TSTP Solution File: LCL447-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL447-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:42:22 EDT 2024
% Result : Unsatisfiable 1.49s 0.59s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1238
% Syntax : Number of formulae : 2137 ( 691 unt; 0 def)
% Number of atoms : 4580 ( 427 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 4240 (1797 ~;1770 |; 0 &)
% ( 673 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 711 ( 709 usr; 674 prp; 0-3 aty)
% Number of functors : 129 ( 129 usr; 22 con; 0-6 aty)
% Number of variables : 3180 (3180 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6164,plain,
$false,
inference(avatar_sat_refutation,[],[f1377,f1382,f1387,f1392,f1397,f1402,f1407,f1412,f1417,f1422,f1427,f1432,f1437,f1442,f1447,f1452,f1457,f1462,f1467,f1472,f1477,f1482,f1487,f1492,f1497,f1502,f1507,f1512,f1517,f1522,f1527,f1532,f1537,f1542,f1547,f1552,f1557,f1562,f1567,f1572,f1577,f1582,f1587,f1592,f1597,f1602,f1607,f1612,f1617,f1622,f1627,f1632,f1636,f1641,f1646,f1650,f1654,f1658,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1703,f1707,f1711,f1715,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1763,f1767,f1771,f1775,f1779,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1815,f1819,f1823,f1827,f1831,f1835,f1839,f1843,f1847,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2143,f2147,f2151,f2155,f2159,f2163,f2167,f2171,f2175,f2179,f2183,f2187,f2191,f2195,f2199,f2203,f2207,f2211,f2215,f2219,f2223,f2227,f2231,f2235,f2239,f2243,f2247,f2251,f2255,f2259,f2263,f2267,f2271,f2275,f2279,f2283,f2287,f2291,f2295,f2299,f2303,f2307,f2311,f2315,f2319,f2323,f2327,f2331,f2335,f2339,f2343,f2347,f2351,f2355,f2359,f2363,f2367,f2371,f2375,f2379,f2383,f2387,f2391,f2395,f2399,f2403,f2407,f2411,f2415,f2419,f2423,f2427,f2431,f2435,f2439,f2443,f2447,f2451,f2455,f2459,f2463,f2467,f2471,f2475,f2479,f2483,f2487,f2491,f2495,f2499,f2503,f2507,f2511,f2515,f2519,f2523,f2527,f2531,f2535,f2539,f2543,f2547,f2551,f2862,f2866,f2871,f2875,f2879,f2883,f2887,f2891,f2895,f2899,f2903,f2907,f2911,f2915,f2919,f2923,f2927,f2931,f2935,f2939,f2944,f2948,f2952,f2956,f2960,f2964,f2968,f2972,f2976,f2980,f2984,f2988,f2992,f2996,f3000,f3004,f3008,f3012,f3016,f3020,f3040,f3044,f3048,f3052,f3056,f3060,f3064,f3068,f3072,f3076,f3080,f3084,f3088,f3092,f3096,f3100,f3104,f3108,f3112,f3116,f3120,f3124,f3135,f3141,f3145,f3149,f3153,f3157,f3161,f3165,f3169,f3173,f3179,f3183,f3187,f3191,f3195,f3199,f3203,f3207,f3211,f3215,f3221,f3242,f3246,f3250,f3254,f3258,f3262,f3266,f3270,f3274,f3278,f3282,f3286,f3290,f3294,f3298,f3302,f3306,f3310,f3314,f3318,f3322,f3326,f3330,f3347,f3380,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3412,f3416,f3420,f3431,f3435,f3439,f3443,f3447,f3451,f3456,f3460,f3464,f3468,f3472,f3476,f3480,f3484,f3488,f3492,f3496,f3504,f3508,f3512,f3516,f3520,f3524,f3528,f3532,f3536,f3540,f3544,f3548,f3552,f3556,f3560,f3564,f3568,f3572,f3576,f3580,f3584,f3588,f3611,f3669,f3673,f3677,f3681,f3685,f3689,f3693,f3697,f3701,f3705,f3709,f3713,f3717,f3721,f3725,f3730,f3734,f3748,f3764,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3796,f3800,f3804,f3808,f3812,f3816,f3820,f3832,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3921,f3925,f3929,f3933,f3937,f3941,f3945,f3949,f3953,f4049,f4053,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4123,f4127,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4167,f4171,f4175,f4179,f4183,f4256,f4260,f4264,f4268,f4283,f4287,f4291,f4296,f4300,f4304,f4329,f4333,f4337,f4341,f4345,f4349,f4353,f4357,f4361,f4365,f4369,f4386,f4451,f4455,f4491,f4495,f4499,f4503,f4507,f4592,f4596,f4600,f4604,f4608,f4612,f4638,f4645,f4649,f4653,f4698,f4702,f4706,f4722,f4728,f4732,f4736,f4748,f4760,f4764,f4784,f4788,f4792,f4796,f4868,f4872,f4879,f4883,f4899,f4941,f4945,f4963,f4967,f5047,f5051,f5063,f5076,f5091,f5095,f5099,f5125,f5140,f5157,f5161,f5188,f5192,f5196,f5200,f5204,f5208,f5212,f5257,f5346,f5350,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5382,f5450,f5454,f5458,f5468,f5472,f5476,f5480,f5484,f5488,f5492,f5525,f5643,f5647,f5651,f5658,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5694,f5698,f5737,f5741,f5745,f5749,f5753,f5757,f5761,f5765,f5769,f5773,f5840,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5893,f5964,f5986,f5990,f5994,f5998,f6002,f6006,f6010,f6014,f6018,f6022,f6107,f6112,f6116,f6120,f6124,f6162,f6163]) ).
fof(f6163,plain,
( ~ spl0_1
| spl0_49
| ~ spl0_672 ),
inference(avatar_split_clause,[],[f6156,f6122,f1614,f1374]) ).
fof(f1374,plain,
( spl0_1
<=> c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1614,plain,
( spl0_49
<=> c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f6122,plain,
( spl0_672
<=> ! [X0,X3,X2,X1] :
( c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f6156,plain,
( ~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| spl0_49
| ~ spl0_672 ),
inference(resolution,[],[f6123,f1616]) ).
fof(f1616,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| spl0_49 ),
inference(avatar_component_clause,[],[f1614]) ).
fof(f6123,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) )
| ~ spl0_672 ),
inference(avatar_component_clause,[],[f6122]) ).
fof(f6162,plain,
( spl0_673
| ~ spl0_392
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f3646,f3574,f3390,f6160]) ).
fof(f6160,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( c_lessequals(c_uminus(X0,tc_set(X1)),X2,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(c_uminus(X0,tc_set(X1)),X2,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f3390,plain,
( spl0_392
<=> ! [X1,X40,X19] :
( ~ c_in(X40,X19,X1)
| ~ c_in(X40,c_uminus(X19,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f3574,plain,
( spl0_435
<=> ! [X21,X1,X19] :
( c_lessequals(X19,X21,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X19,X21,X1),X19,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f3646,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_uminus(X0,tc_set(X1)),X2,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(c_uminus(X0,tc_set(X1)),X2,X1),X0,X1) )
| ~ spl0_392
| ~ spl0_435 ),
inference(resolution,[],[f3575,f3391]) ).
fof(f3391,plain,
( ! [X40,X1,X19] :
( ~ c_in(X40,c_uminus(X19,tc_set(X1)),X1)
| ~ c_in(X40,X19,X1) )
| ~ spl0_392 ),
inference(avatar_component_clause,[],[f3390]) ).
fof(f3575,plain,
( ! [X21,X1,X19] :
( c_in(c_Main_OsubsetI__1(X19,X21,X1),X19,X1)
| c_lessequals(X19,X21,tc_set(X1)) )
| ~ spl0_435 ),
inference(avatar_component_clause,[],[f3574]) ).
fof(f6124,plain,
( spl0_672
| ~ spl0_456
| ~ spl0_554 ),
inference(avatar_split_clause,[],[f4633,f4610,f3732,f6122]) ).
fof(f3732,plain,
( spl0_456
<=> ! [X59,X7,X8,X1] : c_in(c_PropLog_Opl_Oop_A_N_62(X7,c_PropLog_Opl_Oop_A_N_62(X59,X7,X1),X1),c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f4610,plain,
( spl0_554
<=> ! [X59,X7,X8,X1] :
( ~ c_in(X7,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| c_in(X59,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X7,X59,X1),c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f4633,plain,
( ! [X2,X3,X0,X1] :
( c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) )
| ~ spl0_456
| ~ spl0_554 ),
inference(resolution,[],[f4611,f3733]) ).
fof(f3733,plain,
( ! [X59,X1,X8,X7] : c_in(c_PropLog_Opl_Oop_A_N_62(X7,c_PropLog_Opl_Oop_A_N_62(X59,X7,X1),X1),c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| ~ spl0_456 ),
inference(avatar_component_clause,[],[f3732]) ).
fof(f4611,plain,
( ! [X59,X1,X8,X7] :
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(X7,X59,X1),c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| c_in(X59,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| ~ c_in(X7,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1)) )
| ~ spl0_554 ),
inference(avatar_component_clause,[],[f4610]) ).
fof(f6120,plain,
( spl0_671
| ~ spl0_463
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f4559,f4505,f3782,f6118]) ).
fof(f6118,plain,
( spl0_671
<=> ! [X0,X1] :
( ~ c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
| c_less(c_Main_OImageE__1(X1,X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f3782,plain,
( spl0_463
<=> ! [X29,X9] :
( c_less(X9,X29,tc_nat)
| ~ c_in(c_Pair(X9,X29,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f4505,plain,
( spl0_548
<=> ! [X19,X11,X12,X1,X20] :
( ~ c_in(X12,c_Relation_OImage(X20,X19,X11,X1),X1)
| c_in(c_Pair(c_Main_OImageE__1(X19,X12,X20,X11,X1),X12,X11,X1),X20,tc_prod(X11,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f4559,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
| c_less(c_Main_OImageE__1(X1,X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) )
| ~ spl0_463
| ~ spl0_548 ),
inference(resolution,[],[f4506,f3783]) ).
fof(f3783,plain,
( ! [X29,X9] :
( ~ c_in(c_Pair(X9,X29,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
| c_less(X9,X29,tc_nat) )
| ~ spl0_463 ),
inference(avatar_component_clause,[],[f3782]) ).
fof(f4506,plain,
( ! [X11,X1,X19,X12,X20] :
( c_in(c_Pair(c_Main_OImageE__1(X19,X12,X20,X11,X1),X12,X11,X1),X20,tc_prod(X11,X1))
| ~ c_in(X12,c_Relation_OImage(X20,X19,X11,X1),X1) )
| ~ spl0_548 ),
inference(avatar_component_clause,[],[f4505]) ).
fof(f6116,plain,
( spl0_670
| ~ spl0_428
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4011,f3927,f3546,f6114]) ).
fof(f6114,plain,
( spl0_670
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_Pow(X3,X2),X2),X2)
| ~ c_lessequals(X1,X3,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f3546,plain,
( spl0_428
<=> ! [X21,X1,X19] :
( ~ c_lessequals(X19,X21,tc_set(X1))
| c_in(X19,c_Pow(X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f3927,plain,
( spl0_487
<=> ! [X41,X19,X42,X1] :
( ~ c_in(X19,X41,X1)
| ~ c_in(X41,X42,tc_set(X1))
| c_in(X19,c_Union(X42,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f4011,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_Pow(X3,X2),X2),X2)
| ~ c_lessequals(X1,X3,tc_set(X2)) )
| ~ spl0_428
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3547]) ).
fof(f3547,plain,
( ! [X21,X1,X19] :
( c_in(X19,c_Pow(X21,X1),tc_set(X1))
| ~ c_lessequals(X19,X21,tc_set(X1)) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f3546]) ).
fof(f3928,plain,
( ! [X41,X1,X19,X42] :
( ~ c_in(X41,X42,tc_set(X1))
| ~ c_in(X19,X41,X1)
| c_in(X19,c_Union(X42,X1),X1) )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f3927]) ).
fof(f6112,plain,
( spl0_669
| ~ spl0_387
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f3642,f3574,f3328,f6110]) ).
fof(f6110,plain,
( spl0_669
<=> ! [X2,X0,X1] :
( c_lessequals(c_insert(X0,c_emptyset,X1),X2,tc_set(X1))
| c_Main_OsubsetI__1(c_insert(X0,c_emptyset,X1),X2,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f3328,plain,
( spl0_387
<=> ! [X4,X12,X1] :
( X4 = X12
| ~ c_in(X12,c_insert(X4,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f3642,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_insert(X0,c_emptyset,X1),X2,tc_set(X1))
| c_Main_OsubsetI__1(c_insert(X0,c_emptyset,X1),X2,X1) = X0 )
| ~ spl0_387
| ~ spl0_435 ),
inference(resolution,[],[f3575,f3329]) ).
fof(f3329,plain,
( ! [X1,X4,X12] :
( ~ c_in(X12,c_insert(X4,c_emptyset,X1),X1)
| X4 = X12 )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f3328]) ).
fof(f6107,plain,
( spl0_668
| ~ spl0_389
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f3640,f3574,f3378,f6105]) ).
fof(f6105,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( c_lessequals(c_Datatype_Oo2s(X0,X1),X2,tc_set(X1))
| c_Datatype_Ooption_OSome(c_Main_OsubsetI__1(c_Datatype_Oo2s(X0,X1),X2,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f3378,plain,
( spl0_389
<=> ! [X9,X1,X10] :
( c_Datatype_Ooption_OSome(X9,X1) = X10
| ~ c_in(X9,c_Datatype_Oo2s(X10,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f3640,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Datatype_Oo2s(X0,X1),X2,tc_set(X1))
| c_Datatype_Ooption_OSome(c_Main_OsubsetI__1(c_Datatype_Oo2s(X0,X1),X2,X1),X1) = X0 )
| ~ spl0_389
| ~ spl0_435 ),
inference(resolution,[],[f3575,f3379]) ).
fof(f3379,plain,
( ! [X10,X1,X9] :
( ~ c_in(X9,c_Datatype_Oo2s(X10,X1),X1)
| c_Datatype_Ooption_OSome(X9,X1) = X10 )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f3378]) ).
fof(f6022,plain,
( spl0_667
| ~ spl0_534
| ~ spl0_644 ),
inference(avatar_split_clause,[],[f5821,f5767,f4343,f6020]) ).
fof(f6020,plain,
( spl0_667
<=> ! [X0,X1] : c_Main_ORangeE__1(X0,c_Relation_OId,X1,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f4343,plain,
( spl0_534
<=> ! [X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f5767,plain,
( spl0_644
<=> ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
| c_Main_ORangeE__1(X0,c_Relation_OId,X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f5821,plain,
( ! [X0,X1] : c_Main_ORangeE__1(X0,c_Relation_OId,X1,X1) = X0
| ~ spl0_534
| ~ spl0_644 ),
inference(resolution,[],[f5768,f4344]) ).
fof(f4344,plain,
( ! [X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
| ~ spl0_534 ),
inference(avatar_component_clause,[],[f4343]) ).
fof(f5768,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
| c_Main_ORangeE__1(X0,c_Relation_OId,X1,X1) = X0 )
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f5767]) ).
fof(f6018,plain,
( spl0_666
| ~ spl0_61
| ~ spl0_581 ),
inference(avatar_split_clause,[],[f5020,f4965,f1669,f6016]) ).
fof(f6016,plain,
( spl0_666
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Odprod(c_emptyset,X1,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1669,plain,
( spl0_61
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f4965,plain,
( spl0_581
<=> ! [X43,X11,X40,X20,X1] :
( ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdprodE__1(X40,X20,X43,X1,X11),c_Main_OdprodE__3(X40,X20,X43,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f5020,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Odprod(c_emptyset,X1,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
| ~ spl0_61
| ~ spl0_581 ),
inference(resolution,[],[f4966,f1670]) ).
fof(f1670,plain,
( ! [X1,X4] : ~ c_in(X4,c_emptyset,X1)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f4966,plain,
( ! [X40,X11,X1,X43,X20] :
( c_in(c_Pair(c_Main_OdprodE__1(X40,X20,X43,X1,X11),c_Main_OdprodE__3(X40,X20,X43,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) )
| ~ spl0_581 ),
inference(avatar_component_clause,[],[f4965]) ).
fof(f6014,plain,
( spl0_665
| ~ spl0_61
| ~ spl0_580 ),
inference(avatar_split_clause,[],[f4988,f4961,f1669,f6012]) ).
fof(f6012,plain,
( spl0_665
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Odprod(X1,c_emptyset,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f4961,plain,
( spl0_580
<=> ! [X43,X11,X40,X20,X1] :
( ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdprodE__2(X40,X20,X43,X1,X11),c_Main_OdprodE__4(X40,X20,X43,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f4988,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Odprod(X1,c_emptyset,X2,X3),tc_prod(tc_set(tc_Datatype__Universe_Onode(X2,X3)),tc_set(tc_Datatype__Universe_Onode(X2,X3))))
| ~ spl0_61
| ~ spl0_580 ),
inference(resolution,[],[f4962,f1670]) ).
fof(f4962,plain,
( ! [X40,X11,X1,X43,X20] :
( c_in(c_Pair(c_Main_OdprodE__2(X40,X20,X43,X1,X11),c_Main_OdprodE__4(X40,X20,X43,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) )
| ~ spl0_580 ),
inference(avatar_component_clause,[],[f4961]) ).
fof(f6010,plain,
( spl0_664
| ~ spl0_447
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f4558,f4505,f3695,f6008]) ).
fof(f6008,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
| c_Main_OImageE__1(X1,X0,c_Relation_OId,X2,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f3695,plain,
( spl0_447
<=> ! [X4,X12,X1] :
( X4 = X12
| ~ c_in(c_Pair(X4,X12,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f4558,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
| c_Main_OImageE__1(X1,X0,c_Relation_OId,X2,X2) = X0 )
| ~ spl0_447
| ~ spl0_548 ),
inference(resolution,[],[f4506,f3696]) ).
fof(f3696,plain,
( ! [X1,X4,X12] :
( ~ c_in(c_Pair(X4,X12,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| X4 = X12 )
| ~ spl0_447 ),
inference(avatar_component_clause,[],[f3695]) ).
fof(f6006,plain,
( spl0_663
| ~ spl0_464
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f4459,f4449,f3786,f6004]) ).
fof(f6004,plain,
( spl0_663
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
| ~ c_in(X2,X1,tc_nat)
| ~ c_less(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f3786,plain,
( spl0_464
<=> ! [X29,X9] :
( ~ c_less(X9,X29,tc_nat)
| c_in(c_Pair(X9,X29,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f4449,plain,
( spl0_542
<=> ! [X4,X19,X11,X12,X1,X20] :
( ~ c_in(X4,X19,X1)
| c_in(X12,c_Relation_OImage(X20,X19,X1,X11),X11)
| ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f4459,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Wellfounded__Relations_Oless__than,X1,tc_nat,tc_nat),tc_nat)
| ~ c_in(X2,X1,tc_nat)
| ~ c_less(X2,X0,tc_nat) )
| ~ spl0_464
| ~ spl0_542 ),
inference(resolution,[],[f4450,f3787]) ).
fof(f3787,plain,
( ! [X29,X9] :
( c_in(c_Pair(X9,X29,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat))
| ~ c_less(X9,X29,tc_nat) )
| ~ spl0_464 ),
inference(avatar_component_clause,[],[f3786]) ).
fof(f4450,plain,
( ! [X11,X1,X19,X4,X12,X20] :
( ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11))
| c_in(X12,c_Relation_OImage(X20,X19,X1,X11),X11)
| ~ c_in(X4,X19,X1) )
| ~ spl0_542 ),
inference(avatar_component_clause,[],[f4449]) ).
fof(f6002,plain,
( spl0_662
| ~ spl0_313
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4238,f4173,f2986,f6000]) ).
fof(f6000,plain,
( spl0_662
<=> ! [X4,X0,X3,X2,X1] : c_in(X0,c_Relation_ORange(c_insert(c_Pair(X1,X0,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f2986,plain,
( spl0_313
<=> ! [X9,X21,X1] : c_in(X9,c_insert(X9,X21,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f4173,plain,
( spl0_517
<=> ! [X4,X11,X20,X12,X1] :
( c_in(X12,c_Relation_ORange(X20,X1,X11),X11)
| ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f4238,plain,
( ! [X2,X3,X0,X1,X4] : c_in(X0,c_Relation_ORange(c_insert(c_Pair(X1,X0,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X3)
| ~ spl0_313
| ~ spl0_517 ),
inference(resolution,[],[f4174,f2987]) ).
fof(f2987,plain,
( ! [X21,X1,X9] : c_in(X9,c_insert(X9,X21,X1),X1)
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f2986]) ).
fof(f4174,plain,
( ! [X11,X1,X4,X12,X20] :
( ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11))
| c_in(X12,c_Relation_ORange(X20,X1,X11),X11) )
| ~ spl0_517 ),
inference(avatar_component_clause,[],[f4173]) ).
fof(f5998,plain,
( spl0_661
| ~ spl0_313
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4213,f4157,f2986,f5996]) ).
fof(f5996,plain,
( spl0_661
<=> ! [X4,X0,X3,X2,X1] : c_in(X0,c_Relation_ODomain(c_insert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f4157,plain,
( spl0_513
<=> ! [X4,X11,X12,X1,X20] :
( c_in(X4,c_Relation_ODomain(X20,X1,X11),X1)
| ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f4213,plain,
( ! [X2,X3,X0,X1,X4] : c_in(X0,c_Relation_ODomain(c_insert(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)),X2,X3),X2)
| ~ spl0_313
| ~ spl0_513 ),
inference(resolution,[],[f4158,f2987]) ).
fof(f4158,plain,
( ! [X11,X1,X4,X12,X20] :
( ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11))
| c_in(X4,c_Relation_ODomain(X20,X1,X11),X1) )
| ~ spl0_513 ),
inference(avatar_component_clause,[],[f4157]) ).
fof(f5994,plain,
( spl0_660
| ~ spl0_306
| ~ spl0_506 ),
inference(avatar_split_clause,[],[f4186,f4129,f2958,f5992]) ).
fof(f5992,plain,
( spl0_660
<=> ! [X0,X1] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_nat)
| ~ c_Divides_Oop_Advd(c_0,X1,tc_nat)
| c_0 = c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f2958,plain,
( spl0_306
<=> ! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f4129,plain,
( spl0_506
<=> ! [X18,X24,X15] :
( ~ c_Divides_Oop_Advd(X15,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X15,X18,tc_nat)
| c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f4186,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_nat)
| ~ c_Divides_Oop_Advd(c_0,X1,tc_nat)
| c_0 = c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)) )
| ~ spl0_306
| ~ spl0_506 ),
inference(resolution,[],[f4130,f2959]) ).
fof(f2959,plain,
( ! [X18] :
( ~ c_Divides_Oop_Advd(c_0,X18,tc_nat)
| c_0 = X18 )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f2958]) ).
fof(f4130,plain,
( ! [X18,X15,X24] :
( c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat)
| ~ c_Divides_Oop_Advd(X15,X18,tc_nat)
| ~ c_Divides_Oop_Advd(X15,X24,tc_nat) )
| ~ spl0_506 ),
inference(avatar_component_clause,[],[f4129]) ).
fof(f5990,plain,
( spl0_659
| ~ spl0_385
| ~ spl0_499 ),
inference(avatar_split_clause,[],[f4098,f4067,f3320,f5988]) ).
fof(f5988,plain,
( spl0_659
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_less(c_uminus(X0,tc_set(X2)),c_uminus(X1,tc_set(X2)),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f3320,plain,
( spl0_385
<=> ! [X21,X1,X19] :
( ~ c_less(X19,X21,tc_set(X1))
| ~ c_lessequals(X21,X19,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f4067,plain,
( spl0_499
<=> ! [X21,X1,X19] :
( ~ c_lessequals(X21,X19,tc_set(X1))
| c_lessequals(c_uminus(X19,tc_set(X1)),c_uminus(X21,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f4098,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_less(c_uminus(X0,tc_set(X2)),c_uminus(X1,tc_set(X2)),tc_set(X2)) )
| ~ spl0_385
| ~ spl0_499 ),
inference(resolution,[],[f4068,f3321]) ).
fof(f3321,plain,
( ! [X21,X1,X19] :
( ~ c_lessequals(X21,X19,tc_set(X1))
| ~ c_less(X19,X21,tc_set(X1)) )
| ~ spl0_385 ),
inference(avatar_component_clause,[],[f3320]) ).
fof(f4068,plain,
( ! [X21,X1,X19] :
( c_lessequals(c_uminus(X19,tc_set(X1)),c_uminus(X21,tc_set(X1)),tc_set(X1))
| ~ c_lessequals(X21,X19,tc_set(X1)) )
| ~ spl0_499 ),
inference(avatar_component_clause,[],[f4067]) ).
fof(f5986,plain,
( spl0_658
| ~ spl0_324
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4008,f3927,f3046,f5984]) ).
fof(f5984,plain,
( spl0_658
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,tc_set(X2)),tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f3046,plain,
( spl0_324
<=> ! [X9,X1] : c_in(X9,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X9,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f4008,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X1,tc_set(X2)),tc_set(X2)),X2),X2) )
| ~ spl0_324
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3047]) ).
fof(f3047,plain,
( ! [X1,X9] : c_in(X9,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X9,X1),X1),X1)
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3046]) ).
fof(f5964,plain,
( spl0_657
| ~ spl0_520
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f5806,f5759,f4254,f5962]) ).
fof(f5962,plain,
( spl0_657
<=> ! [X0,X1] : c_Main_ODomainE__1(X0,c_Relation_OId,X1,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f4254,plain,
( spl0_520
<=> ! [X0,X1] : c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f5759,plain,
( spl0_642
<=> ! [X0,X1] :
( ~ c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
| c_Main_ODomainE__1(X0,c_Relation_OId,X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f5806,plain,
( ! [X0,X1] : c_Main_ODomainE__1(X0,c_Relation_OId,X1,X1) = X0
| ~ spl0_520
| ~ spl0_642 ),
inference(resolution,[],[f5760,f4255]) ).
fof(f4255,plain,
( ! [X0,X1] : c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f4254]) ).
fof(f5760,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
| c_Main_ODomainE__1(X0,c_Relation_OId,X1,X1) = X0 )
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f5759]) ).
fof(f5893,plain,
( spl0_656
| ~ spl0_517
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f4555,f4505,f4173,f5891]) ).
fof(f5891,plain,
( spl0_656
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
| c_in(X0,c_Relation_ORange(X1,X3,X4),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f4555,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,c_Relation_OImage(X1,X2,X3,X4),X4)
| c_in(X0,c_Relation_ORange(X1,X3,X4),X4) )
| ~ spl0_517
| ~ spl0_548 ),
inference(resolution,[],[f4506,f4174]) ).
fof(f5886,plain,
( spl0_655
| ~ spl0_463
| ~ spl0_539 ),
inference(avatar_split_clause,[],[f4419,f4363,f3782,f5884]) ).
fof(f5884,plain,
( spl0_655
<=> ! [X0] :
( ~ c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| c_less(c_Main_ORangeE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f4363,plain,
( spl0_539
<=> ! [X11,X12,X1,X20] :
( ~ c_in(X12,c_Relation_ORange(X20,X11,X1),X1)
| c_in(c_Pair(c_Main_ORangeE__1(X12,X20,X1,X11),X12,X11,X1),X20,tc_prod(X11,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f4419,plain,
( ! [X0] :
( ~ c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| c_less(c_Main_ORangeE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),X0,tc_nat) )
| ~ spl0_463
| ~ spl0_539 ),
inference(resolution,[],[f4364,f3783]) ).
fof(f4364,plain,
( ! [X11,X1,X12,X20] :
( c_in(c_Pair(c_Main_ORangeE__1(X12,X20,X1,X11),X12,X11,X1),X20,tc_prod(X11,X1))
| ~ c_in(X12,c_Relation_ORange(X20,X11,X1),X1) )
| ~ spl0_539 ),
inference(avatar_component_clause,[],[f4363]) ).
fof(f5882,plain,
( spl0_654
| ~ spl0_463
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f4393,f4359,f3782,f5880]) ).
fof(f5880,plain,
( spl0_654
<=> ! [X0] :
( ~ c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| c_less(X0,c_Main_ODomainE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f4359,plain,
( spl0_538
<=> ! [X4,X11,X1,X20] :
( ~ c_in(X4,c_Relation_ODomain(X20,X1,X11),X1)
| c_in(c_Pair(X4,c_Main_ODomainE__1(X4,X20,X1,X11),X1,X11),X20,tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f4393,plain,
( ! [X0] :
( ~ c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| c_less(X0,c_Main_ODomainE__1(X0,c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) )
| ~ spl0_463
| ~ spl0_538 ),
inference(resolution,[],[f4360,f3783]) ).
fof(f4360,plain,
( ! [X11,X1,X4,X20] :
( c_in(c_Pair(X4,c_Main_ODomainE__1(X4,X20,X1,X11),X1,X11),X20,tc_prod(X1,X11))
| ~ c_in(X4,c_Relation_ODomain(X20,X1,X11),X1) )
| ~ spl0_538 ),
inference(avatar_component_clause,[],[f4359]) ).
fof(f5878,plain,
( spl0_653
| ~ spl0_300
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f4277,f4266,f2933,f5876]) ).
fof(f5876,plain,
( spl0_653
<=> ! [X0,X3,X2,X1] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2933,plain,
( spl0_300
<=> ! [X28,X1] : c_append(c_List_Olist_ONil,X28,X1) = X28 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f4266,plain,
( spl0_523
<=> ! [X28,X9,X29,X27,X1] :
( X9 = X29
| c_append(X27,c_List_Olist_OCons(X9,c_List_Olist_ONil,X1),X1) != c_append(X28,c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f4277,plain,
( ! [X2,X3,X0,X1] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
| X0 = X3 )
| ~ spl0_300
| ~ spl0_523 ),
inference(superposition,[],[f4267,f2934]) ).
fof(f2934,plain,
( ! [X28,X1] : c_append(c_List_Olist_ONil,X28,X1) = X28
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f2933]) ).
fof(f4267,plain,
( ! [X28,X29,X1,X9,X27] :
( c_append(X27,c_List_Olist_OCons(X9,c_List_Olist_ONil,X1),X1) != c_append(X28,c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1)
| X9 = X29 )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f4266]) ).
fof(f5874,plain,
( spl0_652
| ~ spl0_300
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f4274,f4262,f2933,f5872]) ).
fof(f5872,plain,
( spl0_652
<=> ! [X0,X3,X2,X1] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
| c_List_Olist_ONil = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f4262,plain,
( spl0_522
<=> ! [X9,X29,X27,X28,X1] :
( X27 = X28
| c_append(X27,c_List_Olist_OCons(X9,c_List_Olist_ONil,X1),X1) != c_append(X28,c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f4274,plain,
( ! [X2,X3,X0,X1] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) != c_append(X2,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1)
| c_List_Olist_ONil = X2 )
| ~ spl0_300
| ~ spl0_522 ),
inference(superposition,[],[f4263,f2934]) ).
fof(f4263,plain,
( ! [X28,X29,X1,X9,X27] :
( c_append(X27,c_List_Olist_OCons(X9,c_List_Olist_ONil,X1),X1) != c_append(X28,c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1)
| X27 = X28 )
| ~ spl0_522 ),
inference(avatar_component_clause,[],[f4262]) ).
fof(f5870,plain,
( spl0_651
| ~ spl0_491
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f4108,f4083,f3943,f5868]) ).
fof(f5868,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_Main_OdiagE__1(X1,c_Pair(X0,X0,X2,X2),X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f3943,plain,
( spl0_491
<=> ! [X1,X40,X19] :
( c_in(c_Main_OdiagE__1(X19,X40,X1),X19,X1)
| ~ c_in(X40,c_Relation_Odiag(X19,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f4083,plain,
( spl0_503
<=> ! [X4,X1,X19] :
( ~ c_in(X4,X19,X1)
| c_in(c_Pair(X4,X4,X1,X1),c_Relation_Odiag(X19,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f4108,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(c_Main_OdiagE__1(X1,c_Pair(X0,X0,X2,X2),X2),X1,X2) )
| ~ spl0_491
| ~ spl0_503 ),
inference(resolution,[],[f4084,f3944]) ).
fof(f3944,plain,
( ! [X40,X1,X19] :
( ~ c_in(X40,c_Relation_Odiag(X19,X1),tc_prod(X1,X1))
| c_in(c_Main_OdiagE__1(X19,X40,X1),X19,X1) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f3943]) ).
fof(f4084,plain,
( ! [X1,X19,X4] :
( c_in(c_Pair(X4,X4,X1,X1),c_Relation_Odiag(X19,X1),tc_prod(X1,X1))
| ~ c_in(X4,X19,X1) )
| ~ spl0_503 ),
inference(avatar_component_clause,[],[f4083]) ).
fof(f5866,plain,
( spl0_650
| ~ spl0_385
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f3991,f3911,f3320,f5864]) ).
fof(f5864,plain,
( spl0_650
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_less(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X0,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f3911,plain,
( spl0_483
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X9,X29,X1)
| c_lessequals(c_SetInterval_OlessThan(X9,X1),c_SetInterval_OlessThan(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f3991,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_less(c_SetInterval_OlessThan(X1,X2),c_SetInterval_OlessThan(X0,X2),tc_set(X2)) )
| ~ spl0_385
| ~ spl0_483 ),
inference(resolution,[],[f3912,f3321]) ).
fof(f3912,plain,
( ! [X29,X1,X9] :
( c_lessequals(c_SetInterval_OlessThan(X9,X1),c_SetInterval_OlessThan(X29,X1),tc_set(X1))
| ~ c_lessequals(X9,X29,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_483 ),
inference(avatar_component_clause,[],[f3911]) ).
fof(f5862,plain,
( spl0_649
| ~ spl0_385
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f3983,f3903,f3320,f5860]) ).
fof(f5860,plain,
( spl0_649
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_less(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X1,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f3903,plain,
( spl0_481
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X29,X9,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X9,X1),c_SetInterval_OgreaterThan(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f3983,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_less(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X1,X2),tc_set(X2)) )
| ~ spl0_385
| ~ spl0_481 ),
inference(resolution,[],[f3904,f3321]) ).
fof(f3904,plain,
( ! [X29,X1,X9] :
( c_lessequals(c_SetInterval_OgreaterThan(X9,X1),c_SetInterval_OgreaterThan(X29,X1),tc_set(X1))
| ~ c_lessequals(X29,X9,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_481 ),
inference(avatar_component_clause,[],[f3903]) ).
fof(f5858,plain,
( spl0_648
| ~ spl0_385
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f3973,f3895,f3320,f5856]) ).
fof(f5856,plain,
( spl0_648
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X0,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f3895,plain,
( spl0_479
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X9,X29,X1)
| c_lessequals(c_SetInterval_OatMost(X9,X1),c_SetInterval_OatMost(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f3973,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(c_SetInterval_OatMost(X1,X2),c_SetInterval_OatMost(X0,X2),tc_set(X2)) )
| ~ spl0_385
| ~ spl0_479 ),
inference(resolution,[],[f3896,f3321]) ).
fof(f3896,plain,
( ! [X29,X1,X9] :
( c_lessequals(c_SetInterval_OatMost(X9,X1),c_SetInterval_OatMost(X29,X1),tc_set(X1))
| ~ c_lessequals(X9,X29,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f3895]) ).
fof(f5854,plain,
( spl0_647
| ~ spl0_385
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f3965,f3883,f3320,f5852]) ).
fof(f5852,plain,
( spl0_647
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X1,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f3883,plain,
( spl0_476
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X29,X9,X1)
| c_lessequals(c_SetInterval_OatLeast(X9,X1),c_SetInterval_OatLeast(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f3965,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X1,X2),tc_set(X2)) )
| ~ spl0_385
| ~ spl0_476 ),
inference(resolution,[],[f3884,f3321]) ).
fof(f3884,plain,
( ! [X29,X1,X9] :
( c_lessequals(c_SetInterval_OatLeast(X9,X1),c_SetInterval_OatLeast(X29,X1),tc_set(X1))
| ~ c_lessequals(X29,X9,X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_476 ),
inference(avatar_component_clause,[],[f3883]) ).
fof(f5840,plain,
( spl0_646
| ~ spl0_59
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f5412,f5364,f1660,f5837]) ).
fof(f5837,plain,
( spl0_646
<=> c_in(c_1,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1660,plain,
( spl0_59
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f5364,plain,
( spl0_606
<=> ! [X0,X1] :
( c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| ~ c_less(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f5412,plain,
( c_in(c_1,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| ~ spl0_59
| ~ spl0_606 ),
inference(resolution,[],[f5365,f1662]) ).
fof(f1662,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1660]) ).
fof(f5365,plain,
( ! [X0,X1] :
( ~ c_less(X1,X0,tc_nat)
| c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) )
| ~ spl0_606 ),
inference(avatar_component_clause,[],[f5364]) ).
fof(f5773,plain,
( spl0_645
| ~ spl0_437
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f4457,f4449,f3582,f5771]) ).
fof(f5771,plain,
( spl0_645
<=> ! [X0,X3,X2,X1] :
( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X2)
| ~ c_in(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f3582,plain,
( spl0_437
<=> ! [X20,X1,X4] : c_in(c_Pair(X4,X4,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f4457,plain,
( ! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Transitive__Closure_Ortrancl(X1,X2),X3,X2,X2),X2)
| ~ c_in(X0,X3,X2) )
| ~ spl0_437
| ~ spl0_542 ),
inference(resolution,[],[f4450,f3583]) ).
fof(f3583,plain,
( ! [X1,X4,X20] : c_in(c_Pair(X4,X4,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1))
| ~ spl0_437 ),
inference(avatar_component_clause,[],[f3582]) ).
fof(f5769,plain,
( spl0_644
| ~ spl0_447
| ~ spl0_539 ),
inference(avatar_split_clause,[],[f4418,f4363,f3695,f5767]) ).
fof(f4418,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
| c_Main_ORangeE__1(X0,c_Relation_OId,X1,X1) = X0 )
| ~ spl0_447
| ~ spl0_539 ),
inference(resolution,[],[f4364,f3696]) ).
fof(f5765,plain,
( spl0_643
| ~ spl0_290
| ~ spl0_605 ),
inference(avatar_split_clause,[],[f5405,f5360,f2893,f5763]) ).
fof(f5763,plain,
( spl0_643
<=> ! [X0] : c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2893,plain,
( spl0_290
<=> ! [X24] : c_less(X24,c_Suc(X24),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f5360,plain,
( spl0_605
<=> ! [X0,X1] :
( c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| ~ c_less(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f5405,plain,
( ! [X0] : c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| ~ spl0_290
| ~ spl0_605 ),
inference(resolution,[],[f5361,f2894]) ).
fof(f2894,plain,
( ! [X24] : c_less(X24,c_Suc(X24),tc_nat)
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f2893]) ).
fof(f5361,plain,
( ! [X0,X1] :
( ~ c_less(X0,X1,tc_nat)
| c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat) )
| ~ spl0_605 ),
inference(avatar_component_clause,[],[f5360]) ).
fof(f5761,plain,
( spl0_642
| ~ spl0_447
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f4392,f4359,f3695,f5759]) ).
fof(f4392,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
| c_Main_ODomainE__1(X0,c_Relation_OId,X1,X1) = X0 )
| ~ spl0_447
| ~ spl0_538 ),
inference(resolution,[],[f4360,f3696]) ).
fof(f5757,plain,
( spl0_641
| ~ spl0_313
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4009,f3927,f2986,f5755]) ).
fof(f5755,plain,
( spl0_641
<=> ! [X0,X3,X2,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_insert(X1,X3,tc_set(X2)),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f4009,plain,
( ! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_insert(X1,X3,tc_set(X2)),X2),X2) )
| ~ spl0_313
| ~ spl0_487 ),
inference(resolution,[],[f3928,f2987]) ).
fof(f5753,plain,
( spl0_640
| ~ spl0_310
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f3956,f3875,f2974,f5751]) ).
fof(f5751,plain,
( spl0_640
<=> ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_less(c_0,X1,tc_nat)
| c_0 = c_plus(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f2974,plain,
( spl0_310
<=> ! [X24] :
( c_0 = X24
| c_less(c_0,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3875,plain,
( spl0_474
<=> ! [X18,X24] :
( c_less(c_0,X18,tc_nat)
| c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,c_plus(X18,X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f3956,plain,
( ! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| c_less(c_0,X1,tc_nat)
| c_0 = c_plus(X1,X0,tc_nat) )
| ~ spl0_310
| ~ spl0_474 ),
inference(resolution,[],[f3876,f2975]) ).
fof(f2975,plain,
( ! [X24] :
( c_less(c_0,X24,tc_nat)
| c_0 = X24 )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f2974]) ).
fof(f3876,plain,
( ! [X18,X24] :
( ~ c_less(c_0,c_plus(X18,X24,tc_nat),tc_nat)
| c_less(c_0,X24,tc_nat)
| c_less(c_0,X18,tc_nat) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f3875]) ).
fof(f5749,plain,
( spl0_639
| ~ spl0_361
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f3742,f3691,f3205,f5747]) ).
fof(f5747,plain,
( spl0_639
<=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f3205,plain,
( spl0_361
<=> ! [X18,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f3691,plain,
( spl0_446
<=> ! [X18,X24,X15] :
( c_Divides_Oop_Advd(X15,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f3742,plain,
( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X2,tc_nat)
| ~ spl0_361
| ~ spl0_446 ),
inference(resolution,[],[f3692,f3206]) ).
fof(f3206,plain,
( ! [X18,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),X24,tc_nat)
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f3205]) ).
fof(f3692,plain,
( ! [X18,X15,X24] :
( ~ c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat)
| c_Divides_Oop_Advd(X15,X24,tc_nat) )
| ~ spl0_446 ),
inference(avatar_component_clause,[],[f3691]) ).
fof(f5745,plain,
( spl0_638
| ~ spl0_360
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f3741,f3691,f3201,f5743]) ).
fof(f5743,plain,
( spl0_638
<=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f3201,plain,
( spl0_360
<=> ! [X18,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f3741,plain,
( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X1,tc_nat)
| ~ spl0_360
| ~ spl0_446 ),
inference(resolution,[],[f3692,f3202]) ).
fof(f3202,plain,
( ! [X18,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),X18,tc_nat)
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f3201]) ).
fof(f5741,plain,
( spl0_637
| ~ spl0_361
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f3739,f3687,f3205,f5739]) ).
fof(f5739,plain,
( spl0_637
<=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f3687,plain,
( spl0_445
<=> ! [X18,X24,X15] :
( c_Divides_Oop_Advd(X15,X18,tc_nat)
| ~ c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f3739,plain,
( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X0,c_GCD_Ogcd(c_Pair(X1,X2,tc_nat,tc_nat)),tc_nat,tc_nat)),X1,tc_nat)
| ~ spl0_361
| ~ spl0_445 ),
inference(resolution,[],[f3688,f3206]) ).
fof(f3688,plain,
( ! [X18,X15,X24] :
( ~ c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat)
| c_Divides_Oop_Advd(X15,X18,tc_nat) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f3687]) ).
fof(f5737,plain,
( spl0_636
| ~ spl0_360
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f3738,f3687,f3201,f5735]) ).
fof(f5735,plain,
( spl0_636
<=> ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f3738,plain,
( ! [X2,X0,X1] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(c_GCD_Ogcd(c_Pair(X0,X1,tc_nat,tc_nat)),X2,tc_nat,tc_nat)),X0,tc_nat)
| ~ spl0_360
| ~ spl0_445 ),
inference(resolution,[],[f3688,f3202]) ).
fof(f5698,plain,
( spl0_635
| ~ spl0_64
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f5504,f5452,f1681,f5696]) ).
fof(f5696,plain,
( spl0_635
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1681,plain,
( spl0_64
<=> ! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f5452,plain,
( spl0_612
<=> ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f5504,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_64
| ~ spl0_612 ),
inference(resolution,[],[f5453,f1682]) ).
fof(f1682,plain,
( ! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_IntDef_Oint)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f5453,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) )
| ~ spl0_612 ),
inference(avatar_component_clause,[],[f5452]) ).
fof(f5694,plain,
( spl0_634
| ~ spl0_494
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f4560,f4505,f4047,f5692]) ).
fof(f5692,plain,
( spl0_634
<=> ! [X2,X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_OImage(c_List_Olex(X0,X1),X2,tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f4047,plain,
( spl0_494
<=> ! [X20,X27,X1] : ~ c_in(c_Pair(X27,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f4560,plain,
( ! [X2,X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_OImage(c_List_Olex(X0,X1),X2,tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
| ~ spl0_494
| ~ spl0_548 ),
inference(resolution,[],[f4506,f4048]) ).
fof(f4048,plain,
( ! [X1,X27,X20] : ~ c_in(c_Pair(X27,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ spl0_494 ),
inference(avatar_component_clause,[],[f4047]) ).
fof(f5690,plain,
( spl0_633
| ~ spl0_503
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4235,f4173,f4083,f5688]) ).
fof(f5688,plain,
( spl0_633
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Odiag(X1,X2),X2,X2),X2)
| ~ c_in(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f4235,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ORange(c_Relation_Odiag(X1,X2),X2,X2),X2)
| ~ c_in(X0,X1,X2) )
| ~ spl0_503
| ~ spl0_517 ),
inference(resolution,[],[f4174,f4084]) ).
fof(f5686,plain,
( spl0_632
| ~ spl0_503
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4210,f4157,f4083,f5684]) ).
fof(f5684,plain,
( spl0_632
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_ODomain(c_Relation_Odiag(X1,X2),X2,X2),X2)
| ~ c_in(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f4210,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_ODomain(c_Relation_Odiag(X1,X2),X2,X2),X2)
| ~ c_in(X0,X1,X2) )
| ~ spl0_503
| ~ spl0_513 ),
inference(resolution,[],[f4158,f4084]) ).
fof(f5682,plain,
( spl0_631
| ~ spl0_339
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4038,f3927,f3106,f5680]) ).
fof(f5680,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f3106,plain,
( spl0_339
<=> ! [X48,X44] : c_in(c_SetInterval_OgreaterThanLessThan(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f4038,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_339
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3107]) ).
fof(f3107,plain,
( ! [X48,X44] : c_in(c_SetInterval_OgreaterThanLessThan(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f3106]) ).
fof(f5678,plain,
( spl0_630
| ~ spl0_338
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4037,f3927,f3102,f5676]) ).
fof(f5676,plain,
( spl0_630
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f3102,plain,
( spl0_338
<=> ! [X48,X44] : c_in(c_SetInterval_OgreaterThanLessThan(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f4037,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanLessThan(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
| ~ spl0_338
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3103]) ).
fof(f3103,plain,
( ! [X48,X44] : c_in(c_SetInterval_OgreaterThanLessThan(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f3102]) ).
fof(f5674,plain,
( spl0_629
| ~ spl0_337
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4036,f3927,f3098,f5672]) ).
fof(f5672,plain,
( spl0_629
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f3098,plain,
( spl0_337
<=> ! [X48,X44] : c_in(c_SetInterval_OgreaterThanAtMost(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f4036,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_337
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3099]) ).
fof(f3099,plain,
( ! [X48,X44] : c_in(c_SetInterval_OgreaterThanAtMost(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f3098]) ).
fof(f5670,plain,
( spl0_628
| ~ spl0_336
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4035,f3927,f3094,f5668]) ).
fof(f5668,plain,
( spl0_628
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f3094,plain,
( spl0_336
<=> ! [X48,X44] : c_in(c_SetInterval_OgreaterThanAtMost(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f4035,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OgreaterThanAtMost(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
| ~ spl0_336
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3095]) ).
fof(f3095,plain,
( ! [X48,X44] : c_in(c_SetInterval_OgreaterThanAtMost(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f3094]) ).
fof(f5666,plain,
( spl0_627
| ~ spl0_335
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4034,f3927,f3090,f5664]) ).
fof(f5664,plain,
( spl0_627
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f3090,plain,
( spl0_335
<=> ! [X48,X44] : c_in(c_SetInterval_OatLeastLessThan(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f4034,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_335
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3091]) ).
fof(f3091,plain,
( ! [X48,X44] : c_in(c_SetInterval_OatLeastLessThan(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f3090]) ).
fof(f5662,plain,
( spl0_626
| ~ spl0_334
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4033,f3927,f3086,f5660]) ).
fof(f5660,plain,
( spl0_626
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f3086,plain,
( spl0_334
<=> ! [X48,X44] : c_in(c_SetInterval_OatLeastLessThan(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f4033,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastLessThan(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
| ~ spl0_334
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3087]) ).
fof(f3087,plain,
( ! [X48,X44] : c_in(c_SetInterval_OatLeastLessThan(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f5658,plain,
( spl0_625
| ~ spl0_333
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4032,f3927,f3082,f5656]) ).
fof(f5656,plain,
( spl0_625
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f3082,plain,
( spl0_333
<=> ! [X48,X44] : c_in(c_SetInterval_OatLeastAtMost(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4032,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_333
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3083]) ).
fof(f3083,plain,
( ! [X48,X44] : c_in(c_SetInterval_OatLeastAtMost(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint))
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f3082]) ).
fof(f5651,plain,
( spl0_624
| ~ spl0_332
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4031,f3927,f3078,f5649]) ).
fof(f5649,plain,
( spl0_624
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f3078,plain,
( spl0_332
<=> ! [X48,X44] : c_in(c_SetInterval_OatLeastAtMost(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f4031,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_SetInterval_OatLeastAtMost(X1,X2,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
| ~ spl0_332
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3079]) ).
fof(f3079,plain,
( ! [X48,X44] : c_in(c_SetInterval_OatLeastAtMost(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f3078]) ).
fof(f5647,plain,
( spl0_623
| ~ spl0_367
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f3337,f3252,f3248,f5645]) ).
fof(f5645,plain,
( spl0_623
<=> ! [X2,X0,X1] :
( c_Datatype_Ooption_OSome(X2,X1) != X0
| c_Main_Onot__Some__eq__iff1__1(X0,X1) = X2
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f3248,plain,
( spl0_367
<=> ! [X9,X1] :
( c_Datatype_Ooption_ONone = X9
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X9,X1),X1) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f3252,plain,
( spl0_368
<=> ! [X4,X0,X1] :
( X0 = X4
| c_Datatype_Ooption_OSome(X0,X1) != c_Datatype_Ooption_OSome(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f3337,plain,
( ! [X2,X0,X1] :
( c_Datatype_Ooption_OSome(X2,X1) != X0
| c_Main_Onot__Some__eq__iff1__1(X0,X1) = X2
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_367
| ~ spl0_368 ),
inference(superposition,[],[f3253,f3249]) ).
fof(f3249,plain,
( ! [X1,X9] :
( c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X9,X1),X1) = X9
| c_Datatype_Ooption_ONone = X9 )
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f3248]) ).
fof(f3253,plain,
( ! [X0,X1,X4] :
( c_Datatype_Ooption_OSome(X0,X1) != c_Datatype_Ooption_OSome(X4,X1)
| X0 = X4 )
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f3252]) ).
fof(f5643,plain,
( spl0_622
| ~ spl0_366
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f3336,f3252,f3244,f5641]) ).
fof(f5641,plain,
( spl0_622
<=> ! [X2,X0,X1] :
( c_Datatype_Ooption_OSome(X2,X1) != X0
| c_Main_Onot__None__eq__iff1__1(X0,X1) = X2
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f3244,plain,
( spl0_366
<=> ! [X9,X1] :
( c_Datatype_Ooption_ONone = X9
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X9,X1),X1) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f3336,plain,
( ! [X2,X0,X1] :
( c_Datatype_Ooption_OSome(X2,X1) != X0
| c_Main_Onot__None__eq__iff1__1(X0,X1) = X2
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_366
| ~ spl0_368 ),
inference(superposition,[],[f3253,f3245]) ).
fof(f3245,plain,
( ! [X1,X9] :
( c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X9,X1),X1) = X9
| c_Datatype_Ooption_ONone = X9 )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f3244]) ).
fof(f5525,plain,
( spl0_621
| ~ spl0_473
| ~ spl0_591 ),
inference(avatar_split_clause,[],[f5464,f5155,f3830,f5523]) ).
fof(f5523,plain,
( spl0_621
<=> ! [X0] : c_emptyset = c_Union(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f3830,plain,
( spl0_473
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
| c_emptyset = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f5155,plain,
( spl0_591
<=> ! [X0,X1] : c_lessequals(c_Union(c_emptyset,X0),X1,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f5464,plain,
( ! [X0] : c_emptyset = c_Union(c_emptyset,X0)
| ~ spl0_473
| ~ spl0_591 ),
inference(resolution,[],[f5156,f3831]) ).
fof(f3831,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
| c_emptyset = X0 )
| ~ spl0_473 ),
inference(avatar_component_clause,[],[f3830]) ).
fof(f5156,plain,
( ! [X0,X1] : c_lessequals(c_Union(c_emptyset,X0),X1,tc_set(X0))
| ~ spl0_591 ),
inference(avatar_component_clause,[],[f5155]) ).
fof(f5492,plain,
( spl0_620
| ~ spl0_67
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f4468,f4449,f1693,f5490]) ).
fof(f5490,plain,
( spl0_620
<=> ! [X4,X0,X3,X2,X1] :
( c_in(X0,c_Relation_OImage(c_UNIV,X1,X2,X3),X3)
| ~ c_in(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1693,plain,
( spl0_67
<=> ! [X9,X1] : c_in(X9,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f4468,plain,
( ! [X2,X3,X0,X1,X4] :
( c_in(X0,c_Relation_OImage(c_UNIV,X1,X2,X3),X3)
| ~ c_in(X4,X1,X2) )
| ~ spl0_67
| ~ spl0_542 ),
inference(resolution,[],[f4450,f1694]) ).
fof(f1694,plain,
( ! [X1,X9] : c_in(X9,c_UNIV,X1)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1693]) ).
fof(f5488,plain,
( spl0_619
| ~ spl0_384
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f4456,f4449,f3316,f5486]) ).
fof(f5486,plain,
( spl0_619
<=> ! [X2,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
| ~ c_in(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f3316,plain,
( spl0_384
<=> ! [X4,X1] : c_in(c_Pair(X4,X4,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f4456,plain,
( ! [X2,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Relation_OId,X1,X2,X2),X2)
| ~ c_in(X0,X1,X2) )
| ~ spl0_384
| ~ spl0_542 ),
inference(resolution,[],[f4450,f3317]) ).
fof(f3317,plain,
( ! [X1,X4] : c_in(c_Pair(X4,X4,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f3316]) ).
fof(f5484,plain,
( spl0_618
| ~ spl0_494
| ~ spl0_539 ),
inference(avatar_split_clause,[],[f4422,f4363,f4047,f5482]) ).
fof(f5482,plain,
( spl0_618
<=> ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ORange(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f4422,plain,
( ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ORange(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
| ~ spl0_494
| ~ spl0_539 ),
inference(resolution,[],[f4364,f4048]) ).
fof(f5480,plain,
( spl0_617
| ~ spl0_495
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f4396,f4359,f4051,f5478]) ).
fof(f5478,plain,
( spl0_617
<=> ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ODomain(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f4051,plain,
( spl0_495
<=> ! [X20,X1,X28] : ~ c_in(c_Pair(c_List_Olist_ONil,X28,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f4396,plain,
( ! [X0,X1] : ~ c_in(c_List_Olist_ONil,c_Relation_ODomain(c_List_Olex(X0,X1),tc_List_Olist(X1),tc_List_Olist(X1)),tc_List_Olist(X1))
| ~ spl0_495
| ~ spl0_538 ),
inference(resolution,[],[f4360,f4052]) ).
fof(f4052,plain,
( ! [X28,X1,X20] : ~ c_in(c_Pair(c_List_Olist_ONil,X28,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f4051]) ).
fof(f5476,plain,
( spl0_616
| ~ spl0_293
| ~ spl0_510 ),
inference(avatar_split_clause,[],[f4200,f4145,f2905,f5474]) ).
fof(f5474,plain,
( spl0_616
<=> ! [X0,X1] : c_insert(X0,c_emptyset,X1) = c_insert(X0,c_insert(X0,c_emptyset,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2905,plain,
( spl0_293
<=> ! [X1,X19] : c_lessequals(X19,X19,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f4145,plain,
( spl0_510
<=> ! [X9,X1,X19] :
( ~ c_lessequals(X19,c_insert(X9,c_emptyset,X1),tc_set(X1))
| c_insert(X9,c_emptyset,X1) = c_insert(X9,X19,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f4200,plain,
( ! [X0,X1] : c_insert(X0,c_emptyset,X1) = c_insert(X0,c_insert(X0,c_emptyset,X1),X1)
| ~ spl0_293
| ~ spl0_510 ),
inference(resolution,[],[f4146,f2906]) ).
fof(f2906,plain,
( ! [X1,X19] : c_lessequals(X19,X19,tc_set(X1))
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f4146,plain,
( ! [X1,X19,X9] :
( ~ c_lessequals(X19,c_insert(X9,c_emptyset,X1),tc_set(X1))
| c_insert(X9,c_emptyset,X1) = c_insert(X9,X19,X1) )
| ~ spl0_510 ),
inference(avatar_component_clause,[],[f4145]) ).
fof(f5472,plain,
( spl0_615
| ~ spl0_321
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4028,f3927,f3018,f5470]) ).
fof(f5470,plain,
( spl0_615
<=> ! [X0,X1] :
( ~ c_in(X0,c_SetInterval_OlessThan(X1,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f3018,plain,
( spl0_321
<=> ! [X15] : c_in(c_SetInterval_OlessThan(X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f4028,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_SetInterval_OlessThan(X1,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
| ~ spl0_321
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3019]) ).
fof(f3019,plain,
( ! [X15] : c_in(c_SetInterval_OlessThan(X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3018]) ).
fof(f5468,plain,
( spl0_614
| ~ spl0_320
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4027,f3927,f3014,f5466]) ).
fof(f5466,plain,
( spl0_614
<=> ! [X0,X1] :
( ~ c_in(X0,c_SetInterval_OatMost(X1,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f3014,plain,
( spl0_320
<=> ! [X15] : c_in(c_SetInterval_OatMost(X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f4027,plain,
( ! [X0,X1] :
( ~ c_in(X0,c_SetInterval_OatMost(X1,tc_nat),tc_nat)
| c_in(X0,c_Union(c_Finite__Set_OFinites,tc_nat),tc_nat) )
| ~ spl0_320
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3015]) ).
fof(f3015,plain,
( ! [X15] : c_in(c_SetInterval_OatMost(X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3014]) ).
fof(f5458,plain,
( spl0_613
| ~ spl0_318
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4026,f3927,f3006,f5456]) ).
fof(f5456,plain,
( spl0_613
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_List_Oset(X1,X2),X2)
| c_in(X0,c_Union(c_Finite__Set_OFinites,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f3006,plain,
( spl0_318
<=> ! [X27,X1] : c_in(c_List_Oset(X27,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f4026,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,c_List_Oset(X1,X2),X2)
| c_in(X0,c_Union(c_Finite__Set_OFinites,X2),X2) )
| ~ spl0_318
| ~ spl0_487 ),
inference(resolution,[],[f3928,f3007]) ).
fof(f3007,plain,
( ! [X1,X27] : c_in(c_List_Oset(X27,X1),c_Finite__Set_OFinites,tc_set(X1))
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3006]) ).
fof(f5454,plain,
( spl0_612
| ~ spl0_372
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f3353,f3280,f3268,f5452]) ).
fof(f3268,plain,
( spl0_372
<=> ! [X25,X26] :
( c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X25,c_uminus(X26,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f3280,plain,
( spl0_375
<=> ! [X25,X26] :
( ~ c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X25,tc_IntDef_Oint),X26,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f3353,plain,
( ! [X0,X1] :
( ~ c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) )
| ~ spl0_372
| ~ spl0_375 ),
inference(resolution,[],[f3281,f3269]) ).
fof(f3269,plain,
( ! [X26,X25] :
( ~ c_Divides_Oop_Advd(X25,c_uminus(X26,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint) )
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f3268]) ).
fof(f3281,plain,
( ! [X26,X25] :
( c_Divides_Oop_Advd(c_uminus(X25,tc_IntDef_Oint),X26,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint) )
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f3280]) ).
fof(f5450,plain,
( spl0_611
| ~ spl0_373
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3351,f3276,f3272,f5448]) ).
fof(f5448,plain,
( spl0_611
<=> ! [X0,X1] :
( c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f3272,plain,
( spl0_373
<=> ! [X25,X26] :
( ~ c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X25,c_uminus(X26,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f3276,plain,
( spl0_374
<=> ! [X25,X26] :
( c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X25,tc_IntDef_Oint),X26,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f3351,plain,
( ! [X0,X1] :
( c_Divides_Oop_Advd(X0,c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint) )
| ~ spl0_373
| ~ spl0_374 ),
inference(resolution,[],[f3277,f3273]) ).
fof(f3273,plain,
( ! [X26,X25] :
( c_Divides_Oop_Advd(X25,c_uminus(X26,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f3272]) ).
fof(f3277,plain,
( ! [X26,X25] :
( ~ c_Divides_Oop_Advd(c_uminus(X25,tc_IntDef_Oint),X26,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint) )
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f3276]) ).
fof(f5382,plain,
( spl0_610
| ~ spl0_61
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f4843,f4794,f1669,f5380]) ).
fof(f5380,plain,
( spl0_610
<=> ! [X4,X0,X3,X2,X1] : ~ c_in(X0,c_Relation_Orel__comp(X1,c_emptyset,X2,X3,X4),tc_prod(X4,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f4794,plain,
( spl0_572
<=> ! [X43,X51,X11,X50,X1,X20] :
( ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11))
| c_in(c_Pair(c_Main_Orel__compE__1(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__2(X20,X43,X50,X51,X11,X1),X1,X51),X43,tc_prod(X1,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f4843,plain,
( ! [X2,X3,X0,X1,X4] : ~ c_in(X0,c_Relation_Orel__comp(X1,c_emptyset,X2,X3,X4),tc_prod(X4,X3))
| ~ spl0_61
| ~ spl0_572 ),
inference(resolution,[],[f4795,f1670]) ).
fof(f4795,plain,
( ! [X50,X51,X11,X1,X43,X20] :
( c_in(c_Pair(c_Main_Orel__compE__1(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__2(X20,X43,X50,X51,X11,X1),X1,X51),X43,tc_prod(X1,X51))
| ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11)) )
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f4794]) ).
fof(f5378,plain,
( spl0_609
| ~ spl0_61
| ~ spl0_570 ),
inference(avatar_split_clause,[],[f4813,f4786,f1669,f5376]) ).
fof(f5376,plain,
( spl0_609
<=> ! [X4,X0,X3,X2,X1] : ~ c_in(X0,c_Relation_Orel__comp(c_emptyset,X1,X2,X3,X4),tc_prod(X4,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f4786,plain,
( spl0_570
<=> ! [X43,X51,X11,X50,X1,X20] :
( ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11))
| c_in(c_Pair(c_Main_Orel__compE__2(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__3(X20,X43,X50,X51,X11,X1),X51,X11),X20,tc_prod(X51,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f4813,plain,
( ! [X2,X3,X0,X1,X4] : ~ c_in(X0,c_Relation_Orel__comp(c_emptyset,X1,X2,X3,X4),tc_prod(X4,X3))
| ~ spl0_61
| ~ spl0_570 ),
inference(resolution,[],[f4787,f1670]) ).
fof(f4787,plain,
( ! [X50,X51,X11,X1,X43,X20] :
( c_in(c_Pair(c_Main_Orel__compE__2(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__3(X20,X43,X50,X51,X11,X1),X51,X11),X20,tc_prod(X51,X11))
| ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11)) )
| ~ spl0_570 ),
inference(avatar_component_clause,[],[f4786]) ).
fof(f5374,plain,
( spl0_608
| ~ spl0_61
| ~ spl0_547 ),
inference(avatar_split_clause,[],[f4536,f4501,f1669,f5372]) ).
fof(f5372,plain,
( spl0_608
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Ouprod(c_emptyset,X1,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f4501,plain,
( spl0_547
<=> ! [X19,X11,X40,X21,X1] :
( ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OuprodE__1(X19,X21,X40,X1,X11),X19,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f4536,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Ouprod(c_emptyset,X1,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
| ~ spl0_61
| ~ spl0_547 ),
inference(resolution,[],[f4502,f1670]) ).
fof(f4502,plain,
( ! [X40,X21,X11,X1,X19] :
( c_in(c_Main_OuprodE__1(X19,X21,X40,X1,X11),X19,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) )
| ~ spl0_547 ),
inference(avatar_component_clause,[],[f4501]) ).
fof(f5370,plain,
( spl0_607
| ~ spl0_61
| ~ spl0_546 ),
inference(avatar_split_clause,[],[f4516,f4497,f1669,f5368]) ).
fof(f5368,plain,
( spl0_607
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Datatype__Universe_Ouprod(X1,c_emptyset,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f4497,plain,
( spl0_546
<=> ! [X19,X11,X40,X21,X1] :
( ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OuprodE__2(X19,X21,X40,X1,X11),X21,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f4516,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Datatype__Universe_Ouprod(X1,c_emptyset,X2,X3),tc_set(tc_Datatype__Universe_Onode(X2,X3)))
| ~ spl0_61
| ~ spl0_546 ),
inference(resolution,[],[f4498,f1670]) ).
fof(f4498,plain,
( ! [X40,X21,X11,X1,X19] :
( c_in(c_Main_OuprodE__2(X19,X21,X40,X1,X11),X21,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) )
| ~ spl0_546 ),
inference(avatar_component_clause,[],[f4497]) ).
fof(f5366,plain,
( spl0_606
| ~ spl0_464
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4236,f4173,f3786,f5364]) ).
fof(f4236,plain,
( ! [X0,X1] :
( c_in(X0,c_Relation_ORange(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| ~ c_less(X1,X0,tc_nat) )
| ~ spl0_464
| ~ spl0_517 ),
inference(resolution,[],[f4174,f3787]) ).
fof(f5362,plain,
( spl0_605
| ~ spl0_464
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4211,f4157,f3786,f5360]) ).
fof(f4211,plain,
( ! [X0,X1] :
( c_in(X0,c_Relation_ODomain(c_Wellfounded__Relations_Oless__than,tc_nat,tc_nat),tc_nat)
| ~ c_less(X0,X1,tc_nat) )
| ~ spl0_464
| ~ spl0_513 ),
inference(resolution,[],[f4158,f3787]) ).
fof(f5358,plain,
( spl0_604
| ~ spl0_285
| ~ spl0_300
| ~ spl0_497 ),
inference(avatar_split_clause,[],[f4091,f4059,f2933,f2873,f5356]) ).
fof(f5356,plain,
( spl0_604
<=> ! [X0,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2873,plain,
( spl0_285
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f4059,plain,
( spl0_497
<=> ! [X29,X1,X28] : c_List_Olist_OCons(X29,X28,X1) = c_List_Orev(c_append(c_List_Orev(X28,X1),c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f4091,plain,
( ! [X0,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),X0)
| ~ spl0_285
| ~ spl0_300
| ~ spl0_497 ),
inference(forward_demodulation,[],[f4086,f2934]) ).
fof(f4086,plain,
( ! [X0,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil,X0) = c_List_Orev(c_append(c_List_Olist_ONil,c_List_Olist_OCons(X1,c_List_Olist_ONil,X0),X0),X0)
| ~ spl0_285
| ~ spl0_497 ),
inference(superposition,[],[f4060,f2874]) ).
fof(f2874,plain,
( ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1)
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f2873]) ).
fof(f4060,plain,
( ! [X28,X29,X1] : c_List_Olist_OCons(X29,X28,X1) = c_List_Orev(c_append(c_List_Orev(X28,X1),c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1),X1)
| ~ spl0_497 ),
inference(avatar_component_clause,[],[f4059]) ).
fof(f5354,plain,
( spl0_603
| ~ spl0_324
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f3334,f3248,f3046,f5352]) ).
fof(f5352,plain,
( spl0_603
<=> ! [X0,X1] :
( c_in(c_Main_Onot__Some__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f3334,plain,
( ! [X0,X1] :
( c_in(c_Main_Onot__Some__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_324
| ~ spl0_367 ),
inference(superposition,[],[f3047,f3249]) ).
fof(f5350,plain,
( spl0_602
| ~ spl0_324
| ~ spl0_600 ),
inference(avatar_split_clause,[],[f5259,f5255,f3046,f5348]) ).
fof(f5348,plain,
( spl0_602
<=> ! [X0,X1] : c_in(X0,c_Union(c_UNIV,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f5255,plain,
( spl0_600
<=> ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_UNIV,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f5259,plain,
( ! [X0,X1] : c_in(X0,c_Union(c_UNIV,X1),X1)
| ~ spl0_324
| ~ spl0_600 ),
inference(resolution,[],[f5256,f3047]) ).
fof(f5256,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_UNIV,X2),X2) )
| ~ spl0_600 ),
inference(avatar_component_clause,[],[f5255]) ).
fof(f5346,plain,
( spl0_601
| ~ spl0_324
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f3332,f3244,f3046,f5344]) ).
fof(f5344,plain,
( spl0_601
<=> ! [X0,X1] :
( c_in(c_Main_Onot__None__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
| c_Datatype_Ooption_ONone = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f3332,plain,
( ! [X0,X1] :
( c_in(c_Main_Onot__None__eq__iff1__1(X0,X1),c_Datatype_Oo2s(X0,X1),X1)
| c_Datatype_Ooption_ONone = X0 )
| ~ spl0_324
| ~ spl0_366 ),
inference(superposition,[],[f3047,f3245]) ).
fof(f5257,plain,
( spl0_600
| ~ spl0_67
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f4014,f3927,f1693,f5255]) ).
fof(f4014,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,X1,X2)
| c_in(X0,c_Union(c_UNIV,X2),X2) )
| ~ spl0_67
| ~ spl0_487 ),
inference(resolution,[],[f3928,f1694]) ).
fof(f5212,plain,
( spl0_599
| ~ spl0_61
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f4668,f4651,f1669,f5210]) ).
fof(f5210,plain,
( spl0_599
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f4651,plain,
( spl0_558
<=> ! [X11,X20,X49,X1] :
( ~ c_in(X49,c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11))
| c_in(c_Pair(c_Main_OconverseE__1(X20,X49,X11,X1),c_Main_OconverseE__2(X20,X49,X11,X1),X11,X1),X20,tc_prod(X11,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f4668,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_Oconverse(c_emptyset,X1,X2),tc_prod(X2,X1))
| ~ spl0_61
| ~ spl0_558 ),
inference(resolution,[],[f4652,f1670]) ).
fof(f4652,plain,
( ! [X49,X11,X1,X20] :
( c_in(c_Pair(c_Main_OconverseE__1(X20,X49,X11,X1),c_Main_OconverseE__2(X20,X49,X11,X1),X11,X1),X20,tc_prod(X11,X1))
| ~ c_in(X49,c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11)) )
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f4651]) ).
fof(f5208,plain,
( spl0_598
| ~ spl0_437
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4234,f4173,f3582,f5206]) ).
fof(f5206,plain,
( spl0_598
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f4234,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)
| ~ spl0_437
| ~ spl0_517 ),
inference(resolution,[],[f4174,f3583]) ).
fof(f5204,plain,
( spl0_597
| ~ spl0_437
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4209,f4157,f3582,f5202]) ).
fof(f5202,plain,
( spl0_597
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f4209,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),X2)
| ~ spl0_437
| ~ spl0_513 ),
inference(resolution,[],[f4158,f3583]) ).
fof(f5200,plain,
( spl0_596
| ~ spl0_467
| ~ spl0_501 ),
inference(avatar_split_clause,[],[f4107,f4075,f3798,f5198]) ).
fof(f5198,plain,
( spl0_596
<=> ! [X0,X1] : c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f3798,plain,
( spl0_467
<=> ! [X27,X1,X19] :
( ~ c_in(c_Main_Oin__listsI__1(X19,X27,X1),X19,X1)
| c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f4075,plain,
( spl0_501
<=> ! [X27,X1,X19] :
( c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X19,X27,X1),c_List_Oset(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f4107,plain,
( ! [X0,X1] : c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1))
| ~ spl0_467
| ~ spl0_501 ),
inference(duplicate_literal_removal,[],[f4104]) ).
fof(f4104,plain,
( ! [X0,X1] :
( c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1))
| c_in(X0,c_List_Olists(c_List_Oset(X0,X1),X1),tc_List_Olist(X1)) )
| ~ spl0_467
| ~ spl0_501 ),
inference(resolution,[],[f4076,f3799]) ).
fof(f3799,plain,
( ! [X1,X19,X27] :
( ~ c_in(c_Main_Oin__listsI__1(X19,X27,X1),X19,X1)
| c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1)) )
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f3798]) ).
fof(f4076,plain,
( ! [X1,X19,X27] :
( c_in(c_Main_Oin__listsI__1(X19,X27,X1),c_List_Oset(X27,X1),X1)
| c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1)) )
| ~ spl0_501 ),
inference(avatar_component_clause,[],[f4075]) ).
fof(f5196,plain,
( spl0_595
| ~ spl0_298
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f3639,f3570,f2925,f5194]) ).
fof(f5194,plain,
( spl0_595
<=> ! [X0] : c_lessequals(c_Nat_Osize(c_List_Oremdups(c_List_Olist_ONil,X0),tc_List_Olist(X0)),c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2925,plain,
( spl0_298
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f3570,plain,
( spl0_434
<=> ! [X27,X1] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X27,X1),tc_List_Olist(X1)),c_Nat_Osize(X27,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f3639,plain,
( ! [X0] : c_lessequals(c_Nat_Osize(c_List_Oremdups(c_List_Olist_ONil,X0),tc_List_Olist(X0)),c_0,tc_nat)
| ~ spl0_298
| ~ spl0_434 ),
inference(superposition,[],[f3571,f2926]) ).
fof(f2926,plain,
( ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1))
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f2925]) ).
fof(f3571,plain,
( ! [X1,X27] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X27,X1),tc_List_Olist(X1)),c_Nat_Osize(X27,tc_List_Olist(X1)),tc_nat)
| ~ spl0_434 ),
inference(avatar_component_clause,[],[f3570]) ).
fof(f5192,plain,
( spl0_594
| ~ spl0_300
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f3602,f3470,f2933,f5190]) ).
fof(f5190,plain,
( spl0_594
<=> ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f3470,plain,
( spl0_410
<=> ! [X30,X27,X28,X1] :
( X28 = X30
| c_append(X27,X28,X1) != c_append(X27,X30,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f3602,plain,
( ! [X2,X0,X1] :
( c_append(c_List_Olist_ONil,X2,X1) != X0
| X0 = X2 )
| ~ spl0_300
| ~ spl0_410 ),
inference(superposition,[],[f3471,f2934]) ).
fof(f3471,plain,
( ! [X28,X1,X27,X30] :
( c_append(X27,X28,X1) != c_append(X27,X30,X1)
| X28 = X30 )
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f3470]) ).
fof(f5188,plain,
( spl0_593
| ~ spl0_301
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f3596,f3458,f2937,f5186]) ).
fof(f5186,plain,
( spl0_593
<=> ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2937,plain,
( spl0_301
<=> ! [X27,X1] : c_append(X27,c_List_Olist_ONil,X1) = X27 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f3458,plain,
( spl0_407
<=> ! [X30,X27,X28,X1] :
( X28 = X30
| c_append(X28,X27,X1) != c_append(X30,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f3596,plain,
( ! [X2,X0,X1] :
( c_append(X2,c_List_Olist_ONil,X1) != X0
| X0 = X2 )
| ~ spl0_301
| ~ spl0_407 ),
inference(superposition,[],[f3459,f2938]) ).
fof(f2938,plain,
( ! [X1,X27] : c_append(X27,c_List_Olist_ONil,X1) = X27
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f2937]) ).
fof(f3459,plain,
( ! [X28,X1,X27,X30] :
( c_append(X28,X27,X1) != c_append(X30,X27,X1)
| X28 = X30 )
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f3458]) ).
fof(f5161,plain,
( spl0_592
| ~ spl0_61
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f4563,f4505,f1669,f5159]) ).
fof(f5159,plain,
( spl0_592
<=> ! [X2,X0,X1,X3] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f4563,plain,
( ! [X2,X3,X0,X1] : ~ c_in(X0,c_Relation_OImage(c_emptyset,X1,X2,X3),X3)
| ~ spl0_61
| ~ spl0_548 ),
inference(resolution,[],[f4506,f1670]) ).
fof(f5157,plain,
( spl0_591
| ~ spl0_435
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f4045,f3935,f3574,f5155]) ).
fof(f3935,plain,
( spl0_489
<=> ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f4045,plain,
( ! [X0,X1] : c_lessequals(c_Union(c_emptyset,X0),X1,tc_set(X0))
| ~ spl0_435
| ~ spl0_489 ),
inference(resolution,[],[f3936,f3575]) ).
fof(f3936,plain,
( ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1)
| ~ spl0_489 ),
inference(avatar_component_clause,[],[f3935]) ).
fof(f5140,plain,
spl0_590,
inference(avatar_split_clause,[],[f214,f5138]) ).
fof(f5138,plain,
( spl0_590
<=> ! [X17,X43,X11,X14,X13,X16,X1,X20] :
( ~ c_in(c_Pair(X14,X17,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| ~ c_in(c_Pair(X13,X16,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X13,X14,X1,X11),c_Datatype__Universe_OScons(X16,X17,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f214,axiom,
! [X11,X1,X16,X14,X17,X43,X13,X20] :
( ~ c_in(c_Pair(X14,X17,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| ~ c_in(c_Pair(X13,X16,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X13,X14,X1,X11),c_Datatype__Universe_OScons(X16,X17,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
fof(f5125,plain,
spl0_589,
inference(avatar_split_clause,[],[f218,f5123]) ).
fof(f5123,plain,
( spl0_589
<=> ! [X43,X11,X20,X1,X26] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdsumE__3(X43,X26,X1,X11),c_Main_OdsumE__4(X43,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdsumE__1(X20,X26,X1,X11),c_Main_OdsumE__2(X20,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f218,axiom,
! [X11,X1,X26,X43,X20] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdsumE__3(X43,X26,X1,X11),c_Main_OdsumE__4(X43,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdsumE__1(X20,X26,X1,X11),c_Main_OdsumE__2(X20,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).
fof(f5099,plain,
spl0_588,
inference(avatar_split_clause,[],[f217,f5097]) ).
fof(f5097,plain,
( spl0_588
<=> ! [X43,X11,X20,X1,X26] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X43,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X43,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26
| c_in(c_Pair(c_Main_OdsumE__1(X20,X26,X1,X11),c_Main_OdsumE__2(X20,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f217,axiom,
! [X11,X1,X26,X43,X20] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X43,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X43,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26
| c_in(c_Pair(c_Main_OdsumE__1(X20,X26,X1,X11),c_Main_OdsumE__2(X20,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
fof(f5095,plain,
spl0_587,
inference(avatar_split_clause,[],[f216,f5093]) ).
fof(f5093,plain,
( spl0_587
<=> ! [X43,X11,X20,X1,X26] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26
| c_in(c_Pair(c_Main_OdsumE__3(X43,X26,X1,X11),c_Main_OdsumE__4(X43,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f216,axiom,
! [X11,X1,X26,X43,X20] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26
| c_in(c_Pair(c_Main_OdsumE__3(X43,X26,X1,X11),c_Main_OdsumE__4(X43,X26,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
fof(f5091,plain,
( spl0_586
| ~ spl0_436
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f3978,f3891,f3578,f5089]) ).
fof(f5089,plain,
( spl0_586
<=> ! [X0,X1] : c_lessequals(X0,c_Inter(c_emptyset,X1),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f3578,plain,
( spl0_436
<=> ! [X21,X1,X19] :
( c_lessequals(X19,X21,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X19,X21,X1),X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f3891,plain,
( spl0_478
<=> ! [X0,X1] : c_in(X0,c_Inter(c_emptyset,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f3978,plain,
( ! [X0,X1] : c_lessequals(X0,c_Inter(c_emptyset,X1),tc_set(X1))
| ~ spl0_436
| ~ spl0_478 ),
inference(resolution,[],[f3892,f3579]) ).
fof(f3579,plain,
( ! [X21,X1,X19] :
( ~ c_in(c_Main_OsubsetI__1(X19,X21,X1),X21,X1)
| c_lessequals(X19,X21,tc_set(X1)) )
| ~ spl0_436 ),
inference(avatar_component_clause,[],[f3578]) ).
fof(f3892,plain,
( ! [X0,X1] : c_in(X0,c_Inter(c_emptyset,X1),X1)
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f3891]) ).
fof(f5076,plain,
spl0_585,
inference(avatar_split_clause,[],[f215,f5074]) ).
fof(f5074,plain,
( spl0_585
<=> ! [X43,X11,X20,X1,X26] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X43,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X43,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f215,axiom,
! [X11,X1,X26,X43,X20] :
( ~ c_in(X26,c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X43,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X43,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X20,X26,X1,X11),X1,X11),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X20,X26,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
fof(f5063,plain,
spl0_584,
inference(avatar_split_clause,[],[f211,f5061]) ).
fof(f5061,plain,
( spl0_584
<=> ! [X43,X11,X40,X20,X1] :
( ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X40,X20,X43,X1,X11),c_Main_OdprodE__2(X40,X20,X43,X1,X11),X1,X11),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X40,X20,X43,X1,X11),c_Main_OdprodE__4(X40,X20,X43,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f211,axiom,
! [X40,X11,X1,X43,X20] :
( ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X40,X20,X43,X1,X11),c_Main_OdprodE__2(X40,X20,X43,X1,X11),X1,X11),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X40,X20,X43,X1,X11),c_Main_OdprodE__4(X40,X20,X43,X1,X11),X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))) = X40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
fof(f5051,plain,
spl0_583,
inference(avatar_split_clause,[],[f220,f5049]) ).
fof(f5049,plain,
( spl0_583
<=> ! [X17,X43,X11,X14,X1,X20] :
( ~ c_in(c_Pair(X14,X17,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X14,X1,X11),c_Datatype__Universe_OIn1(X17,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f220,axiom,
! [X11,X1,X14,X17,X43,X20] :
( ~ c_in(c_Pair(X14,X17,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X14,X1,X11),c_Datatype__Universe_OIn1(X17,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
fof(f5047,plain,
spl0_582,
inference(avatar_split_clause,[],[f219,f5045]) ).
fof(f5045,plain,
( spl0_582
<=> ! [X43,X11,X20,X13,X16,X1] :
( ~ c_in(c_Pair(X13,X16,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X13,X1,X11),c_Datatype__Universe_OIn0(X16,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f219,axiom,
! [X11,X1,X16,X13,X20,X43] :
( ~ c_in(c_Pair(X13,X16,tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X13,X1,X11),c_Datatype__Universe_OIn0(X16,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),c_Datatype__Universe_Odsum(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
fof(f4967,plain,
spl0_581,
inference(avatar_split_clause,[],[f213,f4965]) ).
fof(f213,axiom,
! [X40,X11,X1,X43,X20] :
( ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdprodE__1(X40,X20,X43,X1,X11),c_Main_OdprodE__3(X40,X20,X43,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
fof(f4963,plain,
spl0_580,
inference(avatar_split_clause,[],[f212,f4961]) ).
fof(f212,axiom,
! [X40,X11,X1,X43,X20] :
( ~ c_in(X40,c_Datatype__Universe_Odprod(X20,X43,X1,X11),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))))
| c_in(c_Pair(c_Main_OdprodE__2(X40,X20,X43,X1,X11),c_Main_OdprodE__4(X40,X20,X43,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11))),X43,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X11)),tc_set(tc_Datatype__Universe_Onode(X1,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
fof(f4945,plain,
spl0_579,
inference(avatar_split_clause,[],[f262,f4943]) ).
fof(f4943,plain,
( spl0_579
<=> ! [X28,X20,X29,X27,X1] :
( ~ c_in(c_Pair(X27,c_List_Olist_OCons(X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X20,X27,X29,X28,X1),X28,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f262,axiom,
! [X28,X29,X1,X27,X20] :
( ~ c_in(c_Pair(X27,c_List_Olist_OCons(X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X20,X27,X29,X28,X1),X28,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
fof(f4941,plain,
spl0_578,
inference(avatar_split_clause,[],[f259,f4939]) ).
fof(f4939,plain,
( spl0_578
<=> ! [X28,X29,X20,X27,X1] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X29,X28,X1),X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(X28,c_Main_Olistrel__Cons1__2(X20,X27,X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f259,axiom,
! [X28,X29,X1,X27,X20] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X29,X28,X1),X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(X28,c_Main_Olistrel__Cons1__2(X20,X27,X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
fof(f4899,plain,
spl0_577,
inference(avatar_split_clause,[],[f293,f4897]) ).
fof(f4897,plain,
( spl0_577
<=> ! [X51,X11,X40,X20,X43,X12,X4,X1] :
( ~ c_in(c_Pair(X12,X40,X11,X51),X20,tc_prod(X11,X51))
| ~ c_in(c_Pair(X4,X12,X1,X11),X43,tc_prod(X1,X11))
| c_in(c_Pair(X4,X40,X1,X51),c_Relation_Orel__comp(X20,X43,X11,X51,X1),tc_prod(X1,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f293,axiom,
! [X40,X51,X11,X1,X4,X12,X43,X20] :
( ~ c_in(c_Pair(X12,X40,X11,X51),X20,tc_prod(X11,X51))
| ~ c_in(c_Pair(X4,X12,X1,X11),X43,tc_prod(X1,X11))
| c_in(c_Pair(X4,X40,X1,X51),c_Relation_Orel__comp(X20,X43,X11,X51,X1),tc_prod(X1,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
fof(f4883,plain,
spl0_576,
inference(avatar_split_clause,[],[f261,f4881]) ).
fof(f4881,plain,
( spl0_576
<=> ! [X28,X20,X29,X27,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X20,X27,X29,X28,X1),c_Main_Olistrel__Cons2__2(X20,X27,X29,X28,X1),X1) = X27
| ~ c_in(c_Pair(X27,c_List_Olist_OCons(X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f261,axiom,
! [X28,X29,X1,X27,X20] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X20,X27,X29,X28,X1),c_Main_Olistrel__Cons2__2(X20,X27,X29,X28,X1),X1) = X27
| ~ c_in(c_Pair(X27,c_List_Olist_OCons(X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
fof(f4879,plain,
spl0_575,
inference(avatar_split_clause,[],[f258,f4877]) ).
fof(f4877,plain,
( spl0_575
<=> ! [X28,X20,X29,X27,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X20,X27,X29,X28,X1),c_Main_Olistrel__Cons1__2(X20,X27,X29,X28,X1),X1) = X27
| ~ c_in(c_Pair(c_List_Olist_OCons(X29,X28,X1),X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f258,axiom,
! [X28,X29,X1,X27,X20] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X20,X27,X29,X28,X1),c_Main_Olistrel__Cons1__2(X20,X27,X29,X28,X1),X1) = X27
| ~ c_in(c_Pair(c_List_Olist_OCons(X29,X28,X1),X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
fof(f4872,plain,
spl0_574,
inference(avatar_split_clause,[],[f263,f4870]) ).
fof(f4870,plain,
( spl0_574
<=> ! [X28,X20,X29,X27,X1] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X20,X27,X29,X28,X1),X29,X1,X1),X20,tc_prod(X1,X1))
| ~ c_in(c_Pair(X27,c_List_Olist_OCons(X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f263,axiom,
! [X28,X29,X1,X27,X20] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X20,X27,X29,X28,X1),X29,X1,X1),X20,tc_prod(X1,X1))
| ~ c_in(c_Pair(X27,c_List_Olist_OCons(X29,X28,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
fof(f4868,plain,
spl0_573,
inference(avatar_split_clause,[],[f260,f4866]) ).
fof(f4866,plain,
( spl0_573
<=> ! [X28,X20,X29,X27,X1] :
( c_in(c_Pair(X29,c_Main_Olistrel__Cons1__1(X20,X27,X29,X28,X1),X1,X1),X20,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X29,X28,X1),X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f260,axiom,
! [X28,X29,X1,X27,X20] :
( c_in(c_Pair(X29,c_Main_Olistrel__Cons1__1(X20,X27,X29,X28,X1),X1,X1),X20,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X29,X28,X1),X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
fof(f4796,plain,
spl0_572,
inference(avatar_split_clause,[],[f291,f4794]) ).
fof(f291,axiom,
! [X50,X51,X11,X1,X43,X20] :
( ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11))
| c_in(c_Pair(c_Main_Orel__compE__1(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__2(X20,X43,X50,X51,X11,X1),X1,X51),X43,tc_prod(X1,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
fof(f4792,plain,
( spl0_571
| ~ spl0_61
| ~ spl0_539 ),
inference(avatar_split_clause,[],[f4425,f4363,f1669,f4790]) ).
fof(f4790,plain,
( spl0_571
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ORange(c_emptyset,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f4425,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ORange(c_emptyset,X1,X2),X2)
| ~ spl0_61
| ~ spl0_539 ),
inference(resolution,[],[f4364,f1670]) ).
fof(f4788,plain,
spl0_570,
inference(avatar_split_clause,[],[f290,f4786]) ).
fof(f290,axiom,
! [X50,X51,X11,X1,X43,X20] :
( ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11))
| c_in(c_Pair(c_Main_Orel__compE__2(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__3(X20,X43,X50,X51,X11,X1),X51,X11),X20,tc_prod(X51,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
fof(f4784,plain,
spl0_569,
inference(avatar_split_clause,[],[f228,f4782]) ).
fof(f4782,plain,
( spl0_569
<=> ! [X44,X19,X11,X21,X1] :
( ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__2(X21,X44,X1,X11),X21,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__1(X19,X44,X1,X11),X19,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f228,axiom,
! [X21,X11,X1,X44,X19] :
( ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__2(X21,X44,X1,X11),X21,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__1(X19,X44,X1,X11),X19,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
fof(f4764,plain,
spl0_568,
inference(avatar_split_clause,[],[f227,f4762]) ).
fof(f4762,plain,
( spl0_568
<=> ! [X44,X19,X11,X21,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X21,X44,X1,X11),X1,X11) = X44
| ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__1(X19,X44,X1,X11),X19,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f227,axiom,
! [X21,X11,X1,X44,X19] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X21,X44,X1,X11),X1,X11) = X44
| ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__1(X19,X44,X1,X11),X19,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f4760,plain,
spl0_567,
inference(avatar_split_clause,[],[f226,f4758]) ).
fof(f4758,plain,
( spl0_567
<=> ! [X44,X19,X11,X21,X1] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X19,X44,X1,X11),X1,X11) = X44
| ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__2(X21,X44,X1,X11),X21,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f226,axiom,
! [X21,X11,X1,X19,X44] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X19,X44,X1,X11),X1,X11) = X44
| ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OusumE__2(X21,X44,X1,X11),X21,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f4748,plain,
spl0_566,
inference(avatar_split_clause,[],[f225,f4746]) ).
fof(f4746,plain,
( spl0_566
<=> ! [X44,X19,X11,X21,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X21,X44,X1,X11),X1,X11) = X44
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X19,X44,X1,X11),X1,X11) = X44
| ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f225,axiom,
! [X21,X11,X1,X44,X19] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X21,X44,X1,X11),X1,X11) = X44
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X19,X44,X1,X11),X1,X11) = X44
| ~ c_in(X44,c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
fof(f4736,plain,
( spl0_565
| ~ spl0_61
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f4399,f4359,f1669,f4734]) ).
fof(f4734,plain,
( spl0_565
<=> ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ODomain(c_emptyset,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f4399,plain,
( ! [X2,X0,X1] : ~ c_in(X0,c_Relation_ODomain(c_emptyset,X1,X2),X1)
| ~ spl0_61
| ~ spl0_538 ),
inference(resolution,[],[f4360,f1670]) ).
fof(f4732,plain,
spl0_564,
inference(avatar_split_clause,[],[f323,f4730]) ).
fof(f4730,plain,
( spl0_564
<=> ! [X44,X19,X11,X21,X1] :
( ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X21,X44,X11,X1),X11,X1) = X44
| c_Sum__Type_OInl(c_Main_OPlusE__1(X19,X44,X1,X11),X1,X11) = X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f323,axiom,
! [X21,X11,X1,X44,X19] :
( ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X21,X44,X11,X1),X11,X1) = X44
| c_Sum__Type_OInl(c_Main_OPlusE__1(X19,X44,X1,X11),X1,X11) = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f4728,plain,
spl0_563,
inference(avatar_split_clause,[],[f292,f4726]) ).
fof(f4726,plain,
( spl0_563
<=> ! [X43,X51,X11,X50,X1,X20] :
( ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11))
| c_Pair(c_Main_Orel__compE__1(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__3(X20,X43,X50,X51,X11,X1),X1,X11) = X50 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f292,axiom,
! [X50,X51,X11,X1,X43,X20] :
( ~ c_in(X50,c_Relation_Orel__comp(X20,X43,X51,X11,X1),tc_prod(X1,X11))
| c_Pair(c_Main_Orel__compE__1(X20,X43,X50,X51,X11,X1),c_Main_Orel__compE__3(X20,X43,X50,X51,X11,X1),X1,X11) = X50 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f4722,plain,
spl0_562,
inference(avatar_split_clause,[],[f224,f4720]) ).
fof(f4720,plain,
( spl0_562
<=> ! [X19,X11,X14,X13,X21,X1] :
( ~ c_in(X14,X21,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| ~ c_in(X13,X19,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Datatype__Universe_OScons(X13,X14,X1,X11),c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f224,axiom,
! [X21,X11,X1,X19,X14,X13] :
( ~ c_in(X14,X21,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| ~ c_in(X13,X19,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Datatype__Universe_OScons(X13,X14,X1,X11),c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f4706,plain,
spl0_561,
inference(avatar_split_clause,[],[f325,f4704]) ).
fof(f4704,plain,
( spl0_561
<=> ! [X44,X19,X11,X21,X1] :
( c_in(c_Main_OPlusE__1(X19,X44,X1,X11),X19,X1)
| ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X21,X44,X11,X1),X11,X1) = X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f325,axiom,
! [X21,X11,X1,X19,X44] :
( c_in(c_Main_OPlusE__1(X19,X44,X1,X11),X19,X1)
| ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X21,X44,X11,X1),X11,X1) = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f4702,plain,
spl0_560,
inference(avatar_split_clause,[],[f324,f4700]) ).
fof(f4700,plain,
( spl0_560
<=> ! [X44,X19,X11,X21,X1] :
( c_in(c_Main_OPlusE__2(X21,X44,X11,X1),X21,X11)
| ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X19,X44,X1,X11),X1,X11) = X44 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f324,axiom,
! [X21,X11,X1,X44,X19] :
( c_in(c_Main_OPlusE__2(X21,X44,X11,X1),X21,X11)
| ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X19,X44,X1,X11),X1,X11) = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f4698,plain,
spl0_559,
inference(avatar_split_clause,[],[f221,f4696]) ).
fof(f4696,plain,
( spl0_559
<=> ! [X19,X11,X40,X21,X1] :
( ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X19,X21,X40,X1,X11),c_Main_OuprodE__2(X19,X21,X40,X1,X11),X1,X11) = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f221,axiom,
! [X40,X21,X11,X1,X19] :
( ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X19,X21,X40,X1,X11),c_Main_OuprodE__2(X19,X21,X40,X1,X11),X1,X11) = X40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f4653,plain,
spl0_558,
inference(avatar_split_clause,[],[f285,f4651]) ).
fof(f285,axiom,
! [X49,X11,X1,X20] :
( ~ c_in(X49,c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11))
| c_in(c_Pair(c_Main_OconverseE__1(X20,X49,X11,X1),c_Main_OconverseE__2(X20,X49,X11,X1),X11,X1),X20,tc_prod(X11,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f4649,plain,
spl0_557,
inference(avatar_split_clause,[],[f206,f4647]) ).
fof(f4647,plain,
( spl0_557
<=> ! [X9,X20,X29,X1] :
( ~ c_Wellfounded__Recursion_Owf(X20,X1)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f206,axiom,
! [X29,X1,X9,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X1)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
fof(f4645,plain,
spl0_556,
inference(avatar_split_clause,[],[f203,f4643]) ).
fof(f4643,plain,
( spl0_556
<=> ! [X9,X20,X29,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X1)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f203,axiom,
! [X29,X1,X9,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X1)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
fof(f4638,plain,
spl0_555,
inference(avatar_split_clause,[],[f326,f4636]) ).
fof(f4636,plain,
( spl0_555
<=> ! [X44,X19,X11,X21,X1] :
( c_in(c_Main_OPlusE__2(X21,X44,X11,X1),X21,X11)
| c_in(c_Main_OPlusE__1(X19,X44,X1,X11),X19,X1)
| ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f326,axiom,
! [X21,X11,X1,X44,X19] :
( c_in(c_Main_OPlusE__2(X21,X44,X11,X1),X21,X11)
| c_in(c_Main_OPlusE__1(X19,X44,X1,X11),X19,X1)
| ~ c_in(X44,c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f4612,plain,
spl0_554,
inference(avatar_split_clause,[],[f1369,f4610]) ).
fof(f1369,axiom,
! [X59,X1,X8,X7] :
( ~ c_in(X7,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| c_in(X59,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X7,X59,X1),c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f4608,plain,
spl0_553,
inference(avatar_split_clause,[],[f330,f4606]) ).
fof(f4606,plain,
( spl0_553
<=> ! [X4,X20,X12,X1] :
( ~ c_in(c_Pair(X4,X12,X1,X1),c_Transitive__Closure_Otrancl(X20,X1),tc_prod(X1,X1))
| c_in(c_Pair(X4,X12,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f330,axiom,
! [X1,X4,X12,X20] :
( ~ c_in(c_Pair(X4,X12,X1,X1),c_Transitive__Closure_Otrancl(X20,X1),tc_prod(X1,X1))
| c_in(c_Pair(X4,X12,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
fof(f4604,plain,
spl0_552,
inference(avatar_split_clause,[],[f286,f4602]) ).
fof(f4602,plain,
( spl0_552
<=> ! [X11,X20,X49,X1] :
( ~ c_in(X49,c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11))
| c_Pair(c_Main_OconverseE__2(X20,X49,X11,X1),c_Main_OconverseE__1(X20,X49,X11,X1),X1,X11) = X49 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f286,axiom,
! [X49,X11,X1,X20] :
( ~ c_in(X49,c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11))
| c_Pair(c_Main_OconverseE__2(X20,X49,X11,X1),c_Main_OconverseE__1(X20,X49,X11,X1),X1,X11) = X49 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f4600,plain,
spl0_551,
inference(avatar_split_clause,[],[f205,f4598]) ).
fof(f4598,plain,
( spl0_551
<=> ! [X9,X20,X29,X1] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f205,axiom,
! [X29,X1,X9,X20] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
fof(f4596,plain,
spl0_550,
inference(avatar_split_clause,[],[f202,f4594]) ).
fof(f4594,plain,
( spl0_550
<=> ! [X9,X20,X29,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f202,axiom,
! [X29,X1,X9,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X9,X29,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
fof(f4592,plain,
spl0_549,
inference(avatar_split_clause,[],[f72,f4590]) ).
fof(f4590,plain,
( spl0_549
<=> ! [X28,X19,X27,X1] :
( ~ c_in(X28,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1))
| c_in(c_append(X27,X28,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f72,axiom,
! [X28,X1,X19,X27] :
( ~ c_in(X28,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1))
| c_in(c_append(X27,X28,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
fof(f4507,plain,
spl0_548,
inference(avatar_split_clause,[],[f281,f4505]) ).
fof(f281,axiom,
! [X11,X1,X19,X12,X20] :
( ~ c_in(X12,c_Relation_OImage(X20,X19,X11,X1),X1)
| c_in(c_Pair(c_Main_OImageE__1(X19,X12,X20,X11,X1),X12,X11,X1),X20,tc_prod(X11,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f4503,plain,
spl0_547,
inference(avatar_split_clause,[],[f223,f4501]) ).
fof(f223,axiom,
! [X40,X21,X11,X1,X19] :
( ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OuprodE__1(X19,X21,X40,X1,X11),X19,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f4499,plain,
spl0_546,
inference(avatar_split_clause,[],[f222,f4497]) ).
fof(f222,axiom,
! [X40,X21,X11,X1,X19] :
( ~ c_in(X40,c_Datatype__Universe_Ouprod(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Main_OuprodE__2(X19,X21,X40,X1,X11),X21,tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f4495,plain,
spl0_545,
inference(avatar_split_clause,[],[f140,f4493]) ).
fof(f4493,plain,
( spl0_545
<=> ! [X4,X11,X12,X1,X20] :
( ~ c_in(c_Pair(X12,X4,X11,X1),X20,tc_prod(X11,X1))
| c_in(c_Pair(X4,X12,X1,X11),c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f140,axiom,
! [X11,X1,X4,X12,X20] :
( ~ c_in(c_Pair(X12,X4,X11,X1),X20,tc_prod(X11,X1))
| c_in(c_Pair(X4,X12,X1,X11),c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
fof(f4491,plain,
spl0_544,
inference(avatar_split_clause,[],[f139,f4489]) ).
fof(f4489,plain,
( spl0_544
<=> ! [X4,X11,X12,X1,X20] :
( c_in(c_Pair(X12,X4,X11,X1),X20,tc_prod(X11,X1))
| ~ c_in(c_Pair(X4,X12,X1,X11),c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f139,axiom,
! [X11,X1,X4,X12,X20] :
( c_in(c_Pair(X12,X4,X11,X1),X20,tc_prod(X11,X1))
| ~ c_in(c_Pair(X4,X12,X1,X11),c_Relation_Oconverse(X20,X11,X1),tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
fof(f4455,plain,
spl0_543,
inference(avatar_split_clause,[],[f329,f4453]) ).
fof(f4453,plain,
( spl0_543
<=> ! [X4,X20,X12,X1] :
( ~ c_in(c_Pair(X4,X12,X1,X1),X20,tc_prod(X1,X1))
| c_in(c_Pair(X4,X12,X1,X1),c_Transitive__Closure_Otrancl(X20,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f329,axiom,
! [X1,X4,X12,X20] :
( ~ c_in(c_Pair(X4,X12,X1,X1),X20,tc_prod(X1,X1))
| c_in(c_Pair(X4,X12,X1,X1),c_Transitive__Closure_Otrancl(X20,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f4451,plain,
spl0_542,
inference(avatar_split_clause,[],[f282,f4449]) ).
fof(f282,axiom,
! [X11,X1,X19,X4,X12,X20] :
( ~ c_in(X4,X19,X1)
| c_in(X12,c_Relation_OImage(X20,X19,X1,X11),X11)
| ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f4386,plain,
( spl0_541
| ~ spl0_67
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4243,f4173,f1693,f4384]) ).
fof(f4384,plain,
( spl0_541
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f4243,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
| ~ spl0_67
| ~ spl0_517 ),
inference(resolution,[],[f4174,f1694]) ).
fof(f4369,plain,
spl0_540,
inference(avatar_split_clause,[],[f287,f4367]) ).
fof(f4367,plain,
( spl0_540
<=> ! [X1,X40,X19] :
( ~ c_in(X40,c_Relation_Odiag(X19,X1),tc_prod(X1,X1))
| c_Pair(c_Main_OdiagE__1(X19,X40,X1),c_Main_OdiagE__1(X19,X40,X1),X1,X1) = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f287,axiom,
! [X40,X1,X19] :
( ~ c_in(X40,c_Relation_Odiag(X19,X1),tc_prod(X1,X1))
| c_Pair(c_Main_OdiagE__1(X19,X40,X1),c_Main_OdiagE__1(X19,X40,X1),X1,X1) = X40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f4365,plain,
spl0_539,
inference(avatar_split_clause,[],[f283,f4363]) ).
fof(f283,axiom,
! [X11,X1,X12,X20] :
( ~ c_in(X12,c_Relation_ORange(X20,X11,X1),X1)
| c_in(c_Pair(c_Main_ORangeE__1(X12,X20,X1,X11),X12,X11,X1),X20,tc_prod(X11,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f4361,plain,
spl0_538,
inference(avatar_split_clause,[],[f277,f4359]) ).
fof(f277,axiom,
! [X11,X1,X4,X20] :
( ~ c_in(X4,c_Relation_ODomain(X20,X1,X11),X1)
| c_in(c_Pair(X4,c_Main_ODomainE__1(X4,X20,X1,X11),X1,X11),X20,tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f4357,plain,
spl0_537,
inference(avatar_split_clause,[],[f268,f4355]) ).
fof(f4355,plain,
( spl0_537
<=> ! [X48,X4,X19,X1] :
( ~ c_in(X4,X19,X1)
| ~ c_in(X48,c_List_Olists(X19,X1),tc_List_Olist(X1))
| c_in(c_List_Olist_OCons(X4,X48,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f268,axiom,
! [X48,X1,X19,X4] :
( ~ c_in(X4,X19,X1)
| ~ c_in(X48,c_List_Olists(X19,X1),tc_List_Olist(X1))
| c_in(c_List_Olist_OCons(X4,X48,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f4353,plain,
spl0_536,
inference(avatar_split_clause,[],[f230,f4351]) ).
fof(f4351,plain,
( spl0_536
<=> ! [X19,X11,X14,X21,X1] :
( ~ c_in(X14,X21,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Datatype__Universe_OIn1(X14,X1,X11),c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f230,axiom,
! [X21,X11,X1,X19,X14] :
( ~ c_in(X14,X21,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Datatype__Universe_OIn1(X14,X1,X11),c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f4349,plain,
spl0_535,
inference(avatar_split_clause,[],[f229,f4347]) ).
fof(f4347,plain,
( spl0_535
<=> ! [X11,X19,X13,X21,X1] :
( ~ c_in(X13,X19,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Datatype__Universe_OIn0(X13,X1,X11),c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f229,axiom,
! [X21,X11,X1,X19,X13] :
( ~ c_in(X13,X19,tc_set(tc_Datatype__Universe_Onode(X1,X11)))
| c_in(c_Datatype__Universe_OIn0(X13,X1,X11),c_Datatype__Universe_Ousum(X19,X21,X1,X11),tc_set(tc_Datatype__Universe_Onode(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f4345,plain,
( spl0_534
| ~ spl0_384
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4233,f4173,f3316,f4343]) ).
fof(f4233,plain,
( ! [X0,X1] : c_in(X0,c_Relation_ORange(c_Relation_OId,X1,X1),X1)
| ~ spl0_384
| ~ spl0_517 ),
inference(resolution,[],[f4174,f3317]) ).
fof(f4341,plain,
spl0_533,
inference(avatar_split_clause,[],[f138,f4339]) ).
fof(f4339,plain,
( spl0_533
<=> ! [X4,X11,X12,X1,X20] :
( ~ c_in(c_Pair(X4,X12,X11,X1),X20,tc_prod(X11,X1))
| c_in(X12,c_Relation_OImage(X20,c_insert(X4,c_emptyset,X11),X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f138,axiom,
! [X11,X1,X4,X12,X20] :
( ~ c_in(c_Pair(X4,X12,X11,X1),X20,tc_prod(X11,X1))
| c_in(X12,c_Relation_OImage(X20,c_insert(X4,c_emptyset,X11),X11,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
fof(f4337,plain,
spl0_532,
inference(avatar_split_clause,[],[f137,f4335]) ).
fof(f4335,plain,
( spl0_532
<=> ! [X4,X11,X12,X1,X20] :
( c_in(c_Pair(X4,X12,X11,X1),X20,tc_prod(X11,X1))
| ~ c_in(X12,c_Relation_OImage(X20,c_insert(X4,c_emptyset,X11),X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f137,axiom,
! [X11,X1,X4,X12,X20] :
( c_in(c_Pair(X4,X12,X11,X1),X20,tc_prod(X11,X1))
| ~ c_in(X12,c_Relation_OImage(X20,c_insert(X4,c_emptyset,X11),X11,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
fof(f4333,plain,
spl0_531,
inference(avatar_split_clause,[],[f42,f4331]) ).
fof(f4331,plain,
( spl0_531
<=> ! [X4,X19,X21,X1] :
( ~ c_in(c_minus(X19,X21,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X19,c_insert(X4,X21,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f42,axiom,
! [X21,X1,X19,X4] :
( ~ c_in(c_minus(X19,X21,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X19,c_insert(X4,X21,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
fof(f4329,plain,
spl0_530,
inference(avatar_split_clause,[],[f41,f4327]) ).
fof(f4327,plain,
( spl0_530
<=> ! [X4,X19,X21,X1] :
( c_in(c_minus(X19,X21,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_minus(X19,c_insert(X4,X21,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f41,axiom,
! [X21,X1,X19,X4] :
( c_in(c_minus(X19,X21,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_minus(X19,c_insert(X4,X21,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
fof(f4304,plain,
spl0_529,
inference(avatar_split_clause,[],[f241,f4302]) ).
fof(f4302,plain,
( spl0_529
<=> ! [X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| ~ c_in(c_Main_Ofinite__Union__1(X19,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Union(X19,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f241,axiom,
! [X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| ~ c_in(c_Main_Ofinite__Union__1(X19,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Union(X19,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f4300,plain,
spl0_528,
inference(avatar_split_clause,[],[f240,f4298]) ).
fof(f4298,plain,
( spl0_528
<=> ! [X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| c_in(c_Main_Ofinite__Union__1(X19,X1),X19,tc_set(X1))
| c_in(c_Union(X19,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f240,axiom,
! [X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| c_in(c_Main_Ofinite__Union__1(X19,X1),X19,tc_set(X1))
| c_in(c_Union(X19,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f4296,plain,
( spl0_527
| ~ spl0_67
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4218,f4157,f1693,f4294]) ).
fof(f4294,plain,
( spl0_527
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f4218,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
| ~ spl0_67
| ~ spl0_513 ),
inference(resolution,[],[f4158,f1694]) ).
fof(f4291,plain,
spl0_526,
inference(avatar_split_clause,[],[f265,f4289]) ).
fof(f4289,plain,
( spl0_526
<=> ! [X20,X27,X1] :
( c_List_Olist_ONil = X27
| ~ c_in(c_Pair(X27,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f265,axiom,
! [X1,X27,X20] :
( c_List_Olist_ONil = X27
| ~ c_in(c_Pair(X27,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f4287,plain,
spl0_525,
inference(avatar_split_clause,[],[f264,f4285]) ).
fof(f4285,plain,
( spl0_525
<=> ! [X20,X27,X1] :
( c_List_Olist_ONil = X27
| ~ c_in(c_Pair(c_List_Olist_ONil,X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f264,axiom,
! [X1,X27,X20] :
( c_List_Olist_ONil = X27
| ~ c_in(c_Pair(c_List_Olist_ONil,X27,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f4283,plain,
spl0_524,
inference(avatar_split_clause,[],[f93,f4281]) ).
fof(f4281,plain,
( spl0_524
<=> ! [X28,X29,X27,X1] :
( c_List_Orev(X27,X1) != c_List_Olist_OCons(X29,X28,X1)
| c_append(c_List_Orev(X28,X1),c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f93,axiom,
! [X28,X29,X1,X27] :
( c_List_Orev(X27,X1) != c_List_Olist_OCons(X29,X28,X1)
| c_append(c_List_Orev(X28,X1),c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff1_0) ).
fof(f4268,plain,
spl0_523,
inference(avatar_split_clause,[],[f69,f4266]) ).
fof(f69,axiom,
! [X28,X29,X1,X9,X27] :
( X9 = X29
| c_append(X27,c_List_Olist_OCons(X9,c_List_Olist_ONil,X1),X1) != c_append(X28,c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
fof(f4264,plain,
spl0_522,
inference(avatar_split_clause,[],[f68,f4262]) ).
fof(f68,axiom,
! [X28,X29,X1,X9,X27] :
( X27 = X28
| c_append(X27,c_List_Olist_OCons(X9,c_List_Olist_ONil,X1),X1) != c_append(X28,c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
fof(f4260,plain,
spl0_521,
inference(avatar_split_clause,[],[f47,f4258]) ).
fof(f4258,plain,
( spl0_521
<=> ! [X22,X1,X23] :
( ~ c_in(X23,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X22,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f47,axiom,
! [X1,X22,X23] :
( ~ c_in(X23,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X22,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
fof(f4256,plain,
( spl0_520
| ~ spl0_384
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4208,f4157,f3316,f4254]) ).
fof(f4208,plain,
( ! [X0,X1] : c_in(X0,c_Relation_ODomain(c_Relation_OId,X1,X1),X1)
| ~ spl0_384
| ~ spl0_513 ),
inference(resolution,[],[f4158,f3317]) ).
fof(f4183,plain,
spl0_519,
inference(avatar_split_clause,[],[f322,f4181]) ).
fof(f4181,plain,
( spl0_519
<=> ! [X19,X11,X12,X21,X1] :
( ~ c_in(X12,X21,X1)
| c_in(c_Sum__Type_OInr(X12,X1,X11),c_Sum__Type_OPlus(X19,X21,X11,X1),tc_sum(X11,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f322,axiom,
! [X21,X11,X1,X19,X12] :
( ~ c_in(X12,X21,X1)
| c_in(c_Sum__Type_OInr(X12,X1,X11),c_Sum__Type_OPlus(X19,X21,X11,X1),tc_sum(X11,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f4179,plain,
spl0_518,
inference(avatar_split_clause,[],[f321,f4177]) ).
fof(f4177,plain,
( spl0_518
<=> ! [X4,X19,X11,X21,X1] :
( ~ c_in(X4,X19,X1)
| c_in(c_Sum__Type_OInl(X4,X1,X11),c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f321,axiom,
! [X21,X11,X1,X19,X4] :
( ~ c_in(X4,X19,X1)
| c_in(c_Sum__Type_OInl(X4,X1,X11),c_Sum__Type_OPlus(X19,X21,X1,X11),tc_sum(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f4175,plain,
spl0_517,
inference(avatar_split_clause,[],[f284,f4173]) ).
fof(f284,axiom,
! [X11,X1,X4,X12,X20] :
( c_in(X12,c_Relation_ORange(X20,X1,X11),X11)
| ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f4171,plain,
spl0_516,
inference(avatar_split_clause,[],[f280,f4169]) ).
fof(f4169,plain,
( spl0_516
<=> ! [X19,X11,X12,X1,X20] :
( ~ c_in(X12,c_Relation_OImage(X20,X19,X11,X1),X1)
| c_in(c_Main_OImageE__1(X19,X12,X20,X11,X1),X19,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f280,axiom,
! [X11,X1,X19,X12,X20] :
( ~ c_in(X12,c_Relation_OImage(X20,X19,X11,X1),X1)
| c_in(c_Main_OImageE__1(X19,X12,X20,X11,X1),X19,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f4167,plain,
spl0_515,
inference(avatar_split_clause,[],[f279,f4165]) ).
fof(f4165,plain,
( spl0_515
<=> ! [X1,X7] :
( ~ c_in(X7,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X7,X1),c_Main_OIdE__1(X7,X1),X1,X1) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f279,axiom,
! [X1,X7] :
( ~ c_in(X7,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X7,X1),c_Main_OIdE__1(X7,X1),X1,X1) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f4163,plain,
( spl0_514
| ~ spl0_67
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f3838,f3798,f1693,f4161]) ).
fof(f4161,plain,
( spl0_514
<=> ! [X0,X1] : c_in(X0,c_List_Olists(c_UNIV,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f3838,plain,
( ! [X0,X1] : c_in(X0,c_List_Olists(c_UNIV,X1),tc_List_Olist(X1))
| ~ spl0_67
| ~ spl0_467 ),
inference(resolution,[],[f3799,f1694]) ).
fof(f4159,plain,
spl0_513,
inference(avatar_split_clause,[],[f278,f4157]) ).
fof(f278,axiom,
! [X11,X1,X4,X12,X20] :
( c_in(X4,c_Relation_ODomain(X20,X1,X11),X1)
| ~ c_in(c_Pair(X4,X12,X1,X11),X20,tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f4155,plain,
spl0_512,
inference(avatar_split_clause,[],[f266,f4153]) ).
fof(f4153,plain,
( spl0_512
<=> ! [X9,X48,X1,X19] :
( c_in(X48,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X9,X48,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f266,axiom,
! [X48,X1,X19,X9] :
( c_in(X48,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X9,X48,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f4151,plain,
spl0_511,
inference(avatar_split_clause,[],[f254,f4149]) ).
fof(f4149,plain,
( spl0_511
<=> ! [X19,X27,X1,X47] :
( c_in(X47,X19,X1)
| ~ c_in(X47,c_List_Oset(X27,X1),X1)
| ~ c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f254,axiom,
! [X47,X1,X19,X27] :
( c_in(X47,X19,X1)
| ~ c_in(X47,c_List_Oset(X27,X1),X1)
| ~ c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f4147,plain,
spl0_510,
inference(avatar_split_clause,[],[f194,f4145]) ).
fof(f194,axiom,
! [X1,X19,X9] :
( ~ c_lessequals(X19,c_insert(X9,c_emptyset,X1),tc_set(X1))
| c_insert(X9,c_emptyset,X1) = c_insert(X9,X19,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
fof(f4143,plain,
spl0_509,
inference(avatar_split_clause,[],[f190,f4141]) ).
fof(f4141,plain,
( spl0_509
<=> ! [X12,X4,X1,X19] :
( c_lessequals(X19,c_insert(X12,c_emptyset,X1),tc_set(X1))
| c_insert(X4,X19,X1) != c_insert(X12,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f190,axiom,
! [X1,X19,X4,X12] :
( c_lessequals(X19,c_insert(X12,c_emptyset,X1),tc_set(X1))
| c_insert(X4,X19,X1) != c_insert(X12,c_emptyset,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
fof(f4139,plain,
spl0_508,
inference(avatar_split_clause,[],[f71,f4137]) ).
fof(f4137,plain,
( spl0_508
<=> ! [X27,X1,X28,X19] :
( c_in(X28,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X27,X28,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f71,axiom,
! [X28,X1,X19,X27] :
( c_in(X28,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X27,X28,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
fof(f4135,plain,
spl0_507,
inference(avatar_split_clause,[],[f70,f4133]) ).
fof(f4133,plain,
( spl0_507
<=> ! [X28,X19,X27,X1] :
( c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X27,X28,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f70,axiom,
! [X28,X1,X19,X27] :
( c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X27,X28,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
fof(f4131,plain,
spl0_506,
inference(avatar_split_clause,[],[f52,f4129]) ).
fof(f52,axiom,
! [X18,X15,X24] :
( ~ c_Divides_Oop_Advd(X15,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X15,X18,tc_nat)
| c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff2_0) ).
fof(f4127,plain,
spl0_505,
inference(avatar_split_clause,[],[f49,f4125]) ).
fof(f4125,plain,
( spl0_505
<=> ! [X11,X20,X1] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X11,X1)))
| c_in(c_Relation_Oconverse(X20,X11,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f49,axiom,
! [X11,X1,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X11,X1)))
| c_in(c_Relation_Oconverse(X20,X11,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
fof(f4123,plain,
spl0_504,
inference(avatar_split_clause,[],[f48,f4121]) ).
fof(f4121,plain,
( spl0_504
<=> ! [X11,X20,X1] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X11,X1)))
| ~ c_in(c_Relation_Oconverse(X20,X11,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f48,axiom,
! [X11,X1,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(tc_prod(X11,X1)))
| ~ c_in(c_Relation_Oconverse(X20,X11,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
fof(f4085,plain,
spl0_503,
inference(avatar_split_clause,[],[f289,f4083]) ).
fof(f289,axiom,
! [X1,X19,X4] :
( ~ c_in(X4,X19,X1)
| c_in(c_Pair(X4,X4,X1,X1),c_Relation_Odiag(X19,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f4081,plain,
( spl0_502
| ~ spl0_293
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f3975,f3899,f2905,f4079]) ).
fof(f4079,plain,
( spl0_502
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f3899,plain,
( spl0_480
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X29,X9,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X9,X1),c_SetInterval_OgreaterThan(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f3975,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_293
| ~ spl0_480 ),
inference(resolution,[],[f3900,f2906]) ).
fof(f3900,plain,
( ! [X29,X1,X9] :
( ~ c_lessequals(c_SetInterval_OgreaterThan(X9,X1),c_SetInterval_OgreaterThan(X29,X1),tc_set(X1))
| c_lessequals(X29,X9,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_480 ),
inference(avatar_component_clause,[],[f3899]) ).
fof(f4077,plain,
spl0_501,
inference(avatar_split_clause,[],[f255,f4075]) ).
fof(f255,axiom,
! [X1,X19,X27] :
( c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X19,X27,X1),c_List_Oset(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f4073,plain,
spl0_500,
inference(avatar_split_clause,[],[f169,f4071]) ).
fof(f4071,plain,
( spl0_500
<=> ! [X40,X19,X21,X1] :
( ~ c_in(X40,X19,X1)
| c_in(X40,X21,X1)
| c_in(X40,c_minus(X19,X21,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f169,axiom,
! [X40,X21,X1,X19] :
( ~ c_in(X40,X19,X1)
| c_in(X40,X21,X1)
| c_in(X40,c_minus(X19,X21,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
fof(f4069,plain,
spl0_499,
inference(avatar_split_clause,[],[f166,f4067]) ).
fof(f166,axiom,
! [X21,X1,X19] :
( ~ c_lessequals(X21,X19,tc_set(X1))
| c_lessequals(c_uminus(X19,tc_set(X1)),c_uminus(X21,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
fof(f4065,plain,
spl0_498,
inference(avatar_split_clause,[],[f165,f4063]) ).
fof(f4063,plain,
( spl0_498
<=> ! [X21,X1,X19] :
( c_lessequals(X21,X19,tc_set(X1))
| ~ c_lessequals(c_uminus(X19,tc_set(X1)),c_uminus(X21,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f165,axiom,
! [X21,X1,X19] :
( c_lessequals(X21,X19,tc_set(X1))
| ~ c_lessequals(c_uminus(X19,tc_set(X1)),c_uminus(X21,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
fof(f4061,plain,
spl0_497,
inference(avatar_split_clause,[],[f94,f4059]) ).
fof(f94,axiom,
! [X28,X29,X1] : c_List_Olist_OCons(X29,X28,X1) = c_List_Orev(c_append(c_List_Orev(X28,X1),c_List_Olist_OCons(X29,c_List_Olist_ONil,X1),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).
fof(f4057,plain,
spl0_496,
inference(avatar_split_clause,[],[f87,f4055]) ).
fof(f4055,plain,
( spl0_496
<=> ! [X27,X1] :
( c_List_Oremdups(X27,X1) = X27
| c_Nat_Osize(X27,tc_List_Olist(X1)) != c_Nat_Osize(c_List_Oremdups(X27,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f87,axiom,
! [X1,X27] :
( c_List_Oremdups(X27,X1) = X27
| c_Nat_Osize(X27,tc_List_Olist(X1)) != c_Nat_Osize(c_List_Oremdups(X27,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).
fof(f4053,plain,
spl0_495,
inference(avatar_split_clause,[],[f67,f4051]) ).
fof(f67,axiom,
! [X28,X1,X20] : ~ c_in(c_Pair(c_List_Olist_ONil,X28,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
fof(f4049,plain,
spl0_494,
inference(avatar_split_clause,[],[f61,f4047]) ).
fof(f61,axiom,
! [X1,X27,X20] : ~ c_in(c_Pair(X27,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X20,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
fof(f3953,plain,
spl0_493,
inference(avatar_split_clause,[],[f335,f3951]) ).
fof(f3951,plain,
( spl0_493
<=> ! [X55,X54,X11,X1] :
( ~ c_Wellfounded__Recursion_Owf(X54,X11)
| ~ c_Wellfounded__Recursion_Owf(X55,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X55,X54,X1,X11),tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f335,axiom,
! [X11,X1,X54,X55] :
( ~ c_Wellfounded__Recursion_Owf(X54,X11)
| ~ c_Wellfounded__Recursion_Owf(X55,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X55,X54,X1,X11),tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f3949,plain,
spl0_492,
inference(avatar_split_clause,[],[f333,f3947]) ).
fof(f3947,plain,
( spl0_492
<=> ! [X53,X11,X52,X1] :
( ~ c_Relation_Otrans(X52,X11)
| ~ c_Relation_Otrans(X53,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X53,X52,X1,X11),tc_prod(X1,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f333,axiom,
! [X11,X1,X52,X53] :
( ~ c_Relation_Otrans(X52,X11)
| ~ c_Relation_Otrans(X53,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X53,X52,X1,X11),tc_prod(X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f3945,plain,
spl0_491,
inference(avatar_split_clause,[],[f288,f3943]) ).
fof(f288,axiom,
! [X40,X1,X19] :
( c_in(c_Main_OdiagE__1(X19,X40,X1),X19,X1)
| ~ c_in(X40,c_Relation_Odiag(X19,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f3941,plain,
spl0_490,
inference(avatar_split_clause,[],[f204,f3939]) ).
fof(f3939,plain,
( spl0_490
<=> ! [X29,X20,X1,X9] :
( c_Wellfounded__Recursion_Owf(X20,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f204,axiom,
! [X29,X1,X9,X20] :
( c_Wellfounded__Recursion_Owf(X20,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
fof(f3937,plain,
( spl0_489
| ~ spl0_61
| ~ spl0_471 ),
inference(avatar_split_clause,[],[f3859,f3814,f1669,f3935]) ).
fof(f3814,plain,
( spl0_471
<=> ! [X1,X19,X42] :
( ~ c_in(X19,c_Union(X42,X1),X1)
| c_in(c_Main_OUnionE__1(X19,X42,X1),X42,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f3859,plain,
( ! [X0,X1] : ~ c_in(X0,c_Union(c_emptyset,X1),X1)
| ~ spl0_61
| ~ spl0_471 ),
inference(resolution,[],[f3815,f1670]) ).
fof(f3815,plain,
( ! [X1,X19,X42] :
( c_in(c_Main_OUnionE__1(X19,X42,X1),X42,tc_set(X1))
| ~ c_in(X19,c_Union(X42,X1),X1) )
| ~ spl0_471 ),
inference(avatar_component_clause,[],[f3814]) ).
fof(f3933,plain,
spl0_488,
inference(avatar_split_clause,[],[f201,f3931]) ).
fof(f3931,plain,
( spl0_488
<=> ! [X29,X20,X1,X9] :
( c_Wellfounded__Recursion_Oacyclic(X20,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f201,axiom,
! [X29,X1,X9,X20] :
( c_Wellfounded__Recursion_Oacyclic(X20,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X29,X9,X1,X1),X20,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
fof(f3929,plain,
spl0_487,
inference(avatar_split_clause,[],[f183,f3927]) ).
fof(f183,axiom,
! [X41,X1,X19,X42] :
( ~ c_in(X19,X41,X1)
| ~ c_in(X41,X42,tc_set(X1))
| c_in(X19,c_Union(X42,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
fof(f3925,plain,
spl0_486,
inference(avatar_split_clause,[],[f179,f3923]) ).
fof(f3923,plain,
( spl0_486
<=> ! [X40,X19,X21,X1] :
( c_in(X40,X19,X1)
| c_in(X40,X21,X1)
| ~ c_in(X40,c_union(X19,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f179,axiom,
! [X40,X21,X1,X19] :
( c_in(X40,X19,X1)
| c_in(X40,X21,X1)
| ~ c_in(X40,c_union(X19,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
fof(f3921,plain,
spl0_485,
inference(avatar_split_clause,[],[f173,f3919]) ).
fof(f3919,plain,
( spl0_485
<=> ! [X41,X19,X42,X1] :
( c_in(X19,X41,X1)
| ~ c_in(X41,X42,tc_set(X1))
| ~ c_in(X19,c_Inter(X42,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f173,axiom,
! [X41,X1,X19,X42] :
( c_in(X19,X41,X1)
| ~ c_in(X41,X42,tc_set(X1))
| ~ c_in(X19,c_Inter(X42,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
fof(f3917,plain,
spl0_484,
inference(avatar_split_clause,[],[f172,f3915]) ).
fof(f3915,plain,
( spl0_484
<=> ! [X40,X19,X21,X1] :
( ~ c_in(X40,X21,X1)
| ~ c_in(X40,X19,X1)
| c_in(X40,c_inter(X19,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f172,axiom,
! [X40,X21,X1,X19] :
( ~ c_in(X40,X21,X1)
| ~ c_in(X40,X19,X1)
| c_in(X40,c_inter(X19,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
fof(f3913,plain,
spl0_483,
inference(avatar_split_clause,[],[f161,f3911]) ).
fof(f161,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X9,X29,X1)
| c_lessequals(c_SetInterval_OlessThan(X9,X1),c_SetInterval_OlessThan(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
fof(f3909,plain,
spl0_482,
inference(avatar_split_clause,[],[f160,f3907]) ).
fof(f3907,plain,
( spl0_482
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X9,X29,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X9,X1),c_SetInterval_OlessThan(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f160,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X9,X29,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X9,X1),c_SetInterval_OlessThan(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
fof(f3905,plain,
spl0_481,
inference(avatar_split_clause,[],[f156,f3903]) ).
fof(f156,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X29,X9,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X9,X1),c_SetInterval_OgreaterThan(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
fof(f3901,plain,
spl0_480,
inference(avatar_split_clause,[],[f155,f3899]) ).
fof(f155,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X29,X9,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X9,X1),c_SetInterval_OgreaterThan(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
fof(f3897,plain,
spl0_479,
inference(avatar_split_clause,[],[f151,f3895]) ).
fof(f151,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X9,X29,X1)
| c_lessequals(c_SetInterval_OatMost(X9,X1),c_SetInterval_OatMost(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
fof(f3893,plain,
( spl0_478
| ~ spl0_61
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f3845,f3806,f1669,f3891]) ).
fof(f3806,plain,
( spl0_469
<=> ! [X1,X19,X42] :
( c_in(X19,c_Inter(X42,X1),X1)
| c_in(c_Main_OInterI__1(X19,X42,X1),X42,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f3845,plain,
( ! [X0,X1] : c_in(X0,c_Inter(c_emptyset,X1),X1)
| ~ spl0_61
| ~ spl0_469 ),
inference(resolution,[],[f3807,f1670]) ).
fof(f3807,plain,
( ! [X1,X19,X42] :
( c_in(c_Main_OInterI__1(X19,X42,X1),X42,tc_set(X1))
| c_in(X19,c_Inter(X42,X1),X1) )
| ~ spl0_469 ),
inference(avatar_component_clause,[],[f3806]) ).
fof(f3889,plain,
spl0_477,
inference(avatar_split_clause,[],[f150,f3887]) ).
fof(f3887,plain,
( spl0_477
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X9,X29,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X9,X1),c_SetInterval_OatMost(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f150,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X9,X29,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X9,X1),c_SetInterval_OatMost(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
fof(f3885,plain,
spl0_476,
inference(avatar_split_clause,[],[f146,f3883]) ).
fof(f146,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X29,X9,X1)
| c_lessequals(c_SetInterval_OatLeast(X9,X1),c_SetInterval_OatLeast(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
fof(f3881,plain,
spl0_475,
inference(avatar_split_clause,[],[f145,f3879]) ).
fof(f3879,plain,
( spl0_475
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X29,X9,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X9,X1),c_SetInterval_OatLeast(X29,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f145,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X29,X9,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X9,X1),c_SetInterval_OatLeast(X29,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
fof(f3877,plain,
spl0_474,
inference(avatar_split_clause,[],[f114,f3875]) ).
fof(f114,axiom,
! [X18,X24] :
( c_less(c_0,X18,tc_nat)
| c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,c_plus(X18,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
fof(f3832,plain,
( spl0_473
| ~ spl0_292
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f3757,f3728,f2901,f3830]) ).
fof(f2901,plain,
( spl0_292
<=> ! [X1,X19] : c_lessequals(c_emptyset,X19,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3728,plain,
( spl0_455
<=> ! [X21,X1,X19] :
( X19 = X21
| ~ c_lessequals(X19,X21,tc_set(X1))
| ~ c_lessequals(X21,X19,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f3757,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
| c_emptyset = X0 )
| ~ spl0_292
| ~ spl0_455 ),
inference(resolution,[],[f3729,f2902]) ).
fof(f2902,plain,
( ! [X1,X19] : c_lessequals(c_emptyset,X19,tc_set(X1))
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f2901]) ).
fof(f3729,plain,
( ! [X21,X1,X19] :
( ~ c_lessequals(X21,X19,tc_set(X1))
| ~ c_lessequals(X19,X21,tc_set(X1))
| X19 = X21 )
| ~ spl0_455 ),
inference(avatar_component_clause,[],[f3728]) ).
fof(f3820,plain,
spl0_472,
inference(avatar_split_clause,[],[f327,f3818]) ).
fof(f3818,plain,
( spl0_472
<=> ! [X20,X1,X7] :
( ~ c_in(X7,X20,tc_prod(X1,X1))
| c_in(X7,c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f327,axiom,
! [X1,X7,X20] :
( ~ c_in(X7,X20,tc_prod(X1,X1))
| c_in(X7,c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f3816,plain,
spl0_471,
inference(avatar_split_clause,[],[f307,f3814]) ).
fof(f307,axiom,
! [X1,X19,X42] :
( ~ c_in(X19,c_Union(X42,X1),X1)
| c_in(c_Main_OUnionE__1(X19,X42,X1),X42,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f3812,plain,
( spl0_470
| ~ spl0_292
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f3749,f3719,f2901,f3810]) ).
fof(f3810,plain,
( spl0_470
<=> ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f3719,plain,
( spl0_453
<=> ! [X21,X1,X19] :
( X19 = X21
| ~ c_lessequals(X19,X21,tc_set(X1))
| c_less(X19,X21,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f3749,plain,
( ! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) )
| ~ spl0_292
| ~ spl0_453 ),
inference(resolution,[],[f3720,f2902]) ).
fof(f3720,plain,
( ! [X21,X1,X19] :
( ~ c_lessequals(X19,X21,tc_set(X1))
| X19 = X21
| c_less(X19,X21,tc_set(X1)) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f3719]) ).
fof(f3808,plain,
spl0_469,
inference(avatar_split_clause,[],[f304,f3806]) ).
fof(f304,axiom,
! [X1,X19,X42] :
( c_in(X19,c_Inter(X42,X1),X1)
| c_in(c_Main_OInterI__1(X19,X42,X1),X42,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f3804,plain,
spl0_468,
inference(avatar_split_clause,[],[f267,f3802]) ).
fof(f3802,plain,
( spl0_468
<=> ! [X48,X19,X9,X1] :
( c_in(X9,X19,X1)
| ~ c_in(c_List_Olist_OCons(X9,X48,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f267,axiom,
! [X48,X1,X19,X9] :
( c_in(X9,X19,X1)
| ~ c_in(c_List_Olist_OCons(X9,X48,X1),c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f3800,plain,
spl0_467,
inference(avatar_split_clause,[],[f256,f3798]) ).
fof(f256,axiom,
! [X1,X19,X27] :
( ~ c_in(c_Main_Oin__listsI__1(X19,X27,X1),X19,X1)
| c_in(X27,c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f3796,plain,
spl0_466,
inference(avatar_split_clause,[],[f251,f3794]) ).
fof(f3794,plain,
( spl0_466
<=> ! [X45,X18] :
( c_0 != c_Divides_Oop_Amod(X18,X45,tc_IntDef_Oint)
| c_times(X45,c_Main_Ozmod__eq__0D__dest__1(X45,X18),tc_IntDef_Oint) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f251,axiom,
! [X18,X45] :
( c_0 != c_Divides_Oop_Amod(X18,X45,tc_IntDef_Oint)
| c_times(X45,c_Main_Ozmod__eq__0D__dest__1(X45,X18),tc_IntDef_Oint) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f3792,plain,
spl0_465,
inference(avatar_split_clause,[],[f235,f3790]) ).
fof(f3790,plain,
( spl0_465
<=> ! [X45,X18] :
( c_0 != c_Divides_Oop_Amod(X18,X45,tc_nat)
| c_times(X45,c_Main_Omod__eq__0D__dest__1(X45,X18),tc_nat) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f235,axiom,
! [X18,X45] :
( c_0 != c_Divides_Oop_Amod(X18,X45,tc_nat)
| c_times(X45,c_Main_Omod__eq__0D__dest__1(X45,X18),tc_nat) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f3788,plain,
spl0_464,
inference(avatar_split_clause,[],[f208,f3786]) ).
fof(f208,axiom,
! [X29,X9] :
( ~ c_less(X9,X29,tc_nat)
| c_in(c_Pair(X9,X29,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
fof(f3784,plain,
spl0_463,
inference(avatar_split_clause,[],[f207,f3782]) ).
fof(f207,axiom,
! [X29,X9] :
( c_less(X9,X29,tc_nat)
| ~ c_in(c_Pair(X9,X29,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
fof(f3780,plain,
spl0_462,
inference(avatar_split_clause,[],[f187,f3778]) ).
fof(f3778,plain,
( spl0_462
<=> ! [X4,X19,X12,X1] :
( X4 = X12
| c_in(X4,X19,X1)
| ~ c_in(X4,c_insert(X12,X19,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f187,axiom,
! [X1,X19,X4,X12] :
( X4 = X12
| c_in(X4,X19,X1)
| ~ c_in(X4,c_insert(X12,X19,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f3776,plain,
spl0_461,
inference(avatar_split_clause,[],[f135,f3774]) ).
fof(f3774,plain,
( spl0_461
<=> ! [X4,X11,X0,X12,X39,X1] :
( X12 = X39
| c_Pair(X4,X12,X1,X11) != c_Pair(X0,X39,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f135,axiom,
! [X39,X0,X11,X1,X4,X12] :
( X12 = X39
| c_Pair(X4,X12,X1,X11) != c_Pair(X0,X39,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
fof(f3772,plain,
spl0_460,
inference(avatar_split_clause,[],[f134,f3770]) ).
fof(f3770,plain,
( spl0_460
<=> ! [X4,X11,X0,X12,X1,X39] :
( X0 = X4
| c_Pair(X4,X12,X1,X11) != c_Pair(X0,X39,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f134,axiom,
! [X39,X0,X11,X1,X4,X12] :
( X0 = X4
| c_Pair(X4,X12,X1,X11) != c_Pair(X0,X39,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
fof(f3768,plain,
spl0_459,
inference(avatar_split_clause,[],[f29,f3766]) ).
fof(f3766,plain,
( spl0_459
<=> ! [X17,X11,X14,X13,X16,X1] :
( X14 = X17
| c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_OScons(X16,X17,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f29,axiom,
! [X11,X1,X16,X14,X17,X13] :
( X14 = X17
| c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_OScons(X16,X17,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
fof(f3764,plain,
spl0_458,
inference(avatar_split_clause,[],[f28,f3762]) ).
fof(f3762,plain,
( spl0_458
<=> ! [X17,X11,X13,X14,X16,X1] :
( X13 = X16
| c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_OScons(X16,X17,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f28,axiom,
! [X11,X1,X16,X14,X17,X13] :
( X13 = X16
| c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_OScons(X16,X17,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
fof(f3748,plain,
( spl0_457
| ~ spl0_385
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f3726,f3683,f3320,f3746]) ).
fof(f3746,plain,
( spl0_457
<=> ! [X0,X1] : ~ c_less(c_UNIV,X0,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f3683,plain,
( spl0_444
<=> ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f3726,plain,
( ! [X0,X1] : ~ c_less(c_UNIV,X0,tc_set(X1))
| ~ spl0_385
| ~ spl0_444 ),
inference(resolution,[],[f3684,f3321]) ).
fof(f3684,plain,
( ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1))
| ~ spl0_444 ),
inference(avatar_component_clause,[],[f3683]) ).
fof(f3734,plain,
spl0_456,
inference(avatar_split_clause,[],[f1368,f3732]) ).
fof(f1368,axiom,
! [X59,X1,X8,X7] : c_in(c_PropLog_Opl_Oop_A_N_62(X7,c_PropLog_Opl_Oop_A_N_62(X59,X7,X1),X1),c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OK_0) ).
fof(f3730,plain,
spl0_455,
inference(avatar_split_clause,[],[f319,f3728]) ).
fof(f319,axiom,
! [X21,X1,X19] :
( X19 = X21
| ~ c_lessequals(X19,X21,tc_set(X1))
| ~ c_lessequals(X21,X19,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f3725,plain,
spl0_454,
inference(avatar_split_clause,[],[f316,f3723]) ).
fof(f3723,plain,
( spl0_454
<=> ! [X40,X19,X21,X1] :
( ~ c_in(X40,X19,X1)
| c_in(X40,X21,X1)
| ~ c_lessequals(X19,X21,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f316,axiom,
! [X40,X21,X1,X19] :
( ~ c_in(X40,X19,X1)
| c_in(X40,X21,X1)
| ~ c_lessequals(X19,X21,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f3721,plain,
spl0_453,
inference(avatar_split_clause,[],[f312,f3719]) ).
fof(f312,axiom,
! [X21,X1,X19] :
( X19 = X21
| ~ c_lessequals(X19,X21,tc_set(X1))
| c_less(X19,X21,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f3717,plain,
spl0_452,
inference(avatar_split_clause,[],[f308,f3715]) ).
fof(f3715,plain,
( spl0_452
<=> ! [X1,X19,X42] :
( ~ c_in(X19,c_Union(X42,X1),X1)
| c_in(X19,c_Main_OUnionE__1(X19,X42,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f308,axiom,
! [X1,X19,X42] :
( ~ c_in(X19,c_Union(X42,X1),X1)
| c_in(X19,c_Main_OUnionE__1(X19,X42,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f3713,plain,
spl0_451,
inference(avatar_split_clause,[],[f305,f3711]) ).
fof(f3711,plain,
( spl0_451
<=> ! [X1,X19,X42] :
( c_in(X19,c_Inter(X42,X1),X1)
| ~ c_in(X19,c_Main_OInterI__1(X19,X42,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f305,axiom,
! [X1,X19,X42] :
( c_in(X19,c_Inter(X42,X1),X1)
| ~ c_in(X19,c_Main_OInterI__1(X19,X42,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f3709,plain,
spl0_450,
inference(avatar_split_clause,[],[f239,f3707]) ).
fof(f3707,plain,
( spl0_450
<=> ! [X22,X1,X23] :
( ~ c_in(X23,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f239,axiom,
! [X1,X22,X23] :
( ~ c_in(X23,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f3705,plain,
spl0_449,
inference(avatar_split_clause,[],[f238,f3703]) ).
fof(f3703,plain,
( spl0_449
<=> ! [X22,X1,X23] :
( ~ c_in(X22,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f238,axiom,
! [X1,X22,X23] :
( ~ c_in(X22,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f3701,plain,
spl0_448,
inference(avatar_split_clause,[],[f237,f3699]) ).
fof(f3699,plain,
( spl0_448
<=> ! [X4,X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X4,X19,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f237,axiom,
! [X1,X19,X4] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X4,X19,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f3697,plain,
spl0_447,
inference(avatar_split_clause,[],[f141,f3695]) ).
fof(f141,axiom,
! [X1,X4,X12] :
( X4 = X12
| ~ c_in(c_Pair(X4,X12,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f3693,plain,
spl0_446,
inference(avatar_split_clause,[],[f51,f3691]) ).
fof(f51,axiom,
! [X18,X15,X24] :
( c_Divides_Oop_Advd(X15,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).
fof(f3689,plain,
spl0_445,
inference(avatar_split_clause,[],[f50,f3687]) ).
fof(f50,axiom,
! [X18,X15,X24] :
( c_Divides_Oop_Advd(X15,X18,tc_nat)
| ~ c_Divides_Oop_Advd(X15,c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).
fof(f3685,plain,
( spl0_444
| ~ spl0_67
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f3659,f3578,f1693,f3683]) ).
fof(f3659,plain,
( ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1))
| ~ spl0_67
| ~ spl0_436 ),
inference(resolution,[],[f3579,f1694]) ).
fof(f3681,plain,
spl0_443,
inference(avatar_split_clause,[],[f46,f3679]) ).
fof(f3679,plain,
( spl0_443
<=> ! [X22,X1,X23] :
( c_in(X23,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f46,axiom,
! [X1,X22,X23] :
( c_in(X23,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
fof(f3677,plain,
spl0_442,
inference(avatar_split_clause,[],[f45,f3675]) ).
fof(f3675,plain,
( spl0_442
<=> ! [X22,X1,X23] :
( c_in(X22,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f45,axiom,
! [X1,X22,X23] :
( c_in(X22,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X22,X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
fof(f3673,plain,
spl0_441,
inference(avatar_split_clause,[],[f44,f3671]) ).
fof(f3671,plain,
( spl0_441
<=> ! [X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X19,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f44,axiom,
! [X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X19,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
fof(f3669,plain,
spl0_440,
inference(avatar_split_clause,[],[f43,f3667]) ).
fof(f3667,plain,
( spl0_440
<=> ! [X1,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X19,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f43,axiom,
! [X1,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X19,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
fof(f3611,plain,
( ~ spl0_439
| spl0_49
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f3591,f3437,f1614,f3608]) ).
fof(f3608,plain,
( spl0_439
<=> c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f3437,plain,
( spl0_402
<=> ! [X1,X8,X7] :
( ~ c_in(X7,X8,tc_PropLog_Opl(X1))
| c_in(X7,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f3591,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),v_H,tc_PropLog_Opl(t_a))
| spl0_49
| ~ spl0_402 ),
inference(resolution,[],[f3438,f1616]) ).
fof(f3438,plain,
( ! [X1,X8,X7] :
( c_in(X7,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1))
| ~ c_in(X7,X8,tc_PropLog_Opl(X1)) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f3437]) ).
fof(f3588,plain,
( spl0_438
| ~ spl0_317
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3350,f3276,f3002,f3586]) ).
fof(f3586,plain,
( spl0_438
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f3002,plain,
( spl0_317
<=> ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X18,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f3350,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_317
| ~ spl0_374 ),
inference(resolution,[],[f3277,f3003]) ).
fof(f3003,plain,
( ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X18,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3002]) ).
fof(f3584,plain,
spl0_437,
inference(avatar_split_clause,[],[f328,f3582]) ).
fof(f328,axiom,
! [X1,X4,X20] : c_in(c_Pair(X4,X4,X1,X1),c_Transitive__Closure_Ortrancl(X20,X1),tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f3580,plain,
spl0_436,
inference(avatar_split_clause,[],[f318,f3578]) ).
fof(f318,axiom,
! [X21,X1,X19] :
( c_lessequals(X19,X21,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X19,X21,X1),X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f3576,plain,
spl0_435,
inference(avatar_split_clause,[],[f317,f3574]) ).
fof(f317,axiom,
! [X21,X1,X19] :
( c_lessequals(X19,X21,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X19,X21,X1),X19,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f3572,plain,
spl0_434,
inference(avatar_split_clause,[],[f257,f3570]) ).
fof(f257,axiom,
! [X1,X27] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X27,X1),tc_List_Olist(X1)),c_Nat_Osize(X27,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f3568,plain,
spl0_433,
inference(avatar_split_clause,[],[f210,f3566]) ).
fof(f3566,plain,
( spl0_433
<=> ! [X9,X11,X29,X1] :
( X9 = X29
| c_Datatype__Universe_ONumb(X9,X1,X11) != c_Datatype__Universe_ONumb(X29,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f210,axiom,
! [X29,X11,X1,X9] :
( X9 = X29
| c_Datatype__Universe_ONumb(X9,X1,X11) != c_Datatype__Universe_ONumb(X29,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f3564,plain,
spl0_432,
inference(avatar_split_clause,[],[f209,f3562]) ).
fof(f3562,plain,
( spl0_432
<=> ! [X9,X11,X29,X1] :
( X9 = X29
| c_Datatype__Universe_OLeaf(X9,X1,X11) != c_Datatype__Universe_OLeaf(X29,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f209,axiom,
! [X29,X11,X1,X9] :
( X9 = X29
| c_Datatype__Universe_OLeaf(X9,X1,X11) != c_Datatype__Universe_OLeaf(X29,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f3560,plain,
spl0_431,
inference(avatar_split_clause,[],[f197,f3558]) ).
fof(f3558,plain,
( spl0_431
<=> ! [X9,X11,X29,X1] :
( X9 = X29
| c_Sum__Type_OInr(X9,X11,X1) != c_Sum__Type_OInr(X29,X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f197,axiom,
! [X29,X11,X1,X9] :
( X9 = X29
| c_Sum__Type_OInr(X9,X11,X1) != c_Sum__Type_OInr(X29,X11,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
fof(f3556,plain,
spl0_430,
inference(avatar_split_clause,[],[f195,f3554]) ).
fof(f3554,plain,
( spl0_430
<=> ! [X9,X11,X29,X1] :
( X9 = X29
| c_Sum__Type_OInl(X9,X1,X11) != c_Sum__Type_OInl(X29,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f195,axiom,
! [X29,X11,X1,X9] :
( X9 = X29
| c_Sum__Type_OInl(X9,X1,X11) != c_Sum__Type_OInl(X29,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
fof(f3552,plain,
spl0_429,
inference(avatar_split_clause,[],[f189,f3550]) ).
fof(f3550,plain,
( spl0_429
<=> ! [X4,X19,X12,X1] :
( X4 = X12
| c_insert(X4,X19,X1) != c_insert(X12,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f189,axiom,
! [X1,X19,X4,X12] :
( X4 = X12
| c_insert(X4,X19,X1) != c_insert(X12,c_emptyset,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
fof(f3548,plain,
spl0_428,
inference(avatar_split_clause,[],[f175,f3546]) ).
fof(f175,axiom,
! [X21,X1,X19] :
( ~ c_lessequals(X19,X21,tc_set(X1))
| c_in(X19,c_Pow(X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
fof(f3544,plain,
( spl0_427
| ~ spl0_316
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3349,f3276,f2998,f3542]) ).
fof(f3542,plain,
( spl0_427
<=> ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2998,plain,
( spl0_316
<=> ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X18,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f3349,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_316
| ~ spl0_374 ),
inference(resolution,[],[f3277,f2999]) ).
fof(f2999,plain,
( ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X18,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f2998]) ).
fof(f3540,plain,
spl0_426,
inference(avatar_split_clause,[],[f174,f3538]) ).
fof(f3538,plain,
( spl0_426
<=> ! [X21,X1,X19] :
( c_lessequals(X19,X21,tc_set(X1))
| ~ c_in(X19,c_Pow(X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f174,axiom,
! [X21,X1,X19] :
( c_lessequals(X19,X21,tc_set(X1))
| ~ c_in(X19,c_Pow(X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
fof(f3536,plain,
spl0_425,
inference(avatar_split_clause,[],[f168,f3534]) ).
fof(f3534,plain,
( spl0_425
<=> ! [X40,X19,X21,X1] :
( c_in(X40,X19,X1)
| ~ c_in(X40,c_minus(X19,X21,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f168,axiom,
! [X40,X21,X1,X19] :
( c_in(X40,X19,X1)
| ~ c_in(X40,c_minus(X19,X21,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
fof(f3532,plain,
spl0_424,
inference(avatar_split_clause,[],[f167,f3530]) ).
fof(f3530,plain,
( spl0_424
<=> ! [X40,X19,X21,X1] :
( ~ c_in(X40,X21,X1)
| ~ c_in(X40,c_minus(X19,X21,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f167,axiom,
! [X40,X21,X1,X19] :
( ~ c_in(X40,X21,X1)
| ~ c_in(X40,c_minus(X19,X21,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
fof(f3528,plain,
spl0_423,
inference(avatar_split_clause,[],[f164,f3526]) ).
fof(f3526,plain,
( spl0_423
<=> ! [X21,X1,X19] :
( X19 = X21
| c_uminus(X19,tc_set(X1)) != c_uminus(X21,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f164,axiom,
! [X21,X1,X19] :
( X19 = X21
| c_uminus(X19,tc_set(X1)) != c_uminus(X21,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
fof(f3524,plain,
spl0_422,
inference(avatar_split_clause,[],[f159,f3522]) ).
fof(f3522,plain,
( spl0_422
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X37,X15,X1)
| c_in(X37,c_SetInterval_OlessThan(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f159,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X37,X15,X1)
| c_in(X37,c_SetInterval_OlessThan(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
fof(f3520,plain,
spl0_421,
inference(avatar_split_clause,[],[f158,f3518]) ).
fof(f3518,plain,
( spl0_421
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| c_less(X37,X15,X1)
| ~ c_in(X37,c_SetInterval_OlessThan(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f158,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| c_less(X37,X15,X1)
| ~ c_in(X37,c_SetInterval_OlessThan(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
fof(f3516,plain,
spl0_420,
inference(avatar_split_clause,[],[f157,f3514]) ).
fof(f3514,plain,
( spl0_420
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OlessThan(X9,X1) != c_SetInterval_OlessThan(X29,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f157,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OlessThan(X9,X1) != c_SetInterval_OlessThan(X29,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
fof(f3512,plain,
spl0_419,
inference(avatar_split_clause,[],[f154,f3510]) ).
fof(f3510,plain,
( spl0_419
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X15,X37,X1)
| c_in(X37,c_SetInterval_OgreaterThan(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f154,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X15,X37,X1)
| c_in(X37,c_SetInterval_OgreaterThan(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
fof(f3508,plain,
spl0_418,
inference(avatar_split_clause,[],[f153,f3506]) ).
fof(f3506,plain,
( spl0_418
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| c_less(X15,X37,X1)
| ~ c_in(X37,c_SetInterval_OgreaterThan(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f153,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| c_less(X15,X37,X1)
| ~ c_in(X37,c_SetInterval_OgreaterThan(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
fof(f3504,plain,
spl0_417,
inference(avatar_split_clause,[],[f152,f3502]) ).
fof(f3502,plain,
( spl0_417
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OgreaterThan(X9,X1) != c_SetInterval_OgreaterThan(X29,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f152,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OgreaterThan(X9,X1) != c_SetInterval_OgreaterThan(X29,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
fof(f3496,plain,
spl0_416,
inference(avatar_split_clause,[],[f149,f3494]) ).
fof(f3494,plain,
( spl0_416
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X37,X15,X1)
| c_in(X37,c_SetInterval_OatMost(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f149,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X37,X15,X1)
| c_in(X37,c_SetInterval_OatMost(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
fof(f3492,plain,
spl0_415,
inference(avatar_split_clause,[],[f148,f3490]) ).
fof(f3490,plain,
( spl0_415
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X37,X15,X1)
| ~ c_in(X37,c_SetInterval_OatMost(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f148,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X37,X15,X1)
| ~ c_in(X37,c_SetInterval_OatMost(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
fof(f3488,plain,
spl0_414,
inference(avatar_split_clause,[],[f147,f3486]) ).
fof(f3486,plain,
( spl0_414
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OatMost(X9,X1) != c_SetInterval_OatMost(X29,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f147,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OatMost(X9,X1) != c_SetInterval_OatMost(X29,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
fof(f3484,plain,
spl0_413,
inference(avatar_split_clause,[],[f144,f3482]) ).
fof(f3482,plain,
( spl0_413
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X15,X37,X1)
| c_in(X37,c_SetInterval_OatLeast(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f144,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X15,X37,X1)
| c_in(X37,c_SetInterval_OatLeast(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
fof(f3480,plain,
spl0_412,
inference(avatar_split_clause,[],[f143,f3478]) ).
fof(f3478,plain,
( spl0_412
<=> ! [X37,X1,X15] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X15,X37,X1)
| ~ c_in(X37,c_SetInterval_OatLeast(X15,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f143,axiom,
! [X1,X37,X15] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X15,X37,X1)
| ~ c_in(X37,c_SetInterval_OatLeast(X15,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
fof(f3476,plain,
spl0_411,
inference(avatar_split_clause,[],[f142,f3474]) ).
fof(f3474,plain,
( spl0_411
<=> ! [X29,X9,X1] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OatLeast(X9,X1) != c_SetInterval_OatLeast(X29,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f142,axiom,
! [X29,X1,X9] :
( ~ class_Orderings_Olinorder(X1)
| X9 = X29
| c_SetInterval_OatLeast(X9,X1) != c_SetInterval_OatLeast(X29,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
fof(f3472,plain,
spl0_410,
inference(avatar_split_clause,[],[f98,f3470]) ).
fof(f98,axiom,
! [X28,X1,X27,X30] :
( X28 = X30
| c_append(X27,X28,X1) != c_append(X27,X30,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
fof(f3468,plain,
spl0_409,
inference(avatar_split_clause,[],[f92,f3466]) ).
fof(f3466,plain,
( spl0_409
<=> ! [X35,X4,X0,X36,X1] :
( X35 = X36
| c_List_Olist_OCons(X0,X35,X1) != c_List_Olist_OCons(X4,X36,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f92,axiom,
! [X0,X36,X1,X4,X35] :
( X35 = X36
| c_List_Olist_OCons(X0,X35,X1) != c_List_Olist_OCons(X4,X36,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
fof(f3464,plain,
spl0_408,
inference(avatar_split_clause,[],[f91,f3462]) ).
fof(f3462,plain,
( spl0_408
<=> ! [X35,X4,X0,X36,X1] :
( X0 = X4
| c_List_Olist_OCons(X0,X35,X1) != c_List_Olist_OCons(X4,X36,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f91,axiom,
! [X0,X36,X1,X4,X35] :
( X0 = X4
| c_List_Olist_OCons(X0,X35,X1) != c_List_Olist_OCons(X4,X36,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
fof(f3460,plain,
spl0_407,
inference(avatar_split_clause,[],[f76,f3458]) ).
fof(f76,axiom,
! [X28,X1,X27,X30] :
( X28 = X30
| c_append(X28,X27,X1) != c_append(X30,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
fof(f3456,plain,
( spl0_406
| ~ spl0_63
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f3367,f3345,f1677,f3453]) ).
fof(f3453,plain,
( spl0_406
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f1677,plain,
( spl0_63
<=> ! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f3345,plain,
( spl0_388
<=> ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f3367,plain,
( c_0 = c_uminus(c_0,tc_IntDef_Oint)
| ~ spl0_63
| ~ spl0_388 ),
inference(resolution,[],[f3346,f1678]) ).
fof(f1678,plain,
( ! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_IntDef_Oint)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1677]) ).
fof(f3346,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f3345]) ).
fof(f3451,plain,
spl0_405,
inference(avatar_split_clause,[],[f22,f3449]) ).
fof(f3449,plain,
( spl0_405
<=> ! [X11,X13,X14,X1] :
( X13 = X14
| c_Datatype__Universe_OIn1(X14,X1,X11) != c_Datatype__Universe_OIn1(X13,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f22,axiom,
! [X11,X1,X14,X13] :
( X13 = X14
| c_Datatype__Universe_OIn1(X14,X1,X11) != c_Datatype__Universe_OIn1(X13,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
fof(f3447,plain,
spl0_404,
inference(avatar_split_clause,[],[f20,f3445]) ).
fof(f3445,plain,
( spl0_404
<=> ! [X11,X13,X14,X1] :
( X13 = X14
| c_Datatype__Universe_OIn0(X13,X1,X11) != c_Datatype__Universe_OIn0(X14,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f20,axiom,
! [X11,X1,X14,X13] :
( X13 = X14
| c_Datatype__Universe_OIn0(X13,X1,X11) != c_Datatype__Universe_OIn0(X14,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
fof(f3443,plain,
spl0_403,
inference(avatar_split_clause,[],[f18,f3441]) ).
fof(f3441,plain,
( spl0_403
<=> ! [X4,X11,X12,X1] :
( X4 = X12
| c_Datatype__Universe_OAtom(X4,X1,X11) != c_Datatype__Universe_OAtom(X12,X1,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f18,axiom,
! [X11,X1,X4,X12] :
( X4 = X12
| c_Datatype__Universe_OAtom(X4,X1,X11) != c_Datatype__Universe_OAtom(X12,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq__iff1_0) ).
fof(f3439,plain,
spl0_402,
inference(avatar_split_clause,[],[f10,f3437]) ).
fof(f10,axiom,
! [X1,X8,X7] :
( ~ c_in(X7,X8,tc_PropLog_Opl(X1))
| c_in(X7,c_PropLog_Othms(X8,X1),tc_PropLog_Opl(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f3435,plain,
spl0_401,
inference(avatar_split_clause,[],[f9,f3433]) ).
fof(f3433,plain,
( spl0_401
<=> ! [X5,X3,X2,X6,X1] :
( X3 = X6
| c_PropLog_Opl_Oop_A_N_62(X2,X3,X1) != c_PropLog_Opl_Oop_A_N_62(X5,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f9,axiom,
! [X2,X3,X1,X6,X5] :
( X3 = X6
| c_PropLog_Opl_Oop_A_N_62(X2,X3,X1) != c_PropLog_Opl_Oop_A_N_62(X5,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Opl_Oinject__2__iff1_1) ).
fof(f3431,plain,
spl0_400,
inference(avatar_split_clause,[],[f8,f3429]) ).
fof(f3429,plain,
( spl0_400
<=> ! [X5,X3,X6,X2,X1] :
( X2 = X5
| c_PropLog_Opl_Oop_A_N_62(X2,X3,X1) != c_PropLog_Opl_Oop_A_N_62(X5,X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f8,axiom,
! [X2,X3,X1,X6,X5] :
( X2 = X5
| c_PropLog_Opl_Oop_A_N_62(X2,X3,X1) != c_PropLog_Opl_Oop_A_N_62(X5,X6,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Opl_Oinject__2__iff1_0) ).
fof(f3420,plain,
spl0_399,
inference(avatar_split_clause,[],[f185,f3418]) ).
fof(f3418,plain,
( spl0_399
<=> ! [X4,X12,X21,X1] :
( ~ c_in(X4,X21,X1)
| c_in(X4,c_insert(X12,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f185,axiom,
! [X21,X1,X4,X12] :
( ~ c_in(X4,X21,X1)
| c_in(X4,c_insert(X12,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
fof(f3416,plain,
spl0_398,
inference(avatar_split_clause,[],[f178,f3414]) ).
fof(f3414,plain,
( spl0_398
<=> ! [X40,X19,X21,X1] :
( ~ c_in(X40,X19,X1)
| c_in(X40,c_union(X19,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f178,axiom,
! [X40,X21,X1,X19] :
( ~ c_in(X40,X19,X1)
| c_in(X40,c_union(X19,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
fof(f3412,plain,
spl0_397,
inference(avatar_split_clause,[],[f177,f3410]) ).
fof(f3410,plain,
( spl0_397
<=> ! [X40,X19,X21,X1] :
( ~ c_in(X40,X21,X1)
| c_in(X40,c_union(X19,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f177,axiom,
! [X40,X21,X1,X19] :
( ~ c_in(X40,X21,X1)
| c_in(X40,c_union(X19,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
fof(f3408,plain,
spl0_396,
inference(avatar_split_clause,[],[f171,f3406]) ).
fof(f3406,plain,
( spl0_396
<=> ! [X40,X19,X21,X1] :
( c_in(X40,X19,X1)
| ~ c_in(X40,c_inter(X19,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f171,axiom,
! [X40,X21,X1,X19] :
( c_in(X40,X19,X1)
| ~ c_in(X40,c_inter(X19,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
fof(f3404,plain,
( spl0_395
| ~ spl0_293
| ~ spl0_385 ),
inference(avatar_split_clause,[],[f3374,f3320,f2905,f3402]) ).
fof(f3402,plain,
( spl0_395
<=> ! [X0,X1] : ~ c_less(X0,X0,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f3374,plain,
( ! [X0,X1] : ~ c_less(X0,X0,tc_set(X1))
| ~ spl0_293
| ~ spl0_385 ),
inference(resolution,[],[f3321,f2906]) ).
fof(f3400,plain,
spl0_394,
inference(avatar_split_clause,[],[f170,f3398]) ).
fof(f3398,plain,
( spl0_394
<=> ! [X40,X19,X21,X1] :
( c_in(X40,X21,X1)
| ~ c_in(X40,c_inter(X19,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f170,axiom,
! [X40,X21,X1,X19] :
( c_in(X40,X21,X1)
| ~ c_in(X40,c_inter(X19,X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
fof(f3396,plain,
spl0_393,
inference(avatar_split_clause,[],[f163,f3394]) ).
fof(f3394,plain,
( spl0_393
<=> ! [X1,X40,X19] :
( c_in(X40,X19,X1)
| c_in(X40,c_uminus(X19,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f163,axiom,
! [X40,X1,X19] :
( c_in(X40,X19,X1)
| c_in(X40,c_uminus(X19,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
fof(f3392,plain,
spl0_392,
inference(avatar_split_clause,[],[f162,f3390]) ).
fof(f162,axiom,
! [X40,X1,X19] :
( ~ c_in(X40,X19,X1)
| ~ c_in(X40,c_uminus(X19,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f3388,plain,
spl0_391,
inference(avatar_split_clause,[],[f116,f3386]) ).
fof(f3386,plain,
( spl0_391
<=> ! [X18,X24] :
( ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_plus(X18,X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f116,axiom,
! [X18,X24] :
( ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_plus(X18,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
fof(f3384,plain,
spl0_390,
inference(avatar_split_clause,[],[f115,f3382]) ).
fof(f3382,plain,
( spl0_390
<=> ! [X18,X24] :
( ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_plus(X18,X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f115,axiom,
! [X18,X24] :
( ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_plus(X18,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
fof(f3380,plain,
spl0_389,
inference(avatar_split_clause,[],[f11,f3378]) ).
fof(f11,axiom,
! [X10,X1,X9] :
( c_Datatype_Ooption_OSome(X9,X1) = X10
| ~ c_in(X9,c_Datatype_Oo2s(X10,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
fof(f3347,plain,
( spl0_388
| ~ spl0_307
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3342,f3272,f2962,f3345]) ).
fof(f2962,plain,
( spl0_307
<=> ! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f3342,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_307
| ~ spl0_373 ),
inference(resolution,[],[f3273,f2963]) ).
fof(f2963,plain,
( ! [X18] :
( ~ c_Divides_Oop_Advd(c_0,X18,tc_IntDef_Oint)
| c_0 = X18 )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f2962]) ).
fof(f3330,plain,
spl0_387,
inference(avatar_split_clause,[],[f313,f3328]) ).
fof(f313,axiom,
! [X1,X4,X12] :
( X4 = X12
| ~ c_in(X12,c_insert(X4,c_emptyset,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f3326,plain,
spl0_386,
inference(avatar_split_clause,[],[f311,f3324]) ).
fof(f3324,plain,
( spl0_386
<=> ! [X21,X1,X19] :
( ~ c_less(X19,X21,tc_set(X1))
| c_lessequals(X19,X21,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f311,axiom,
! [X21,X1,X19] :
( ~ c_less(X19,X21,tc_set(X1))
| c_lessequals(X19,X21,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f3322,plain,
spl0_385,
inference(avatar_split_clause,[],[f310,f3320]) ).
fof(f310,axiom,
! [X21,X1,X19] :
( ~ c_less(X19,X21,tc_set(X1))
| ~ c_lessequals(X21,X19,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f3318,plain,
spl0_384,
inference(avatar_split_clause,[],[f136,f3316]) ).
fof(f136,axiom,
! [X1,X4] : c_in(c_Pair(X4,X4,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
fof(f3314,plain,
spl0_383,
inference(avatar_split_clause,[],[f111,f3312]) ).
fof(f3312,plain,
( spl0_383
<=> ! [X18,X24] :
( ~ c_less(X18,X24,tc_nat)
| c_less(c_Suc(X18),c_Suc(X24),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f111,axiom,
! [X18,X24] :
( ~ c_less(X18,X24,tc_nat)
| c_less(c_Suc(X18),c_Suc(X24),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
fof(f3310,plain,
spl0_382,
inference(avatar_split_clause,[],[f110,f3308]) ).
fof(f3308,plain,
( spl0_382
<=> ! [X18,X24] :
( c_less(X18,X24,tc_nat)
| ~ c_less(c_Suc(X18),c_Suc(X24),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f110,axiom,
! [X18,X24] :
( c_less(X18,X24,tc_nat)
| ~ c_less(c_Suc(X18),c_Suc(X24),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
fof(f3306,plain,
spl0_381,
inference(avatar_split_clause,[],[f109,f3304]) ).
fof(f3304,plain,
( spl0_381
<=> ! [X18,X24] :
( ~ c_lessequals(X24,X18,tc_nat)
| c_lessequals(c_Suc(X24),c_Suc(X18),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f109,axiom,
! [X18,X24] :
( ~ c_lessequals(X24,X18,tc_nat)
| c_lessequals(c_Suc(X24),c_Suc(X18),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
fof(f3302,plain,
spl0_380,
inference(avatar_split_clause,[],[f108,f3300]) ).
fof(f3300,plain,
( spl0_380
<=> ! [X18,X24] :
( c_lessequals(X24,X18,tc_nat)
| ~ c_lessequals(c_Suc(X24),c_Suc(X18),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f108,axiom,
! [X18,X24] :
( c_lessequals(X24,X18,tc_nat)
| ~ c_lessequals(c_Suc(X24),c_Suc(X18),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
fof(f3298,plain,
spl0_379,
inference(avatar_split_clause,[],[f97,f3296]) ).
fof(f3296,plain,
( spl0_379
<=> ! [X27,X28,X1] :
( X27 = X28
| c_List_Orev(X27,X1) != c_List_Orev(X28,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f97,axiom,
! [X28,X1,X27] :
( X27 = X28
| c_List_Orev(X27,X1) != c_List_Orev(X28,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).
fof(f3294,plain,
spl0_378,
inference(avatar_split_clause,[],[f86,f3292]) ).
fof(f3292,plain,
( spl0_378
<=> ! [X27,X1] :
( c_List_Olist_ONil = X27
| c_less(c_0,c_Nat_Osize(X27,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f86,axiom,
! [X1,X27] :
( c_List_Olist_ONil = X27
| c_less(c_0,c_Nat_Osize(X27,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
fof(f3290,plain,
spl0_377,
inference(avatar_split_clause,[],[f82,f3288]) ).
fof(f3288,plain,
( spl0_377
<=> ! [X34,X32,X31,X33] :
( X32 = X34
| c_List_Ochar_OChar(X31,X32) != c_List_Ochar_OChar(X33,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f82,axiom,
! [X31,X34,X32,X33] :
( X32 = X34
| c_List_Ochar_OChar(X31,X32) != c_List_Ochar_OChar(X33,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_1) ).
fof(f3286,plain,
spl0_376,
inference(avatar_split_clause,[],[f81,f3284]) ).
fof(f3284,plain,
( spl0_376
<=> ! [X31,X34,X33,X32] :
( X31 = X33
| c_List_Ochar_OChar(X31,X32) != c_List_Ochar_OChar(X33,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f81,axiom,
! [X31,X34,X32,X33] :
( X31 = X33
| c_List_Ochar_OChar(X31,X32) != c_List_Ochar_OChar(X33,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_0) ).
fof(f3282,plain,
spl0_375,
inference(avatar_split_clause,[],[f60,f3280]) ).
fof(f60,axiom,
! [X26,X25] :
( ~ c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X25,tc_IntDef_Oint),X26,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
fof(f3278,plain,
spl0_374,
inference(avatar_split_clause,[],[f59,f3276]) ).
fof(f59,axiom,
! [X26,X25] :
( c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X25,tc_IntDef_Oint),X26,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
fof(f3274,plain,
spl0_373,
inference(avatar_split_clause,[],[f56,f3272]) ).
fof(f56,axiom,
! [X26,X25] :
( ~ c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X25,c_uminus(X26,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
fof(f3270,plain,
spl0_372,
inference(avatar_split_clause,[],[f55,f3268]) ).
fof(f55,axiom,
! [X26,X25] :
( c_Divides_Oop_Advd(X25,X26,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X25,c_uminus(X26,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
fof(f3266,plain,
spl0_371,
inference(avatar_split_clause,[],[f30,f3264]) ).
fof(f3264,plain,
( spl0_371
<=> ! [X4,X11,X13,X14,X1] : c_Datatype__Universe_OAtom(X4,X1,X11) != c_Datatype__Universe_OScons(X13,X14,X1,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f30,axiom,
! [X11,X1,X14,X4,X13] : c_Datatype__Universe_OAtom(X4,X1,X11) != c_Datatype__Universe_OScons(X13,X14,X1,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).
fof(f3262,plain,
spl0_370,
inference(avatar_split_clause,[],[f27,f3260]) ).
fof(f3260,plain,
( spl0_370
<=> ! [X15,X11,X14,X13,X1] : c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_ONumb(X15,X1,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f27,axiom,
! [X11,X1,X14,X15,X13] : c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_ONumb(X15,X1,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons__iff1_0) ).
fof(f3258,plain,
spl0_369,
inference(avatar_split_clause,[],[f25,f3256]) ).
fof(f3256,plain,
( spl0_369
<=> ! [X4,X11,X14,X13,X1] : c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_OLeaf(X4,X1,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f25,axiom,
! [X11,X1,X14,X4,X13] : c_Datatype__Universe_OScons(X13,X14,X1,X11) != c_Datatype__Universe_OLeaf(X4,X1,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons__iff1_0) ).
fof(f3254,plain,
spl0_368,
inference(avatar_split_clause,[],[f17,f3252]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( X0 = X4
| c_Datatype_Ooption_OSome(X0,X1) != c_Datatype_Ooption_OSome(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
fof(f3250,plain,
spl0_367,
inference(avatar_split_clause,[],[f14,f3248]) ).
fof(f14,axiom,
! [X1,X9] :
( c_Datatype_Ooption_ONone = X9
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X9,X1),X1) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq__iff1_0) ).
fof(f3246,plain,
spl0_366,
inference(avatar_split_clause,[],[f13,f3244]) ).
fof(f13,axiom,
! [X1,X9] :
( c_Datatype_Ooption_ONone = X9
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X9,X1),X1) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq__iff1_0) ).
fof(f3242,plain,
spl0_365,
inference(avatar_split_clause,[],[f7,f3240]) ).
fof(f3240,plain,
( spl0_365
<=> ! [X4,X0,X1] :
( X0 = X4
| c_PropLog_Opl_Ovar(X0,X1) != c_PropLog_Opl_Ovar(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f7,axiom,
! [X0,X1,X4] :
( X0 = X4
| c_PropLog_Opl_Ovar(X0,X1) != c_PropLog_Opl_Ovar(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Opl_Oinject__1__iff1_0) ).
fof(f3221,plain,
spl0_364,
inference(avatar_split_clause,[],[f271,f3219]) ).
fof(f3219,plain,
( spl0_364
<=> ! [X20,X1] :
( ~ c_Wellfounded__Recursion_Owf(X20,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X20,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f271,axiom,
! [X1,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X20,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f3215,plain,
spl0_363,
inference(avatar_split_clause,[],[f270,f3213]) ).
fof(f3213,plain,
( spl0_363
<=> ! [X20,X1] :
( ~ c_Wellfounded__Recursion_Owf(X20,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X20,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f270,axiom,
! [X1,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X20,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f3211,plain,
spl0_362,
inference(avatar_split_clause,[],[f246,f3209]) ).
fof(f3209,plain,
( spl0_362
<=> ! [X18,X24] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X24)),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f246,axiom,
! [X18,X24] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X24)),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f3207,plain,
spl0_361,
inference(avatar_split_clause,[],[f243,f3205]) ).
fof(f243,axiom,
! [X18,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),X24,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f3203,plain,
spl0_360,
inference(avatar_split_clause,[],[f242,f3201]) ).
fof(f242,axiom,
! [X18,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X24,tc_nat,tc_nat)),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f3199,plain,
spl0_359,
inference(avatar_split_clause,[],[f200,f3197]) ).
fof(f3197,plain,
( spl0_359
<=> ! [X20,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f200,axiom,
! [X1,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
fof(f3195,plain,
spl0_358,
inference(avatar_split_clause,[],[f199,f3193]) ).
fof(f3193,plain,
( spl0_358
<=> ! [X20,X1] :
( c_Wellfounded__Recursion_Oacyclic(X20,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f199,axiom,
! [X1,X20] :
( c_Wellfounded__Recursion_Oacyclic(X20,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
fof(f3191,plain,
spl0_357,
inference(avatar_split_clause,[],[f196,f3189]) ).
fof(f3189,plain,
( spl0_357
<=> ! [X11,X12,X1,X4] : c_Sum__Type_OInl(X4,X1,X11) != c_Sum__Type_OInr(X12,X11,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f196,axiom,
! [X11,X1,X4,X12] : c_Sum__Type_OInl(X4,X1,X11) != c_Sum__Type_OInr(X12,X11,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
fof(f3187,plain,
spl0_356,
inference(avatar_split_clause,[],[f181,f3185]) ).
fof(f3185,plain,
( spl0_356
<=> ! [X21,X1,X19] :
( c_emptyset = X21
| c_emptyset != c_union(X19,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f181,axiom,
! [X21,X1,X19] :
( c_emptyset = X21
| c_emptyset != c_union(X19,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
fof(f3183,plain,
spl0_355,
inference(avatar_split_clause,[],[f180,f3181]) ).
fof(f3181,plain,
( spl0_355
<=> ! [X21,X1,X19] :
( c_emptyset = X19
| c_emptyset != c_union(X19,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f180,axiom,
! [X21,X1,X19] :
( c_emptyset = X19
| c_emptyset != c_union(X19,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
fof(f3179,plain,
spl0_354,
inference(avatar_split_clause,[],[f118,f3177]) ).
fof(f3177,plain,
( spl0_354
<=> ! [X18,X24] :
( c_0 = X24
| c_0 != c_plus(X18,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f118,axiom,
! [X18,X24] :
( c_0 = X24
| c_0 != c_plus(X18,X24,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
fof(f3173,plain,
spl0_353,
inference(avatar_split_clause,[],[f117,f3171]) ).
fof(f3171,plain,
( spl0_353
<=> ! [X18,X24] :
( c_0 = X18
| c_0 != c_plus(X18,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f117,axiom,
! [X18,X24] :
( c_0 = X18
| c_0 != c_plus(X18,X24,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
fof(f3169,plain,
spl0_352,
inference(avatar_split_clause,[],[f101,f3167]) ).
fof(f3167,plain,
( spl0_352
<=> ! [X27,X28,X1] :
( c_List_Olist_ONil = X28
| c_append(X27,X28,X1) != X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f101,axiom,
! [X28,X1,X27] :
( c_List_Olist_ONil = X28
| c_append(X27,X28,X1) != X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
fof(f3165,plain,
spl0_351,
inference(avatar_split_clause,[],[f83,f3163]) ).
fof(f3163,plain,
( spl0_351
<=> ! [X27,X1] :
( c_List_Olist_ONil = X27
| c_0 != c_Nat_Osize(X27,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f83,axiom,
! [X1,X27] :
( c_List_Olist_ONil = X27
| c_0 != c_Nat_Osize(X27,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
fof(f3161,plain,
spl0_350,
inference(avatar_split_clause,[],[f77,f3159]) ).
fof(f3159,plain,
( spl0_350
<=> ! [X27,X28,X1] :
( c_List_Olist_ONil = X27
| c_append(X27,X28,X1) != X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f77,axiom,
! [X28,X1,X27] :
( c_List_Olist_ONil = X27
| c_append(X27,X28,X1) != X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
fof(f3157,plain,
spl0_349,
inference(avatar_split_clause,[],[f73,f3155]) ).
fof(f3155,plain,
( spl0_349
<=> ! [X27,X1,X28] :
( c_List_Olist_ONil = X27
| c_List_Olist_ONil != c_append(X27,X28,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f73,axiom,
! [X28,X1,X27] :
( c_List_Olist_ONil = X27
| c_List_Olist_ONil != c_append(X27,X28,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
fof(f3153,plain,
spl0_348,
inference(avatar_split_clause,[],[f63,f3151]) ).
fof(f3151,plain,
( spl0_348
<=> ! [X27,X28,X1] :
( c_List_Olist_ONil = X28
| c_List_Olist_ONil != c_append(X27,X28,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f63,axiom,
! [X28,X1,X27] :
( c_List_Olist_ONil = X28
| c_List_Olist_ONil != c_append(X27,X28,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
fof(f3149,plain,
spl0_347,
inference(avatar_split_clause,[],[f37,f3147]) ).
fof(f3147,plain,
( spl0_347
<=> ! [X20,X1,X19] :
( c_emptyset = X19
| c_emptyset != c_Equiv__Relations_Oquotient(X19,X20,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f37,axiom,
! [X1,X19,X20] :
( c_emptyset = X19
| c_emptyset != c_Equiv__Relations_Oquotient(X19,X20,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty__iff1_0) ).
fof(f3145,plain,
spl0_346,
inference(avatar_split_clause,[],[f24,f3143]) ).
fof(f3143,plain,
( spl0_346
<=> ! [X4,X11,X1,X15] : c_Datatype__Universe_OLeaf(X4,X1,X11) != c_Datatype__Universe_ONumb(X15,X1,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f24,axiom,
! [X11,X1,X4,X15] : c_Datatype__Universe_OLeaf(X4,X1,X11) != c_Datatype__Universe_ONumb(X15,X1,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).
fof(f3141,plain,
spl0_345,
inference(avatar_split_clause,[],[f21,f3139]) ).
fof(f3139,plain,
( spl0_345
<=> ! [X13,X11,X1,X14] : c_Datatype__Universe_OIn0(X13,X1,X11) != c_Datatype__Universe_OIn1(X14,X1,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f21,axiom,
! [X11,X1,X14,X13] : c_Datatype__Universe_OIn0(X13,X1,X11) != c_Datatype__Universe_OIn1(X14,X1,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
fof(f3135,plain,
( spl0_344
| ~ spl0_307
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f3035,f3002,f2962,f3133]) ).
fof(f3133,plain,
( spl0_344
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f3035,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_307
| ~ spl0_317 ),
inference(resolution,[],[f3003,f2963]) ).
fof(f3124,plain,
spl0_343,
inference(avatar_split_clause,[],[f460,f3122]) ).
fof(f3122,plain,
( spl0_343
<=> ! [X57,X56] :
( ~ class_Finite__Set_Ofinite(X57)
| ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_sum(X57,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f460,axiom,
! [X56,X57] :
( ~ class_Finite__Set_Ofinite(X57)
| ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_sum(X57,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f3120,plain,
spl0_342,
inference(avatar_split_clause,[],[f454,f3118]) ).
fof(f3118,plain,
( spl0_342
<=> ! [X57,X56] :
( ~ class_Finite__Set_Ofinite(X57)
| ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_prod(X57,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f454,axiom,
! [X56,X57] :
( ~ class_Finite__Set_Ofinite(X57)
| ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_prod(X57,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f3116,plain,
( spl0_341
| ~ spl0_307
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3034,f2998,f2962,f3114]) ).
fof(f3114,plain,
( spl0_341
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f3034,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_307
| ~ spl0_316 ),
inference(resolution,[],[f2999,f2963]) ).
fof(f3112,plain,
spl0_340,
inference(avatar_split_clause,[],[f404,f3110]) ).
fof(f3110,plain,
( spl0_340
<=> ! [X57,X56] :
( ~ class_Finite__Set_Ofinite(X57)
| ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_fun(X57,X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f404,axiom,
! [X56,X57] :
( ~ class_Finite__Set_Ofinite(X57)
| ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_fun(X57,X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f3108,plain,
spl0_339,
inference(avatar_split_clause,[],[f302,f3106]) ).
fof(f302,axiom,
! [X48,X44] : c_in(c_SetInterval_OgreaterThanLessThan(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f3104,plain,
spl0_338,
inference(avatar_split_clause,[],[f301,f3102]) ).
fof(f301,axiom,
! [X48,X44] : c_in(c_SetInterval_OgreaterThanLessThan(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f3100,plain,
spl0_337,
inference(avatar_split_clause,[],[f300,f3098]) ).
fof(f300,axiom,
! [X48,X44] : c_in(c_SetInterval_OgreaterThanAtMost(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f3096,plain,
spl0_336,
inference(avatar_split_clause,[],[f299,f3094]) ).
fof(f299,axiom,
! [X48,X44] : c_in(c_SetInterval_OgreaterThanAtMost(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f3092,plain,
spl0_335,
inference(avatar_split_clause,[],[f297,f3090]) ).
fof(f297,axiom,
! [X48,X44] : c_in(c_SetInterval_OatLeastLessThan(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f3088,plain,
spl0_334,
inference(avatar_split_clause,[],[f296,f3086]) ).
fof(f296,axiom,
! [X48,X44] : c_in(c_SetInterval_OatLeastLessThan(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f3084,plain,
spl0_333,
inference(avatar_split_clause,[],[f295,f3082]) ).
fof(f295,axiom,
! [X48,X44] : c_in(c_SetInterval_OatLeastAtMost(X48,X44,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f3080,plain,
spl0_332,
inference(avatar_split_clause,[],[f294,f3078]) ).
fof(f294,axiom,
! [X48,X44] : c_in(c_SetInterval_OatLeastAtMost(X48,X44,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f3076,plain,
spl0_331,
inference(avatar_split_clause,[],[f245,f3074]) ).
fof(f3074,plain,
( spl0_331
<=> ! [X18,X24] : c_lessequals(c_uminus(c_IntDef_Oint(X24),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f245,axiom,
! [X18,X24] : c_lessequals(c_uminus(c_IntDef_Oint(X24),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f3072,plain,
( spl0_330
| ~ spl0_306
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3033,f2994,f2958,f3070]) ).
fof(f3070,plain,
( spl0_330
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2994,plain,
( spl0_315
<=> ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X18,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3033,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_nat)
| ~ spl0_306
| ~ spl0_315 ),
inference(resolution,[],[f2995,f2959]) ).
fof(f2995,plain,
( ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X18,X15,tc_nat),tc_nat)
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f2994]) ).
fof(f3068,plain,
spl0_329,
inference(avatar_split_clause,[],[f122,f3066]) ).
fof(f3066,plain,
( spl0_329
<=> ! [X24] :
( c_0 = X24
| ~ c_less(X24,c_Suc(c_0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f122,axiom,
! [X24] :
( c_0 = X24
| ~ c_less(X24,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
fof(f3064,plain,
spl0_328,
inference(avatar_split_clause,[],[f107,f3062]) ).
fof(f3062,plain,
( spl0_328
<=> ! [X18,X24] :
( X18 = X24
| c_Suc(X18) != c_Suc(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f107,axiom,
! [X18,X24] :
( X18 = X24
| c_Suc(X18) != c_Suc(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
fof(f3060,plain,
spl0_327,
inference(avatar_split_clause,[],[f103,f3058]) ).
fof(f3058,plain,
( spl0_327
<=> ! [X27,X1] :
( c_List_Olist_ONil = X27
| c_emptyset != c_List_Oset(X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f103,axiom,
! [X1,X27] :
( c_List_Olist_ONil = X27
| c_emptyset != c_List_Oset(X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
fof(f3056,plain,
spl0_326,
inference(avatar_split_clause,[],[f65,f3054]) ).
fof(f3054,plain,
( spl0_326
<=> ! [X27,X1] :
( c_List_Olist_ONil = X27
| c_List_Olist_ONil != c_List_Orev(X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f65,axiom,
! [X1,X27] :
( c_List_Olist_ONil = X27
| c_List_Olist_ONil != c_List_Orev(X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff1_0) ).
fof(f3052,plain,
spl0_325,
inference(avatar_split_clause,[],[f54,f3050]) ).
fof(f3050,plain,
( spl0_325
<=> ! [X18,X24] :
( X18 = X24
| c_IntDef_Oint(X18) != c_IntDef_Oint(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f54,axiom,
! [X18,X24] :
( X18 = X24
| c_IntDef_Oint(X18) != c_IntDef_Oint(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
fof(f3048,plain,
spl0_324,
inference(avatar_split_clause,[],[f12,f3046]) ).
fof(f12,axiom,
! [X1,X9] : c_in(X9,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X9,X1),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
fof(f3044,plain,
spl0_323,
inference(avatar_split_clause,[],[f5,f3042]) ).
fof(f3042,plain,
( spl0_323
<=> ! [X2,X4,X1,X3] : c_PropLog_Opl_Oop_A_N_62(X2,X3,X1) != c_PropLog_Opl_Ovar(X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f5,axiom,
! [X2,X3,X1,X4] : c_PropLog_Opl_Oop_A_N_62(X2,X3,X1) != c_PropLog_Opl_Ovar(X4,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__5__iff1_0) ).
fof(f3040,plain,
( spl0_322
| ~ spl0_306
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f3032,f2990,f2958,f3038]) ).
fof(f3038,plain,
( spl0_322
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2990,plain,
( spl0_314
<=> ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f3032,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_nat)
| ~ spl0_306
| ~ spl0_314 ),
inference(resolution,[],[f2991,f2959]) ).
fof(f2991,plain,
( ! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X18,tc_nat),tc_nat)
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f2990]) ).
fof(f3020,plain,
spl0_321,
inference(avatar_split_clause,[],[f303,f3018]) ).
fof(f303,axiom,
! [X15] : c_in(c_SetInterval_OlessThan(X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f3016,plain,
spl0_320,
inference(avatar_split_clause,[],[f298,f3014]) ).
fof(f298,axiom,
! [X15] : c_in(c_SetInterval_OatMost(X15,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f3012,plain,
spl0_319,
inference(avatar_split_clause,[],[f269,f3010]) ).
fof(f3010,plain,
( spl0_319
<=> ! [X1,X19] : c_in(c_List_Olist_ONil,c_List_Olists(X19,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f269,axiom,
! [X1,X19] : c_in(c_List_Olist_ONil,c_List_Olists(X19,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f3008,plain,
spl0_318,
inference(avatar_split_clause,[],[f253,f3006]) ).
fof(f253,axiom,
! [X1,X27] : c_in(c_List_Oset(X27,X1),c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f3004,plain,
spl0_317,
inference(avatar_split_clause,[],[f250,f3002]) ).
fof(f250,axiom,
! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X18,X15,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f3000,plain,
spl0_316,
inference(avatar_split_clause,[],[f249,f2998]) ).
fof(f249,axiom,
! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X18,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f2996,plain,
spl0_315,
inference(avatar_split_clause,[],[f234,f2994]) ).
fof(f234,axiom,
! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X18,X15,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f2992,plain,
spl0_314,
inference(avatar_split_clause,[],[f233,f2990]) ).
fof(f233,axiom,
! [X18,X15] : c_Divides_Oop_Advd(X15,c_times(X15,X18,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f2988,plain,
spl0_313,
inference(avatar_split_clause,[],[f186,f2986]) ).
fof(f186,axiom,
! [X21,X1,X9] : c_in(X9,c_insert(X9,X21,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f2984,plain,
spl0_312,
inference(avatar_split_clause,[],[f129,f2982]) ).
fof(f2982,plain,
( spl0_312
<=> ! [X38,X37] : ~ c_less(c_plus(X38,X37,tc_nat),X37,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f129,axiom,
! [X38,X37] : ~ c_less(c_plus(X38,X37,tc_nat),X37,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
fof(f2980,plain,
spl0_311,
inference(avatar_split_clause,[],[f128,f2978]) ).
fof(f2978,plain,
( spl0_311
<=> ! [X38,X37] : ~ c_less(c_plus(X37,X38,tc_nat),X37,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f128,axiom,
! [X38,X37] : ~ c_less(c_plus(X37,X38,tc_nat),X37,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
fof(f2976,plain,
spl0_310,
inference(avatar_split_clause,[],[f126,f2974]) ).
fof(f126,axiom,
! [X24] :
( c_0 = X24
| c_less(c_0,X24,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
fof(f2972,plain,
spl0_309,
inference(avatar_split_clause,[],[f124,f2970]) ).
fof(f2970,plain,
( spl0_309
<=> ! [X24] :
( c_0 = X24
| ~ c_less(X24,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f124,axiom,
! [X24] :
( c_0 = X24
| ~ c_less(X24,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).
fof(f2968,plain,
spl0_308,
inference(avatar_split_clause,[],[f120,f2966]) ).
fof(f2966,plain,
( spl0_308
<=> ! [X37] :
( c_0 = X37
| ~ c_lessequals(X37,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f120,axiom,
! [X37] :
( c_0 = X37
| ~ c_lessequals(X37,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
fof(f2964,plain,
spl0_307,
inference(avatar_split_clause,[],[f57,f2962]) ).
fof(f57,axiom,
! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
fof(f2960,plain,
spl0_306,
inference(avatar_split_clause,[],[f33,f2958]) ).
fof(f33,axiom,
! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
fof(f2956,plain,
spl0_305,
inference(avatar_split_clause,[],[f276,f2954]) ).
fof(f2954,plain,
( spl0_305
<=> ! [X9,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X9,X9,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f276,axiom,
! [X1,X9] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X9,X9,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f2952,plain,
spl0_304,
inference(avatar_split_clause,[],[f182,f2950]) ).
fof(f2950,plain,
( spl0_304
<=> ! [X1] : c_emptyset = c_union(c_emptyset,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f182,axiom,
! [X1] : c_emptyset = c_union(c_emptyset,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
fof(f2948,plain,
spl0_303,
inference(avatar_split_clause,[],[f133,f2946]) ).
fof(f2946,plain,
( spl0_303
<=> ! [X9,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X9,X9,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f133,axiom,
! [X1,X9] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X9,X9,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f2944,plain,
spl0_302,
inference(avatar_split_clause,[],[f119,f2941]) ).
fof(f2941,plain,
( spl0_302
<=> c_0 = c_plus(c_0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f119,axiom,
c_0 = c_plus(c_0,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
fof(f2939,plain,
spl0_301,
inference(avatar_split_clause,[],[f102,f2937]) ).
fof(f102,axiom,
! [X1,X27] : c_append(X27,c_List_Olist_ONil,X1) = X27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
fof(f2935,plain,
spl0_300,
inference(avatar_split_clause,[],[f100,f2933]) ).
fof(f100,axiom,
! [X28,X1] : c_append(c_List_Olist_ONil,X28,X1) = X28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
fof(f2931,plain,
spl0_299,
inference(avatar_split_clause,[],[f89,f2929]) ).
fof(f2929,plain,
( spl0_299
<=> ! [X0,X1,X35] : c_List_Olist_ONil != c_List_Olist_OCons(X0,X35,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f89,axiom,
! [X0,X1,X35] : c_List_Olist_ONil != c_List_Olist_OCons(X0,X35,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
fof(f2927,plain,
spl0_298,
inference(avatar_split_clause,[],[f84,f2925]) ).
fof(f84,axiom,
! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
fof(f2923,plain,
spl0_297,
inference(avatar_split_clause,[],[f36,f2921]) ).
fof(f2921,plain,
( spl0_297
<=> ! [X20,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X20,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f36,axiom,
! [X1,X20] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X20,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff2_0) ).
fof(f2919,plain,
spl0_296,
inference(avatar_split_clause,[],[f3,f2917]) ).
fof(f2917,plain,
( spl0_296
<=> ! [X2,X1,X3] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Oop_A_N_62(X2,X3,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3,axiom,
! [X2,X3,X1] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Oop_A_N_62(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__3__iff1_0) ).
fof(f2915,plain,
spl0_295,
inference(avatar_split_clause,[],[f458,f2913]) ).
fof(f2913,plain,
( spl0_295
<=> ! [X56] :
( ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_set(X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f458,axiom,
! [X56] :
( ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_set(X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f2911,plain,
spl0_294,
inference(avatar_split_clause,[],[f336,f2909]) ).
fof(f2909,plain,
( spl0_294
<=> ! [X56] :
( ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X56)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f336,axiom,
! [X56] :
( ~ class_Finite__Set_Ofinite(X56)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f2907,plain,
spl0_293,
inference(avatar_split_clause,[],[f320,f2905]) ).
fof(f320,axiom,
! [X1,X19] : c_lessequals(X19,X19,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f2903,plain,
spl0_292,
inference(avatar_split_clause,[],[f309,f2901]) ).
fof(f309,axiom,
! [X1,X19] : c_lessequals(c_emptyset,X19,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f2899,plain,
spl0_291,
inference(avatar_split_clause,[],[f275,f2897]) ).
fof(f2897,plain,
( spl0_291
<=> ! [X24] : c_less(c_0,c_Suc(X24),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f275,axiom,
! [X24] : c_less(c_0,c_Suc(X24),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f2895,plain,
spl0_290,
inference(avatar_split_clause,[],[f273,f2893]) ).
fof(f273,axiom,
! [X24] : c_less(X24,c_Suc(X24),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f2891,plain,
spl0_289,
inference(avatar_split_clause,[],[f236,f2889]) ).
fof(f2889,plain,
( spl0_289
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f236,axiom,
! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f2887,plain,
spl0_288,
inference(avatar_split_clause,[],[f232,f2885]) ).
fof(f2885,plain,
( spl0_288
<=> ! [X15] : c_Divides_Oop_Advd(c_Suc(c_0),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f232,axiom,
! [X15] : c_Divides_Oop_Advd(c_Suc(c_0),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f2883,plain,
spl0_287,
inference(avatar_split_clause,[],[f188,f2881]) ).
fof(f2881,plain,
( spl0_287
<=> ! [X1,X19] : ~ c_less(X19,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f188,axiom,
! [X1,X19] : ~ c_less(X19,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
fof(f2879,plain,
spl0_286,
inference(avatar_split_clause,[],[f104,f2877]) ).
fof(f2877,plain,
( spl0_286
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f104,axiom,
! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
fof(f2875,plain,
spl0_285,
inference(avatar_split_clause,[],[f96,f2873]) ).
fof(f96,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff2_0) ).
fof(f2871,plain,
~ spl0_284,
inference(avatar_split_clause,[],[f53,f2868]) ).
fof(f2868,plain,
( spl0_284
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f53,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
fof(f2866,plain,
spl0_283,
inference(avatar_split_clause,[],[f15,f2864]) ).
fof(f2864,plain,
( spl0_283
<=> ! [X0,X1] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f15,axiom,
! [X0,X1] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1__iff1_0) ).
fof(f2862,plain,
spl0_282,
inference(avatar_split_clause,[],[f1,f2860]) ).
fof(f2860,plain,
( spl0_282
<=> ! [X0,X1] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Ovar(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f1,axiom,
! [X0,X1] : c_PropLog_Opl_Ofalse != c_PropLog_Opl_Ovar(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Opl_Odistinct__1__iff1_0) ).
fof(f2551,plain,
spl0_281,
inference(avatar_split_clause,[],[f1367,f2549]) ).
fof(f2549,plain,
( spl0_281
<=> ! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_Orderings_Olinorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f1367,axiom,
! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_Orderings_Olinorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f2547,plain,
spl0_280,
inference(avatar_split_clause,[],[f1366,f2545]) ).
fof(f2545,plain,
( spl0_280
<=> ! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f1366,axiom,
! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f2543,plain,
spl0_279,
inference(avatar_split_clause,[],[f1365,f2541]) ).
fof(f2541,plain,
( spl0_279
<=> ! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f1365,axiom,
! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f2539,plain,
spl0_278,
inference(avatar_split_clause,[],[f1364,f2537]) ).
fof(f2537,plain,
( spl0_278
<=> ! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f1364,axiom,
! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f2535,plain,
spl0_277,
inference(avatar_split_clause,[],[f1363,f2533]) ).
fof(f2533,plain,
( spl0_277
<=> ! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f1363,axiom,
! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f2531,plain,
spl0_276,
inference(avatar_split_clause,[],[f1362,f2529]) ).
fof(f2529,plain,
( spl0_276
<=> ! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f1362,axiom,
! [X58] :
( ~ class_Wellfounded__Recursion_Owellorder(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f2527,plain,
spl0_275,
inference(avatar_split_clause,[],[f1275,f2525]) ).
fof(f2525,plain,
( spl0_275
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f1275,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f2523,plain,
spl0_274,
inference(avatar_split_clause,[],[f1267,f2521]) ).
fof(f2521,plain,
( spl0_274
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__semiring(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1267,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__semiring(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f2519,plain,
spl0_273,
inference(avatar_split_clause,[],[f1266,f2517]) ).
fof(f2517,plain,
( spl0_273
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__semiring(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f1266,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__semiring(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f2515,plain,
spl0_272,
inference(avatar_split_clause,[],[f1256,f2513]) ).
fof(f2513,plain,
( spl0_272
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f1256,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f2511,plain,
spl0_271,
inference(avatar_split_clause,[],[f1255,f2509]) ).
fof(f2509,plain,
( spl0_271
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1255,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f2507,plain,
spl0_270,
inference(avatar_split_clause,[],[f1254,f2505]) ).
fof(f2505,plain,
( spl0_270
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1254,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f2503,plain,
spl0_269,
inference(avatar_split_clause,[],[f1252,f2501]) ).
fof(f2501,plain,
( spl0_269
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1252,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f2499,plain,
spl0_268,
inference(avatar_split_clause,[],[f1251,f2497]) ).
fof(f2497,plain,
( spl0_268
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1251,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f2495,plain,
spl0_267,
inference(avatar_split_clause,[],[f1250,f2493]) ).
fof(f2493,plain,
( spl0_267
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1250,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f2491,plain,
spl0_266,
inference(avatar_split_clause,[],[f1249,f2489]) ).
fof(f2489,plain,
( spl0_266
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1249,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f2487,plain,
spl0_265,
inference(avatar_split_clause,[],[f1248,f2485]) ).
fof(f2485,plain,
( spl0_265
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1248,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__ring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f2483,plain,
spl0_264,
inference(avatar_split_clause,[],[f1232,f2481]) ).
fof(f2481,plain,
( spl0_264
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f1232,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f2479,plain,
spl0_263,
inference(avatar_split_clause,[],[f1231,f2477]) ).
fof(f2477,plain,
( spl0_263
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1231,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f2475,plain,
spl0_262,
inference(avatar_split_clause,[],[f1230,f2473]) ).
fof(f2473,plain,
( spl0_262
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1230,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f2471,plain,
spl0_261,
inference(avatar_split_clause,[],[f1229,f2469]) ).
fof(f2469,plain,
( spl0_261
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1229,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f2467,plain,
spl0_260,
inference(avatar_split_clause,[],[f1197,f2465]) ).
fof(f2465,plain,
( spl0_260
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1197,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f2463,plain,
spl0_259,
inference(avatar_split_clause,[],[f1188,f2461]) ).
fof(f2461,plain,
( spl0_259
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1188,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f2459,plain,
spl0_258,
inference(avatar_split_clause,[],[f1187,f2457]) ).
fof(f2457,plain,
( spl0_258
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1187,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f2455,plain,
spl0_257,
inference(avatar_split_clause,[],[f1184,f2453]) ).
fof(f2453,plain,
( spl0_257
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1184,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f2451,plain,
spl0_256,
inference(avatar_split_clause,[],[f1174,f2449]) ).
fof(f2449,plain,
( spl0_256
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1174,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f2447,plain,
spl0_255,
inference(avatar_split_clause,[],[f1173,f2445]) ).
fof(f2445,plain,
( spl0_255
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1173,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f2443,plain,
spl0_254,
inference(avatar_split_clause,[],[f1170,f2441]) ).
fof(f2441,plain,
( spl0_254
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1170,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f2439,plain,
spl0_253,
inference(avatar_split_clause,[],[f1169,f2437]) ).
fof(f2437,plain,
( spl0_253
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1169,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f2435,plain,
spl0_252,
inference(avatar_split_clause,[],[f1165,f2433]) ).
fof(f2433,plain,
( spl0_252
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1165,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f2431,plain,
spl0_251,
inference(avatar_split_clause,[],[f1163,f2429]) ).
fof(f2429,plain,
( spl0_251
<=> ! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1163,axiom,
! [X58] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f2427,plain,
spl0_250,
inference(avatar_split_clause,[],[f1162,f2425]) ).
fof(f2425,plain,
( spl0_250
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1162,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f2423,plain,
spl0_249,
inference(avatar_split_clause,[],[f1155,f2421]) ).
fof(f2421,plain,
( spl0_249
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f1155,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f2419,plain,
spl0_248,
inference(avatar_split_clause,[],[f1154,f2417]) ).
fof(f2417,plain,
( spl0_248
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1154,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f2415,plain,
spl0_247,
inference(avatar_split_clause,[],[f1149,f2413]) ).
fof(f2413,plain,
( spl0_247
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1149,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f2411,plain,
spl0_246,
inference(avatar_split_clause,[],[f1148,f2409]) ).
fof(f2409,plain,
( spl0_246
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1148,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f2407,plain,
spl0_245,
inference(avatar_split_clause,[],[f1147,f2405]) ).
fof(f2405,plain,
( spl0_245
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f1147,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f2403,plain,
spl0_244,
inference(avatar_split_clause,[],[f1146,f2401]) ).
fof(f2401,plain,
( spl0_244
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1146,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f2399,plain,
spl0_243,
inference(avatar_split_clause,[],[f1145,f2397]) ).
fof(f2397,plain,
( spl0_243
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f1145,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f2395,plain,
spl0_242,
inference(avatar_split_clause,[],[f1144,f2393]) ).
fof(f2393,plain,
( spl0_242
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f1144,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f2391,plain,
spl0_241,
inference(avatar_split_clause,[],[f1143,f2389]) ).
fof(f2389,plain,
( spl0_241
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1143,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f2387,plain,
spl0_240,
inference(avatar_split_clause,[],[f1142,f2385]) ).
fof(f2385,plain,
( spl0_240
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1142,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f2383,plain,
spl0_239,
inference(avatar_split_clause,[],[f1141,f2381]) ).
fof(f2381,plain,
( spl0_239
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Orderings_Olinorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1141,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X58)
| class_Orderings_Olinorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f2379,plain,
spl0_238,
inference(avatar_split_clause,[],[f1132,f2377]) ).
fof(f2377,plain,
( spl0_238
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1132,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f2375,plain,
spl0_237,
inference(avatar_split_clause,[],[f1131,f2373]) ).
fof(f2373,plain,
( spl0_237
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1131,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f2371,plain,
spl0_236,
inference(avatar_split_clause,[],[f1130,f2369]) ).
fof(f2369,plain,
( spl0_236
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1130,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f2367,plain,
spl0_235,
inference(avatar_split_clause,[],[f1129,f2365]) ).
fof(f2365,plain,
( spl0_235
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1129,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f2363,plain,
spl0_234,
inference(avatar_split_clause,[],[f1128,f2361]) ).
fof(f2361,plain,
( spl0_234
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1128,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f2359,plain,
spl0_233,
inference(avatar_split_clause,[],[f1127,f2357]) ).
fof(f2357,plain,
( spl0_233
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1127,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f2355,plain,
spl0_232,
inference(avatar_split_clause,[],[f1126,f2353]) ).
fof(f2353,plain,
( spl0_232
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1126,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f2351,plain,
spl0_231,
inference(avatar_split_clause,[],[f1125,f2349]) ).
fof(f2349,plain,
( spl0_231
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1125,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f2347,plain,
spl0_230,
inference(avatar_split_clause,[],[f1124,f2345]) ).
fof(f2345,plain,
( spl0_230
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1124,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f2343,plain,
spl0_229,
inference(avatar_split_clause,[],[f1123,f2341]) ).
fof(f2341,plain,
( spl0_229
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1123,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f2339,plain,
spl0_228,
inference(avatar_split_clause,[],[f1121,f2337]) ).
fof(f2337,plain,
( spl0_228
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1121,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f2335,plain,
spl0_227,
inference(avatar_split_clause,[],[f1120,f2333]) ).
fof(f2333,plain,
( spl0_227
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1120,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f2331,plain,
spl0_226,
inference(avatar_split_clause,[],[f1119,f2329]) ).
fof(f2329,plain,
( spl0_226
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Orderings_Olinorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1119,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Orderings_Olinorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f2327,plain,
spl0_225,
inference(avatar_split_clause,[],[f1118,f2325]) ).
fof(f2325,plain,
( spl0_225
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1118,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f2323,plain,
spl0_224,
inference(avatar_split_clause,[],[f1117,f2321]) ).
fof(f2321,plain,
( spl0_224
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1117,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f2319,plain,
spl0_223,
inference(avatar_split_clause,[],[f1116,f2317]) ).
fof(f2317,plain,
( spl0_223
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1116,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__semidom(X58)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f2315,plain,
spl0_222,
inference(avatar_split_clause,[],[f1091,f2313]) ).
fof(f2313,plain,
( spl0_222
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group__join(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1091,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group__join(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f2311,plain,
spl0_221,
inference(avatar_split_clause,[],[f1090,f2309]) ).
fof(f2309,plain,
( spl0_221
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group__meet(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1090,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group__meet(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f2307,plain,
spl0_220,
inference(avatar_split_clause,[],[f1089,f2305]) ).
fof(f2305,plain,
( spl0_220
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group__abs(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1089,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group__abs(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f2303,plain,
spl0_219,
inference(avatar_split_clause,[],[f1088,f2301]) ).
fof(f2301,plain,
( spl0_219
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Opordered__ring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1088,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Opordered__ring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f2299,plain,
spl0_218,
inference(avatar_split_clause,[],[f1087,f2297]) ).
fof(f2297,plain,
( spl0_218
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Olordered__ring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1087,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Olordered__ring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f2295,plain,
spl0_217,
inference(avatar_split_clause,[],[f1086,f2293]) ).
fof(f2293,plain,
( spl0_217
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1086,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f2291,plain,
spl0_216,
inference(avatar_split_clause,[],[f1084,f2289]) ).
fof(f2289,plain,
( spl0_216
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1084,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f2287,plain,
spl0_215,
inference(avatar_split_clause,[],[f1083,f2285]) ).
fof(f2285,plain,
( spl0_215
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Oaxclass__abs__if(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1083,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Oaxclass__abs__if(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f2283,plain,
spl0_214,
inference(avatar_split_clause,[],[f1082,f2281]) ).
fof(f2281,plain,
( spl0_214
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1082,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f2279,plain,
spl0_213,
inference(avatar_split_clause,[],[f1081,f2277]) ).
fof(f2277,plain,
( spl0_213
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1081,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f2275,plain,
spl0_212,
inference(avatar_split_clause,[],[f1080,f2273]) ).
fof(f2273,plain,
( spl0_212
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1080,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f2271,plain,
spl0_211,
inference(avatar_split_clause,[],[f1079,f2269]) ).
fof(f2269,plain,
( spl0_211
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1079,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f2267,plain,
spl0_210,
inference(avatar_split_clause,[],[f1078,f2265]) ).
fof(f2265,plain,
( spl0_210
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1078,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f2263,plain,
spl0_209,
inference(avatar_split_clause,[],[f1077,f2261]) ).
fof(f2261,plain,
( spl0_209
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1077,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f2259,plain,
spl0_208,
inference(avatar_split_clause,[],[f1076,f2257]) ).
fof(f2257,plain,
( spl0_208
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1076,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f2255,plain,
spl0_207,
inference(avatar_split_clause,[],[f1075,f2253]) ).
fof(f2253,plain,
( spl0_207
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1075,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f2251,plain,
spl0_206,
inference(avatar_split_clause,[],[f1073,f2249]) ).
fof(f2249,plain,
( spl0_206
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1073,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f2247,plain,
spl0_205,
inference(avatar_split_clause,[],[f1072,f2245]) ).
fof(f2245,plain,
( spl0_205
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1072,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f2243,plain,
spl0_204,
inference(avatar_split_clause,[],[f1071,f2241]) ).
fof(f2241,plain,
( spl0_204
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Orderings_Olinorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1071,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Orderings_Olinorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f2239,plain,
spl0_203,
inference(avatar_split_clause,[],[f1070,f2237]) ).
fof(f2237,plain,
( spl0_203
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1070,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f2235,plain,
spl0_202,
inference(avatar_split_clause,[],[f1069,f2233]) ).
fof(f2233,plain,
( spl0_202
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1069,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f2231,plain,
spl0_201,
inference(avatar_split_clause,[],[f1055,f2229]) ).
fof(f2229,plain,
( spl0_201
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__semidom(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1055,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__semidom(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f2227,plain,
spl0_200,
inference(avatar_split_clause,[],[f1054,f2225]) ).
fof(f2225,plain,
( spl0_200
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1054,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f2223,plain,
spl0_199,
inference(avatar_split_clause,[],[f1053,f2221]) ).
fof(f2221,plain,
( spl0_199
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1053,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f2219,plain,
spl0_198,
inference(avatar_split_clause,[],[f1052,f2217]) ).
fof(f2217,plain,
( spl0_198
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group__join(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1052,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group__join(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f2215,plain,
spl0_197,
inference(avatar_split_clause,[],[f1051,f2213]) ).
fof(f2213,plain,
( spl0_197
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group__meet(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1051,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group__meet(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f2211,plain,
spl0_196,
inference(avatar_split_clause,[],[f1050,f2209]) ).
fof(f2209,plain,
( spl0_196
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group__abs(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1050,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Olordered__ab__group__abs(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f2207,plain,
spl0_195,
inference(avatar_split_clause,[],[f1048,f2205]) ).
fof(f2205,plain,
( spl0_195
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__ring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1048,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__ring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f2203,plain,
spl0_194,
inference(avatar_split_clause,[],[f1047,f2201]) ).
fof(f2201,plain,
( spl0_194
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Olordered__ring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1047,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Olordered__ring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f2199,plain,
spl0_193,
inference(avatar_split_clause,[],[f1046,f2197]) ).
fof(f2197,plain,
( spl0_193
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__ring__strict(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1046,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__ring__strict(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f2195,plain,
spl0_192,
inference(avatar_split_clause,[],[f1045,f2193]) ).
fof(f2193,plain,
( spl0_192
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oaxclass__abs__if(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1045,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oaxclass__abs__if(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f2191,plain,
spl0_191,
inference(avatar_split_clause,[],[f1044,f2189]) ).
fof(f2189,plain,
( spl0_191
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1044,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f2187,plain,
spl0_190,
inference(avatar_split_clause,[],[f1043,f2185]) ).
fof(f2185,plain,
( spl0_190
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1043,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f2183,plain,
spl0_189,
inference(avatar_split_clause,[],[f1042,f2181]) ).
fof(f2181,plain,
( spl0_189
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1042,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f2179,plain,
spl0_188,
inference(avatar_split_clause,[],[f1041,f2177]) ).
fof(f2177,plain,
( spl0_188
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1041,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f2175,plain,
spl0_187,
inference(avatar_split_clause,[],[f1040,f2173]) ).
fof(f2173,plain,
( spl0_187
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1040,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f2171,plain,
spl0_186,
inference(avatar_split_clause,[],[f1039,f2169]) ).
fof(f2169,plain,
( spl0_186
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1039,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f2167,plain,
spl0_185,
inference(avatar_split_clause,[],[f1037,f2165]) ).
fof(f2165,plain,
( spl0_185
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1037,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f2163,plain,
spl0_184,
inference(avatar_split_clause,[],[f1036,f2161]) ).
fof(f2161,plain,
( spl0_184
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1036,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f2159,plain,
spl0_183,
inference(avatar_split_clause,[],[f1035,f2157]) ).
fof(f2157,plain,
( spl0_183
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1035,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f2155,plain,
spl0_182,
inference(avatar_split_clause,[],[f1034,f2153]) ).
fof(f2153,plain,
( spl0_182
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1034,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f2151,plain,
spl0_181,
inference(avatar_split_clause,[],[f1033,f2149]) ).
fof(f2149,plain,
( spl0_181
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1033,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f2147,plain,
spl0_180,
inference(avatar_split_clause,[],[f1032,f2145]) ).
fof(f2145,plain,
( spl0_180
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1032,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f2143,plain,
spl0_179,
inference(avatar_split_clause,[],[f1031,f2141]) ).
fof(f2141,plain,
( spl0_179
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Orderings_Olinorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1031,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Orderings_Olinorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f2139,plain,
spl0_178,
inference(avatar_split_clause,[],[f1030,f2137]) ).
fof(f2137,plain,
( spl0_178
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1030,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f2135,plain,
spl0_177,
inference(avatar_split_clause,[],[f1029,f2133]) ).
fof(f2133,plain,
( spl0_177
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1029,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f2131,plain,
spl0_176,
inference(avatar_split_clause,[],[f1028,f2129]) ).
fof(f2129,plain,
( spl0_176
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1028,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__idom(X58)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f2127,plain,
spl0_175,
inference(avatar_split_clause,[],[f935,f2125]) ).
fof(f2125,plain,
( spl0_175
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f935,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__comm__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f2123,plain,
spl0_174,
inference(avatar_split_clause,[],[f934,f2121]) ).
fof(f2121,plain,
( spl0_174
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f934,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f2119,plain,
spl0_173,
inference(avatar_split_clause,[],[f933,f2117]) ).
fof(f2117,plain,
( spl0_173
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f933,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f2115,plain,
spl0_172,
inference(avatar_split_clause,[],[f931,f2113]) ).
fof(f2113,plain,
( spl0_172
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f931,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f2111,plain,
spl0_171,
inference(avatar_split_clause,[],[f930,f2109]) ).
fof(f2109,plain,
( spl0_171
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f930,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Ring__and__Field_Oordered__semiring__strict(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f2107,plain,
spl0_170,
inference(avatar_split_clause,[],[f927,f2105]) ).
fof(f2105,plain,
( spl0_170
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f927,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f2103,plain,
spl0_169,
inference(avatar_split_clause,[],[f926,f2101]) ).
fof(f2101,plain,
( spl0_169
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f926,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f2099,plain,
spl0_168,
inference(avatar_split_clause,[],[f924,f2097]) ).
fof(f2097,plain,
( spl0_168
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f924,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f2095,plain,
spl0_167,
inference(avatar_split_clause,[],[f923,f2093]) ).
fof(f2093,plain,
( spl0_167
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f923,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f2091,plain,
spl0_166,
inference(avatar_split_clause,[],[f922,f2089]) ).
fof(f2089,plain,
( spl0_166
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f922,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f2087,plain,
spl0_165,
inference(avatar_split_clause,[],[f921,f2085]) ).
fof(f2085,plain,
( spl0_165
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f921,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f2083,plain,
spl0_164,
inference(avatar_split_clause,[],[f920,f2081]) ).
fof(f2081,plain,
( spl0_164
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f920,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f2079,plain,
spl0_163,
inference(avatar_split_clause,[],[f919,f2077]) ).
fof(f2077,plain,
( spl0_163
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f919,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f2075,plain,
spl0_162,
inference(avatar_split_clause,[],[f918,f2073]) ).
fof(f2073,plain,
( spl0_162
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Orderings_Olinorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f918,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_Orderings_Olinorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f2071,plain,
spl0_161,
inference(avatar_split_clause,[],[f917,f2069]) ).
fof(f2069,plain,
( spl0_161
<=> ! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f917,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X58)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f2067,plain,
spl0_160,
inference(avatar_split_clause,[],[f912,f2065]) ).
fof(f2065,plain,
( spl0_160
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f912,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f2063,plain,
spl0_159,
inference(avatar_split_clause,[],[f911,f2061]) ).
fof(f2061,plain,
( spl0_159
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f911,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Ring__and__Field_Opordered__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f2059,plain,
spl0_158,
inference(avatar_split_clause,[],[f910,f2057]) ).
fof(f2057,plain,
( spl0_158
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f910,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Ring__and__Field_Opordered__cancel__semiring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f2055,plain,
spl0_157,
inference(avatar_split_clause,[],[f909,f2053]) ).
fof(f2053,plain,
( spl0_157
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f909,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f2051,plain,
spl0_156,
inference(avatar_split_clause,[],[f908,f2049]) ).
fof(f2049,plain,
( spl0_156
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f908,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f2047,plain,
spl0_155,
inference(avatar_split_clause,[],[f906,f2045]) ).
fof(f2045,plain,
( spl0_155
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group__join(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f906,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group__join(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f2043,plain,
spl0_154,
inference(avatar_split_clause,[],[f904,f2041]) ).
fof(f2041,plain,
( spl0_154
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group__meet(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f904,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group__meet(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f2039,plain,
spl0_153,
inference(avatar_split_clause,[],[f903,f2037]) ).
fof(f2037,plain,
( spl0_153
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f903,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f2035,plain,
spl0_152,
inference(avatar_split_clause,[],[f902,f2033]) ).
fof(f2033,plain,
( spl0_152
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f902,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f2031,plain,
spl0_151,
inference(avatar_split_clause,[],[f901,f2029]) ).
fof(f2029,plain,
( spl0_151
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f901,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f2027,plain,
spl0_150,
inference(avatar_split_clause,[],[f900,f2025]) ).
fof(f2025,plain,
( spl0_150
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f900,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f2023,plain,
spl0_149,
inference(avatar_split_clause,[],[f899,f2021]) ).
fof(f2021,plain,
( spl0_149
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group__abs(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f899,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Olordered__ab__group__abs(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f2019,plain,
spl0_148,
inference(avatar_split_clause,[],[f894,f2017]) ).
fof(f2017,plain,
( spl0_148
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f894,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f2015,plain,
spl0_147,
inference(avatar_split_clause,[],[f885,f2013]) ).
fof(f2013,plain,
( spl0_147
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f885,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f2011,plain,
spl0_146,
inference(avatar_split_clause,[],[f884,f2009]) ).
fof(f2009,plain,
( spl0_146
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f884,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f2007,plain,
spl0_145,
inference(avatar_split_clause,[],[f882,f2005]) ).
fof(f2005,plain,
( spl0_145
<=> ! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Ring__and__Field_Opordered__ring(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f882,axiom,
! [X58] :
( ~ class_Ring__and__Field_Olordered__ring(X58)
| class_Ring__and__Field_Opordered__ring(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f2003,plain,
spl0_144,
inference(avatar_split_clause,[],[f691,f2001]) ).
fof(f2001,plain,
( spl0_144
<=> ! [X58] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f691,axiom,
! [X58] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f1999,plain,
spl0_143,
inference(avatar_split_clause,[],[f662,f1997]) ).
fof(f1997,plain,
( spl0_143
<=> ! [X58] :
( ~ class_Orderings_Oorder(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f662,axiom,
! [X58] :
( ~ class_Orderings_Oorder(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f1995,plain,
spl0_142,
inference(avatar_split_clause,[],[f661,f1993]) ).
fof(f1993,plain,
( spl0_142
<=> ! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f661,axiom,
! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f1991,plain,
spl0_141,
inference(avatar_split_clause,[],[f660,f1989]) ).
fof(f1989,plain,
( spl0_141
<=> ! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f660,axiom,
! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f1987,plain,
spl0_140,
inference(avatar_split_clause,[],[f659,f1985]) ).
fof(f1985,plain,
( spl0_140
<=> ! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f659,axiom,
! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f1983,plain,
spl0_139,
inference(avatar_split_clause,[],[f658,f1981]) ).
fof(f1981,plain,
( spl0_139
<=> ! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f658,axiom,
! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f1979,plain,
spl0_138,
inference(avatar_split_clause,[],[f657,f1977]) ).
fof(f1977,plain,
( spl0_138
<=> ! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f657,axiom,
! [X58] :
( ~ class_Orderings_Olinorder(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f1975,plain,
spl0_137,
inference(avatar_split_clause,[],[f649,f1973]) ).
fof(f1973,plain,
( spl0_137
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f649,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f1971,plain,
spl0_136,
inference(avatar_split_clause,[],[f648,f1969]) ).
fof(f1969,plain,
( spl0_136
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f648,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f1967,plain,
spl0_135,
inference(avatar_split_clause,[],[f647,f1965]) ).
fof(f1965,plain,
( spl0_135
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f647,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f1963,plain,
spl0_134,
inference(avatar_split_clause,[],[f641,f1961]) ).
fof(f1961,plain,
( spl0_134
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f641,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f1959,plain,
spl0_133,
inference(avatar_split_clause,[],[f640,f1957]) ).
fof(f1957,plain,
( spl0_133
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f640,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f1955,plain,
spl0_132,
inference(avatar_split_clause,[],[f639,f1953]) ).
fof(f1953,plain,
( spl0_132
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f639,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f1951,plain,
spl0_131,
inference(avatar_split_clause,[],[f638,f1949]) ).
fof(f1949,plain,
( spl0_131
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f638,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f1947,plain,
spl0_130,
inference(avatar_split_clause,[],[f634,f1945]) ).
fof(f1945,plain,
( spl0_130
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f634,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f1943,plain,
spl0_129,
inference(avatar_split_clause,[],[f633,f1941]) ).
fof(f1941,plain,
( spl0_129
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f633,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f1939,plain,
spl0_128,
inference(avatar_split_clause,[],[f632,f1937]) ).
fof(f1937,plain,
( spl0_128
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f632,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f1935,plain,
spl0_127,
inference(avatar_split_clause,[],[f624,f1933]) ).
fof(f1933,plain,
( spl0_127
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f624,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f1931,plain,
spl0_126,
inference(avatar_split_clause,[],[f623,f1929]) ).
fof(f1929,plain,
( spl0_126
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f623,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f1927,plain,
spl0_125,
inference(avatar_split_clause,[],[f622,f1925]) ).
fof(f1925,plain,
( spl0_125
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f622,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f1923,plain,
spl0_124,
inference(avatar_split_clause,[],[f621,f1921]) ).
fof(f1921,plain,
( spl0_124
<=> ! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f621,axiom,
! [X58] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f1919,plain,
spl0_123,
inference(avatar_split_clause,[],[f618,f1917]) ).
fof(f1917,plain,
( spl0_123
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Olinorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f618,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Olinorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f1915,plain,
spl0_122,
inference(avatar_split_clause,[],[f612,f1913]) ).
fof(f1913,plain,
( spl0_122
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f612,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f1911,plain,
spl0_121,
inference(avatar_split_clause,[],[f611,f1909]) ).
fof(f1909,plain,
( spl0_121
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f611,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f1907,plain,
spl0_120,
inference(avatar_split_clause,[],[f610,f1905]) ).
fof(f1905,plain,
( spl0_120
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f610,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f1903,plain,
spl0_119,
inference(avatar_split_clause,[],[f609,f1901]) ).
fof(f1901,plain,
( spl0_119
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f609,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f1899,plain,
spl0_118,
inference(avatar_split_clause,[],[f608,f1897]) ).
fof(f1897,plain,
( spl0_118
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f608,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f1895,plain,
spl0_117,
inference(avatar_split_clause,[],[f607,f1893]) ).
fof(f1893,plain,
( spl0_117
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f607,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f1891,plain,
spl0_116,
inference(avatar_split_clause,[],[f606,f1889]) ).
fof(f1889,plain,
( spl0_116
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f606,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f1887,plain,
spl0_115,
inference(avatar_split_clause,[],[f605,f1885]) ).
fof(f1885,plain,
( spl0_115
<=> ! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f605,axiom,
! [X58] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f1883,plain,
spl0_114,
inference(avatar_split_clause,[],[f601,f1881]) ).
fof(f1881,plain,
( spl0_114
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f601,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f1879,plain,
spl0_113,
inference(avatar_split_clause,[],[f600,f1877]) ).
fof(f1877,plain,
( spl0_113
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f600,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f1875,plain,
spl0_112,
inference(avatar_split_clause,[],[f599,f1873]) ).
fof(f1873,plain,
( spl0_112
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f599,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f1871,plain,
spl0_111,
inference(avatar_split_clause,[],[f598,f1869]) ).
fof(f1869,plain,
( spl0_111
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f598,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f1867,plain,
spl0_110,
inference(avatar_split_clause,[],[f597,f1865]) ).
fof(f1865,plain,
( spl0_110
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f597,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f1863,plain,
spl0_109,
inference(avatar_split_clause,[],[f593,f1861]) ).
fof(f1861,plain,
( spl0_109
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f593,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f1859,plain,
spl0_108,
inference(avatar_split_clause,[],[f592,f1857]) ).
fof(f1857,plain,
( spl0_108
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f592,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f1855,plain,
spl0_107,
inference(avatar_split_clause,[],[f591,f1853]) ).
fof(f1853,plain,
( spl0_107
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f591,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f1851,plain,
spl0_106,
inference(avatar_split_clause,[],[f590,f1849]) ).
fof(f1849,plain,
( spl0_106
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f590,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f1847,plain,
spl0_105,
inference(avatar_split_clause,[],[f583,f1845]) ).
fof(f1845,plain,
( spl0_105
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f583,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f1843,plain,
spl0_104,
inference(avatar_split_clause,[],[f582,f1841]) ).
fof(f1841,plain,
( spl0_104
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f582,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f1839,plain,
spl0_103,
inference(avatar_split_clause,[],[f581,f1837]) ).
fof(f1837,plain,
( spl0_103
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f581,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f1835,plain,
spl0_102,
inference(avatar_split_clause,[],[f580,f1833]) ).
fof(f1833,plain,
( spl0_102
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f580,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f1831,plain,
spl0_101,
inference(avatar_split_clause,[],[f579,f1829]) ).
fof(f1829,plain,
( spl0_101
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f579,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f1827,plain,
spl0_100,
inference(avatar_split_clause,[],[f578,f1825]) ).
fof(f1825,plain,
( spl0_100
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f578,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f1823,plain,
spl0_99,
inference(avatar_split_clause,[],[f574,f1821]) ).
fof(f1821,plain,
( spl0_99
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f574,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f1819,plain,
spl0_98,
inference(avatar_split_clause,[],[f573,f1817]) ).
fof(f1817,plain,
( spl0_98
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f573,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f1815,plain,
spl0_97,
inference(avatar_split_clause,[],[f572,f1813]) ).
fof(f1813,plain,
( spl0_97
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f572,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f1811,plain,
spl0_96,
inference(avatar_split_clause,[],[f571,f1809]) ).
fof(f1809,plain,
( spl0_96
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f571,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f1807,plain,
spl0_95,
inference(avatar_split_clause,[],[f564,f1805]) ).
fof(f1805,plain,
( spl0_95
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f564,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f1803,plain,
spl0_94,
inference(avatar_split_clause,[],[f562,f1801]) ).
fof(f1801,plain,
( spl0_94
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f562,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f1799,plain,
spl0_93,
inference(avatar_split_clause,[],[f561,f1797]) ).
fof(f1797,plain,
( spl0_93
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f561,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f1795,plain,
spl0_92,
inference(avatar_split_clause,[],[f560,f1793]) ).
fof(f1793,plain,
( spl0_92
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f560,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f1791,plain,
spl0_91,
inference(avatar_split_clause,[],[f555,f1789]) ).
fof(f1789,plain,
( spl0_91
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f555,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f1787,plain,
spl0_90,
inference(avatar_split_clause,[],[f554,f1785]) ).
fof(f1785,plain,
( spl0_90
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f554,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f1783,plain,
spl0_89,
inference(avatar_split_clause,[],[f553,f1781]) ).
fof(f1781,plain,
( spl0_89
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f553,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f1779,plain,
spl0_88,
inference(avatar_split_clause,[],[f552,f1777]) ).
fof(f1777,plain,
( spl0_88
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f552,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f1775,plain,
spl0_87,
inference(avatar_split_clause,[],[f551,f1773]) ).
fof(f1773,plain,
( spl0_87
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f551,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f1771,plain,
spl0_86,
inference(avatar_split_clause,[],[f546,f1769]) ).
fof(f1769,plain,
( spl0_86
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f546,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f1767,plain,
spl0_85,
inference(avatar_split_clause,[],[f545,f1765]) ).
fof(f1765,plain,
( spl0_85
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f545,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X58)
| class_OrderedGroup_Olordered__ab__group(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f1763,plain,
spl0_84,
inference(avatar_split_clause,[],[f544,f1761]) ).
fof(f1761,plain,
( spl0_84
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f544,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f1759,plain,
spl0_83,
inference(avatar_split_clause,[],[f543,f1757]) ).
fof(f1757,plain,
( spl0_83
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f543,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f1755,plain,
spl0_82,
inference(avatar_split_clause,[],[f542,f1753]) ).
fof(f1753,plain,
( spl0_82
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f542,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f1751,plain,
spl0_81,
inference(avatar_split_clause,[],[f541,f1749]) ).
fof(f1749,plain,
( spl0_81
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f541,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f1747,plain,
spl0_80,
inference(avatar_split_clause,[],[f540,f1745]) ).
fof(f1745,plain,
( spl0_80
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f540,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f1743,plain,
spl0_79,
inference(avatar_split_clause,[],[f536,f1741]) ).
fof(f1741,plain,
( spl0_79
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f536,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f1739,plain,
spl0_78,
inference(avatar_split_clause,[],[f535,f1737]) ).
fof(f1737,plain,
( spl0_78
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f535,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f1735,plain,
spl0_77,
inference(avatar_split_clause,[],[f534,f1733]) ).
fof(f1733,plain,
( spl0_77
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_LOrder_Olorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f534,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_LOrder_Olorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f1731,plain,
spl0_76,
inference(avatar_split_clause,[],[f527,f1729]) ).
fof(f1729,plain,
( spl0_76
<=> ! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f527,axiom,
! [X58] :
( ~ class_OrderedGroup_Olordered__ab__group(X58)
| class_OrderedGroup_Opordered__ab__group__add(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f1727,plain,
spl0_75,
inference(avatar_split_clause,[],[f468,f1725]) ).
fof(f1725,plain,
( spl0_75
<=> ! [X58] :
( ~ class_LOrder_Omeet__semilorder(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f468,axiom,
! [X58] :
( ~ class_LOrder_Omeet__semilorder(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f1723,plain,
spl0_74,
inference(avatar_split_clause,[],[f467,f1721]) ).
fof(f1721,plain,
( spl0_74
<=> ! [X58] :
( ~ class_LOrder_Omeet__semilorder(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f467,axiom,
! [X58] :
( ~ class_LOrder_Omeet__semilorder(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f1719,plain,
spl0_73,
inference(avatar_split_clause,[],[f466,f1717]) ).
fof(f1717,plain,
( spl0_73
<=> ! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_LOrder_Ojoin__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f466,axiom,
! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_LOrder_Ojoin__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f1715,plain,
spl0_72,
inference(avatar_split_clause,[],[f465,f1713]) ).
fof(f1713,plain,
( spl0_72
<=> ! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f465,axiom,
! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f1711,plain,
spl0_71,
inference(avatar_split_clause,[],[f464,f1709]) ).
fof(f1709,plain,
( spl0_71
<=> ! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f464,axiom,
! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f1707,plain,
spl0_70,
inference(avatar_split_clause,[],[f463,f1705]) ).
fof(f1705,plain,
( spl0_70
<=> ! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_LOrder_Omeet__semilorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f463,axiom,
! [X58] :
( ~ class_LOrder_Olorder(X58)
| class_LOrder_Omeet__semilorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f1703,plain,
spl0_69,
inference(avatar_split_clause,[],[f462,f1701]) ).
fof(f1701,plain,
( spl0_69
<=> ! [X58] :
( ~ class_LOrder_Ojoin__semilorder(X58)
| class_Orderings_Oorder(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f462,axiom,
! [X58] :
( ~ class_LOrder_Ojoin__semilorder(X58)
| class_Orderings_Oorder(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f1699,plain,
spl0_68,
inference(avatar_split_clause,[],[f461,f1697]) ).
fof(f1697,plain,
( spl0_68
<=> ! [X58] :
( ~ class_LOrder_Ojoin__semilorder(X58)
| class_Orderings_Oord(X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f461,axiom,
! [X58] :
( ~ class_LOrder_Ojoin__semilorder(X58)
| class_Orderings_Oord(X58) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f1695,plain,
spl0_67,
inference(avatar_split_clause,[],[f306,f1693]) ).
fof(f306,axiom,
! [X1,X9] : c_in(X9,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f1691,plain,
spl0_66,
inference(avatar_split_clause,[],[f274,f1689]) ).
fof(f1689,plain,
( spl0_66
<=> ! [X24] : ~ c_less(X24,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f274,axiom,
! [X24] : ~ c_less(X24,X24,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f1687,plain,
spl0_65,
inference(avatar_split_clause,[],[f272,f1685]) ).
fof(f1685,plain,
( spl0_65
<=> ! [X24] : c_lessequals(c_0,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f272,axiom,
! [X24] : c_lessequals(c_0,X24,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f1683,plain,
spl0_64,
inference(avatar_split_clause,[],[f248,f1681]) ).
fof(f248,axiom,
! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f1679,plain,
spl0_63,
inference(avatar_split_clause,[],[f247,f1677]) ).
fof(f247,axiom,
! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f1675,plain,
spl0_62,
inference(avatar_split_clause,[],[f231,f1673]) ).
fof(f1673,plain,
( spl0_62
<=> ! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f231,axiom,
! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f1671,plain,
spl0_61,
inference(avatar_split_clause,[],[f184,f1669]) ).
fof(f184,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f1667,plain,
spl0_60,
inference(avatar_split_clause,[],[f130,f1665]) ).
fof(f1665,plain,
( spl0_60
<=> ! [X24] : ~ c_less(X24,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f130,axiom,
! [X24] : ~ c_less(X24,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
fof(f1663,plain,
spl0_59,
inference(avatar_split_clause,[],[f125,f1660]) ).
fof(f125,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).
fof(f1658,plain,
spl0_58,
inference(avatar_split_clause,[],[f113,f1656]) ).
fof(f1656,plain,
( spl0_58
<=> ! [X18] : c_0 != c_Suc(X18) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f113,axiom,
! [X18] : c_0 != c_Suc(X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
fof(f1654,plain,
spl0_57,
inference(avatar_split_clause,[],[f457,f1652]) ).
fof(f1652,plain,
( spl0_57
<=> ! [X56] : class_Orderings_Oorder(tc_set(X56)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f457,axiom,
! [X56] : class_Orderings_Oorder(tc_set(X56)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f1650,plain,
spl0_56,
inference(avatar_split_clause,[],[f456,f1648]) ).
fof(f1648,plain,
( spl0_56
<=> ! [X56] : class_Orderings_Oord(tc_set(X56)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f456,axiom,
! [X56] : class_Orderings_Oord(tc_set(X56)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f1646,plain,
spl0_55,
inference(avatar_split_clause,[],[f334,f1643]) ).
fof(f1643,plain,
( spl0_55
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f334,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f1641,plain,
spl0_54,
inference(avatar_split_clause,[],[f332,f1638]) ).
fof(f1638,plain,
( spl0_54
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f332,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f1636,plain,
spl0_53,
inference(avatar_split_clause,[],[f331,f1634]) ).
fof(f1634,plain,
( spl0_53
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f331,axiom,
! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f1632,plain,
~ spl0_52,
inference(avatar_split_clause,[],[f176,f1629]) ).
fof(f1629,plain,
( spl0_52
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f176,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
fof(f1627,plain,
~ spl0_51,
inference(avatar_split_clause,[],[f132,f1624]) ).
fof(f1624,plain,
( spl0_51
<=> c_Numeral_Obit_OB0 = c_Numeral_Obit_OB1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f132,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2__iff1_0) ).
fof(f1622,plain,
~ spl0_50,
inference(avatar_split_clause,[],[f39,f1619]) ).
fof(f1619,plain,
( spl0_50
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f39,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).
fof(f1617,plain,
~ spl0_49,
inference(avatar_split_clause,[],[f1371,f1614]) ).
fof(f1371,axiom,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1612,plain,
spl0_48,
inference(avatar_split_clause,[],[f452,f1609]) ).
fof(f1609,plain,
( spl0_48
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f452,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f1607,plain,
spl0_47,
inference(avatar_split_clause,[],[f451,f1604]) ).
fof(f1604,plain,
( spl0_47
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f451,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f1602,plain,
spl0_46,
inference(avatar_split_clause,[],[f450,f1599]) ).
fof(f1599,plain,
( spl0_46
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f450,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f1597,plain,
spl0_45,
inference(avatar_split_clause,[],[f449,f1594]) ).
fof(f1594,plain,
( spl0_45
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f449,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f1592,plain,
spl0_44,
inference(avatar_split_clause,[],[f444,f1589]) ).
fof(f1589,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f444,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f1587,plain,
spl0_43,
inference(avatar_split_clause,[],[f443,f1584]) ).
fof(f1584,plain,
( spl0_43
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f443,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f1582,plain,
spl0_42,
inference(avatar_split_clause,[],[f442,f1579]) ).
fof(f1579,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f442,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f1577,plain,
spl0_41,
inference(avatar_split_clause,[],[f441,f1574]) ).
fof(f1574,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f441,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f1572,plain,
spl0_40,
inference(avatar_split_clause,[],[f440,f1569]) ).
fof(f1569,plain,
( spl0_40
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f440,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f1567,plain,
spl0_39,
inference(avatar_split_clause,[],[f439,f1564]) ).
fof(f1564,plain,
( spl0_39
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f439,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f1562,plain,
spl0_38,
inference(avatar_split_clause,[],[f438,f1559]) ).
fof(f1559,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f438,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f1557,plain,
spl0_37,
inference(avatar_split_clause,[],[f437,f1554]) ).
fof(f1554,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f437,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f1552,plain,
spl0_36,
inference(avatar_split_clause,[],[f436,f1549]) ).
fof(f1549,plain,
( spl0_36
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f436,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f1547,plain,
spl0_35,
inference(avatar_split_clause,[],[f435,f1544]) ).
fof(f1544,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f435,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f1542,plain,
spl0_34,
inference(avatar_split_clause,[],[f434,f1539]) ).
fof(f1539,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f434,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f1537,plain,
spl0_33,
inference(avatar_split_clause,[],[f433,f1534]) ).
fof(f1534,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f433,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f1532,plain,
spl0_32,
inference(avatar_split_clause,[],[f429,f1529]) ).
fof(f1529,plain,
( spl0_32
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f429,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f1527,plain,
spl0_31,
inference(avatar_split_clause,[],[f418,f1524]) ).
fof(f1524,plain,
( spl0_31
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f418,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f1522,plain,
spl0_30,
inference(avatar_split_clause,[],[f403,f1519]) ).
fof(f1519,plain,
( spl0_30
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f403,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f1517,plain,
spl0_29,
inference(avatar_split_clause,[],[f402,f1514]) ).
fof(f1514,plain,
( spl0_29
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f402,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f1512,plain,
spl0_28,
inference(avatar_split_clause,[],[f391,f1509]) ).
fof(f1509,plain,
( spl0_28
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f391,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f1507,plain,
spl0_27,
inference(avatar_split_clause,[],[f389,f1504]) ).
fof(f1504,plain,
( spl0_27
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f389,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f1502,plain,
spl0_26,
inference(avatar_split_clause,[],[f388,f1499]) ).
fof(f1499,plain,
( spl0_26
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f388,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f1497,plain,
spl0_25,
inference(avatar_split_clause,[],[f386,f1494]) ).
fof(f1494,plain,
( spl0_25
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f386,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f1492,plain,
spl0_24,
inference(avatar_split_clause,[],[f385,f1489]) ).
fof(f1489,plain,
( spl0_24
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f385,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f1487,plain,
spl0_23,
inference(avatar_split_clause,[],[f384,f1484]) ).
fof(f1484,plain,
( spl0_23
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f384,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f1482,plain,
spl0_22,
inference(avatar_split_clause,[],[f383,f1479]) ).
fof(f1479,plain,
( spl0_22
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f383,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f1477,plain,
spl0_21,
inference(avatar_split_clause,[],[f382,f1474]) ).
fof(f1474,plain,
( spl0_21
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f382,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f1472,plain,
spl0_20,
inference(avatar_split_clause,[],[f381,f1469]) ).
fof(f1469,plain,
( spl0_20
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f381,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f1467,plain,
spl0_19,
inference(avatar_split_clause,[],[f380,f1464]) ).
fof(f1464,plain,
( spl0_19
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f380,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f1462,plain,
spl0_18,
inference(avatar_split_clause,[],[f379,f1459]) ).
fof(f1459,plain,
( spl0_18
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f379,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f1457,plain,
spl0_17,
inference(avatar_split_clause,[],[f378,f1454]) ).
fof(f1454,plain,
( spl0_17
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f378,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f1452,plain,
spl0_16,
inference(avatar_split_clause,[],[f377,f1449]) ).
fof(f1449,plain,
( spl0_16
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f377,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f1447,plain,
spl0_15,
inference(avatar_split_clause,[],[f376,f1444]) ).
fof(f1444,plain,
( spl0_15
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f376,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f1442,plain,
spl0_14,
inference(avatar_split_clause,[],[f375,f1439]) ).
fof(f1439,plain,
( spl0_14
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f375,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f1437,plain,
spl0_13,
inference(avatar_split_clause,[],[f374,f1434]) ).
fof(f1434,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f374,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f1432,plain,
spl0_12,
inference(avatar_split_clause,[],[f373,f1429]) ).
fof(f1429,plain,
( spl0_12
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f373,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f1427,plain,
spl0_11,
inference(avatar_split_clause,[],[f372,f1424]) ).
fof(f1424,plain,
( spl0_11
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f372,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f1422,plain,
spl0_10,
inference(avatar_split_clause,[],[f370,f1419]) ).
fof(f1419,plain,
( spl0_10
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f370,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f1417,plain,
spl0_9,
inference(avatar_split_clause,[],[f369,f1414]) ).
fof(f1414,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f369,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f1412,plain,
spl0_8,
inference(avatar_split_clause,[],[f368,f1409]) ).
fof(f1409,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f368,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f1407,plain,
spl0_7,
inference(avatar_split_clause,[],[f367,f1404]) ).
fof(f1404,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f367,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f1402,plain,
spl0_6,
inference(avatar_split_clause,[],[f366,f1399]) ).
fof(f1399,plain,
( spl0_6
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f366,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f1397,plain,
spl0_5,
inference(avatar_split_clause,[],[f365,f1394]) ).
fof(f1394,plain,
( spl0_5
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f365,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f1392,plain,
spl0_4,
inference(avatar_split_clause,[],[f364,f1389]) ).
fof(f1389,plain,
( spl0_4
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f364,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f1387,plain,
spl0_3,
inference(avatar_split_clause,[],[f363,f1384]) ).
fof(f1384,plain,
( spl0_3
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f363,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f1382,plain,
spl0_2,
inference(avatar_split_clause,[],[f362,f1379]) ).
fof(f1379,plain,
( spl0_2
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f362,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f1377,plain,
spl0_1,
inference(avatar_split_clause,[],[f1370,f1374]) ).
fof(f1370,axiom,
c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL447-1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 23:12:18 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (2390)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.41 % (2393)WARNING: value z3 for option sas not known
% 0.22/0.41 % (2394)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.41 % (2392)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.41 % (2395)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)
% 0.22/0.41 % (2393)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)
% 0.22/0.41 % (2391)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.41 % (2396)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)
% 0.22/0.41 % (2397)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.47 TRYING [1]
% 0.22/0.49 TRYING [2]
% 0.22/0.57 % (2395)First to succeed.
% 0.22/0.58 TRYING [3]
% 1.49/0.59 % (2395)Refutation found. Thanks to Tanya!
% 1.49/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.49/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.56/0.61 % (2395)------------------------------
% 1.56/0.61 % (2395)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.56/0.61 % (2395)Termination reason: Refutation
% 1.56/0.61
% 1.56/0.61 % (2395)Memory used [KB]: 4354
% 1.56/0.61 % (2395)Time elapsed: 0.179 s
% 1.56/0.61 % (2395)Instructions burned: 361 (million)
% 1.56/0.61 % (2395)------------------------------
% 1.56/0.61 % (2395)------------------------------
% 1.56/0.61 % (2390)Success in time 0.241 s
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