],[f876,f3051]) ).
fof(f3051,plain,
( spl0_348
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f876,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
fof(f3049,plain,
spl0_347,
inference(avatar_split_clause,[],[f875,f3047]) ).
fof(f3047,plain,
( spl0_347
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f875,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
fof(f3045,plain,
spl0_346,
inference(avatar_split_clause,[],[f874,f3043]) ).
fof(f3043,plain,
( spl0_346
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f874,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
fof(f3041,plain,
spl0_345,
inference(avatar_split_clause,[],[f873,f3039]) ).
fof(f3039,plain,
( spl0_345
<=> ! [X5,X0,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f873,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X7,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
fof(f3037,plain,
spl0_344,
inference(avatar_split_clause,[],[f832,f3035]) ).
fof(f832,axiom,
! [X10,X0,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,X10,X0)
| c_HOL_Oabs__class_Oabs(X30,X0) != c_HOL_Oabs__class_Oabs(X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
fof(f3033,plain,
spl0_343,
inference(avatar_split_clause,[],[f825,f3031]) ).
fof(f3031,plain,
( spl0_343
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X5,X6,X0),X0),c_Polynomial_Odegree(X6,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f825,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(X5,X6,X0),X0),c_Polynomial_Odegree(X6,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__le_0) ).
fof(f3029,plain,
spl0_342,
inference(avatar_split_clause,[],[f818,f3027]) ).
fof(f3027,plain,
( spl0_342
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f818,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f3025,plain,
spl0_341,
inference(avatar_split_clause,[],[f817,f3023]) ).
fof(f3023,plain,
( spl0_341
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f817,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f3021,plain,
spl0_340,
inference(avatar_split_clause,[],[f749,f3019]) ).
fof(f3019,plain,
( spl0_340
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f749,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X5,X7,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Oinverse(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f3017,plain,
spl0_339,
inference(avatar_split_clause,[],[f721,f3015]) ).
fof(f3015,plain,
( spl0_339
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X7,X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f721,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X7,X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f3013,plain,
spl0_338,
inference(avatar_split_clause,[],[f690,f3011]) ).
fof(f3011,plain,
( spl0_338
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f690,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f3009,plain,
spl0_337,
inference(avatar_split_clause,[],[f621,f3007]) ).
fof(f3007,plain,
( spl0_337
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f621,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f3005,plain,
( spl0_336
| ~ spl0_60
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1990,f1875,f1333,f3003]) ).
fof(f3003,plain,
( spl0_336
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f1875,plain,
( spl0_189
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1990,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = X0
| ~ spl0_60
| ~ spl0_189 ),
inference(resolution,[],[f1876,f1335]) ).
fof(f1876,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1875]) ).
fof(f3001,plain,
spl0_335,
inference(avatar_split_clause,[],[f620,f2999]) ).
fof(f2999,plain,
( spl0_335
<=> ! [X2,X0,X17] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X17,X0),c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f620,axiom,
! [X2,X0,X17] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X17,X0),c_HOL_Oplus__class_Oplus(X2,X17,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f2997,plain,
spl0_334,
inference(avatar_split_clause,[],[f521,f2995]) ).
fof(f2995,plain,
( spl0_334
<=> ! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f521,axiom,
! [X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
fof(f2993,plain,
spl0_333,
inference(avatar_split_clause,[],[f520,f2991]) ).
fof(f2991,plain,
( spl0_333
<=> ! [X13,X14] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f520,axiom,
! [X14,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X13,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
fof(f2989,plain,
spl0_332,
inference(avatar_split_clause,[],[f479,f2987]) ).
fof(f2987,plain,
( spl0_332
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f479,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
fof(f2985,plain,
spl0_331,
inference(avatar_split_clause,[],[f422,f2983]) ).
fof(f2983,plain,
( spl0_331
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f422,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f2981,plain,
spl0_330,
inference(avatar_split_clause,[],[f414,f2979]) ).
fof(f2979,plain,
( spl0_330
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f414,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f2977,plain,
spl0_329,
inference(avatar_split_clause,[],[f413,f2975]) ).
fof(f2975,plain,
( spl0_329
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f413,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f2973,plain,
spl0_328,
inference(avatar_split_clause,[],[f412,f2971]) ).
fof(f2971,plain,
( spl0_328
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f412,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f2969,plain,
spl0_327,
inference(avatar_split_clause,[],[f411,f2967]) ).
fof(f2967,plain,
( spl0_327
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f411,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f2965,plain,
spl0_326,
inference(avatar_split_clause,[],[f402,f2963]) ).
fof(f2963,plain,
( spl0_326
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f402,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f2961,plain,
( spl0_325
| ~ spl0_28
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1989,f1875,f1173,f2959]) ).
fof(f2959,plain,
( spl0_325
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f1989,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_28
| ~ spl0_189 ),
inference(resolution,[],[f1876,f1175]) ).
fof(f2957,plain,
spl0_324,
inference(avatar_split_clause,[],[f368,f2955]) ).
fof(f2955,plain,
( spl0_324
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f368,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f2953,plain,
spl0_323,
inference(avatar_split_clause,[],[f367,f2951]) ).
fof(f2951,plain,
( spl0_323
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f367,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
fof(f2949,plain,
spl0_322,
inference(avatar_split_clause,[],[f366,f2947]) ).
fof(f2947,plain,
( spl0_322
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f366,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
fof(f2945,plain,
spl0_321,
inference(avatar_split_clause,[],[f334,f2943]) ).
fof(f2943,plain,
( spl0_321
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f334,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f2941,plain,
spl0_320,
inference(avatar_split_clause,[],[f333,f2939]) ).
fof(f2939,plain,
( spl0_320
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(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_320])]) ).
fof(f333,axiom,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(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/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f2937,plain,
spl0_319,
inference(avatar_split_clause,[],[f332,f2935]) ).
fof(f2935,plain,
( spl0_319
<=> ! [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_319])]) ).
fof(f332,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/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
fof(f2933,plain,
spl0_318,
inference(avatar_split_clause,[],[f251,f2931]) ).
fof(f2931,plain,
( spl0_318
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f251,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_3) ).
fof(f2929,plain,
spl0_317,
inference(avatar_split_clause,[],[f237,f2927]) ).
fof(f2927,plain,
( spl0_317
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f237,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f2925,plain,
spl0_316,
inference(avatar_split_clause,[],[f136,f2923]) ).
fof(f2923,plain,
( spl0_316
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f136,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f2921,plain,
spl0_315,
inference(avatar_split_clause,[],[f123,f2919]) ).
fof(f2919,plain,
( spl0_315
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f123,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f2917,plain,
( spl0_314
| ~ spl0_63
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1986,f1863,f1348,f2914]) ).
fof(f2914,plain,
( spl0_314
<=> 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_314])]) ).
fof(f1348,plain,
( spl0_63
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1863,plain,
( spl0_186
<=> ! [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_186])]) ).
fof(f1986,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_63
| ~ spl0_186 ),
inference(resolution,[],[f1864,f1350]) ).
fof(f1350,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1348]) ).
fof(f1864,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_186 ),
inference(avatar_component_clause,[],[f1863]) ).
fof(f2912,plain,
spl0_313,
inference(avatar_split_clause,[],[f116,f2910]) ).
fof(f2910,plain,
( spl0_313
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f116,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f2908,plain,
spl0_312,
inference(avatar_split_clause,[],[f115,f2906]) ).
fof(f2906,plain,
( spl0_312
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f115,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f2904,plain,
spl0_311,
inference(avatar_split_clause,[],[f70,f2902]) ).
fof(f2902,plain,
( spl0_311
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0),X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f70,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0),X0) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f2900,plain,
spl0_310,
inference(avatar_split_clause,[],[f22,f2898]) ).
fof(f2898,plain,
( spl0_310
<=> ! [X5,X0,X7] :
( ~ class_Orderings_Oorder(X0)
| X5 = X7
| ~ c_lessequals(X7,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f22,axiom,
! [X0,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| X5 = X7
| ~ c_lessequals(X7,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
fof(f2896,plain,
spl0_309,
inference(avatar_split_clause,[],[f20,f2894]) ).
fof(f2894,plain,
( spl0_309
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f2858,plain,
( spl0_308
| ~ spl0_31
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1978,f1855,f1188,f2856]) ).
fof(f2856,plain,
( spl0_308
<=> ! [X0] : c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f1855,plain,
( spl0_184
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1978,plain,
( ! [X0] : c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_184 ),
inference(resolution,[],[f1856,f1190]) ).
fof(f1856,plain,
( ! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1855]) ).
fof(f2800,plain,
( spl0_307
| ~ spl0_63
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1976,f1851,f1348,f2798]) ).
fof(f2798,plain,
( spl0_307
<=> ! [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_307])]) ).
fof(f1851,plain,
( spl0_183
<=> ! [X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1976,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_63
| ~ spl0_183 ),
inference(resolution,[],[f1852,f1350]) ).
fof(f1852,plain,
( ! [X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = X7 )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1851]) ).
fof(f2733,plain,
spl0_306,
inference(avatar_split_clause,[],[f863,f2731]) ).
fof(f2731,plain,
( spl0_306
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f863,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
fof(f2729,plain,
spl0_305,
inference(avatar_split_clause,[],[f862,f2727]) ).
fof(f2727,plain,
( spl0_305
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f862,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
fof(f2725,plain,
spl0_304,
inference(avatar_split_clause,[],[f861,f2723]) ).
fof(f861,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
fof(f2721,plain,
spl0_303,
inference(avatar_split_clause,[],[f860,f2719]) ).
fof(f2719,plain,
( spl0_303
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f860,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
fof(f2717,plain,
spl0_302,
inference(avatar_split_clause,[],[f846,f2715]) ).
fof(f846,axiom,
! [X10,X0,X13] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X13,X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
fof(f2713,plain,
spl0_301,
inference(avatar_split_clause,[],[f845,f2711]) ).
fof(f2711,plain,
( spl0_301
<=> ! [X13,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X13,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f845,axiom,
! [X10,X0,X13] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X13,X0),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
fof(f2709,plain,
( spl0_300
| ~ spl0_62
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1958,f1831,f1343,f2707]) ).
fof(f2707,plain,
( spl0_300
<=> ! [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_300])]) ).
fof(f1343,plain,
( spl0_62
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1831,plain,
( spl0_178
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1958,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_62
| ~ spl0_178 ),
inference(resolution,[],[f1832,f1345]) ).
fof(f1345,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1343]) ).
fof(f1832,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1831]) ).
fof(f2705,plain,
spl0_299,
inference(avatar_split_clause,[],[f844,f2703]) ).
fof(f844,axiom,
! [X10,X0,X13] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oabs__class_Oabs(X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
fof(f2701,plain,
spl0_298,
inference(avatar_split_clause,[],[f843,f2699]) ).
fof(f2699,plain,
( spl0_298
<=> ! [X13,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oabs__class_Oabs(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f843,axiom,
! [X10,X0,X13] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X13,c_HOL_Oabs__class_Oabs(X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
fof(f2697,plain,
spl0_297,
inference(avatar_split_clause,[],[f810,f2695]) ).
fof(f2695,plain,
( spl0_297
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X7,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f810,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X7,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
fof(f2693,plain,
spl0_296,
inference(avatar_split_clause,[],[f801,f2691]) ).
fof(f2691,plain,
( spl0_296
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f801,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f2689,plain,
spl0_295,
inference(avatar_split_clause,[],[f800,f2687]) ).
fof(f2687,plain,
( spl0_295
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f800,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f2685,plain,
spl0_294,
inference(avatar_split_clause,[],[f788,f2683]) ).
fof(f2683,plain,
( spl0_294
<=> ! [X16,X10,X15] :
( ~ c_lessequals(X15,X16,tc_nat)
| ~ c_lessequals(X16,X10,tc_nat)
| c_lessequals(X15,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f788,axiom,
! [X10,X16,X15] :
( ~ c_lessequals(X15,X16,tc_nat)
| ~ c_lessequals(X16,X10,tc_nat)
| c_lessequals(X15,X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2681,plain,
spl0_293,
inference(avatar_split_clause,[],[f773,f2679]) ).
fof(f2679,plain,
( spl0_293
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f773,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f2677,plain,
spl0_292,
inference(avatar_split_clause,[],[f760,f2675]) ).
fof(f760,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f2673,plain,
spl0_291,
inference(avatar_split_clause,[],[f755,f2671]) ).
fof(f2671,plain,
( spl0_291
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f755,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
fof(f2669,plain,
spl0_290,
inference(avatar_split_clause,[],[f753,f2667]) ).
fof(f2667,plain,
( spl0_290
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f753,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
fof(f2665,plain,
( spl0_289
| ~ spl0_30
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1957,f1831,f1183,f2663]) ).
fof(f2663,plain,
( spl0_289
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f1183,plain,
( spl0_30
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1957,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0
| ~ spl0_30
| ~ spl0_178 ),
inference(resolution,[],[f1832,f1185]) ).
fof(f1185,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1183]) ).
fof(f2661,plain,
spl0_288,
inference(avatar_split_clause,[],[f738,f2659]) ).
fof(f2659,plain,
( spl0_288
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f738,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f2657,plain,
spl0_287,
inference(avatar_split_clause,[],[f647,f2655]) ).
fof(f2655,plain,
( spl0_287
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f647,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f2653,plain,
spl0_286,
inference(avatar_split_clause,[],[f570,f2651]) ).
fof(f2651,plain,
( spl0_286
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f570,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2649,plain,
spl0_285,
inference(avatar_split_clause,[],[f539,f2647]) ).
fof(f2647,plain,
( spl0_285
<=> ! [X5,X0,X7] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f539,axiom,
! [X0,X7,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f2645,plain,
spl0_284,
inference(avatar_split_clause,[],[f525,f2643]) ).
fof(f2643,plain,
( spl0_284
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f525,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f2641,plain,
spl0_283,
inference(avatar_split_clause,[],[f524,f2639]) ).
fof(f2639,plain,
( spl0_283
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f524,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X5 = X7
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f2637,plain,
spl0_282,
inference(avatar_split_clause,[],[f468,f2635]) ).
fof(f2635,plain,
( spl0_282
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f468,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f2633,plain,
spl0_281,
inference(avatar_split_clause,[],[f390,f2631]) ).
fof(f2631,plain,
( spl0_281
<=> ! [X5,X0,X14] :
( ~ 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(X5,X0),X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f390,axiom,
! [X0,X14,X5] :
( ~ 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(X5,X0),X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
fof(f2629,plain,
spl0_280,
inference(avatar_split_clause,[],[f318,f2627]) ).
fof(f318,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X5,X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f2625,plain,
spl0_279,
inference(avatar_split_clause,[],[f257,f2623]) ).
fof(f2623,plain,
( spl0_279
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f257,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_0) ).
fof(f2621,plain,
( spl0_278
| ~ spl0_62
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1955,f1827,f1343,f2619]) ).
fof(f2619,plain,
( spl0_278
<=> ! [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_278])]) ).
fof(f1827,plain,
( spl0_177
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1955,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_62
| ~ spl0_177 ),
inference(resolution,[],[f1828,f1345]) ).
fof(f1828,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1827]) ).
fof(f2617,plain,
spl0_277,
inference(avatar_split_clause,[],[f185,f2615]) ).
fof(f2615,plain,
( spl0_277
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f185,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f2613,plain,
spl0_276,
inference(avatar_split_clause,[],[f128,f2611]) ).
fof(f2611,plain,
( spl0_276
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X5 = X7
| c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ouminus__class_Ouminus(X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f128,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X5 = X7
| c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ouminus__class_Ouminus(X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2609,plain,
spl0_275,
inference(avatar_split_clause,[],[f114,f2607]) ).
fof(f114,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f2575,plain,
( spl0_274
| ~ spl0_30
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1954,f1827,f1183,f2573]) ).
fof(f2573,plain,
( spl0_274
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1954,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_30
| ~ spl0_177 ),
inference(resolution,[],[f1828,f1185]) ).
fof(f2550,plain,
( spl0_273
| ~ spl0_50
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1953,f1819,f1283,f2547]) ).
fof(f2547,plain,
( spl0_273
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f1283,plain,
( spl0_50
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1819,plain,
( spl0_175
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1953,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_50
| ~ spl0_175 ),
inference(resolution,[],[f1820,f1285]) ).
fof(f1285,plain,
( class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f1820,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1819]) ).
fof(f2518,plain,
( spl0_272
| ~ spl0_31
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f1931,f1803,f1188,f2516]) ).
fof(f2516,plain,
( spl0_272
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f1803,plain,
( spl0_171
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1931,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_31
| ~ spl0_171 ),
inference(resolution,[],[f1804,f1190]) ).
fof(f1804,plain,
( ! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,X5,X0) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f2449,plain,
spl0_271,
inference(avatar_split_clause,[],[f902,f2447]) ).
fof(f2447,plain,
( spl0_271
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f902,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f2445,plain,
spl0_270,
inference(avatar_split_clause,[],[f859,f2443]) ).
fof(f2443,plain,
( spl0_270
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f859,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f2441,plain,
spl0_269,
inference(avatar_split_clause,[],[f822,f2439]) ).
fof(f2439,plain,
( spl0_269
<=> ! [X13,X14] :
( c_HOL_Oone__class_Oone(tc_nat) = X13
| c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f822,axiom,
! [X14,X13] :
( c_HOL_Oone__class_Oone(tc_nat) = X13
| c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
fof(f2437,plain,
spl0_268,
inference(avatar_split_clause,[],[f821,f2435]) ).
fof(f2435,plain,
( spl0_268
<=> ! [X13,X14] :
( c_HOL_Oone__class_Oone(tc_nat) = X14
| c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f821,axiom,
! [X14,X13] :
( c_HOL_Oone__class_Oone(tc_nat) = X14
| c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
fof(f2433,plain,
spl0_267,
inference(avatar_split_clause,[],[f756,f2431]) ).
fof(f2431,plain,
( spl0_267
<=> ! [X6,X0] :
( ~ 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),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f756,axiom,
! [X0,X6] :
( ~ 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),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
fof(f2429,plain,
spl0_266,
inference(avatar_split_clause,[],[f754,f2427]) ).
fof(f2427,plain,
( spl0_266
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f754,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
fof(f2425,plain,
( spl0_265
| ~ spl0_31
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1929,f1799,f1188,f2423]) ).
fof(f2423,plain,
( spl0_265
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1799,plain,
( spl0_170
<=> ! [X5,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1929,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_170 ),
inference(resolution,[],[f1800,f1190]) ).
fof(f1800,plain,
( ! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1799]) ).
fof(f2421,plain,
spl0_264,
inference(avatar_split_clause,[],[f743,f2419]) ).
fof(f2419,plain,
( spl0_264
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f743,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__commute_0) ).
fof(f2417,plain,
spl0_263,
inference(avatar_split_clause,[],[f710,f2415]) ).
fof(f2415,plain,
( spl0_263
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f710,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2413,plain,
spl0_262,
inference(avatar_split_clause,[],[f699,f2411]) ).
fof(f2411,plain,
( spl0_262
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f699,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2409,plain,
spl0_261,
inference(avatar_split_clause,[],[f631,f2407]) ).
fof(f2407,plain,
( spl0_261
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f631,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
fof(f2405,plain,
spl0_260,
inference(avatar_split_clause,[],[f622,f2403]) ).
fof(f2403,plain,
( spl0_260
<=> ! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f622,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
fof(f2401,plain,
spl0_259,
inference(avatar_split_clause,[],[f519,f2399]) ).
fof(f2399,plain,
( spl0_259
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f519,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f2397,plain,
spl0_258,
inference(avatar_split_clause,[],[f518,f2395]) ).
fof(f2395,plain,
( spl0_258
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f518,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2393,plain,
spl0_257,
inference(avatar_split_clause,[],[f517,f2391]) ).
fof(f2391,plain,
( spl0_257
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f517,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2389,plain,
spl0_256,
inference(avatar_split_clause,[],[f453,f2387]) ).
fof(f2387,plain,
( spl0_256
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,X7,X0) = c_HOL_Otimes__class_Otimes(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f453,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,X7,X0) = c_HOL_Otimes__class_Otimes(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2385,plain,
spl0_255,
inference(avatar_split_clause,[],[f446,f2383]) ).
fof(f2383,plain,
( spl0_255
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f446,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X5,X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f2381,plain,
( spl0_254
| ~ spl0_66
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1928,f1795,f1363,f2379]) ).
fof(f2379,plain,
( spl0_254
<=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1795,plain,
( spl0_169
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1928,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_66
| ~ spl0_169 ),
inference(resolution,[],[f1796,f1365]) ).
fof(f1796,plain,
( ! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1795]) ).
fof(f2377,plain,
spl0_253,
inference(avatar_split_clause,[],[f445,f2375]) ).
fof(f2375,plain,
( spl0_253
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X7,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f445,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X7,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2373,plain,
spl0_252,
inference(avatar_split_clause,[],[f429,f2371]) ).
fof(f2371,plain,
( spl0_252
<=> ! [X5,X0,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f429,axiom,
! [X0,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2369,plain,
spl0_251,
inference(avatar_split_clause,[],[f428,f2367]) ).
fof(f2367,plain,
( spl0_251
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f428,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f2365,plain,
spl0_250,
inference(avatar_split_clause,[],[f417,f2363]) ).
fof(f2363,plain,
( spl0_250
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f417,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f2361,plain,
spl0_249,
inference(avatar_split_clause,[],[f348,f2359]) ).
fof(f2359,plain,
( spl0_249
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f348,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f2357,plain,
spl0_248,
inference(avatar_split_clause,[],[f320,f2355]) ).
fof(f2355,plain,
( spl0_248
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X5,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f320,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X5,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f2353,plain,
spl0_247,
inference(avatar_split_clause,[],[f312,f2351]) ).
fof(f2351,plain,
( spl0_247
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X5,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f312,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X5,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f2349,plain,
spl0_246,
inference(avatar_split_clause,[],[f283,f2347]) ).
fof(f2347,plain,
( spl0_246
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f283,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2345,plain,
spl0_245,
inference(avatar_split_clause,[],[f230,f2343]) ).
fof(f2343,plain,
( spl0_245
<=> ! [X0,X1] :
( ~ 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)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f230,axiom,
! [X0,X1] :
( ~ 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)),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
fof(f2341,plain,
spl0_244,
inference(avatar_split_clause,[],[f223,f2339]) ).
fof(f2339,plain,
( spl0_244
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f223,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2337,plain,
( spl0_243
| ~ spl0_60
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1920,f1783,f1333,f2335]) ).
fof(f1783,plain,
( spl0_166
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1920,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_60
| ~ spl0_166 ),
inference(resolution,[],[f1784,f1335]) ).
fof(f1784,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1783]) ).
fof(f2333,plain,
spl0_242,
inference(avatar_split_clause,[],[f177,f2331]) ).
fof(f2331,plain,
( spl0_242
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f177,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
fof(f2329,plain,
spl0_241,
inference(avatar_split_clause,[],[f176,f2327]) ).
fof(f2327,plain,
( spl0_241
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ouminus__class_Ouminus(X5,X0) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f176,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ouminus__class_Ouminus(X5,X0) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2325,plain,
spl0_240,
inference(avatar_split_clause,[],[f121,f2323]) ).
fof(f2323,plain,
( spl0_240
<=> ! [X13,X14] :
( X13 = X14
| c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X14,X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f121,axiom,
! [X14,X13] :
( X13 = X14
| c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X14,X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f2321,plain,
spl0_239,
inference(avatar_split_clause,[],[f120,f2319]) ).
fof(f2319,plain,
( spl0_239
<=> ! [X13,X14] :
( X13 = X14
| ~ c_lessequals(X13,X14,tc_nat)
| ~ c_lessequals(X14,X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f120,axiom,
! [X14,X13] :
( X13 = X14
| ~ c_lessequals(X13,X14,tc_nat)
| ~ c_lessequals(X14,X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f2317,plain,
spl0_238,
inference(avatar_split_clause,[],[f17,f2315]) ).
fof(f2315,plain,
( spl0_238
<=> ! [X13,X14] :
( X13 = X14
| ~ c_lessequals(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f17,axiom,
! [X14,X13] :
( X13 = X14
| ~ c_lessequals(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
fof(f2263,plain,
( spl0_237
| ~ spl0_136
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2228,f2066,f1654,f2261]) ).
fof(f2261,plain,
( spl0_237
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1654,plain,
( spl0_136
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f2066,plain,
( spl0_209
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f2228,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_136
| ~ spl0_209 ),
inference(duplicate_literal_removal,[],[f2224]) ).
fof(f2224,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_136
| ~ spl0_209 ),
inference(resolution,[],[f2067,f1655]) ).
fof(f1655,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1654]) ).
fof(f2067,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f2218,plain,
( spl0_236
| ~ spl0_60
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1917,f1779,f1333,f2216]) ).
fof(f1779,plain,
( spl0_165
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1917,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_60
| ~ spl0_165 ),
inference(resolution,[],[f1780,f1335]) ).
fof(f1780,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1779]) ).
fof(f2176,plain,
( spl0_235
| ~ spl0_63
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1914,f1775,f1348,f2174]) ).
fof(f2174,plain,
( spl0_235
<=> ! [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_235])]) ).
fof(f1775,plain,
( spl0_164
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1914,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_63
| ~ spl0_164 ),
inference(resolution,[],[f1776,f1350]) ).
fof(f1776,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1775]) ).
fof(f2168,plain,
spl0_234,
inference(avatar_split_clause,[],[f857,f2166]) ).
fof(f857,axiom,
! [X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f2164,plain,
spl0_233,
inference(avatar_split_clause,[],[f841,f2162]) ).
fof(f2162,plain,
( spl0_233
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X2,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f841,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X2,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd2_0) ).
fof(f2160,plain,
spl0_232,
inference(avatar_split_clause,[],[f840,f2158]) ).
fof(f2158,plain,
( spl0_232
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X1,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f840,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X1,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd1_0) ).
fof(f2156,plain,
spl0_231,
inference(avatar_split_clause,[],[f831,f2154]) ).
fof(f2154,plain,
( spl0_231
<=> ! [X5,X0,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f831,axiom,
! [X0,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2152,plain,
spl0_230,
inference(avatar_split_clause,[],[f830,f2150]) ).
fof(f2150,plain,
( spl0_230
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f830,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2148,plain,
spl0_229,
inference(avatar_split_clause,[],[f828,f2146]) ).
fof(f2146,plain,
( spl0_229
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f828,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2144,plain,
spl0_228,
inference(avatar_split_clause,[],[f826,f2142]) ).
fof(f2142,plain,
( spl0_228
<=> ! [X5,X0,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f826,axiom,
! [X0,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X7,X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f2140,plain,
spl0_227,
inference(avatar_split_clause,[],[f774,f2138]) ).
fof(f2138,plain,
( spl0_227
<=> ! [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_227])]) ).
fof(f774,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f2136,plain,
spl0_226,
inference(avatar_split_clause,[],[f655,f2134]) ).
fof(f655,axiom,
! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__0_0) ).
fof(f2132,plain,
( spl0_225
| ~ spl0_57
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1910,f1767,f1318,f2130]) ).
fof(f2130,plain,
( spl0_225
<=> ! [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_225])]) ).
fof(f1318,plain,
( spl0_57
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1767,plain,
( spl0_162
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1910,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_57
| ~ spl0_162 ),
inference(resolution,[],[f1768,f1320]) ).
fof(f1320,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f1768,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1767]) ).
fof(f2128,plain,
spl0_224,
inference(avatar_split_clause,[],[f637,f2126]) ).
fof(f2126,plain,
( spl0_224
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f637,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f2124,plain,
spl0_223,
inference(avatar_split_clause,[],[f634,f2122]) ).
fof(f634,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f2120,plain,
spl0_222,
inference(avatar_split_clause,[],[f618,f2118]) ).
fof(f2118,plain,
( spl0_222
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f618,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2116,plain,
spl0_221,
inference(avatar_split_clause,[],[f616,f2114]) ).
fof(f2114,plain,
( spl0_221
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f616,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2112,plain,
spl0_220,
inference(avatar_split_clause,[],[f598,f2110]) ).
fof(f598,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f2108,plain,
spl0_219,
inference(avatar_split_clause,[],[f594,f2106]) ).
fof(f2106,plain,
( spl0_219
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f594,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f2104,plain,
spl0_218,
inference(avatar_split_clause,[],[f593,f2102]) ).
fof(f2102,plain,
( spl0_218
<=> ! [X0,X7] :
( ~ 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),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f593,axiom,
! [X0,X7] :
( ~ 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),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f2100,plain,
spl0_217,
inference(avatar_split_clause,[],[f592,f2098]) ).
fof(f2098,plain,
( spl0_217
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f592,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2096,plain,
spl0_216,
inference(avatar_split_clause,[],[f591,f2094]) ).
fof(f2094,plain,
( spl0_216
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f591,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2092,plain,
spl0_215,
inference(avatar_split_clause,[],[f589,f2090]) ).
fof(f2090,plain,
( spl0_215
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(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_215])]) ).
fof(f589,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f2088,plain,
spl0_214,
inference(avatar_split_clause,[],[f585,f2086]) ).
fof(f2086,plain,
( spl0_214
<=> ! [X0,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f585,axiom,
! [X0,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f2084,plain,
spl0_213,
inference(avatar_split_clause,[],[f583,f2082]) ).
fof(f583,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2080,plain,
spl0_212,
inference(avatar_split_clause,[],[f582,f2078]) ).
fof(f582,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f2076,plain,
spl0_211,
inference(avatar_split_clause,[],[f557,f2074]) ).
fof(f2074,plain,
( spl0_211
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f557,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f2072,plain,
spl0_210,
inference(avatar_split_clause,[],[f475,f2070]) ).
fof(f2070,plain,
( spl0_210
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f475,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f2068,plain,
spl0_209,
inference(avatar_split_clause,[],[f472,f2066]) ).
fof(f472,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f2064,plain,
spl0_208,
inference(avatar_split_clause,[],[f471,f2062]) ).
fof(f2062,plain,
( spl0_208
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f471,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2060,plain,
spl0_207,
inference(avatar_split_clause,[],[f438,f2058]) ).
fof(f438,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f2056,plain,
spl0_206,
inference(avatar_split_clause,[],[f363,f2054]) ).
fof(f363,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/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f2052,plain,
spl0_205,
inference(avatar_split_clause,[],[f353,f2050]) ).
fof(f353,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f2048,plain,
( ~ spl0_32
| spl0_204
| ~ spl0_143
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2012,f1891,f1682,f2046,f1193]) ).
fof(f1682,plain,
( spl0_143
<=> ! [X14] : c_HOL_Otimes__class_Otimes(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f2012,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_143
| ~ spl0_193 ),
inference(superposition,[],[f1892,f1683]) ).
fof(f1683,plain,
( ! [X14] : c_HOL_Otimes__class_Otimes(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1682]) ).
fof(f2044,plain,
spl0_203,
inference(avatar_split_clause,[],[f275,f2042]) ).
fof(f275,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f2040,plain,
spl0_202,
inference(avatar_split_clause,[],[f274,f2038]) ).
fof(f274,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f2036,plain,
spl0_201,
inference(avatar_split_clause,[],[f196,f2034]) ).
fof(f2034,plain,
( spl0_201
<=> ! [X13] : c_lessequals(X13,c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X13,X13,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f196,axiom,
! [X13] : c_lessequals(X13,c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X13,X13,tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).
fof(f2032,plain,
spl0_200,
inference(avatar_split_clause,[],[f92,f2030]) ).
fof(f2030,plain,
( spl0_200
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f92,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f2028,plain,
spl0_199,
inference(avatar_split_clause,[],[f86,f2026]) ).
fof(f2026,plain,
( spl0_199
<=> ! [X5,X0] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f86,axiom,
! [X0,X5] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f2024,plain,
spl0_198,
inference(avatar_split_clause,[],[f85,f2022]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f2020,plain,
spl0_197,
inference(avatar_split_clause,[],[f31,f2018]) ).
fof(f2018,plain,
( spl0_197
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f31,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X5,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1998,plain,
( spl0_196
| ~ spl0_44
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1908,f1763,f1253,f1996]) ).
fof(f1996,plain,
( spl0_196
<=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1763,plain,
( spl0_161
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X6,X0) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1908,plain,
( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_44
| ~ spl0_161 ),
inference(resolution,[],[f1764,f1255]) ).
fof(f1764,plain,
( ! [X0,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X6,X0) = X6 )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1763]) ).
fof(f1969,plain,
( spl0_195
| ~ spl0_16
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1907,f1763,f1113,f1967]) ).
fof(f1967,plain,
( spl0_195
<=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1907,plain,
( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
| ~ spl0_16
| ~ spl0_161 ),
inference(resolution,[],[f1764,f1115]) ).
fof(f1906,plain,
( spl0_194
| ~ spl0_43
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1894,f1751,f1248,f1903]) ).
fof(f1903,plain,
( spl0_194
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1248,plain,
( spl0_43
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1751,plain,
( spl0_158
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1894,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_43
| ~ spl0_158 ),
inference(resolution,[],[f1752,f1250]) ).
fof(f1250,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f1752,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1751]) ).
fof(f1893,plain,
spl0_193,
inference(avatar_split_clause,[],[f893,f1891]) ).
fof(f893,axiom,
! [X10,X0,X7] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X7,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f1889,plain,
spl0_192,
inference(avatar_split_clause,[],[f892,f1887]) ).
fof(f1887,plain,
( spl0_192
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f892,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f1885,plain,
spl0_191,
inference(avatar_split_clause,[],[f891,f1883]) ).
fof(f1883,plain,
( spl0_191
<=> ! [X5,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f891,axiom,
! [X0,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f1881,plain,
spl0_190,
inference(avatar_split_clause,[],[f850,f1879]) ).
fof(f1879,plain,
( spl0_190
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f850,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1877,plain,
spl0_189,
inference(avatar_split_clause,[],[f849,f1875]) ).
fof(f849,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
fof(f1873,plain,
spl0_188,
inference(avatar_split_clause,[],[f819,f1871]) ).
fof(f1871,plain,
( spl0_188
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f819,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1869,plain,
spl0_187,
inference(avatar_split_clause,[],[f748,f1867]) ).
fof(f1867,plain,
( spl0_187
<=> ! [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_187])]) ).
fof(f748,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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1865,plain,
spl0_186,
inference(avatar_split_clause,[],[f747,f1863]) ).
fof(f747,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/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f1861,plain,
spl0_185,
inference(avatar_split_clause,[],[f742,f1859]) ).
fof(f1859,plain,
( spl0_185
<=> ! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f742,axiom,
! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1857,plain,
spl0_184,
inference(avatar_split_clause,[],[f720,f1855]) ).
fof(f720,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f1853,plain,
spl0_183,
inference(avatar_split_clause,[],[f717,f1851]) ).
fof(f717,axiom,
! [X0,X7] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
fof(f1849,plain,
spl0_182,
inference(avatar_split_clause,[],[f702,f1847]) ).
fof(f1847,plain,
( spl0_182
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f702,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1845,plain,
spl0_181,
inference(avatar_split_clause,[],[f701,f1843]) ).
fof(f1843,plain,
( spl0_181
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f701,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1841,plain,
spl0_180,
inference(avatar_split_clause,[],[f700,f1839]) ).
fof(f1839,plain,
( spl0_180
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f700,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f1837,plain,
spl0_179,
inference(avatar_split_clause,[],[f698,f1835]) ).
fof(f1835,plain,
( spl0_179
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f698,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1833,plain,
spl0_178,
inference(avatar_split_clause,[],[f697,f1831]) ).
fof(f697,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1829,plain,
spl0_177,
inference(avatar_split_clause,[],[f696,f1827]) ).
fof(f696,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1825,plain,
spl0_176,
inference(avatar_split_clause,[],[f630,f1823]) ).
fof(f1823,plain,
( spl0_176
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f630,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1821,plain,
spl0_175,
inference(avatar_split_clause,[],[f624,f1819]) ).
fof(f624,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
fof(f1817,plain,
spl0_174,
inference(avatar_split_clause,[],[f458,f1815]) ).
fof(f1815,plain,
( spl0_174
<=> ! [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_174])]) ).
fof(f458,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/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1813,plain,
spl0_173,
inference(avatar_split_clause,[],[f452,f1811]) ).
fof(f1811,plain,
( spl0_173
<=> ! [X13,X14] : c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) = c_HOL_Otimes__class_Otimes(X14,X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f452,axiom,
! [X14,X13] : c_HOL_Otimes__class_Otimes(X13,X14,tc_nat) = c_HOL_Otimes__class_Otimes(X14,X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1809,plain,
spl0_172,
inference(avatar_split_clause,[],[f432,f1807]) ).
fof(f1807,plain,
( spl0_172
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f432,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(f1805,plain,
spl0_171,
inference(avatar_split_clause,[],[f426,f1803]) ).
fof(f426,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1801,plain,
spl0_170,
inference(avatar_split_clause,[],[f425,f1799]) ).
fof(f425,axiom,
! [X0,X5] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1797,plain,
spl0_169,
inference(avatar_split_clause,[],[f344,f1795]) ).
fof(f344,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f1793,plain,
spl0_168,
inference(avatar_split_clause,[],[f331,f1791]) ).
fof(f1791,plain,
( spl0_168
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f331,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f1789,plain,
spl0_167,
inference(avatar_split_clause,[],[f327,f1787]) ).
fof(f1787,plain,
( spl0_167
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f327,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f1785,plain,
spl0_166,
inference(avatar_split_clause,[],[f326,f1783]) ).
fof(f326,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f1781,plain,
spl0_165,
inference(avatar_split_clause,[],[f325,f1779]) ).
fof(f325,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f1777,plain,
spl0_164,
inference(avatar_split_clause,[],[f281,f1775]) ).
fof(f281,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1773,plain,
spl0_163,
inference(avatar_split_clause,[],[f280,f1771]) ).
fof(f1771,plain,
( spl0_163
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f280,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f1769,plain,
spl0_162,
inference(avatar_split_clause,[],[f279,f1767]) ).
fof(f279,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1765,plain,
spl0_161,
inference(avatar_split_clause,[],[f219,f1763]) ).
fof(f219,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X6,X0) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
fof(f1761,plain,
spl0_160,
inference(avatar_split_clause,[],[f182,f1759]) ).
fof(f1759,plain,
( spl0_160
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f182,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f1757,plain,
spl0_159,
inference(avatar_split_clause,[],[f129,f1755]) ).
fof(f1755,plain,
( spl0_159
<=> ! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f129,axiom,
! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1753,plain,
spl0_158,
inference(avatar_split_clause,[],[f32,f1751]) ).
fof(f32,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f1743,plain,
spl0_157,
inference(avatar_split_clause,[],[f829,f1741]) ).
fof(f1741,plain,
( spl0_157
<=> ! [X13,X14] :
( c_lessequals(X13,X14,tc_nat)
| c_lessequals(X14,X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f829,axiom,
! [X14,X13] :
( c_lessequals(X13,X14,tc_nat)
| c_lessequals(X14,X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1739,plain,
spl0_156,
inference(avatar_split_clause,[],[f732,f1737]) ).
fof(f1737,plain,
( spl0_156
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f732,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1735,plain,
spl0_155,
inference(avatar_split_clause,[],[f619,f1733]) ).
fof(f1733,plain,
( spl0_155
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f619,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
fof(f1731,plain,
spl0_154,
inference(avatar_split_clause,[],[f608,f1729]) ).
fof(f1729,plain,
( spl0_154
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f608,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1727,plain,
spl0_153,
inference(avatar_split_clause,[],[f587,f1725]) ).
fof(f1725,plain,
( spl0_153
<=> ! [X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f587,axiom,
! [X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f1723,plain,
spl0_152,
inference(avatar_split_clause,[],[f586,f1721]) ).
fof(f586,axiom,
! [X13] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f1719,plain,
spl0_151,
inference(avatar_split_clause,[],[f581,f1717]) ).
fof(f1717,plain,
( spl0_151
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f581,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1715,plain,
spl0_150,
inference(avatar_split_clause,[],[f569,f1713]) ).
fof(f1713,plain,
( spl0_150
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f569,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1711,plain,
spl0_149,
inference(avatar_split_clause,[],[f558,f1709]) ).
fof(f1709,plain,
( spl0_149
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X5,c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f558,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X5,c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1705,plain,
spl0_148,
inference(avatar_split_clause,[],[f904,f1702]) ).
fof(f904,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
fof(f1700,plain,
spl0_147,
inference(avatar_split_clause,[],[f877,f1698]) ).
fof(f1698,plain,
( spl0_147
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f877,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
fof(f1696,plain,
spl0_146,
inference(avatar_split_clause,[],[f847,f1694]) ).
fof(f1694,plain,
( spl0_146
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f847,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1692,plain,
spl0_145,
inference(avatar_split_clause,[],[f665,f1690]) ).
fof(f1690,plain,
( spl0_145
<=> ! [X13] : c_lessequals(X13,c_HOL_Otimes__class_Otimes(X13,X13,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f665,axiom,
! [X13] : c_lessequals(X13,c_HOL_Otimes__class_Otimes(X13,X13,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).
fof(f1688,plain,
spl0_144,
inference(avatar_split_clause,[],[f373,f1686]) ).
fof(f1686,plain,
( spl0_144
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f373,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f1684,plain,
spl0_143,
inference(avatar_split_clause,[],[f330,f1682]) ).
fof(f330,axiom,
! [X14] : c_HOL_Otimes__class_Otimes(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
fof(f1680,plain,
spl0_142,
inference(avatar_split_clause,[],[f329,f1678]) ).
fof(f329,axiom,
! [X14] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X14,tc_nat) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
fof(f1676,plain,
spl0_141,
inference(avatar_split_clause,[],[f881,f1674]) ).
fof(f1674,plain,
( spl0_141
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f881,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1672,plain,
spl0_140,
inference(avatar_split_clause,[],[f786,f1670]) ).
fof(f1670,plain,
( spl0_140
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f786,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1668,plain,
spl0_139,
inference(avatar_split_clause,[],[f785,f1666]) ).
fof(f1666,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f785,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1664,plain,
spl0_138,
inference(avatar_split_clause,[],[f605,f1662]) ).
fof(f1662,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f605,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1660,plain,
spl0_137,
inference(avatar_split_clause,[],[f602,f1658]) ).
fof(f1658,plain,
( spl0_137
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f602,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1656,plain,
spl0_136,
inference(avatar_split_clause,[],[f601,f1654]) ).
fof(f601,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1652,plain,
spl0_135,
inference(avatar_split_clause,[],[f1033,f1650]) ).
fof(f1650,plain,
( spl0_135
<=> ! [X34] :
( ~ class_HOL_Ozero(X34)
| class_HOL_Ozero(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1033,axiom,
! [X34] :
( ~ class_HOL_Ozero(X34)
| class_HOL_Ozero(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(f1648,plain,
spl0_134,
inference(avatar_split_clause,[],[f1032,f1646]) ).
fof(f1646,plain,
( spl0_134
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Power_Opower(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1032,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Power_Opower(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(f1644,plain,
spl0_133,
inference(avatar_split_clause,[],[f1031,f1642]) ).
fof(f1642,plain,
( spl0_133
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1031,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f1640,plain,
spl0_132,
inference(avatar_split_clause,[],[f1030,f1638]) ).
fof(f1638,plain,
( spl0_132
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1030,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f1636,plain,
spl0_131,
inference(avatar_split_clause,[],[f1029,f1634]) ).
fof(f1634,plain,
( spl0_131
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1029,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(f1632,plain,
spl0_130,
inference(avatar_split_clause,[],[f1028,f1630]) ).
fof(f1630,plain,
( spl0_130
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1028,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f1628,plain,
spl0_129,
inference(avatar_split_clause,[],[f1027,f1626]) ).
fof(f1626,plain,
( spl0_129
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1027,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f1624,plain,
spl0_128,
inference(avatar_split_clause,[],[f1026,f1622]) ).
fof(f1622,plain,
( spl0_128
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1026,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(f1620,plain,
spl0_127,
inference(avatar_split_clause,[],[f1025,f1618]) ).
fof(f1618,plain,
( spl0_127
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1025,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(f1616,plain,
spl0_126,
inference(avatar_split_clause,[],[f1024,f1614]) ).
fof(f1614,plain,
( spl0_126
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1024,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(f1612,plain,
spl0_125,
inference(avatar_split_clause,[],[f1023,f1610]) ).
fof(f1610,plain,
( spl0_125
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1023,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f1608,plain,
spl0_124,
inference(avatar_split_clause,[],[f1022,f1606]) ).
fof(f1606,plain,
( spl0_124
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1022,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
fof(f1604,plain,
spl0_123,
inference(avatar_split_clause,[],[f1021,f1602]) ).
fof(f1602,plain,
( spl0_123
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1021,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
fof(f1600,plain,
spl0_122,
inference(avatar_split_clause,[],[f1020,f1598]) ).
fof(f1598,plain,
( spl0_122
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1020,axiom,
! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(f1596,plain,
spl0_121,
inference(avatar_split_clause,[],[f1019,f1594]) ).
fof(f1594,plain,
( spl0_121
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1019,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(f1592,plain,
spl0_120,
inference(avatar_split_clause,[],[f1018,f1590]) ).
fof(f1590,plain,
( spl0_120
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1018,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(f1588,plain,
spl0_119,
inference(avatar_split_clause,[],[f1017,f1586]) ).
fof(f1586,plain,
( spl0_119
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1017,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(f1584,plain,
spl0_118,
inference(avatar_split_clause,[],[f1016,f1582]) ).
fof(f1582,plain,
( spl0_118
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1016,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(f1580,plain,
spl0_117,
inference(avatar_split_clause,[],[f1015,f1578]) ).
fof(f1578,plain,
( spl0_117
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1015,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(f1576,plain,
spl0_116,
inference(avatar_split_clause,[],[f1014,f1574]) ).
fof(f1574,plain,
( spl0_116
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1014,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(f1572,plain,
spl0_115,
inference(avatar_split_clause,[],[f1013,f1570]) ).
fof(f1570,plain,
( spl0_115
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1013,axiom,
! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(f1568,plain,
spl0_114,
inference(avatar_split_clause,[],[f1012,f1566]) ).
fof(f1566,plain,
( spl0_114
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1012,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(f1564,plain,
spl0_113,
inference(avatar_split_clause,[],[f1011,f1562]) ).
fof(f1562,plain,
( spl0_113
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1011,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
fof(f1560,plain,
spl0_112,
inference(avatar_split_clause,[],[f1010,f1558]) ).
fof(f1558,plain,
( spl0_112
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1010,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(f1556,plain,
spl0_111,
inference(avatar_split_clause,[],[f1009,f1554]) ).
fof(f1554,plain,
( spl0_111
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1009,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(f1552,plain,
spl0_110,
inference(avatar_split_clause,[],[f1008,f1550]) ).
fof(f1550,plain,
( spl0_110
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1008,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(f1548,plain,
spl0_109,
inference(avatar_split_clause,[],[f1007,f1546]) ).
fof(f1546,plain,
( spl0_109
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1007,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(f1544,plain,
spl0_108,
inference(avatar_split_clause,[],[f1006,f1542]) ).
fof(f1542,plain,
( spl0_108
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1006,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(f1540,plain,
spl0_107,
inference(avatar_split_clause,[],[f1005,f1538]) ).
fof(f1538,plain,
( spl0_107
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1005,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(f1536,plain,
spl0_106,
inference(avatar_split_clause,[],[f1004,f1534]) ).
fof(f1534,plain,
( spl0_106
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1004,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(f1532,plain,
spl0_105,
inference(avatar_split_clause,[],[f1003,f1530]) ).
fof(f1530,plain,
( spl0_105
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1003,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1528,plain,
spl0_104,
inference(avatar_split_clause,[],[f1002,f1526]) ).
fof(f1526,plain,
( spl0_104
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1002,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(f1524,plain,
spl0_103,
inference(avatar_split_clause,[],[f1001,f1522]) ).
fof(f1522,plain,
( spl0_103
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1001,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1520,plain,
spl0_102,
inference(avatar_split_clause,[],[f1000,f1518]) ).
fof(f1518,plain,
( spl0_102
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1000,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1516,plain,
spl0_101,
inference(avatar_split_clause,[],[f999,f1514]) ).
fof(f1514,plain,
( spl0_101
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f999,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(f1512,plain,
spl0_100,
inference(avatar_split_clause,[],[f998,f1510]) ).
fof(f1510,plain,
( spl0_100
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f998,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(f1508,plain,
spl0_99,
inference(avatar_split_clause,[],[f997,f1506]) ).
fof(f1506,plain,
( spl0_99
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f997,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(f1504,plain,
spl0_98,
inference(avatar_split_clause,[],[f996,f1502]) ).
fof(f1502,plain,
( spl0_98
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f996,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
fof(f1500,plain,
spl0_97,
inference(avatar_split_clause,[],[f995,f1498]) ).
fof(f1498,plain,
( spl0_97
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f995,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(f1496,plain,
spl0_96,
inference(avatar_split_clause,[],[f994,f1494]) ).
fof(f1494,plain,
( spl0_96
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f994,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1492,plain,
spl0_95,
inference(avatar_split_clause,[],[f993,f1490]) ).
fof(f1490,plain,
( spl0_95
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f993,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(f1488,plain,
spl0_94,
inference(avatar_split_clause,[],[f992,f1486]) ).
fof(f1486,plain,
( spl0_94
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f992,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(f1484,plain,
spl0_93,
inference(avatar_split_clause,[],[f991,f1482]) ).
fof(f1482,plain,
( spl0_93
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f991,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(f1480,plain,
spl0_92,
inference(avatar_split_clause,[],[f990,f1478]) ).
fof(f1478,plain,
( spl0_92
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f990,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1476,plain,
spl0_91,
inference(avatar_split_clause,[],[f989,f1474]) ).
fof(f1474,plain,
( spl0_91
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f989,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1472,plain,
spl0_90,
inference(avatar_split_clause,[],[f988,f1470]) ).
fof(f1470,plain,
( spl0_90
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f988,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1468,plain,
spl0_89,
inference(avatar_split_clause,[],[f987,f1466]) ).
fof(f1466,plain,
( spl0_89
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f987,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1464,plain,
spl0_88,
inference(avatar_split_clause,[],[f986,f1462]) ).
fof(f1462,plain,
( spl0_88
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f986,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1460,plain,
spl0_87,
inference(avatar_split_clause,[],[f985,f1458]) ).
fof(f1458,plain,
( spl0_87
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f985,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1456,plain,
spl0_86,
inference(avatar_split_clause,[],[f984,f1454]) ).
fof(f1454,plain,
( spl0_86
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f984,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1452,plain,
spl0_85,
inference(avatar_split_clause,[],[f983,f1450]) ).
fof(f1450,plain,
( spl0_85
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f983,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1448,plain,
spl0_84,
inference(avatar_split_clause,[],[f982,f1446]) ).
fof(f1446,plain,
( spl0_84
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f982,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1444,plain,
spl0_83,
inference(avatar_split_clause,[],[f981,f1442]) ).
fof(f1442,plain,
( spl0_83
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f981,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1440,plain,
spl0_82,
inference(avatar_split_clause,[],[f980,f1438]) ).
fof(f1438,plain,
( spl0_82
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f980,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1436,plain,
spl0_81,
inference(avatar_split_clause,[],[f907,f1434]) ).
fof(f1434,plain,
( spl0_81
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f907,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1432,plain,
~ spl0_80,
inference(avatar_split_clause,[],[f883,f1429]) ).
fof(f883,axiom,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pne_0) ).
fof(f1427,plain,
spl0_79,
inference(avatar_split_clause,[],[f867,f1424]) ).
fof(f1424,plain,
( spl0_79
<=> v_na____ = c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f867,axiom,
v_na____ = c_Polynomial_Odegree(v_pa____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dpn_0) ).
fof(f1422,plain,
spl0_78,
inference(avatar_split_clause,[],[f640,f1420]) ).
fof(f640,axiom,
! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1418,plain,
spl0_77,
inference(avatar_split_clause,[],[f384,f1416]) ).
fof(f384,axiom,
! [X13] : ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f1414,plain,
~ spl0_76,
inference(avatar_split_clause,[],[f858,f1411]) ).
fof(f1411,plain,
( spl0_76
<=> c_HOL_Ozero__class_Ozero(tc_nat) = v_na____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f858,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != v_na____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n0_0) ).
fof(f1409,plain,
spl0_75,
inference(avatar_split_clause,[],[f789,f1407]) ).
fof(f1407,plain,
( spl0_75
<=> ! [X14] : c_lessequals(X14,X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f789,axiom,
! [X14] : c_lessequals(X14,X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f1405,plain,
spl0_74,
inference(avatar_split_clause,[],[f603,f1403]) ).
fof(f1403,plain,
( spl0_74
<=> ! [X14] : ~ c_HOL_Oord__class_Oless(X14,X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f603,axiom,
! [X14] : ~ c_HOL_Oord__class_Oless(X14,X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f1401,plain,
~ spl0_73,
inference(avatar_split_clause,[],[f906,f1398]) ).
fof(f906,axiom,
~ c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1396,plain,
spl0_72,
inference(avatar_split_clause,[],[f979,f1393]) ).
fof(f979,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f1391,plain,
spl0_71,
inference(avatar_split_clause,[],[f978,f1388]) ).
fof(f1388,plain,
( spl0_71
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f978,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f1386,plain,
spl0_70,
inference(avatar_split_clause,[],[f977,f1383]) ).
fof(f1383,plain,
( spl0_70
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f977,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1381,plain,
spl0_69,
inference(avatar_split_clause,[],[f976,f1378]) ).
fof(f976,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
fof(f1376,plain,
spl0_68,
inference(avatar_split_clause,[],[f975,f1373]) ).
fof(f975,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1371,plain,
spl0_67,
inference(avatar_split_clause,[],[f974,f1368]) ).
fof(f1368,plain,
( spl0_67
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f974,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1366,plain,
spl0_66,
inference(avatar_split_clause,[],[f973,f1363]) ).
fof(f973,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1361,plain,
spl0_65,
inference(avatar_split_clause,[],[f972,f1358]) ).
fof(f1358,plain,
( spl0_65
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f972,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1356,plain,
spl0_64,
inference(avatar_split_clause,[],[f971,f1353]) ).
fof(f1353,plain,
( spl0_64
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f971,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(f1351,plain,
spl0_63,
inference(avatar_split_clause,[],[f970,f1348]) ).
fof(f970,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1346,plain,
spl0_62,
inference(avatar_split_clause,[],[f969,f1343]) ).
fof(f969,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1341,plain,
spl0_61,
inference(avatar_split_clause,[],[f968,f1338]) ).
fof(f1338,plain,
( spl0_61
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f968,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1336,plain,
spl0_60,
inference(avatar_split_clause,[],[f967,f1333]) ).
fof(f967,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1331,plain,
spl0_59,
inference(avatar_split_clause,[],[f966,f1328]) ).
fof(f1328,plain,
( spl0_59
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f966,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f1326,plain,
spl0_58,
inference(avatar_split_clause,[],[f965,f1323]) ).
fof(f1323,plain,
( spl0_58
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f965,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f1321,plain,
spl0_57,
inference(avatar_split_clause,[],[f964,f1318]) ).
fof(f964,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1316,plain,
spl0_56,
inference(avatar_split_clause,[],[f963,f1313]) ).
fof(f1313,plain,
( spl0_56
<=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f963,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
fof(f1311,plain,
spl0_55,
inference(avatar_split_clause,[],[f962,f1308]) ).
fof(f1308,plain,
( spl0_55
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f962,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f1306,plain,
spl0_54,
inference(avatar_split_clause,[],[f961,f1303]) ).
fof(f1303,plain,
( spl0_54
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f961,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1301,plain,
spl0_53,
inference(avatar_split_clause,[],[f960,f1298]) ).
fof(f1298,plain,
( spl0_53
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f960,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1296,plain,
spl0_52,
inference(avatar_split_clause,[],[f959,f1293]) ).
fof(f1293,plain,
( spl0_52
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f959,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1291,plain,
spl0_51,
inference(avatar_split_clause,[],[f958,f1288]) ).
fof(f1288,plain,
( spl0_51
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f958,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f1286,plain,
spl0_50,
inference(avatar_split_clause,[],[f957,f1283]) ).
fof(f957,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f1281,plain,
spl0_49,
inference(avatar_split_clause,[],[f956,f1278]) ).
fof(f1278,plain,
( spl0_49
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f956,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1276,plain,
spl0_48,
inference(avatar_split_clause,[],[f955,f1273]) ).
fof(f1273,plain,
( spl0_48
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f955,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1271,plain,
spl0_47,
inference(avatar_split_clause,[],[f954,f1268]) ).
fof(f1268,plain,
( spl0_47
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f954,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1266,plain,
spl0_46,
inference(avatar_split_clause,[],[f953,f1263]) ).
fof(f1263,plain,
( spl0_46
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f953,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1261,plain,
spl0_45,
inference(avatar_split_clause,[],[f952,f1258]) ).
fof(f1258,plain,
( spl0_45
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f952,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1256,plain,
spl0_44,
inference(avatar_split_clause,[],[f951,f1253]) ).
fof(f951,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1251,plain,
spl0_43,
inference(avatar_split_clause,[],[f950,f1248]) ).
fof(f950,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1246,plain,
spl0_42,
inference(avatar_split_clause,[],[f949,f1243]) ).
fof(f1243,plain,
( spl0_42
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f949,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f1241,plain,
spl0_41,
inference(avatar_split_clause,[],[f948,f1238]) ).
fof(f1238,plain,
( spl0_41
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f948,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1236,plain,
spl0_40,
inference(avatar_split_clause,[],[f947,f1233]) ).
fof(f1233,plain,
( spl0_40
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f947,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1231,plain,
spl0_39,
inference(avatar_split_clause,[],[f946,f1228]) ).
fof(f1228,plain,
( spl0_39
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f946,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1226,plain,
spl0_38,
inference(avatar_split_clause,[],[f945,f1223]) ).
fof(f1223,plain,
( spl0_38
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f945,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1221,plain,
spl0_37,
inference(avatar_split_clause,[],[f944,f1218]) ).
fof(f944,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
fof(f1216,plain,
spl0_36,
inference(avatar_split_clause,[],[f943,f1213]) ).
fof(f1213,plain,
( spl0_36
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f943,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1211,plain,
spl0_35,
inference(avatar_split_clause,[],[f942,f1208]) ).
fof(f1208,plain,
( spl0_35
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f942,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1206,plain,
spl0_34,
inference(avatar_split_clause,[],[f941,f1203]) ).
fof(f1203,plain,
( spl0_34
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f941,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1201,plain,
spl0_33,
inference(avatar_split_clause,[],[f940,f1198]) ).
fof(f1198,plain,
( spl0_33
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f940,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1196,plain,
spl0_32,
inference(avatar_split_clause,[],[f939,f1193]) ).
fof(f939,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f1191,plain,
spl0_31,
inference(avatar_split_clause,[],[f938,f1188]) ).
fof(f938,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f1186,plain,
spl0_30,
inference(avatar_split_clause,[],[f937,f1183]) ).
fof(f937,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1181,plain,
spl0_29,
inference(avatar_split_clause,[],[f936,f1178]) ).
fof(f1178,plain,
( spl0_29
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f936,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1176,plain,
spl0_28,
inference(avatar_split_clause,[],[f935,f1173]) ).
fof(f935,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1171,plain,
spl0_27,
inference(avatar_split_clause,[],[f934,f1168]) ).
fof(f1168,plain,
( spl0_27
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f934,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1166,plain,
spl0_26,
inference(avatar_split_clause,[],[f933,f1163]) ).
fof(f1163,plain,
( spl0_26
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f933,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1161,plain,
spl0_25,
inference(avatar_split_clause,[],[f932,f1158]) ).
fof(f1158,plain,
( spl0_25
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f932,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1156,plain,
spl0_24,
inference(avatar_split_clause,[],[f931,f1153]) ).
fof(f1153,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f931,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1151,plain,
spl0_23,
inference(avatar_split_clause,[],[f930,f1148]) ).
fof(f1148,plain,
( spl0_23
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f930,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1146,plain,
spl0_22,
inference(avatar_split_clause,[],[f929,f1143]) ).
fof(f1143,plain,
( spl0_22
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f929,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1141,plain,
spl0_21,
inference(avatar_split_clause,[],[f928,f1138]) ).
fof(f1138,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f928,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1136,plain,
spl0_20,
inference(avatar_split_clause,[],[f927,f1133]) ).
fof(f1133,plain,
( spl0_20
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f927,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1131,plain,
spl0_19,
inference(avatar_split_clause,[],[f926,f1128]) ).
fof(f1128,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f926,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1126,plain,
spl0_18,
inference(avatar_split_clause,[],[f925,f1123]) ).
fof(f1123,plain,
( spl0_18
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f925,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1121,plain,
spl0_17,
inference(avatar_split_clause,[],[f924,f1118]) ).
fof(f1118,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f924,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1116,plain,
spl0_16,
inference(avatar_split_clause,[],[f923,f1113]) ).
fof(f923,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1111,plain,
spl0_15,
inference(avatar_split_clause,[],[f922,f1108]) ).
fof(f1108,plain,
( spl0_15
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f922,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1106,plain,
spl0_14,
inference(avatar_split_clause,[],[f921,f1103]) ).
fof(f1103,plain,
( spl0_14
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f921,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1101,plain,
spl0_13,
inference(avatar_split_clause,[],[f920,f1098]) ).
fof(f1098,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f920,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1096,plain,
spl0_12,
inference(avatar_split_clause,[],[f919,f1093]) ).
fof(f1093,plain,
( spl0_12
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f919,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1091,plain,
spl0_11,
inference(avatar_split_clause,[],[f918,f1088]) ).
fof(f1088,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f918,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1086,plain,
spl0_10,
inference(avatar_split_clause,[],[f917,f1083]) ).
fof(f1083,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f917,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1081,plain,
spl0_9,
inference(avatar_split_clause,[],[f916,f1078]) ).
fof(f1078,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f916,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1076,plain,
spl0_8,
inference(avatar_split_clause,[],[f915,f1073]) ).
fof(f1073,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f915,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1071,plain,
spl0_7,
inference(avatar_split_clause,[],[f914,f1068]) ).
fof(f1068,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f914,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1066,plain,
spl0_6,
inference(avatar_split_clause,[],[f913,f1063]) ).
fof(f1063,plain,
( spl0_6
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f913,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1061,plain,
spl0_5,
inference(avatar_split_clause,[],[f912,f1058]) ).
fof(f1058,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f912,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1056,plain,
spl0_4,
inference(avatar_split_clause,[],[f911,f1053]) ).
fof(f1053,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f911,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1051,plain,
spl0_3,
inference(avatar_split_clause,[],[f910,f1048]) ).
fof(f1048,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f910,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1046,plain,
spl0_2,
inference(avatar_split_clause,[],[f909,f1043]) ).
fof(f1043,plain,
( spl0_2
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f909,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1041,plain,
spl0_1,
inference(avatar_split_clause,[],[f908,f1038]) ).
fof(f1038,plain,
( spl0_1
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f908,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG424-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 20:00:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (28458)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.41 % (28462)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.41 % (28461)WARNING: value z3 for option sas not known
% 0.21/0.42 % (28459)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.42 % (28461)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)
% 0.21/0.42 % (28460)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.42 % (28464)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)
% 0.21/0.42 % (28465)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)
% 0.21/0.42 % (28463)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)
% 0.21/0.45 TRYING [1]
% 0.21/0.46 TRYING [2]
% 1.80/0.64 TRYING [3]
% 1.87/0.70 TRYING [1]
% 2.30/0.71 % (28463)First to succeed.
% 2.30/0.73 % (28463)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28458"
% 2.30/0.73 % (28463)Refutation found. Thanks to Tanya!
% 2.30/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.30/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.30/0.74 % (28463)------------------------------
% 2.30/0.74 % (28463)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.30/0.74 % (28463)Termination reason: Refutation
% 2.30/0.74
% 2.30/0.74 % (28463)Memory used [KB]: 6731
% 2.30/0.74 % (28463)Time elapsed: 0.312 s
% 2.30/0.74 % (28463)Instructions burned: 746 (million)
% 2.30/0.74 % (28458)Success in time 0.367 s
%------------------------------------------------------------------------------