TSTP Solution File: SET851-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET851-1 : 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:19:19 EDT 2024
% Result : Unsatisfiable 0.23s 0.48s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 980
% Syntax : Number of formulae : 1524 ( 603 unt; 0 def)
% Number of atoms : 2946 ( 269 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 2372 ( 950 ~; 922 |; 0 &)
% ( 500 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 538 ( 536 usr; 501 prp; 0-3 aty)
% Number of functors : 86 ( 86 usr; 21 con; 0-4 aty)
% Number of variables : 1597 (1597 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4077,plain,
$false,
inference(avatar_sat_refutation,[],[f1373,f1378,f1383,f1388,f1393,f1398,f1403,f1408,f1413,f1418,f1423,f1428,f1433,f1438,f1443,f1448,f1453,f1458,f1463,f1468,f1473,f1478,f1483,f1488,f1493,f1498,f1503,f1508,f1513,f1518,f1523,f1528,f1533,f1538,f1543,f1548,f1553,f1558,f1563,f1568,f1573,f1578,f1583,f1588,f1593,f1598,f1603,f1608,f1613,f1618,f1623,f1628,f1633,f1638,f1642,f1647,f1652,f1656,f1660,f1669,f1673,f1678,f1682,f1686,f1690,f1694,f1698,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1866,f1870,f1874,f1878,f1882,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f1918,f1922,f1926,f1930,f1934,f1938,f1942,f1946,f1950,f1954,f1958,f1962,f1966,f1970,f1974,f1978,f1982,f1986,f1990,f1994,f1998,f2002,f2006,f2010,f2014,f2018,f2022,f2026,f2030,f2034,f2038,f2042,f2046,f2050,f2054,f2058,f2062,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2094,f2098,f2102,f2106,f2110,f2114,f2118,f2122,f2126,f2130,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2162,f2166,f2170,f2174,f2178,f2182,f2186,f2190,f2194,f2198,f2202,f2206,f2210,f2214,f2218,f2222,f2226,f2230,f2234,f2238,f2242,f2246,f2250,f2254,f2258,f2262,f2266,f2270,f2274,f2278,f2282,f2286,f2290,f2294,f2298,f2302,f2306,f2310,f2314,f2318,f2322,f2326,f2330,f2334,f2338,f2342,f2346,f2350,f2354,f2358,f2362,f2366,f2370,f2374,f2378,f2382,f2386,f2390,f2394,f2398,f2402,f2406,f2410,f2414,f2418,f2422,f2426,f2430,f2434,f2438,f2442,f2446,f2450,f2454,f2458,f2462,f2466,f2470,f2474,f2478,f2482,f2486,f2490,f2494,f2498,f2502,f2506,f2510,f2514,f2518,f2522,f2526,f2530,f2534,f2538,f2542,f2546,f2550,f2554,f2558,f2562,f2566,f2877,f2882,f2886,f2890,f2894,f2898,f2902,f2906,f2910,f2914,f2918,f2922,f2926,f2930,f2934,f2938,f2942,f2946,f2951,f2955,f2959,f2963,f2967,f2972,f2976,f2981,f2985,f2989,f2993,f2997,f3001,f3005,f3009,f3013,f3017,f3021,f3031,f3035,f3039,f3043,f3058,f3068,f3072,f3076,f3080,f3084,f3088,f3092,f3096,f3100,f3104,f3109,f3113,f3117,f3121,f3125,f3129,f3133,f3137,f3141,f3145,f3155,f3159,f3163,f3167,f3171,f3175,f3179,f3183,f3187,f3191,f3195,f3199,f3203,f3207,f3211,f3215,f3219,f3223,f3227,f3231,f3235,f3239,f3243,f3261,f3266,f3270,f3276,f3280,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3318,f3322,f3326,f3330,f3334,f3338,f3342,f3346,f3350,f3354,f3399,f3404,f3408,f3412,f3416,f3420,f3424,f3428,f3432,f3436,f3440,f3449,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3491,f3495,f3499,f3503,f3507,f3511,f3515,f3519,f3523,f3527,f3531,f3535,f3539,f3543,f3547,f3551,f3555,f3559,f3563,f3567,f3571,f3575,f3579,f3583,f3587,f3600,f3617,f3629,f3663,f3667,f3671,f3675,f3679,f3683,f3687,f3691,f3695,f3699,f3703,f3707,f3711,f3716,f3720,f3724,f3738,f3760,f3764,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3796,f3800,f3804,f3808,f3813,f3817,f3834,f3880,f3884,f3888,f3892,f3896,f3900,f3904,f3908,f3912,f3916,f3920,f3924,f3928,f3932,f3937,f3941,f3945,f3949,f3953,f3979,f4055,f4059,f4063,f4067,f4071,f4075,f4076]) ).
fof(f4076,plain,
( ~ spl0_60
| spl0_51
| ~ spl0_493 ),
inference(avatar_split_clause,[],[f4050,f3951,f1620,f1662]) ).
fof(f1662,plain,
( spl0_60
<=> c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1620,plain,
( spl0_51
<=> c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f3951,plain,
( spl0_493
<=> ! [X40,X0,X23,X2] :
( ~ c_lessequals(X0,X23,tc_set(tc_set(X2)))
| c_lessequals(X0,c_Zorn_Osucc(X40,X23,X2),tc_set(tc_set(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f4050,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| spl0_51
| ~ spl0_493 ),
inference(resolution,[],[f3952,f1622]) ).
fof(f1622,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| spl0_51 ),
inference(avatar_component_clause,[],[f1620]) ).
fof(f3952,plain,
( ! [X40,X2,X0,X23] :
( c_lessequals(X0,c_Zorn_Osucc(X40,X23,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X23,tc_set(tc_set(X2))) )
| ~ spl0_493 ),
inference(avatar_component_clause,[],[f3951]) ).
fof(f4075,plain,
spl0_500,
inference(avatar_split_clause,[],[f156,f4073]) ).
fof(f4073,plain,
( spl0_500
<=> ! [X13,X2,X15] :
( ~ c_lessequals(X15,X13,tc_set(X2))
| c_lessequals(c_uminus(X13,tc_set(X2)),c_uminus(X15,tc_set(X2)),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f156,axiom,
! [X2,X15,X13] :
( ~ c_lessequals(X15,X13,tc_set(X2))
| c_lessequals(c_uminus(X13,tc_set(X2)),c_uminus(X15,tc_set(X2)),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
fof(f4071,plain,
spl0_499,
inference(avatar_split_clause,[],[f155,f4069]) ).
fof(f4069,plain,
( spl0_499
<=> ! [X13,X2,X15] :
( c_lessequals(X15,X13,tc_set(X2))
| ~ c_lessequals(c_uminus(X13,tc_set(X2)),c_uminus(X15,tc_set(X2)),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f155,axiom,
! [X2,X15,X13] :
( c_lessequals(X15,X13,tc_set(X2))
| ~ c_lessequals(c_uminus(X13,tc_set(X2)),c_uminus(X15,tc_set(X2)),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
fof(f4067,plain,
spl0_498,
inference(avatar_split_clause,[],[f84,f4065]) ).
fof(f4065,plain,
( spl0_498
<=> ! [X22,X2,X23] : c_List_Olist_OCons(X23,X22,X2) = c_List_Orev(c_append(c_List_Orev(X22,X2),c_List_Olist_OCons(X23,c_List_Olist_ONil,X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f84,axiom,
! [X2,X22,X23] : c_List_Olist_OCons(X23,X22,X2) = c_List_Orev(c_append(c_List_Orev(X22,X2),c_List_Olist_OCons(X23,c_List_Olist_ONil,X2),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff__iff2_0) ).
fof(f4063,plain,
spl0_497,
inference(avatar_split_clause,[],[f77,f4061]) ).
fof(f4061,plain,
( spl0_497
<=> ! [X2,X21] :
( c_List_Oremdups(X21,X2) = X21
| c_Nat_Osize(X21,tc_List_Olist(X2)) != c_Nat_Osize(c_List_Oremdups(X21,X2),tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f77,axiom,
! [X2,X21] :
( c_List_Oremdups(X21,X2) = X21
| c_Nat_Osize(X21,tc_List_Olist(X2)) != c_Nat_Osize(c_List_Oremdups(X21,X2),tc_List_Olist(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq__iff1_0) ).
fof(f4059,plain,
spl0_496,
inference(avatar_split_clause,[],[f57,f4057]) ).
fof(f4057,plain,
( spl0_496
<=> ! [X22,X2,X14] : ~ c_in(c_Pair(c_List_Olist_ONil,X22,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X14,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f57,axiom,
! [X2,X14,X22] : ~ c_in(c_Pair(c_List_Olist_ONil,X22,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X14,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
fof(f4055,plain,
spl0_495,
inference(avatar_split_clause,[],[f51,f4053]) ).
fof(f4053,plain,
( spl0_495
<=> ! [X2,X21,X14] : ~ c_in(c_Pair(X21,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X14,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f51,axiom,
! [X2,X21,X14] : ~ c_in(c_Pair(X21,c_List_Olist_ONil,tc_List_Olist(X2),tc_List_Olist(X2)),c_List_Olex(X14,X2),tc_prod(tc_List_Olist(X2),tc_List_Olist(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
fof(f3979,plain,
( spl0_474
| ~ spl0_494
| ~ spl0_60
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f3756,f3722,f1662,f3976,f3831]) ).
fof(f3831,plain,
( spl0_474
<=> v_x = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f3976,plain,
( spl0_494
<=> c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f3722,plain,
( spl0_456
<=> ! [X13,X2,X15] :
( X13 = X15
| ~ c_lessequals(X13,X15,tc_set(X2))
| ~ c_lessequals(X15,X13,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f3756,plain,
( ~ c_lessequals(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| v_x = c_Zorn_Osucc(v_S,v_m,t_a)
| ~ spl0_60
| ~ spl0_456 ),
inference(resolution,[],[f3723,f1664]) ).
fof(f1664,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1662]) ).
fof(f3723,plain,
( ! [X2,X15,X13] :
( ~ c_lessequals(X15,X13,tc_set(X2))
| ~ c_lessequals(X13,X15,tc_set(X2))
| X13 = X15 )
| ~ spl0_456 ),
inference(avatar_component_clause,[],[f3722]) ).
fof(f3953,plain,
spl0_493,
inference(avatar_split_clause,[],[f1361,f3951]) ).
fof(f1361,axiom,
! [X2,X40,X0,X23] :
( ~ c_lessequals(X0,X23,tc_set(tc_set(X2)))
| c_lessequals(X0,c_Zorn_Osucc(X40,X23,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f3949,plain,
spl0_492,
inference(avatar_split_clause,[],[f325,f3947]) ).
fof(f3947,plain,
( spl0_492
<=> ! [X49,X50,X5,X2] :
( ~ c_Wellfounded__Recursion_Owf(X49,X5)
| ~ c_Wellfounded__Recursion_Owf(X50,X2)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X50,X49,X2,X5),tc_prod(X2,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f325,axiom,
! [X50,X2,X49,X5] :
( ~ c_Wellfounded__Recursion_Owf(X49,X5)
| ~ c_Wellfounded__Recursion_Owf(X50,X2)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X50,X49,X2,X5),tc_prod(X2,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f3945,plain,
spl0_491,
inference(avatar_split_clause,[],[f323,f3943]) ).
fof(f3943,plain,
( spl0_491
<=> ! [X48,X47,X5,X2] :
( ~ c_Relation_Otrans(X47,X5)
| ~ c_Relation_Otrans(X48,X2)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X48,X47,X2,X5),tc_prod(X2,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f323,axiom,
! [X2,X48,X47,X5] :
( ~ c_Relation_Otrans(X47,X5)
| ~ c_Relation_Otrans(X48,X2)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X48,X47,X2,X5),tc_prod(X2,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f3941,plain,
spl0_490,
inference(avatar_split_clause,[],[f278,f3939]) ).
fof(f3939,plain,
( spl0_490
<=> ! [X13,X2,X34] :
( c_in(c_Main_OdiagE__1(X13,X34,X2),X13,X2)
| ~ c_in(X34,c_Relation_Odiag(X13,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f278,axiom,
! [X2,X34,X13] :
( c_in(c_Main_OdiagE__1(X13,X34,X2),X13,X2)
| ~ c_in(X34,c_Relation_Odiag(X13,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f3937,plain,
spl0_489,
inference(avatar_split_clause,[],[f194,f3935]) ).
fof(f3935,plain,
( spl0_489
<=> ! [X2,X0,X23,X14] :
( c_Wellfounded__Recursion_Owf(X14,X2)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X23,X0,X2,X2),X14,tc_prod(X2,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f194,axiom,
! [X2,X0,X14,X23] :
( c_Wellfounded__Recursion_Owf(X14,X2)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X23,X0,X2,X2),X14,tc_prod(X2,X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
fof(f3932,plain,
spl0_488,
inference(avatar_split_clause,[],[f191,f3930]) ).
fof(f3930,plain,
( spl0_488
<=> ! [X2,X0,X23,X14] :
( c_Wellfounded__Recursion_Oacyclic(X14,X2)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X23,X0,X2,X2),X14,tc_prod(X2,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f191,axiom,
! [X2,X0,X14,X23] :
( c_Wellfounded__Recursion_Oacyclic(X14,X2)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X23,X0,X2,X2),X14,tc_prod(X2,X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
fof(f3928,plain,
spl0_487,
inference(avatar_split_clause,[],[f173,f3926]) ).
fof(f3926,plain,
( spl0_487
<=> ! [X35,X13,X36,X2] :
( ~ c_in(X13,X35,X2)
| ~ c_in(X35,X36,tc_set(X2))
| c_in(X13,c_Union(X36,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f173,axiom,
! [X2,X36,X35,X13] :
( ~ c_in(X13,X35,X2)
| ~ c_in(X35,X36,tc_set(X2))
| c_in(X13,c_Union(X36,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
fof(f3924,plain,
spl0_486,
inference(avatar_split_clause,[],[f169,f3922]) ).
fof(f3922,plain,
( spl0_486
<=> ! [X15,X34,X13,X2] :
( c_in(X34,X13,X2)
| c_in(X34,X15,X2)
| ~ c_in(X34,c_union(X13,X15,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f169,axiom,
! [X2,X34,X15,X13] :
( c_in(X34,X13,X2)
| c_in(X34,X15,X2)
| ~ c_in(X34,c_union(X13,X15,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
fof(f3920,plain,
spl0_485,
inference(avatar_split_clause,[],[f163,f3918]) ).
fof(f3918,plain,
( spl0_485
<=> ! [X35,X13,X36,X2] :
( c_in(X13,X35,X2)
| ~ c_in(X35,X36,tc_set(X2))
| ~ c_in(X13,c_Inter(X36,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f163,axiom,
! [X2,X36,X35,X13] :
( c_in(X13,X35,X2)
| ~ c_in(X35,X36,tc_set(X2))
| ~ c_in(X13,c_Inter(X36,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
fof(f3916,plain,
spl0_484,
inference(avatar_split_clause,[],[f162,f3914]) ).
fof(f3914,plain,
( spl0_484
<=> ! [X15,X34,X13,X2] :
( ~ c_in(X34,X15,X2)
| ~ c_in(X34,X13,X2)
| c_in(X34,c_inter(X13,X15,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f162,axiom,
! [X2,X34,X15,X13] :
( ~ c_in(X34,X15,X2)
| ~ c_in(X34,X13,X2)
| c_in(X34,c_inter(X13,X15,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
fof(f3912,plain,
spl0_483,
inference(avatar_split_clause,[],[f151,f3910]) ).
fof(f3910,plain,
( spl0_483
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X23,X2)
| c_lessequals(c_SetInterval_OlessThan(X0,X2),c_SetInterval_OlessThan(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f151,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X23,X2)
| c_lessequals(c_SetInterval_OlessThan(X0,X2),c_SetInterval_OlessThan(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
fof(f3908,plain,
spl0_482,
inference(avatar_split_clause,[],[f150,f3906]) ).
fof(f3906,plain,
( spl0_482
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X23,X2)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X2),c_SetInterval_OlessThan(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f150,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X23,X2)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X2),c_SetInterval_OlessThan(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
fof(f3904,plain,
spl0_481,
inference(avatar_split_clause,[],[f146,f3902]) ).
fof(f3902,plain,
( spl0_481
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X23,X0,X2)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f146,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X23,X0,X2)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
fof(f3900,plain,
spl0_480,
inference(avatar_split_clause,[],[f145,f3898]) ).
fof(f3898,plain,
( spl0_480
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X23,X0,X2)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f145,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X23,X0,X2)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X2),c_SetInterval_OgreaterThan(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
fof(f3896,plain,
spl0_479,
inference(avatar_split_clause,[],[f141,f3894]) ).
fof(f3894,plain,
( spl0_479
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X0,X23,X2)
| c_lessequals(c_SetInterval_OatMost(X0,X2),c_SetInterval_OatMost(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f141,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X0,X23,X2)
| c_lessequals(c_SetInterval_OatMost(X0,X2),c_SetInterval_OatMost(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
fof(f3892,plain,
spl0_478,
inference(avatar_split_clause,[],[f140,f3890]) ).
fof(f3890,plain,
( spl0_478
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X23,X2)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X2),c_SetInterval_OatMost(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f140,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X23,X2)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X2),c_SetInterval_OatMost(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
fof(f3888,plain,
spl0_477,
inference(avatar_split_clause,[],[f136,f3886]) ).
fof(f3886,plain,
( spl0_477
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X23,X0,X2)
| c_lessequals(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f136,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X23,X0,X2)
| c_lessequals(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
fof(f3884,plain,
spl0_476,
inference(avatar_split_clause,[],[f135,f3882]) ).
fof(f3882,plain,
( spl0_476
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X23,X0,X2)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X23,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f135,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X23,X0,X2)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X2),c_SetInterval_OatLeast(X23,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
fof(f3880,plain,
spl0_475,
inference(avatar_split_clause,[],[f104,f3878]) ).
fof(f3878,plain,
( spl0_475
<=> ! [X18,X12] :
( c_less(c_0,X12,tc_nat)
| c_less(c_0,X18,tc_nat)
| ~ c_less(c_0,c_plus(X12,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f104,axiom,
! [X18,X12] :
( c_less(c_0,X12,tc_nat)
| c_less(c_0,X18,tc_nat)
| ~ c_less(c_0,c_plus(X12,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
fof(f3834,plain,
( spl0_473
| spl0_474
| ~ spl0_60
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f3744,f3714,f1662,f3831,f3827]) ).
fof(f3827,plain,
( spl0_473
<=> c_less(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f3714,plain,
( spl0_454
<=> ! [X13,X2,X15] :
( X13 = X15
| ~ c_lessequals(X13,X15,tc_set(X2))
| c_less(X13,X15,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f3744,plain,
( v_x = c_Zorn_Osucc(v_S,v_m,t_a)
| c_less(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| ~ spl0_60
| ~ spl0_454 ),
inference(resolution,[],[f3715,f1664]) ).
fof(f3715,plain,
( ! [X2,X15,X13] :
( ~ c_lessequals(X13,X15,tc_set(X2))
| X13 = X15
| c_less(X13,X15,tc_set(X2)) )
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f3714]) ).
fof(f3817,plain,
spl0_472,
inference(avatar_split_clause,[],[f317,f3815]) ).
fof(f3815,plain,
( spl0_472
<=> ! [X2,X43,X14] :
( ~ c_in(X43,X14,tc_prod(X2,X2))
| c_in(X43,c_Transitive__Closure_Ortrancl(X14,X2),tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f317,axiom,
! [X2,X14,X43] :
( ~ c_in(X43,X14,tc_prod(X2,X2))
| c_in(X43,c_Transitive__Closure_Ortrancl(X14,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f3813,plain,
spl0_471,
inference(avatar_split_clause,[],[f297,f3811]) ).
fof(f3811,plain,
( spl0_471
<=> ! [X13,X2,X36] :
( ~ c_in(X13,c_Union(X36,X2),X2)
| c_in(c_Main_OUnionE__1(X13,X36,X2),X36,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f297,axiom,
! [X2,X36,X13] :
( ~ c_in(X13,c_Union(X36,X2),X2)
| c_in(c_Main_OUnionE__1(X13,X36,X2),X36,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f3808,plain,
spl0_470,
inference(avatar_split_clause,[],[f294,f3806]) ).
fof(f3806,plain,
( spl0_470
<=> ! [X13,X2,X36] :
( c_in(X13,c_Inter(X36,X2),X2)
| c_in(c_Main_OInterI__1(X13,X36,X2),X36,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f294,axiom,
! [X2,X36,X13] :
( c_in(X13,c_Inter(X36,X2),X2)
| c_in(c_Main_OInterI__1(X13,X36,X2),X36,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f3804,plain,
spl0_469,
inference(avatar_split_clause,[],[f257,f3802]) ).
fof(f3802,plain,
( spl0_469
<=> ! [X42,X13,X0,X2] :
( c_in(X0,X13,X2)
| ~ c_in(c_List_Olist_OCons(X0,X42,X2),c_List_Olists(X13,X2),tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f257,axiom,
! [X2,X0,X42,X13] :
( c_in(X0,X13,X2)
| ~ c_in(c_List_Olist_OCons(X0,X42,X2),c_List_Olists(X13,X2),tc_List_Olist(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f3800,plain,
spl0_468,
inference(avatar_split_clause,[],[f246,f3798]) ).
fof(f3798,plain,
( spl0_468
<=> ! [X13,X2,X21] :
( ~ c_in(c_Main_Oin__listsI__1(X13,X21,X2),X13,X2)
| c_in(X21,c_List_Olists(X13,X2),tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f246,axiom,
! [X2,X21,X13] :
( ~ c_in(c_Main_Oin__listsI__1(X13,X21,X2),X13,X2)
| c_in(X21,c_List_Olists(X13,X2),tc_List_Olist(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f3796,plain,
spl0_467,
inference(avatar_split_clause,[],[f241,f3794]) ).
fof(f3794,plain,
( spl0_467
<=> ! [X12,X39] :
( c_0 != c_Divides_Oop_Amod(X12,X39,tc_IntDef_Oint)
| c_times(X39,c_Main_Ozmod__eq__0D__dest__1(X39,X12),tc_IntDef_Oint) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f241,axiom,
! [X39,X12] :
( c_0 != c_Divides_Oop_Amod(X12,X39,tc_IntDef_Oint)
| c_times(X39,c_Main_Ozmod__eq__0D__dest__1(X39,X12),tc_IntDef_Oint) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f3792,plain,
spl0_466,
inference(avatar_split_clause,[],[f225,f3790]) ).
fof(f3790,plain,
( spl0_466
<=> ! [X12,X39] :
( c_0 != c_Divides_Oop_Amod(X12,X39,tc_nat)
| c_times(X39,c_Main_Omod__eq__0D__dest__1(X39,X12),tc_nat) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f225,axiom,
! [X39,X12] :
( c_0 != c_Divides_Oop_Amod(X12,X39,tc_nat)
| c_times(X39,c_Main_Omod__eq__0D__dest__1(X39,X12),tc_nat) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f3788,plain,
spl0_465,
inference(avatar_split_clause,[],[f198,f3786]) ).
fof(f3786,plain,
( spl0_465
<=> ! [X0,X23] :
( ~ c_less(X0,X23,tc_nat)
| c_in(c_Pair(X0,X23,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f198,axiom,
! [X0,X23] :
( ~ c_less(X0,X23,tc_nat)
| c_in(c_Pair(X0,X23,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_464,
inference(avatar_split_clause,[],[f197,f3782]) ).
fof(f3782,plain,
( spl0_464
<=> ! [X0,X23] :
( c_less(X0,X23,tc_nat)
| ~ c_in(c_Pair(X0,X23,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f197,axiom,
! [X0,X23] :
( c_less(X0,X23,tc_nat)
| ~ c_in(c_Pair(X0,X23,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_463,
inference(avatar_split_clause,[],[f177,f3778]) ).
fof(f3778,plain,
( spl0_463
<=> ! [X4,X13,X6,X2] :
( X4 = X6
| c_in(X4,X13,X2)
| ~ c_in(X4,c_insert(X6,X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f177,axiom,
! [X2,X6,X4,X13] :
( X4 = X6
| c_in(X4,X13,X2)
| ~ c_in(X4,c_insert(X6,X13,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f3776,plain,
spl0_462,
inference(avatar_split_clause,[],[f125,f3774]) ).
fof(f3774,plain,
( spl0_462
<=> ! [X5,X3,X33,X4,X6,X2] :
( X6 = X33
| c_Pair(X4,X6,X2,X5) != c_Pair(X3,X33,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f125,axiom,
! [X2,X3,X6,X4,X5,X33] :
( X6 = X33
| c_Pair(X4,X6,X2,X5) != c_Pair(X3,X33,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
fof(f3772,plain,
spl0_461,
inference(avatar_split_clause,[],[f124,f3770]) ).
fof(f3770,plain,
( spl0_461
<=> ! [X3,X4,X6,X5,X33,X2] :
( X3 = X4
| c_Pair(X4,X6,X2,X5) != c_Pair(X3,X33,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f124,axiom,
! [X2,X3,X6,X4,X5,X33] :
( X3 = X4
| c_Pair(X4,X6,X2,X5) != c_Pair(X3,X33,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
fof(f3768,plain,
( spl0_460
| ~ spl0_60
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f3750,f3718,f1662,f3766]) ).
fof(f3766,plain,
( spl0_460
<=> ! [X0] :
( c_in(X0,v_x,tc_set(t_a))
| ~ c_in(X0,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f3718,plain,
( spl0_455
<=> ! [X15,X34,X13,X2] :
( ~ c_in(X34,X13,X2)
| c_in(X34,X15,X2)
| ~ c_lessequals(X13,X15,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f3750,plain,
( ! [X0] :
( c_in(X0,v_x,tc_set(t_a))
| ~ c_in(X0,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(t_a)) )
| ~ spl0_60
| ~ spl0_455 ),
inference(resolution,[],[f3719,f1664]) ).
fof(f3719,plain,
( ! [X2,X34,X15,X13] :
( ~ c_lessequals(X13,X15,tc_set(X2))
| c_in(X34,X15,X2)
| ~ c_in(X34,X13,X2) )
| ~ spl0_455 ),
inference(avatar_component_clause,[],[f3718]) ).
fof(f3764,plain,
spl0_459,
inference(avatar_split_clause,[],[f19,f3762]) ).
fof(f3762,plain,
( spl0_459
<=> ! [X10,X11,X8,X5,X2,X7] :
( X8 = X11
| c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_OScons(X10,X11,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f19,axiom,
! [X2,X10,X11,X8,X7,X5] :
( X8 = X11
| c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_OScons(X10,X11,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
fof(f3760,plain,
spl0_458,
inference(avatar_split_clause,[],[f18,f3758]) ).
fof(f3758,plain,
( spl0_458
<=> ! [X10,X11,X7,X8,X5,X2] :
( X7 = X10
| c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_OScons(X10,X11,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f18,axiom,
! [X2,X10,X11,X8,X7,X5] :
( X7 = X10
| c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_OScons(X10,X11,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
fof(f3738,plain,
( spl0_457
| ~ spl0_389
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f3712,f3669,f3344,f3736]) ).
fof(f3736,plain,
( spl0_457
<=> ! [X0,X1] : ~ c_less(c_UNIV,X0,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f3344,plain,
( spl0_389
<=> ! [X13,X2,X15] :
( ~ c_less(X13,X15,tc_set(X2))
| ~ c_lessequals(X15,X13,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f3669,plain,
( spl0_443
<=> ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f3712,plain,
( ! [X0,X1] : ~ c_less(c_UNIV,X0,tc_set(X1))
| ~ spl0_389
| ~ spl0_443 ),
inference(resolution,[],[f3670,f3345]) ).
fof(f3345,plain,
( ! [X2,X15,X13] :
( ~ c_lessequals(X15,X13,tc_set(X2))
| ~ c_less(X13,X15,tc_set(X2)) )
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f3344]) ).
fof(f3670,plain,
( ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1))
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f3669]) ).
fof(f3724,plain,
spl0_456,
inference(avatar_split_clause,[],[f309,f3722]) ).
fof(f309,axiom,
! [X2,X15,X13] :
( X13 = X15
| ~ c_lessequals(X13,X15,tc_set(X2))
| ~ c_lessequals(X15,X13,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f3720,plain,
spl0_455,
inference(avatar_split_clause,[],[f306,f3718]) ).
fof(f306,axiom,
! [X2,X34,X15,X13] :
( ~ c_in(X34,X13,X2)
| c_in(X34,X15,X2)
| ~ c_lessequals(X13,X15,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f3716,plain,
spl0_454,
inference(avatar_split_clause,[],[f302,f3714]) ).
fof(f302,axiom,
! [X2,X15,X13] :
( X13 = X15
| ~ c_lessequals(X13,X15,tc_set(X2))
| c_less(X13,X15,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f3711,plain,
spl0_453,
inference(avatar_split_clause,[],[f298,f3709]) ).
fof(f3709,plain,
( spl0_453
<=> ! [X13,X2,X36] :
( ~ c_in(X13,c_Union(X36,X2),X2)
| c_in(X13,c_Main_OUnionE__1(X13,X36,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f298,axiom,
! [X2,X36,X13] :
( ~ c_in(X13,c_Union(X36,X2),X2)
| c_in(X13,c_Main_OUnionE__1(X13,X36,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f3707,plain,
spl0_452,
inference(avatar_split_clause,[],[f295,f3705]) ).
fof(f3705,plain,
( spl0_452
<=> ! [X13,X2,X36] :
( c_in(X13,c_Inter(X36,X2),X2)
| ~ c_in(X13,c_Main_OInterI__1(X13,X36,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f295,axiom,
! [X2,X36,X13] :
( c_in(X13,c_Inter(X36,X2),X2)
| ~ c_in(X13,c_Main_OInterI__1(X13,X36,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f3703,plain,
spl0_451,
inference(avatar_split_clause,[],[f229,f3701]) ).
fof(f3701,plain,
( spl0_451
<=> ! [X2,X16,X17] :
( ~ c_in(X17,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_inter(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f229,axiom,
! [X2,X16,X17] :
( ~ c_in(X17,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_inter(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f3699,plain,
spl0_450,
inference(avatar_split_clause,[],[f228,f3697]) ).
fof(f3697,plain,
( spl0_450
<=> ! [X2,X16,X17] :
( ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_inter(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f228,axiom,
! [X2,X16,X17] :
( ~ c_in(X16,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_inter(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f3695,plain,
spl0_449,
inference(avatar_split_clause,[],[f227,f3693]) ).
fof(f3693,plain,
( spl0_449
<=> ! [X13,X2,X4] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_insert(X4,X13,X2),c_Finite__Set_OFinites,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f227,axiom,
! [X2,X4,X13] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_insert(X4,X13,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f3691,plain,
spl0_448,
inference(avatar_split_clause,[],[f131,f3689]) ).
fof(f3689,plain,
( spl0_448
<=> ! [X6,X4,X2] :
( X4 = X6
| ~ c_in(c_Pair(X4,X6,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f131,axiom,
! [X2,X6,X4] :
( X4 = X6
| ~ c_in(c_Pair(X4,X6,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f3687,plain,
spl0_447,
inference(avatar_split_clause,[],[f41,f3685]) ).
fof(f3685,plain,
( spl0_447
<=> ! [X18,X9,X12] :
( c_Divides_Oop_Advd(X9,X18,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f41,axiom,
! [X18,X9,X12] :
( c_Divides_Oop_Advd(X9,X18,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_1) ).
fof(f3683,plain,
spl0_446,
inference(avatar_split_clause,[],[f40,f3681]) ).
fof(f3681,plain,
( spl0_446
<=> ! [X9,X12,X18] :
( c_Divides_Oop_Advd(X9,X12,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f40,axiom,
! [X18,X9,X12] :
( c_Divides_Oop_Advd(X9,X12,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff__iff1_0) ).
fof(f3679,plain,
spl0_445,
inference(avatar_split_clause,[],[f36,f3677]) ).
fof(f3677,plain,
( spl0_445
<=> ! [X2,X16,X17] :
( c_in(X17,c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_union(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f36,axiom,
! [X2,X16,X17] :
( c_in(X17,c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_union(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
fof(f3675,plain,
spl0_444,
inference(avatar_split_clause,[],[f35,f3673]) ).
fof(f3673,plain,
( spl0_444
<=> ! [X2,X16,X17] :
( c_in(X16,c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_union(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f35,axiom,
! [X2,X16,X17] :
( c_in(X16,c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_union(X16,X17,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
fof(f3671,plain,
( spl0_443
| ~ spl0_71
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f3653,f3581,f1708,f3669]) ).
fof(f1708,plain,
( spl0_71
<=> ! [X2,X0] : c_in(X0,c_UNIV,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f3581,plain,
( spl0_436
<=> ! [X13,X2,X15] :
( c_lessequals(X13,X15,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X13,X15,X2),X15,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f3653,plain,
( ! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1))
| ~ spl0_71
| ~ spl0_436 ),
inference(resolution,[],[f3582,f1709]) ).
fof(f1709,plain,
( ! [X2,X0] : c_in(X0,c_UNIV,X2)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1708]) ).
fof(f3582,plain,
( ! [X2,X15,X13] :
( ~ c_in(c_Main_OsubsetI__1(X13,X15,X2),X15,X2)
| c_lessequals(X13,X15,tc_set(X2)) )
| ~ spl0_436 ),
inference(avatar_component_clause,[],[f3581]) ).
fof(f3667,plain,
spl0_442,
inference(avatar_split_clause,[],[f34,f3665]) ).
fof(f3665,plain,
( spl0_442
<=> ! [X13,X2] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_Pow(X13,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f34,axiom,
! [X2,X13] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X2))
| c_in(c_Pow(X13,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
fof(f3663,plain,
spl0_441,
inference(avatar_split_clause,[],[f33,f3661]) ).
fof(f3661,plain,
( spl0_441
<=> ! [X13,X2] :
( c_in(X13,c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_Pow(X13,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f33,axiom,
! [X2,X13] :
( c_in(X13,c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_Pow(X13,X2),c_Finite__Set_OFinites,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
fof(f3629,plain,
( spl0_440
| ~ spl0_321
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f3371,f3298,f3019,f3627]) ).
fof(f3627,plain,
( spl0_440
<=> ! [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_440])]) ).
fof(f3019,plain,
( spl0_321
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f3298,plain,
( spl0_378
<=> ! [X20,X19] :
( c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X19,tc_IntDef_Oint),X20,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f3371,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_321
| ~ spl0_378 ),
inference(resolution,[],[f3299,f3020]) ).
fof(f3020,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3019]) ).
fof(f3299,plain,
( ! [X19,X20] :
( ~ c_Divides_Oop_Advd(c_uminus(X19,tc_IntDef_Oint),X20,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f3298]) ).
fof(f3617,plain,
( spl0_439
| ~ spl0_320
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f3370,f3298,f3015,f3615]) ).
fof(f3615,plain,
( spl0_439
<=> ! [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_439])]) ).
fof(f3015,plain,
( spl0_320
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3370,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_320
| ~ spl0_378 ),
inference(resolution,[],[f3299,f3016]) ).
fof(f3016,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3015]) ).
fof(f3600,plain,
( spl0_438
| ~ spl0_310
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f3367,f3294,f2974,f3598]) ).
fof(f3598,plain,
( spl0_438
<=> ! [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_438])]) ).
fof(f2974,plain,
( spl0_310
<=> ! [X12] :
( c_0 = X12
| ~ c_Divides_Oop_Advd(c_0,X12,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3294,plain,
( spl0_377
<=> ! [X20,X19] :
( ~ c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X19,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f3367,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_310
| ~ spl0_377 ),
inference(resolution,[],[f3295,f2975]) ).
fof(f2975,plain,
( ! [X12] :
( ~ c_Divides_Oop_Advd(c_0,X12,tc_IntDef_Oint)
| c_0 = X12 )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f2974]) ).
fof(f3295,plain,
( ! [X19,X20] :
( c_Divides_Oop_Advd(X19,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f3294]) ).
fof(f3587,plain,
spl0_437,
inference(avatar_split_clause,[],[f318,f3585]) ).
fof(f3585,plain,
( spl0_437
<=> ! [X2,X4,X14] : c_in(c_Pair(X4,X4,X2,X2),c_Transitive__Closure_Ortrancl(X14,X2),tc_prod(X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f318,axiom,
! [X2,X14,X4] : c_in(c_Pair(X4,X4,X2,X2),c_Transitive__Closure_Ortrancl(X14,X2),tc_prod(X2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f3583,plain,
spl0_436,
inference(avatar_split_clause,[],[f308,f3581]) ).
fof(f308,axiom,
! [X2,X15,X13] :
( c_lessequals(X13,X15,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X13,X15,X2),X15,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f3579,plain,
spl0_435,
inference(avatar_split_clause,[],[f307,f3577]) ).
fof(f3577,plain,
( spl0_435
<=> ! [X13,X2,X15] :
( c_lessequals(X13,X15,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X13,X15,X2),X13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f307,axiom,
! [X2,X15,X13] :
( c_lessequals(X13,X15,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X13,X15,X2),X13,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f3575,plain,
spl0_434,
inference(avatar_split_clause,[],[f247,f3573]) ).
fof(f3573,plain,
( spl0_434
<=> ! [X2,X21] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X21,X2),tc_List_Olist(X2)),c_Nat_Osize(X21,tc_List_Olist(X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f247,axiom,
! [X2,X21] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X21,X2),tc_List_Olist(X2)),c_Nat_Osize(X21,tc_List_Olist(X2)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f3571,plain,
spl0_433,
inference(avatar_split_clause,[],[f200,f3569]) ).
fof(f3569,plain,
( spl0_433
<=> ! [X23,X0,X5,X2] :
( X0 = X23
| c_Datatype__Universe_ONumb(X0,X2,X5) != c_Datatype__Universe_ONumb(X23,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f200,axiom,
! [X2,X0,X5,X23] :
( X0 = X23
| c_Datatype__Universe_ONumb(X0,X2,X5) != c_Datatype__Universe_ONumb(X23,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f3567,plain,
spl0_432,
inference(avatar_split_clause,[],[f199,f3565]) ).
fof(f3565,plain,
( spl0_432
<=> ! [X23,X0,X5,X2] :
( X0 = X23
| c_Datatype__Universe_OLeaf(X0,X2,X5) != c_Datatype__Universe_OLeaf(X23,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f199,axiom,
! [X2,X0,X5,X23] :
( X0 = X23
| c_Datatype__Universe_OLeaf(X0,X2,X5) != c_Datatype__Universe_OLeaf(X23,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f3563,plain,
spl0_431,
inference(avatar_split_clause,[],[f187,f3561]) ).
fof(f3561,plain,
( spl0_431
<=> ! [X23,X0,X5,X2] :
( X0 = X23
| c_Sum__Type_OInr(X0,X5,X2) != c_Sum__Type_OInr(X23,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f187,axiom,
! [X2,X0,X5,X23] :
( X0 = X23
| c_Sum__Type_OInr(X0,X5,X2) != c_Sum__Type_OInr(X23,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
fof(f3559,plain,
spl0_430,
inference(avatar_split_clause,[],[f185,f3557]) ).
fof(f3557,plain,
( spl0_430
<=> ! [X23,X0,X5,X2] :
( X0 = X23
| c_Sum__Type_OInl(X0,X2,X5) != c_Sum__Type_OInl(X23,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f185,axiom,
! [X2,X0,X5,X23] :
( X0 = X23
| c_Sum__Type_OInl(X0,X2,X5) != c_Sum__Type_OInl(X23,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
fof(f3555,plain,
spl0_429,
inference(avatar_split_clause,[],[f179,f3553]) ).
fof(f3553,plain,
( spl0_429
<=> ! [X4,X13,X6,X2] :
( X4 = X6
| c_insert(X4,X13,X2) != c_insert(X6,c_emptyset,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f179,axiom,
! [X2,X6,X4,X13] :
( X4 = X6
| c_insert(X4,X13,X2) != c_insert(X6,c_emptyset,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
fof(f3551,plain,
spl0_428,
inference(avatar_split_clause,[],[f165,f3549]) ).
fof(f3549,plain,
( spl0_428
<=> ! [X13,X2,X15] :
( ~ c_lessequals(X13,X15,tc_set(X2))
| c_in(X13,c_Pow(X15,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f165,axiom,
! [X2,X15,X13] :
( ~ c_lessequals(X13,X15,tc_set(X2))
| c_in(X13,c_Pow(X15,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
fof(f3547,plain,
spl0_427,
inference(avatar_split_clause,[],[f164,f3545]) ).
fof(f3545,plain,
( spl0_427
<=> ! [X13,X2,X15] :
( c_lessequals(X13,X15,tc_set(X2))
| ~ c_in(X13,c_Pow(X15,X2),tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f164,axiom,
! [X2,X15,X13] :
( c_lessequals(X13,X15,tc_set(X2))
| ~ c_in(X13,c_Pow(X15,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
fof(f3543,plain,
spl0_426,
inference(avatar_split_clause,[],[f158,f3541]) ).
fof(f3541,plain,
( spl0_426
<=> ! [X15,X34,X13,X2] :
( c_in(X34,X13,X2)
| ~ c_in(X34,c_minus(X13,X15,tc_set(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f158,axiom,
! [X2,X34,X15,X13] :
( c_in(X34,X13,X2)
| ~ c_in(X34,c_minus(X13,X15,tc_set(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
fof(f3539,plain,
spl0_425,
inference(avatar_split_clause,[],[f157,f3537]) ).
fof(f3537,plain,
( spl0_425
<=> ! [X15,X34,X13,X2] :
( ~ c_in(X34,X15,X2)
| ~ c_in(X34,c_minus(X13,X15,tc_set(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f157,axiom,
! [X2,X34,X15,X13] :
( ~ c_in(X34,X15,X2)
| ~ c_in(X34,c_minus(X13,X15,tc_set(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
fof(f3535,plain,
spl0_424,
inference(avatar_split_clause,[],[f154,f3533]) ).
fof(f3533,plain,
( spl0_424
<=> ! [X13,X2,X15] :
( X13 = X15
| c_uminus(X13,tc_set(X2)) != c_uminus(X15,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f154,axiom,
! [X2,X15,X13] :
( X13 = X15
| c_uminus(X13,tc_set(X2)) != c_uminus(X15,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
fof(f3531,plain,
spl0_423,
inference(avatar_split_clause,[],[f149,f3529]) ).
fof(f3529,plain,
( spl0_423
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| ~ c_less(X31,X9,X2)
| c_in(X31,c_SetInterval_OlessThan(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f149,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| ~ c_less(X31,X9,X2)
| c_in(X31,c_SetInterval_OlessThan(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
fof(f3527,plain,
( spl0_422
| ~ spl0_308
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f3393,f3344,f2965,f3525]) ).
fof(f3525,plain,
( spl0_422
<=> ! [X0] :
( ~ c_less(v_m,c_Zorn_Osucc(v_S,X0,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2965,plain,
( spl0_308
<=> ! [X41] :
( v_m = X41
| ~ c_lessequals(X41,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X41,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X41,t_a),v_m,tc_set(tc_set(t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f3393,plain,
( ! [X0] :
( ~ c_less(v_m,c_Zorn_Osucc(v_S,X0,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = X0 )
| ~ spl0_308
| ~ spl0_389 ),
inference(resolution,[],[f3345,f2966]) ).
fof(f2966,plain,
( ! [X41] :
( c_lessequals(c_Zorn_Osucc(v_S,X41,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_lessequals(X41,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X41,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = X41 )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f2965]) ).
fof(f3523,plain,
spl0_421,
inference(avatar_split_clause,[],[f148,f3521]) ).
fof(f3521,plain,
( spl0_421
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| c_less(X31,X9,X2)
| ~ c_in(X31,c_SetInterval_OlessThan(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f148,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| c_less(X31,X9,X2)
| ~ c_in(X31,c_SetInterval_OlessThan(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
fof(f3519,plain,
spl0_420,
inference(avatar_split_clause,[],[f147,f3517]) ).
fof(f3517,plain,
( spl0_420
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OlessThan(X0,X2) != c_SetInterval_OlessThan(X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f147,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OlessThan(X0,X2) != c_SetInterval_OlessThan(X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
fof(f3515,plain,
spl0_419,
inference(avatar_split_clause,[],[f144,f3513]) ).
fof(f3513,plain,
( spl0_419
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| ~ c_less(X9,X31,X2)
| c_in(X31,c_SetInterval_OgreaterThan(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f144,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| ~ c_less(X9,X31,X2)
| c_in(X31,c_SetInterval_OgreaterThan(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
fof(f3511,plain,
spl0_418,
inference(avatar_split_clause,[],[f143,f3509]) ).
fof(f3509,plain,
( spl0_418
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| c_less(X9,X31,X2)
| ~ c_in(X31,c_SetInterval_OgreaterThan(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f143,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| c_less(X9,X31,X2)
| ~ c_in(X31,c_SetInterval_OgreaterThan(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
fof(f3507,plain,
spl0_417,
inference(avatar_split_clause,[],[f142,f3505]) ).
fof(f3505,plain,
( spl0_417
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OgreaterThan(X0,X2) != c_SetInterval_OgreaterThan(X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f142,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OgreaterThan(X0,X2) != c_SetInterval_OgreaterThan(X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
fof(f3503,plain,
spl0_416,
inference(avatar_split_clause,[],[f139,f3501]) ).
fof(f3501,plain,
( spl0_416
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| ~ c_lessequals(X31,X9,X2)
| c_in(X31,c_SetInterval_OatMost(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f139,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| ~ c_lessequals(X31,X9,X2)
| c_in(X31,c_SetInterval_OatMost(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
fof(f3499,plain,
spl0_415,
inference(avatar_split_clause,[],[f138,f3497]) ).
fof(f3497,plain,
( spl0_415
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| c_lessequals(X31,X9,X2)
| ~ c_in(X31,c_SetInterval_OatMost(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f138,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| c_lessequals(X31,X9,X2)
| ~ c_in(X31,c_SetInterval_OatMost(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
fof(f3495,plain,
spl0_414,
inference(avatar_split_clause,[],[f137,f3493]) ).
fof(f3493,plain,
( spl0_414
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OatMost(X0,X2) != c_SetInterval_OatMost(X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f137,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OatMost(X0,X2) != c_SetInterval_OatMost(X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
fof(f3491,plain,
spl0_413,
inference(avatar_split_clause,[],[f134,f3489]) ).
fof(f3489,plain,
( spl0_413
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| ~ c_lessequals(X9,X31,X2)
| c_in(X31,c_SetInterval_OatLeast(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f134,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| ~ c_lessequals(X9,X31,X2)
| c_in(X31,c_SetInterval_OatLeast(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
fof(f3487,plain,
spl0_412,
inference(avatar_split_clause,[],[f133,f3485]) ).
fof(f3485,plain,
( spl0_412
<=> ! [X2,X9,X31] :
( ~ class_Orderings_Oord(X2)
| c_lessequals(X9,X31,X2)
| ~ c_in(X31,c_SetInterval_OatLeast(X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f133,axiom,
! [X2,X31,X9] :
( ~ class_Orderings_Oord(X2)
| c_lessequals(X9,X31,X2)
| ~ c_in(X31,c_SetInterval_OatLeast(X9,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
fof(f3483,plain,
spl0_411,
inference(avatar_split_clause,[],[f132,f3481]) ).
fof(f3481,plain,
( spl0_411
<=> ! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OatLeast(X0,X2) != c_SetInterval_OatLeast(X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f132,axiom,
! [X2,X0,X23] :
( ~ class_Orderings_Olinorder(X2)
| X0 = X23
| c_SetInterval_OatLeast(X0,X2) != c_SetInterval_OatLeast(X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
fof(f3479,plain,
spl0_410,
inference(avatar_split_clause,[],[f88,f3477]) ).
fof(f3477,plain,
( spl0_410
<=> ! [X2,X24,X21,X22] :
( X22 = X24
| c_append(X21,X22,X2) != c_append(X21,X24,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f88,axiom,
! [X2,X21,X24,X22] :
( X22 = X24
| c_append(X21,X22,X2) != c_append(X21,X24,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
fof(f3475,plain,
spl0_409,
inference(avatar_split_clause,[],[f82,f3473]) ).
fof(f3473,plain,
( spl0_409
<=> ! [X3,X4,X29,X2,X30] :
( X29 = X30
| c_List_Olist_OCons(X3,X29,X2) != c_List_Olist_OCons(X4,X30,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f82,axiom,
! [X2,X3,X29,X4,X30] :
( X29 = X30
| c_List_Olist_OCons(X3,X29,X2) != c_List_Olist_OCons(X4,X30,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
fof(f3471,plain,
spl0_408,
inference(avatar_split_clause,[],[f81,f3469]) ).
fof(f3469,plain,
( spl0_408
<=> ! [X3,X4,X29,X30,X2] :
( X3 = X4
| c_List_Olist_OCons(X3,X29,X2) != c_List_Olist_OCons(X4,X30,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f81,axiom,
! [X2,X3,X29,X4,X30] :
( X3 = X4
| c_List_Olist_OCons(X3,X29,X2) != c_List_Olist_OCons(X4,X30,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
fof(f3467,plain,
spl0_407,
inference(avatar_split_clause,[],[f66,f3465]) ).
fof(f3465,plain,
( spl0_407
<=> ! [X2,X24,X21,X22] :
( X22 = X24
| c_append(X22,X21,X2) != c_append(X24,X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f66,axiom,
! [X2,X21,X24,X22] :
( X22 = X24
| c_append(X22,X21,X2) != c_append(X24,X21,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
fof(f3463,plain,
spl0_406,
inference(avatar_split_clause,[],[f12,f3461]) ).
fof(f3461,plain,
( spl0_406
<=> ! [X7,X8,X5,X2] :
( X7 = X8
| c_Datatype__Universe_OIn1(X8,X2,X5) != c_Datatype__Universe_OIn1(X7,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f12,axiom,
! [X2,X8,X7,X5] :
( X7 = X8
| c_Datatype__Universe_OIn1(X8,X2,X5) != c_Datatype__Universe_OIn1(X7,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
fof(f3459,plain,
spl0_405,
inference(avatar_split_clause,[],[f10,f3457]) ).
fof(f3457,plain,
( spl0_405
<=> ! [X7,X8,X5,X2] :
( X7 = X8
| c_Datatype__Universe_OIn0(X7,X2,X5) != c_Datatype__Universe_OIn0(X8,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f10,axiom,
! [X2,X8,X7,X5] :
( X7 = X8
| c_Datatype__Universe_OIn0(X7,X2,X5) != c_Datatype__Universe_OIn0(X8,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
fof(f3455,plain,
spl0_404,
inference(avatar_split_clause,[],[f8,f3453]) ).
fof(f3453,plain,
( spl0_404
<=> ! [X5,X4,X6,X2] :
( X4 = X6
| c_Datatype__Universe_OAtom(X4,X2,X5) != c_Datatype__Universe_OAtom(X6,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f8,axiom,
! [X2,X6,X4,X5] :
( X4 = X6
| c_Datatype__Universe_OAtom(X4,X2,X5) != c_Datatype__Universe_OAtom(X6,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq__iff1_0) ).
fof(f3449,plain,
( spl0_403
| ~ spl0_296
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f3390,f3344,f2916,f3447]) ).
fof(f3447,plain,
( spl0_403
<=> ! [X0,X1] : ~ c_less(X0,X0,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2916,plain,
( spl0_296
<=> ! [X13,X2] : c_lessequals(X13,X13,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3390,plain,
( ! [X0,X1] : ~ c_less(X0,X0,tc_set(X1))
| ~ spl0_296
| ~ spl0_389 ),
inference(resolution,[],[f3345,f2917]) ).
fof(f2917,plain,
( ! [X2,X13] : c_lessequals(X13,X13,tc_set(X2))
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f2916]) ).
fof(f3440,plain,
spl0_402,
inference(avatar_split_clause,[],[f175,f3438]) ).
fof(f3438,plain,
( spl0_402
<=> ! [X15,X4,X6,X2] :
( ~ c_in(X4,X15,X2)
| c_in(X4,c_insert(X6,X15,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f175,axiom,
! [X2,X6,X4,X15] :
( ~ c_in(X4,X15,X2)
| c_in(X4,c_insert(X6,X15,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
fof(f3436,plain,
spl0_401,
inference(avatar_split_clause,[],[f168,f3434]) ).
fof(f3434,plain,
( spl0_401
<=> ! [X15,X34,X13,X2] :
( ~ c_in(X34,X13,X2)
| c_in(X34,c_union(X13,X15,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f168,axiom,
! [X2,X34,X15,X13] :
( ~ c_in(X34,X13,X2)
| c_in(X34,c_union(X13,X15,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
fof(f3432,plain,
spl0_400,
inference(avatar_split_clause,[],[f167,f3430]) ).
fof(f3430,plain,
( spl0_400
<=> ! [X15,X34,X13,X2] :
( ~ c_in(X34,X15,X2)
| c_in(X34,c_union(X13,X15,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f167,axiom,
! [X2,X34,X15,X13] :
( ~ c_in(X34,X15,X2)
| c_in(X34,c_union(X13,X15,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
fof(f3428,plain,
spl0_399,
inference(avatar_split_clause,[],[f161,f3426]) ).
fof(f3426,plain,
( spl0_399
<=> ! [X15,X34,X13,X2] :
( c_in(X34,X13,X2)
| ~ c_in(X34,c_inter(X13,X15,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f161,axiom,
! [X2,X34,X15,X13] :
( c_in(X34,X13,X2)
| ~ c_in(X34,c_inter(X13,X15,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
fof(f3424,plain,
spl0_398,
inference(avatar_split_clause,[],[f160,f3422]) ).
fof(f3422,plain,
( spl0_398
<=> ! [X15,X34,X13,X2] :
( c_in(X34,X15,X2)
| ~ c_in(X34,c_inter(X13,X15,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f160,axiom,
! [X2,X34,X15,X13] :
( c_in(X34,X15,X2)
| ~ c_in(X34,c_inter(X13,X15,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
fof(f3420,plain,
spl0_397,
inference(avatar_split_clause,[],[f153,f3418]) ).
fof(f3418,plain,
( spl0_397
<=> ! [X13,X2,X34] :
( c_in(X34,X13,X2)
| c_in(X34,c_uminus(X13,tc_set(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f153,axiom,
! [X2,X34,X13] :
( c_in(X34,X13,X2)
| c_in(X34,c_uminus(X13,tc_set(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
fof(f3416,plain,
spl0_396,
inference(avatar_split_clause,[],[f152,f3414]) ).
fof(f3414,plain,
( spl0_396
<=> ! [X13,X2,X34] :
( ~ c_in(X34,X13,X2)
| ~ c_in(X34,c_uminus(X13,tc_set(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f152,axiom,
! [X2,X34,X13] :
( ~ c_in(X34,X13,X2)
| ~ c_in(X34,c_uminus(X13,tc_set(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f3412,plain,
spl0_395,
inference(avatar_split_clause,[],[f106,f3410]) ).
fof(f3410,plain,
( spl0_395
<=> ! [X18,X12] :
( ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_plus(X12,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f106,axiom,
! [X18,X12] :
( ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_plus(X12,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
fof(f3408,plain,
spl0_394,
inference(avatar_split_clause,[],[f105,f3406]) ).
fof(f3406,plain,
( spl0_394
<=> ! [X18,X12] :
( ~ c_less(c_0,X12,tc_nat)
| c_less(c_0,c_plus(X12,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f105,axiom,
! [X18,X12] :
( ~ c_less(c_0,X12,tc_nat)
| c_less(c_0,c_plus(X12,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
fof(f3404,plain,
spl0_393,
inference(avatar_split_clause,[],[f1,f3402]) ).
fof(f3402,plain,
( spl0_393
<=> ! [X2,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X2) = X1
| ~ c_in(X0,c_Datatype_Oo2s(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X2) = X1
| ~ c_in(X0,c_Datatype_Oo2s(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
fof(f3399,plain,
( ~ spl0_392
| ~ spl0_60
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f3394,f3344,f1662,f3396]) ).
fof(f3396,plain,
( spl0_392
<=> c_less(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f3394,plain,
( ~ c_less(v_x,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ spl0_60
| ~ spl0_389 ),
inference(resolution,[],[f3345,f1664]) ).
fof(f3354,plain,
spl0_391,
inference(avatar_split_clause,[],[f303,f3352]) ).
fof(f3352,plain,
( spl0_391
<=> ! [X6,X4,X2] :
( X4 = X6
| ~ c_in(X6,c_insert(X4,c_emptyset,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f303,axiom,
! [X2,X6,X4] :
( X4 = X6
| ~ c_in(X6,c_insert(X4,c_emptyset,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f3350,plain,
spl0_390,
inference(avatar_split_clause,[],[f301,f3348]) ).
fof(f3348,plain,
( spl0_390
<=> ! [X13,X2,X15] :
( ~ c_less(X13,X15,tc_set(X2))
| c_lessequals(X13,X15,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f301,axiom,
! [X2,X15,X13] :
( ~ c_less(X13,X15,tc_set(X2))
| c_lessequals(X13,X15,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f3346,plain,
spl0_389,
inference(avatar_split_clause,[],[f300,f3344]) ).
fof(f300,axiom,
! [X2,X15,X13] :
( ~ c_less(X13,X15,tc_set(X2))
| ~ c_lessequals(X15,X13,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f3342,plain,
spl0_388,
inference(avatar_split_clause,[],[f126,f3340]) ).
fof(f3340,plain,
( spl0_388
<=> ! [X2,X4] : c_in(c_Pair(X4,X4,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f126,axiom,
! [X2,X4] : c_in(c_Pair(X4,X4,X2,X2),c_Relation_OId,tc_prod(X2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
fof(f3338,plain,
spl0_387,
inference(avatar_split_clause,[],[f101,f3336]) ).
fof(f3336,plain,
( spl0_387
<=> ! [X18,X12] :
( ~ c_less(X12,X18,tc_nat)
| c_less(c_Suc(X12),c_Suc(X18),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f101,axiom,
! [X18,X12] :
( ~ c_less(X12,X18,tc_nat)
| c_less(c_Suc(X12),c_Suc(X18),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
fof(f3334,plain,
spl0_386,
inference(avatar_split_clause,[],[f100,f3332]) ).
fof(f3332,plain,
( spl0_386
<=> ! [X18,X12] :
( c_less(X12,X18,tc_nat)
| ~ c_less(c_Suc(X12),c_Suc(X18),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f100,axiom,
! [X18,X12] :
( c_less(X12,X18,tc_nat)
| ~ c_less(c_Suc(X12),c_Suc(X18),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
fof(f3330,plain,
spl0_385,
inference(avatar_split_clause,[],[f99,f3328]) ).
fof(f3328,plain,
( spl0_385
<=> ! [X18,X12] :
( ~ c_lessequals(X18,X12,tc_nat)
| c_lessequals(c_Suc(X18),c_Suc(X12),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f99,axiom,
! [X18,X12] :
( ~ c_lessequals(X18,X12,tc_nat)
| c_lessequals(c_Suc(X18),c_Suc(X12),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
fof(f3326,plain,
spl0_384,
inference(avatar_split_clause,[],[f98,f3324]) ).
fof(f3324,plain,
( spl0_384
<=> ! [X18,X12] :
( c_lessequals(X18,X12,tc_nat)
| ~ c_lessequals(c_Suc(X18),c_Suc(X12),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f98,axiom,
! [X18,X12] :
( c_lessequals(X18,X12,tc_nat)
| ~ c_lessequals(c_Suc(X18),c_Suc(X12),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
fof(f3322,plain,
spl0_383,
inference(avatar_split_clause,[],[f87,f3320]) ).
fof(f3320,plain,
( spl0_383
<=> ! [X22,X2,X21] :
( X21 = X22
| c_List_Orev(X21,X2) != c_List_Orev(X22,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f87,axiom,
! [X2,X21,X22] :
( X21 = X22
| c_List_Orev(X21,X2) != c_List_Orev(X22,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv__iff1_0) ).
fof(f3318,plain,
spl0_382,
inference(avatar_split_clause,[],[f76,f3316]) ).
fof(f3316,plain,
( spl0_382
<=> ! [X2,X21] :
( c_List_Olist_ONil = X21
| c_less(c_0,c_Nat_Osize(X21,tc_List_Olist(X2)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f76,axiom,
! [X2,X21] :
( c_List_Olist_ONil = X21
| c_less(c_0,c_Nat_Osize(X21,tc_List_Olist(X2)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
fof(f3312,plain,
spl0_381,
inference(avatar_split_clause,[],[f72,f3310]) ).
fof(f3310,plain,
( spl0_381
<=> ! [X25,X27,X28,X26] :
( X26 = X28
| c_List_Ochar_OChar(X25,X26) != c_List_Ochar_OChar(X27,X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f72,axiom,
! [X28,X26,X27,X25] :
( X26 = X28
| c_List_Ochar_OChar(X25,X26) != c_List_Ochar_OChar(X27,X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_1) ).
fof(f3308,plain,
spl0_380,
inference(avatar_split_clause,[],[f71,f3306]) ).
fof(f3306,plain,
( spl0_380
<=> ! [X28,X27,X25,X26] :
( X25 = X27
| c_List_Ochar_OChar(X25,X26) != c_List_Ochar_OChar(X27,X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f71,axiom,
! [X28,X26,X27,X25] :
( X25 = X27
| c_List_Ochar_OChar(X25,X26) != c_List_Ochar_OChar(X27,X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject__iff1_0) ).
fof(f3304,plain,
spl0_379,
inference(avatar_split_clause,[],[f50,f3302]) ).
fof(f3302,plain,
( spl0_379
<=> ! [X20,X19] :
( ~ c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X19,tc_IntDef_Oint),X20,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f50,axiom,
! [X19,X20] :
( ~ c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X19,tc_IntDef_Oint),X20,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
fof(f3300,plain,
spl0_378,
inference(avatar_split_clause,[],[f49,f3298]) ).
fof(f49,axiom,
! [X19,X20] :
( c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X19,tc_IntDef_Oint),X20,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
fof(f3296,plain,
spl0_377,
inference(avatar_split_clause,[],[f46,f3294]) ).
fof(f46,axiom,
! [X19,X20] :
( ~ c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X19,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
fof(f3292,plain,
spl0_376,
inference(avatar_split_clause,[],[f45,f3290]) ).
fof(f3290,plain,
( spl0_376
<=> ! [X20,X19] :
( c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X19,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f45,axiom,
! [X19,X20] :
( c_Divides_Oop_Advd(X19,X20,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X19,c_uminus(X20,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
fof(f3288,plain,
spl0_375,
inference(avatar_split_clause,[],[f22,f3286]) ).
fof(f3286,plain,
( spl0_375
<=> ! [X9,X7,X8,X5,X2] : c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_ONumb(X9,X2,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f22,axiom,
! [X2,X8,X9,X7,X5] : c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_ONumb(X9,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb__iff1_0) ).
fof(f3284,plain,
spl0_374,
inference(avatar_split_clause,[],[f21,f3282]) ).
fof(f3282,plain,
( spl0_374
<=> ! [X4,X7,X8,X5,X2] : c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_OLeaf(X4,X2,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f21,axiom,
! [X2,X8,X7,X4,X5] : c_Datatype__Universe_OScons(X7,X8,X2,X5) != c_Datatype__Universe_OLeaf(X4,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf__iff1_0) ).
fof(f3280,plain,
spl0_373,
inference(avatar_split_clause,[],[f20,f3278]) ).
fof(f3278,plain,
( spl0_373
<=> ! [X4,X7,X8,X5,X2] : c_Datatype__Universe_OAtom(X4,X2,X5) != c_Datatype__Universe_OScons(X7,X8,X2,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f20,axiom,
! [X2,X8,X7,X4,X5] : c_Datatype__Universe_OAtom(X4,X2,X5) != c_Datatype__Universe_OScons(X7,X8,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom__iff1_0) ).
fof(f3276,plain,
spl0_372,
inference(avatar_split_clause,[],[f7,f3274]) ).
fof(f3274,plain,
( spl0_372
<=> ! [X4,X2,X3] :
( X3 = X4
| c_Datatype_Ooption_OSome(X3,X2) != c_Datatype_Ooption_OSome(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f7,axiom,
! [X2,X3,X4] :
( X3 = X4
| c_Datatype_Ooption_OSome(X3,X2) != c_Datatype_Ooption_OSome(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
fof(f3270,plain,
spl0_371,
inference(avatar_split_clause,[],[f4,f3268]) ).
fof(f3268,plain,
( spl0_371
<=> ! [X2,X0] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X0,X2),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f4,axiom,
! [X2,X0] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__iff1__1(X0,X2),X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq__iff1_0) ).
fof(f3266,plain,
spl0_370,
inference(avatar_split_clause,[],[f3,f3264]) ).
fof(f3264,plain,
( spl0_370
<=> ! [X2,X0] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X0,X2),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f3,axiom,
! [X2,X0] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__iff1__1(X0,X2),X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq__iff1_0) ).
fof(f3261,plain,
( spl0_369
| ~ spl0_310
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3063,f3019,f2974,f3259]) ).
fof(f3259,plain,
( spl0_369
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f3063,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_310
| ~ spl0_321 ),
inference(resolution,[],[f3020,f2975]) ).
fof(f3243,plain,
( spl0_368
| ~ spl0_310
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3062,f3015,f2974,f3241]) ).
fof(f3241,plain,
( spl0_368
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f3062,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_310
| ~ spl0_320 ),
inference(resolution,[],[f3016,f2975]) ).
fof(f3239,plain,
spl0_367,
inference(avatar_split_clause,[],[f261,f3237]) ).
fof(f3237,plain,
( spl0_367
<=> ! [X2,X14] :
( ~ c_Wellfounded__Recursion_Owf(X14,X2)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X14,X2),tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f261,axiom,
! [X2,X14] :
( ~ c_Wellfounded__Recursion_Owf(X14,X2)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X14,X2),tc_List_Olist(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f3235,plain,
spl0_366,
inference(avatar_split_clause,[],[f260,f3233]) ).
fof(f3233,plain,
( spl0_366
<=> ! [X2,X14] :
( ~ c_Wellfounded__Recursion_Owf(X14,X2)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X14,X2),tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f260,axiom,
! [X2,X14] :
( ~ c_Wellfounded__Recursion_Owf(X14,X2)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X14,X2),tc_List_Olist(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f3231,plain,
spl0_365,
inference(avatar_split_clause,[],[f236,f3229]) ).
fof(f3229,plain,
( spl0_365
<=> ! [X18,X12] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X18)),tc_IntDef_Oint),c_IntDef_Oint(X12),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f236,axiom,
! [X18,X12] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X18)),tc_IntDef_Oint),c_IntDef_Oint(X12),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f3227,plain,
spl0_364,
inference(avatar_split_clause,[],[f233,f3225]) ).
fof(f3225,plain,
( spl0_364
<=> ! [X18,X12] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f233,axiom,
! [X18,X12] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f3223,plain,
spl0_363,
inference(avatar_split_clause,[],[f232,f3221]) ).
fof(f3221,plain,
( spl0_363
<=> ! [X18,X12] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),X12,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f232,axiom,
! [X18,X12] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X12,X18,tc_nat,tc_nat)),X12,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f3219,plain,
spl0_362,
inference(avatar_split_clause,[],[f190,f3217]) ).
fof(f3217,plain,
( spl0_362
<=> ! [X2,X14] :
( ~ c_Wellfounded__Recursion_Oacyclic(X14,X2)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f190,axiom,
! [X2,X14] :
( ~ c_Wellfounded__Recursion_Oacyclic(X14,X2)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
fof(f3215,plain,
spl0_361,
inference(avatar_split_clause,[],[f189,f3213]) ).
fof(f3213,plain,
( spl0_361
<=> ! [X2,X14] :
( c_Wellfounded__Recursion_Oacyclic(X14,X2)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X2,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f189,axiom,
! [X2,X14] :
( c_Wellfounded__Recursion_Oacyclic(X14,X2)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X14,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
fof(f3211,plain,
spl0_360,
inference(avatar_split_clause,[],[f188,f3209]) ).
fof(f3209,plain,
( spl0_360
<=> ! [X6,X2,X5,X4] : c_Sum__Type_OInl(X4,X2,X5) != c_Sum__Type_OInr(X6,X5,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f188,axiom,
! [X2,X6,X4,X5] : c_Sum__Type_OInl(X4,X2,X5) != c_Sum__Type_OInr(X6,X5,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
fof(f3207,plain,
( spl0_359
| ~ spl0_309
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3061,f3011,f2970,f3205]) ).
fof(f3205,plain,
( spl0_359
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2970,plain,
( spl0_309
<=> ! [X12] :
( c_0 = X12
| ~ c_Divides_Oop_Advd(c_0,X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f3011,plain,
( spl0_319
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f3061,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_nat)
| ~ spl0_309
| ~ spl0_319 ),
inference(resolution,[],[f3012,f2971]) ).
fof(f2971,plain,
( ! [X12] :
( ~ c_Divides_Oop_Advd(c_0,X12,tc_nat)
| c_0 = X12 )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f2970]) ).
fof(f3012,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_nat),tc_nat)
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f3011]) ).
fof(f3203,plain,
spl0_358,
inference(avatar_split_clause,[],[f171,f3201]) ).
fof(f3201,plain,
( spl0_358
<=> ! [X13,X2,X15] :
( c_emptyset = X15
| c_emptyset != c_union(X13,X15,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f171,axiom,
! [X2,X15,X13] :
( c_emptyset = X15
| c_emptyset != c_union(X13,X15,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
fof(f3199,plain,
spl0_357,
inference(avatar_split_clause,[],[f170,f3197]) ).
fof(f3197,plain,
( spl0_357
<=> ! [X13,X2,X15] :
( c_emptyset = X13
| c_emptyset != c_union(X13,X15,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f170,axiom,
! [X2,X15,X13] :
( c_emptyset = X13
| c_emptyset != c_union(X13,X15,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
fof(f3195,plain,
spl0_356,
inference(avatar_split_clause,[],[f108,f3193]) ).
fof(f3193,plain,
( spl0_356
<=> ! [X18,X12] :
( c_0 = X18
| c_0 != c_plus(X12,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f108,axiom,
! [X18,X12] :
( c_0 = X18
| c_0 != c_plus(X12,X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
fof(f3191,plain,
spl0_355,
inference(avatar_split_clause,[],[f107,f3189]) ).
fof(f3189,plain,
( spl0_355
<=> ! [X18,X12] :
( c_0 = X12
| c_0 != c_plus(X12,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f107,axiom,
! [X18,X12] :
( c_0 = X12
| c_0 != c_plus(X12,X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
fof(f3187,plain,
spl0_354,
inference(avatar_split_clause,[],[f73,f3185]) ).
fof(f3185,plain,
( spl0_354
<=> ! [X2,X21] :
( c_List_Olist_ONil = X21
| c_0 != c_Nat_Osize(X21,tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f73,axiom,
! [X2,X21] :
( c_List_Olist_ONil = X21
| c_0 != c_Nat_Osize(X21,tc_List_Olist(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
fof(f3183,plain,
spl0_353,
inference(avatar_split_clause,[],[f69,f3181]) ).
fof(f3181,plain,
( spl0_353
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X22
| c_append(X21,X22,X2) != X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f69,axiom,
! [X2,X21,X22] :
( c_List_Olist_ONil = X22
| c_append(X21,X22,X2) != X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
fof(f3179,plain,
spl0_352,
inference(avatar_split_clause,[],[f67,f3177]) ).
fof(f3177,plain,
( spl0_352
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X21
| c_append(X21,X22,X2) != X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f67,axiom,
! [X2,X21,X22] :
( c_List_Olist_ONil = X21
| c_append(X21,X22,X2) != X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
fof(f3175,plain,
spl0_351,
inference(avatar_split_clause,[],[f64,f3173]) ).
fof(f3173,plain,
( spl0_351
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X22
| c_List_Olist_ONil != c_append(X21,X22,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f64,axiom,
! [X2,X21,X22] :
( c_List_Olist_ONil = X22
| c_List_Olist_ONil != c_append(X21,X22,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
fof(f3171,plain,
spl0_350,
inference(avatar_split_clause,[],[f52,f3169]) ).
fof(f3169,plain,
( spl0_350
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X21
| c_List_Olist_ONil != c_append(X21,X22,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f52,axiom,
! [X2,X21,X22] :
( c_List_Olist_ONil = X21
| c_List_Olist_ONil != c_append(X21,X22,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
fof(f3167,plain,
spl0_349,
inference(avatar_split_clause,[],[f25,f3165]) ).
fof(f3165,plain,
( spl0_349
<=> ! [X13,X2,X14] :
( c_emptyset = X13
| c_emptyset != c_Equiv__Relations_Oquotient(X13,X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f25,axiom,
! [X2,X14,X13] :
( c_emptyset = X13
| c_emptyset != c_Equiv__Relations_Oquotient(X13,X14,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff1_0) ).
fof(f3163,plain,
( spl0_348
| ~ spl0_309
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3060,f3007,f2970,f3161]) ).
fof(f3161,plain,
( spl0_348
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f3007,plain,
( spl0_318
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f3060,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_nat)
| ~ spl0_309
| ~ spl0_318 ),
inference(resolution,[],[f3008,f2971]) ).
fof(f3008,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_nat),tc_nat)
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3007]) ).
fof(f3159,plain,
spl0_347,
inference(avatar_split_clause,[],[f14,f3157]) ).
fof(f3157,plain,
( spl0_347
<=> ! [X2,X5,X9,X4] : c_Datatype__Universe_OLeaf(X4,X2,X5) != c_Datatype__Universe_ONumb(X9,X2,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f14,axiom,
! [X2,X9,X4,X5] : c_Datatype__Universe_OLeaf(X4,X2,X5) != c_Datatype__Universe_ONumb(X9,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb__iff1_0) ).
fof(f3155,plain,
spl0_346,
inference(avatar_split_clause,[],[f11,f3153]) ).
fof(f3153,plain,
( spl0_346
<=> ! [X2,X5,X8,X7] : c_Datatype__Universe_OIn0(X7,X2,X5) != c_Datatype__Universe_OIn1(X8,X2,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f11,axiom,
! [X2,X8,X7,X5] : c_Datatype__Universe_OIn0(X7,X2,X5) != c_Datatype__Universe_OIn1(X8,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
fof(f3145,plain,
( ~ spl0_296
| spl0_337 ),
inference(avatar_contradiction_clause,[],[f3143]) ).
fof(f3143,plain,
( $false
| ~ spl0_296
| spl0_337 ),
inference(resolution,[],[f3108,f2917]) ).
fof(f3108,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| spl0_337 ),
inference(avatar_component_clause,[],[f3106]) ).
fof(f3106,plain,
( spl0_337
<=> c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f3141,plain,
spl0_345,
inference(avatar_split_clause,[],[f450,f3139]) ).
fof(f3139,plain,
( spl0_345
<=> ! [X52,X51] :
( ~ class_Finite__Set_Ofinite(X52)
| ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_sum(X52,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f450,axiom,
! [X51,X52] :
( ~ class_Finite__Set_Ofinite(X52)
| ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_sum(X52,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f3137,plain,
spl0_344,
inference(avatar_split_clause,[],[f444,f3135]) ).
fof(f3135,plain,
( spl0_344
<=> ! [X52,X51] :
( ~ class_Finite__Set_Ofinite(X52)
| ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_prod(X52,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f444,axiom,
! [X51,X52] :
( ~ class_Finite__Set_Ofinite(X52)
| ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_prod(X52,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f3133,plain,
spl0_343,
inference(avatar_split_clause,[],[f394,f3131]) ).
fof(f3131,plain,
( spl0_343
<=> ! [X52,X51] :
( ~ class_Finite__Set_Ofinite(X52)
| ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_fun(X52,X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f394,axiom,
! [X51,X52] :
( ~ class_Finite__Set_Ofinite(X52)
| ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_fun(X52,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f3129,plain,
spl0_342,
inference(avatar_split_clause,[],[f292,f3127]) ).
fof(f3127,plain,
( spl0_342
<=> ! [X38,X42] : c_in(c_SetInterval_OgreaterThanLessThan(X42,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f292,axiom,
! [X38,X42] : c_in(c_SetInterval_OgreaterThanLessThan(X42,X38,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(f3125,plain,
spl0_341,
inference(avatar_split_clause,[],[f291,f3123]) ).
fof(f3123,plain,
( spl0_341
<=> ! [X38,X42] : c_in(c_SetInterval_OgreaterThanLessThan(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f291,axiom,
! [X38,X42] : c_in(c_SetInterval_OgreaterThanLessThan(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f3121,plain,
spl0_340,
inference(avatar_split_clause,[],[f290,f3119]) ).
fof(f3119,plain,
( spl0_340
<=> ! [X38,X42] : c_in(c_SetInterval_OgreaterThanAtMost(X42,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f290,axiom,
! [X38,X42] : c_in(c_SetInterval_OgreaterThanAtMost(X42,X38,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(f3117,plain,
spl0_339,
inference(avatar_split_clause,[],[f289,f3115]) ).
fof(f3115,plain,
( spl0_339
<=> ! [X38,X42] : c_in(c_SetInterval_OgreaterThanAtMost(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f289,axiom,
! [X38,X42] : c_in(c_SetInterval_OgreaterThanAtMost(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f3113,plain,
spl0_338,
inference(avatar_split_clause,[],[f287,f3111]) ).
fof(f3111,plain,
( spl0_338
<=> ! [X38,X42] : c_in(c_SetInterval_OatLeastLessThan(X42,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f287,axiom,
! [X38,X42] : c_in(c_SetInterval_OatLeastLessThan(X42,X38,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(f3109,plain,
( ~ spl0_337
| spl0_51
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3024,f2978,f1620,f3106]) ).
fof(f2978,plain,
( spl0_311
<=> v_m = v_x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f3024,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| spl0_51
| ~ spl0_311 ),
inference(superposition,[],[f1622,f2980]) ).
fof(f2980,plain,
( v_m = v_x
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f2978]) ).
fof(f3104,plain,
spl0_336,
inference(avatar_split_clause,[],[f286,f3102]) ).
fof(f3102,plain,
( spl0_336
<=> ! [X38,X42] : c_in(c_SetInterval_OatLeastLessThan(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f286,axiom,
! [X38,X42] : c_in(c_SetInterval_OatLeastLessThan(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f3100,plain,
spl0_335,
inference(avatar_split_clause,[],[f285,f3098]) ).
fof(f3098,plain,
( spl0_335
<=> ! [X38,X42] : c_in(c_SetInterval_OatLeastAtMost(X42,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f285,axiom,
! [X38,X42] : c_in(c_SetInterval_OatLeastAtMost(X42,X38,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(f3096,plain,
spl0_334,
inference(avatar_split_clause,[],[f284,f3094]) ).
fof(f3094,plain,
( spl0_334
<=> ! [X38,X42] : c_in(c_SetInterval_OatLeastAtMost(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f284,axiom,
! [X38,X42] : c_in(c_SetInterval_OatLeastAtMost(X42,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f3092,plain,
spl0_333,
inference(avatar_split_clause,[],[f235,f3090]) ).
fof(f3090,plain,
( spl0_333
<=> ! [X18,X12] : c_lessequals(c_uminus(c_IntDef_Oint(X18),tc_IntDef_Oint),c_IntDef_Oint(X12),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f235,axiom,
! [X18,X12] : c_lessequals(c_uminus(c_IntDef_Oint(X18),tc_IntDef_Oint),c_IntDef_Oint(X12),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f3088,plain,
spl0_332,
inference(avatar_split_clause,[],[f112,f3086]) ).
fof(f3086,plain,
( spl0_332
<=> ! [X18] :
( c_0 = X18
| ~ c_less(X18,c_Suc(c_0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f112,axiom,
! [X18] :
( c_0 = X18
| ~ c_less(X18,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
fof(f3084,plain,
spl0_331,
inference(avatar_split_clause,[],[f97,f3082]) ).
fof(f3082,plain,
( spl0_331
<=> ! [X18,X12] :
( X12 = X18
| c_Suc(X12) != c_Suc(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f97,axiom,
! [X18,X12] :
( X12 = X18
| c_Suc(X12) != c_Suc(X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
fof(f3080,plain,
spl0_330,
inference(avatar_split_clause,[],[f93,f3078]) ).
fof(f3078,plain,
( spl0_330
<=> ! [X2,X21] :
( c_List_Olist_ONil = X21
| c_emptyset != c_List_Oset(X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f93,axiom,
! [X2,X21] :
( c_List_Olist_ONil = X21
| c_emptyset != c_List_Oset(X21,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
fof(f3076,plain,
spl0_329,
inference(avatar_split_clause,[],[f85,f3074]) ).
fof(f3074,plain,
( spl0_329
<=> ! [X2,X21] :
( c_List_Olist_ONil = X21
| c_List_Olist_ONil != c_List_Orev(X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f85,axiom,
! [X2,X21] :
( c_List_Olist_ONil = X21
| c_List_Olist_ONil != c_List_Orev(X21,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv__iff1_0) ).
fof(f3072,plain,
spl0_328,
inference(avatar_split_clause,[],[f44,f3070]) ).
fof(f3070,plain,
( spl0_328
<=> ! [X18,X12] :
( X12 = X18
| c_IntDef_Oint(X12) != c_IntDef_Oint(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f44,axiom,
! [X18,X12] :
( X12 = X18
| c_IntDef_Oint(X12) != c_IntDef_Oint(X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
fof(f3068,plain,
spl0_327,
inference(avatar_split_clause,[],[f2,f3066]) ).
fof(f3066,plain,
( spl0_327
<=> ! [X2,X0] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2,axiom,
! [X2,X0] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X2),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
fof(f3058,plain,
( ~ spl0_326
| spl0_50
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3023,f2978,f1615,f3055]) ).
fof(f3055,plain,
( spl0_326
<=> c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f1615,plain,
( spl0_50
<=> c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f3023,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| spl0_50
| ~ spl0_311 ),
inference(superposition,[],[f1617,f2980]) ).
fof(f1617,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a)))
| spl0_50 ),
inference(avatar_component_clause,[],[f1615]) ).
fof(f3043,plain,
spl0_325,
inference(avatar_split_clause,[],[f293,f3041]) ).
fof(f3041,plain,
( spl0_325
<=> ! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f293,axiom,
! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f3039,plain,
spl0_324,
inference(avatar_split_clause,[],[f288,f3037]) ).
fof(f3037,plain,
( spl0_324
<=> ! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f288,axiom,
! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f3035,plain,
spl0_323,
inference(avatar_split_clause,[],[f259,f3033]) ).
fof(f3033,plain,
( spl0_323
<=> ! [X13,X2] : c_in(c_List_Olist_ONil,c_List_Olists(X13,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f259,axiom,
! [X2,X13] : c_in(c_List_Olist_ONil,c_List_Olists(X13,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f3031,plain,
spl0_322,
inference(avatar_split_clause,[],[f243,f3029]) ).
fof(f3029,plain,
( spl0_322
<=> ! [X2,X21] : c_in(c_List_Oset(X21,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f243,axiom,
! [X2,X21] : c_in(c_List_Oset(X21,X2),c_Finite__Set_OFinites,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f3021,plain,
spl0_321,
inference(avatar_split_clause,[],[f240,f3019]) ).
fof(f240,axiom,
! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f3017,plain,
spl0_320,
inference(avatar_split_clause,[],[f239,f3015]) ).
fof(f239,axiom,
! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f3013,plain,
spl0_319,
inference(avatar_split_clause,[],[f224,f3011]) ).
fof(f224,axiom,
! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f3009,plain,
spl0_318,
inference(avatar_split_clause,[],[f223,f3007]) ).
fof(f223,axiom,
! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f3005,plain,
spl0_317,
inference(avatar_split_clause,[],[f176,f3003]) ).
fof(f3003,plain,
( spl0_317
<=> ! [X2,X0,X15] : c_in(X0,c_insert(X0,X15,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f176,axiom,
! [X2,X0,X15] : c_in(X0,c_insert(X0,X15,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f3001,plain,
spl0_316,
inference(avatar_split_clause,[],[f119,f2999]) ).
fof(f2999,plain,
( spl0_316
<=> ! [X32,X31] : ~ c_less(c_plus(X32,X31,tc_nat),X31,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f119,axiom,
! [X31,X32] : ~ c_less(c_plus(X32,X31,tc_nat),X31,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
fof(f2997,plain,
spl0_315,
inference(avatar_split_clause,[],[f118,f2995]) ).
fof(f2995,plain,
( spl0_315
<=> ! [X32,X31] : ~ c_less(c_plus(X31,X32,tc_nat),X31,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f118,axiom,
! [X31,X32] : ~ c_less(c_plus(X31,X32,tc_nat),X31,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
fof(f2993,plain,
spl0_314,
inference(avatar_split_clause,[],[f116,f2991]) ).
fof(f2991,plain,
( spl0_314
<=> ! [X18] :
( c_0 = X18
| c_less(c_0,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f116,axiom,
! [X18] :
( c_0 = X18
| c_less(c_0,X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
fof(f2989,plain,
spl0_313,
inference(avatar_split_clause,[],[f114,f2987]) ).
fof(f2987,plain,
( spl0_313
<=> ! [X18] :
( c_0 = X18
| ~ c_less(X18,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f114,axiom,
! [X18] :
( c_0 = X18
| ~ c_less(X18,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff1_0) ).
fof(f2985,plain,
spl0_312,
inference(avatar_split_clause,[],[f110,f2983]) ).
fof(f2983,plain,
( spl0_312
<=> ! [X31] :
( c_0 = X31
| ~ c_lessequals(X31,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f110,axiom,
! [X31] :
( c_0 = X31
| ~ c_lessequals(X31,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
fof(f2981,plain,
( spl0_311
| ~ spl0_2
| ~ spl0_61
| spl0_50
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f2968,f2965,f1615,f1666,f1375,f2978]) ).
fof(f1375,plain,
( spl0_2
<=> c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1666,plain,
( spl0_61
<=> c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f2968,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = v_x
| spl0_50
| ~ spl0_308 ),
inference(resolution,[],[f2966,f1617]) ).
fof(f2976,plain,
spl0_310,
inference(avatar_split_clause,[],[f47,f2974]) ).
fof(f47,axiom,
! [X12] :
( c_0 = X12
| ~ c_Divides_Oop_Advd(c_0,X12,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
fof(f2972,plain,
spl0_309,
inference(avatar_split_clause,[],[f23,f2970]) ).
fof(f23,axiom,
! [X12] :
( c_0 = X12
| ~ c_Divides_Oop_Advd(c_0,X12,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
fof(f2967,plain,
spl0_308,
inference(avatar_split_clause,[],[f1367,f2965]) ).
fof(f1367,axiom,
! [X41] :
( v_m = X41
| ~ c_lessequals(X41,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X41,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X41,t_a),v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f2963,plain,
spl0_307,
inference(avatar_split_clause,[],[f266,f2961]) ).
fof(f2961,plain,
( spl0_307
<=> ! [X2,X0] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f266,axiom,
! [X2,X0] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X0,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f2959,plain,
spl0_306,
inference(avatar_split_clause,[],[f172,f2957]) ).
fof(f2957,plain,
( spl0_306
<=> ! [X2] : c_emptyset = c_union(c_emptyset,c_emptyset,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f172,axiom,
! [X2] : c_emptyset = c_union(c_emptyset,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
fof(f2955,plain,
spl0_305,
inference(avatar_split_clause,[],[f123,f2953]) ).
fof(f2953,plain,
( spl0_305
<=> ! [X2,X0] :
( ~ class_Orderings_Oorder(X2)
| ~ c_less(X0,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f123,axiom,
! [X2,X0] :
( ~ class_Orderings_Oorder(X2)
| ~ c_less(X0,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f2951,plain,
spl0_304,
inference(avatar_split_clause,[],[f109,f2948]) ).
fof(f2948,plain,
( spl0_304
<=> c_0 = c_plus(c_0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f109,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(f2946,plain,
spl0_303,
inference(avatar_split_clause,[],[f92,f2944]) ).
fof(f2944,plain,
( spl0_303
<=> ! [X2,X21] : c_append(X21,c_List_Olist_ONil,X2) = X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f92,axiom,
! [X2,X21] : c_append(X21,c_List_Olist_ONil,X2) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
fof(f2942,plain,
spl0_302,
inference(avatar_split_clause,[],[f90,f2940]) ).
fof(f2940,plain,
( spl0_302
<=> ! [X22,X2] : c_append(c_List_Olist_ONil,X22,X2) = X22 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f90,axiom,
! [X2,X22] : c_append(c_List_Olist_ONil,X22,X2) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
fof(f2938,plain,
spl0_301,
inference(avatar_split_clause,[],[f80,f2936]) ).
fof(f2936,plain,
( spl0_301
<=> ! [X29,X2,X3] : c_List_Olist_ONil != c_List_Olist_OCons(X3,X29,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f80,axiom,
! [X2,X3,X29] : c_List_Olist_ONil != c_List_Olist_OCons(X3,X29,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
fof(f2934,plain,
spl0_300,
inference(avatar_split_clause,[],[f74,f2932]) ).
fof(f2932,plain,
( spl0_300
<=> ! [X2] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f74,axiom,
! [X2] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
fof(f2930,plain,
spl0_299,
inference(avatar_split_clause,[],[f26,f2928]) ).
fof(f2928,plain,
( spl0_299
<=> ! [X2,X14] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X14,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f26,axiom,
! [X2,X14] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X14,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2__iff2_0) ).
fof(f2926,plain,
spl0_298,
inference(avatar_split_clause,[],[f448,f2924]) ).
fof(f2924,plain,
( spl0_298
<=> ! [X51] :
( ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_set(X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f448,axiom,
! [X51] :
( ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_set(X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f2922,plain,
spl0_297,
inference(avatar_split_clause,[],[f326,f2920]) ).
fof(f2920,plain,
( spl0_297
<=> ! [X51] :
( ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f326,axiom,
! [X51] :
( ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f2918,plain,
spl0_296,
inference(avatar_split_clause,[],[f310,f2916]) ).
fof(f310,axiom,
! [X2,X13] : c_lessequals(X13,X13,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f2914,plain,
spl0_295,
inference(avatar_split_clause,[],[f299,f2912]) ).
fof(f2912,plain,
( spl0_295
<=> ! [X13,X2] : c_lessequals(c_emptyset,X13,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f299,axiom,
! [X2,X13] : c_lessequals(c_emptyset,X13,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f2910,plain,
spl0_294,
inference(avatar_split_clause,[],[f265,f2908]) ).
fof(f2908,plain,
( spl0_294
<=> ! [X18] : c_less(c_0,c_Suc(X18),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f265,axiom,
! [X18] : c_less(c_0,c_Suc(X18),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f2906,plain,
spl0_293,
inference(avatar_split_clause,[],[f263,f2904]) ).
fof(f2904,plain,
( spl0_293
<=> ! [X18] : c_less(X18,c_Suc(X18),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f263,axiom,
! [X18] : c_less(X18,c_Suc(X18),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f2902,plain,
spl0_292,
inference(avatar_split_clause,[],[f226,f2900]) ).
fof(f2900,plain,
( spl0_292
<=> ! [X2] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f226,axiom,
! [X2] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f2898,plain,
spl0_291,
inference(avatar_split_clause,[],[f222,f2896]) ).
fof(f2896,plain,
( spl0_291
<=> ! [X9] : c_Divides_Oop_Advd(c_Suc(c_0),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f222,axiom,
! [X9] : c_Divides_Oop_Advd(c_Suc(c_0),X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f2894,plain,
spl0_290,
inference(avatar_split_clause,[],[f178,f2892]) ).
fof(f2892,plain,
( spl0_290
<=> ! [X13,X2] : ~ c_less(X13,c_emptyset,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f178,axiom,
! [X2,X13] : ~ c_less(X13,c_emptyset,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
fof(f2890,plain,
spl0_289,
inference(avatar_split_clause,[],[f96,f2888]) ).
fof(f2888,plain,
( spl0_289
<=> ! [X2] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f96,axiom,
! [X2] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
fof(f2886,plain,
spl0_288,
inference(avatar_split_clause,[],[f56,f2884]) ).
fof(f2884,plain,
( spl0_288
<=> ! [X2] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f56,axiom,
! [X2] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv__iff2_0) ).
fof(f2882,plain,
~ spl0_287,
inference(avatar_split_clause,[],[f43,f2879]) ).
fof(f2879,plain,
( spl0_287
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f43,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(f2877,plain,
spl0_286,
inference(avatar_split_clause,[],[f6,f2875]) ).
fof(f2875,plain,
( spl0_286
<=> ! [X2,X3] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f6,axiom,
! [X2,X3] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2__iff1_0) ).
fof(f2566,plain,
spl0_285,
inference(avatar_split_clause,[],[f1357,f2564]) ).
fof(f2564,plain,
( spl0_285
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f1357,axiom,
! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Olinorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f2562,plain,
spl0_284,
inference(avatar_split_clause,[],[f1356,f2560]) ).
fof(f2560,plain,
( spl0_284
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f1356,axiom,
! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f2558,plain,
spl0_283,
inference(avatar_split_clause,[],[f1355,f2556]) ).
fof(f2556,plain,
( spl0_283
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f1355,axiom,
! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f2554,plain,
spl0_282,
inference(avatar_split_clause,[],[f1354,f2552]) ).
fof(f2552,plain,
( spl0_282
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f1354,axiom,
! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f2550,plain,
spl0_281,
inference(avatar_split_clause,[],[f1353,f2548]) ).
fof(f2548,plain,
( spl0_281
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f1353,axiom,
! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f2546,plain,
spl0_280,
inference(avatar_split_clause,[],[f1352,f2544]) ).
fof(f2544,plain,
( spl0_280
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f1352,axiom,
! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f2542,plain,
spl0_279,
inference(avatar_split_clause,[],[f1265,f2540]) ).
fof(f2540,plain,
( spl0_279
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f1265,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f2538,plain,
spl0_278,
inference(avatar_split_clause,[],[f1257,f2536]) ).
fof(f2536,plain,
( spl0_278
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f1257,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f2534,plain,
spl0_277,
inference(avatar_split_clause,[],[f1256,f2532]) ).
fof(f2532,plain,
( spl0_277
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f1256,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f2530,plain,
spl0_276,
inference(avatar_split_clause,[],[f1246,f2528]) ).
fof(f2528,plain,
( spl0_276
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f1246,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f2526,plain,
spl0_275,
inference(avatar_split_clause,[],[f1245,f2524]) ).
fof(f2524,plain,
( spl0_275
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f1245,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f2522,plain,
spl0_274,
inference(avatar_split_clause,[],[f1244,f2520]) ).
fof(f2520,plain,
( spl0_274
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1244,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f2518,plain,
spl0_273,
inference(avatar_split_clause,[],[f1242,f2516]) ).
fof(f2516,plain,
( spl0_273
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f1242,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f2514,plain,
spl0_272,
inference(avatar_split_clause,[],[f1241,f2512]) ).
fof(f2512,plain,
( spl0_272
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f1241,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f2510,plain,
spl0_271,
inference(avatar_split_clause,[],[f1240,f2508]) ).
fof(f2508,plain,
( spl0_271
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1240,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f2506,plain,
spl0_270,
inference(avatar_split_clause,[],[f1239,f2504]) ).
fof(f2504,plain,
( spl0_270
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1239,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f2502,plain,
spl0_269,
inference(avatar_split_clause,[],[f1238,f2500]) ).
fof(f2500,plain,
( spl0_269
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1238,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f2498,plain,
spl0_268,
inference(avatar_split_clause,[],[f1222,f2496]) ).
fof(f2496,plain,
( spl0_268
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1222,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f2494,plain,
spl0_267,
inference(avatar_split_clause,[],[f1221,f2492]) ).
fof(f2492,plain,
( spl0_267
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1221,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f2490,plain,
spl0_266,
inference(avatar_split_clause,[],[f1220,f2488]) ).
fof(f2488,plain,
( spl0_266
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1220,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f2486,plain,
spl0_265,
inference(avatar_split_clause,[],[f1219,f2484]) ).
fof(f2484,plain,
( spl0_265
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1219,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f2482,plain,
spl0_264,
inference(avatar_split_clause,[],[f1187,f2480]) ).
fof(f2480,plain,
( spl0_264
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f1187,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f2478,plain,
spl0_263,
inference(avatar_split_clause,[],[f1178,f2476]) ).
fof(f2476,plain,
( spl0_263
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1178,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f2474,plain,
spl0_262,
inference(avatar_split_clause,[],[f1177,f2472]) ).
fof(f2472,plain,
( spl0_262
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1177,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f2470,plain,
spl0_261,
inference(avatar_split_clause,[],[f1174,f2468]) ).
fof(f2468,plain,
( spl0_261
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1174,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f2466,plain,
spl0_260,
inference(avatar_split_clause,[],[f1164,f2464]) ).
fof(f2464,plain,
( spl0_260
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1164,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f2462,plain,
spl0_259,
inference(avatar_split_clause,[],[f1163,f2460]) ).
fof(f2460,plain,
( spl0_259
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1163,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f2458,plain,
spl0_258,
inference(avatar_split_clause,[],[f1160,f2456]) ).
fof(f2456,plain,
( spl0_258
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1160,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f2454,plain,
spl0_257,
inference(avatar_split_clause,[],[f1159,f2452]) ).
fof(f2452,plain,
( spl0_257
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1159,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f2450,plain,
spl0_256,
inference(avatar_split_clause,[],[f1155,f2448]) ).
fof(f2448,plain,
( spl0_256
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1155,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f2446,plain,
spl0_255,
inference(avatar_split_clause,[],[f1153,f2444]) ).
fof(f2444,plain,
( spl0_255
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1153,axiom,
! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f2442,plain,
spl0_254,
inference(avatar_split_clause,[],[f1152,f2440]) ).
fof(f2440,plain,
( spl0_254
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1152,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f2438,plain,
spl0_253,
inference(avatar_split_clause,[],[f1145,f2436]) ).
fof(f2436,plain,
( spl0_253
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1145,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f2434,plain,
spl0_252,
inference(avatar_split_clause,[],[f1144,f2432]) ).
fof(f2432,plain,
( spl0_252
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1144,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f2430,plain,
spl0_251,
inference(avatar_split_clause,[],[f1139,f2428]) ).
fof(f2428,plain,
( spl0_251
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1139,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f2426,plain,
spl0_250,
inference(avatar_split_clause,[],[f1138,f2424]) ).
fof(f2424,plain,
( spl0_250
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1138,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f2422,plain,
spl0_249,
inference(avatar_split_clause,[],[f1137,f2420]) ).
fof(f2420,plain,
( spl0_249
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f1137,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f2418,plain,
spl0_248,
inference(avatar_split_clause,[],[f1136,f2416]) ).
fof(f2416,plain,
( spl0_248
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1136,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f2414,plain,
spl0_247,
inference(avatar_split_clause,[],[f1135,f2412]) ).
fof(f2412,plain,
( spl0_247
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1135,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f2410,plain,
spl0_246,
inference(avatar_split_clause,[],[f1134,f2408]) ).
fof(f2408,plain,
( spl0_246
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1134,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f2406,plain,
spl0_245,
inference(avatar_split_clause,[],[f1133,f2404]) ).
fof(f2404,plain,
( spl0_245
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f1133,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f2402,plain,
spl0_244,
inference(avatar_split_clause,[],[f1132,f2400]) ).
fof(f2400,plain,
( spl0_244
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1132,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f2398,plain,
spl0_243,
inference(avatar_split_clause,[],[f1131,f2396]) ).
fof(f2396,plain,
( spl0_243
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f1131,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Olinorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f2394,plain,
spl0_242,
inference(avatar_split_clause,[],[f1122,f2392]) ).
fof(f2392,plain,
( spl0_242
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f1122,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f2390,plain,
spl0_241,
inference(avatar_split_clause,[],[f1121,f2388]) ).
fof(f2388,plain,
( spl0_241
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1121,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f2386,plain,
spl0_240,
inference(avatar_split_clause,[],[f1120,f2384]) ).
fof(f2384,plain,
( spl0_240
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1120,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f2382,plain,
spl0_239,
inference(avatar_split_clause,[],[f1119,f2380]) ).
fof(f2380,plain,
( spl0_239
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1119,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f2378,plain,
spl0_238,
inference(avatar_split_clause,[],[f1118,f2376]) ).
fof(f2376,plain,
( spl0_238
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1118,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f2374,plain,
spl0_237,
inference(avatar_split_clause,[],[f1117,f2372]) ).
fof(f2372,plain,
( spl0_237
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1117,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f2370,plain,
spl0_236,
inference(avatar_split_clause,[],[f1116,f2368]) ).
fof(f2368,plain,
( spl0_236
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1116,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f2366,plain,
spl0_235,
inference(avatar_split_clause,[],[f1115,f2364]) ).
fof(f2364,plain,
( spl0_235
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1115,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f2362,plain,
spl0_234,
inference(avatar_split_clause,[],[f1114,f2360]) ).
fof(f2360,plain,
( spl0_234
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1114,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f2358,plain,
spl0_233,
inference(avatar_split_clause,[],[f1113,f2356]) ).
fof(f2356,plain,
( spl0_233
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1113,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f2354,plain,
spl0_232,
inference(avatar_split_clause,[],[f1111,f2352]) ).
fof(f2352,plain,
( spl0_232
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1111,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f2350,plain,
spl0_231,
inference(avatar_split_clause,[],[f1110,f2348]) ).
fof(f2348,plain,
( spl0_231
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1110,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f2346,plain,
spl0_230,
inference(avatar_split_clause,[],[f1109,f2344]) ).
fof(f2344,plain,
( spl0_230
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1109,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Olinorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f2342,plain,
spl0_229,
inference(avatar_split_clause,[],[f1108,f2340]) ).
fof(f2340,plain,
( spl0_229
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1108,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f2338,plain,
spl0_228,
inference(avatar_split_clause,[],[f1107,f2336]) ).
fof(f2336,plain,
( spl0_228
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1107,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f2334,plain,
spl0_227,
inference(avatar_split_clause,[],[f1106,f2332]) ).
fof(f2332,plain,
( spl0_227
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1106,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f2330,plain,
spl0_226,
inference(avatar_split_clause,[],[f1081,f2328]) ).
fof(f2328,plain,
( spl0_226
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1081,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f2326,plain,
spl0_225,
inference(avatar_split_clause,[],[f1080,f2324]) ).
fof(f2324,plain,
( spl0_225
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1080,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f2322,plain,
spl0_224,
inference(avatar_split_clause,[],[f1079,f2320]) ).
fof(f2320,plain,
( spl0_224
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1079,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f2318,plain,
spl0_223,
inference(avatar_split_clause,[],[f1078,f2316]) ).
fof(f2316,plain,
( spl0_223
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1078,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__ring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f2314,plain,
spl0_222,
inference(avatar_split_clause,[],[f1077,f2312]) ).
fof(f2312,plain,
( spl0_222
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Olordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1077,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Olordered__ring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f2310,plain,
spl0_221,
inference(avatar_split_clause,[],[f1076,f2308]) ).
fof(f2308,plain,
( spl0_221
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1076,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f2306,plain,
spl0_220,
inference(avatar_split_clause,[],[f1074,f2304]) ).
fof(f2304,plain,
( spl0_220
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1074,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f2302,plain,
spl0_219,
inference(avatar_split_clause,[],[f1073,f2300]) ).
fof(f2300,plain,
( spl0_219
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Oaxclass__abs__if(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1073,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Oaxclass__abs__if(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f2298,plain,
spl0_218,
inference(avatar_split_clause,[],[f1072,f2296]) ).
fof(f2296,plain,
( spl0_218
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1072,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f2294,plain,
spl0_217,
inference(avatar_split_clause,[],[f1071,f2292]) ).
fof(f2292,plain,
( spl0_217
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1071,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f2290,plain,
spl0_216,
inference(avatar_split_clause,[],[f1070,f2288]) ).
fof(f2288,plain,
( spl0_216
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1070,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f2286,plain,
spl0_215,
inference(avatar_split_clause,[],[f1069,f2284]) ).
fof(f2284,plain,
( spl0_215
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1069,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f2282,plain,
spl0_214,
inference(avatar_split_clause,[],[f1068,f2280]) ).
fof(f2280,plain,
( spl0_214
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1068,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f2278,plain,
spl0_213,
inference(avatar_split_clause,[],[f1067,f2276]) ).
fof(f2276,plain,
( spl0_213
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1067,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f2274,plain,
spl0_212,
inference(avatar_split_clause,[],[f1066,f2272]) ).
fof(f2272,plain,
( spl0_212
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1066,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f2270,plain,
spl0_211,
inference(avatar_split_clause,[],[f1065,f2268]) ).
fof(f2268,plain,
( spl0_211
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1065,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f2266,plain,
spl0_210,
inference(avatar_split_clause,[],[f1063,f2264]) ).
fof(f2264,plain,
( spl0_210
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1063,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f2262,plain,
spl0_209,
inference(avatar_split_clause,[],[f1062,f2260]) ).
fof(f2260,plain,
( spl0_209
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1062,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f2258,plain,
spl0_208,
inference(avatar_split_clause,[],[f1061,f2256]) ).
fof(f2256,plain,
( spl0_208
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1061,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Olinorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f2254,plain,
spl0_207,
inference(avatar_split_clause,[],[f1060,f2252]) ).
fof(f2252,plain,
( spl0_207
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1060,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f2250,plain,
spl0_206,
inference(avatar_split_clause,[],[f1059,f2248]) ).
fof(f2248,plain,
( spl0_206
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1059,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f2246,plain,
spl0_205,
inference(avatar_split_clause,[],[f1045,f2244]) ).
fof(f2244,plain,
( spl0_205
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__semidom(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1045,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__semidom(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f2242,plain,
spl0_204,
inference(avatar_split_clause,[],[f1044,f2240]) ).
fof(f2240,plain,
( spl0_204
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1044,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f2238,plain,
spl0_203,
inference(avatar_split_clause,[],[f1043,f2236]) ).
fof(f2236,plain,
( spl0_203
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1043,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f2234,plain,
spl0_202,
inference(avatar_split_clause,[],[f1042,f2232]) ).
fof(f2232,plain,
( spl0_202
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1042,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f2230,plain,
spl0_201,
inference(avatar_split_clause,[],[f1041,f2228]) ).
fof(f2228,plain,
( spl0_201
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1041,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f2226,plain,
spl0_200,
inference(avatar_split_clause,[],[f1040,f2224]) ).
fof(f2224,plain,
( spl0_200
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1040,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f2222,plain,
spl0_199,
inference(avatar_split_clause,[],[f1038,f2220]) ).
fof(f2220,plain,
( spl0_199
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1038,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__ring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f2218,plain,
spl0_198,
inference(avatar_split_clause,[],[f1037,f2216]) ).
fof(f2216,plain,
( spl0_198
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Olordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1037,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Olordered__ring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f2214,plain,
spl0_197,
inference(avatar_split_clause,[],[f1036,f2212]) ).
fof(f2212,plain,
( spl0_197
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__ring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1036,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__ring__strict(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f2210,plain,
spl0_196,
inference(avatar_split_clause,[],[f1035,f2208]) ).
fof(f2208,plain,
( spl0_196
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oaxclass__abs__if(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1035,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oaxclass__abs__if(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f2206,plain,
spl0_195,
inference(avatar_split_clause,[],[f1034,f2204]) ).
fof(f2204,plain,
( spl0_195
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1034,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f2202,plain,
spl0_194,
inference(avatar_split_clause,[],[f1033,f2200]) ).
fof(f2200,plain,
( spl0_194
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1033,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f2198,plain,
spl0_193,
inference(avatar_split_clause,[],[f1032,f2196]) ).
fof(f2196,plain,
( spl0_193
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1032,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f2194,plain,
spl0_192,
inference(avatar_split_clause,[],[f1031,f2192]) ).
fof(f2192,plain,
( spl0_192
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1031,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f2190,plain,
spl0_191,
inference(avatar_split_clause,[],[f1030,f2188]) ).
fof(f2188,plain,
( spl0_191
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1030,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f2186,plain,
spl0_190,
inference(avatar_split_clause,[],[f1029,f2184]) ).
fof(f2184,plain,
( spl0_190
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1029,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f2182,plain,
spl0_189,
inference(avatar_split_clause,[],[f1027,f2180]) ).
fof(f2180,plain,
( spl0_189
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1027,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f2178,plain,
spl0_188,
inference(avatar_split_clause,[],[f1026,f2176]) ).
fof(f2176,plain,
( spl0_188
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1026,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f2174,plain,
spl0_187,
inference(avatar_split_clause,[],[f1025,f2172]) ).
fof(f2172,plain,
( spl0_187
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1025,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f2170,plain,
spl0_186,
inference(avatar_split_clause,[],[f1024,f2168]) ).
fof(f2168,plain,
( spl0_186
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1024,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f2166,plain,
spl0_185,
inference(avatar_split_clause,[],[f1023,f2164]) ).
fof(f2164,plain,
( spl0_185
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1023,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f2162,plain,
spl0_184,
inference(avatar_split_clause,[],[f1022,f2160]) ).
fof(f2160,plain,
( spl0_184
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1022,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f2158,plain,
spl0_183,
inference(avatar_split_clause,[],[f1021,f2156]) ).
fof(f2156,plain,
( spl0_183
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1021,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Olinorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f2154,plain,
spl0_182,
inference(avatar_split_clause,[],[f1020,f2152]) ).
fof(f2152,plain,
( spl0_182
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1020,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f2150,plain,
spl0_181,
inference(avatar_split_clause,[],[f1019,f2148]) ).
fof(f2148,plain,
( spl0_181
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1019,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f2146,plain,
spl0_180,
inference(avatar_split_clause,[],[f1018,f2144]) ).
fof(f2144,plain,
( spl0_180
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1018,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f2142,plain,
spl0_179,
inference(avatar_split_clause,[],[f925,f2140]) ).
fof(f2140,plain,
( spl0_179
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f925,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f2138,plain,
spl0_178,
inference(avatar_split_clause,[],[f924,f2136]) ).
fof(f2136,plain,
( spl0_178
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f924,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f2134,plain,
spl0_177,
inference(avatar_split_clause,[],[f923,f2132]) ).
fof(f2132,plain,
( spl0_177
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f923,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f2130,plain,
spl0_176,
inference(avatar_split_clause,[],[f921,f2128]) ).
fof(f2128,plain,
( spl0_176
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f921,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f2126,plain,
spl0_175,
inference(avatar_split_clause,[],[f920,f2124]) ).
fof(f2124,plain,
( spl0_175
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f920,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f2122,plain,
spl0_174,
inference(avatar_split_clause,[],[f917,f2120]) ).
fof(f2120,plain,
( spl0_174
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f917,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f2118,plain,
spl0_173,
inference(avatar_split_clause,[],[f916,f2116]) ).
fof(f2116,plain,
( spl0_173
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f916,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f2114,plain,
spl0_172,
inference(avatar_split_clause,[],[f914,f2112]) ).
fof(f2112,plain,
( spl0_172
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f914,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f2110,plain,
spl0_171,
inference(avatar_split_clause,[],[f913,f2108]) ).
fof(f2108,plain,
( spl0_171
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f913,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f2106,plain,
spl0_170,
inference(avatar_split_clause,[],[f912,f2104]) ).
fof(f2104,plain,
( spl0_170
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f912,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f2102,plain,
spl0_169,
inference(avatar_split_clause,[],[f911,f2100]) ).
fof(f2100,plain,
( spl0_169
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f911,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f2098,plain,
spl0_168,
inference(avatar_split_clause,[],[f910,f2096]) ).
fof(f2096,plain,
( spl0_168
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f910,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f2094,plain,
spl0_167,
inference(avatar_split_clause,[],[f909,f2092]) ).
fof(f2092,plain,
( spl0_167
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f909,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f2090,plain,
spl0_166,
inference(avatar_split_clause,[],[f908,f2088]) ).
fof(f2088,plain,
( spl0_166
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f908,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Olinorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f2086,plain,
spl0_165,
inference(avatar_split_clause,[],[f907,f2084]) ).
fof(f2084,plain,
( spl0_165
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f907,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f2082,plain,
spl0_164,
inference(avatar_split_clause,[],[f902,f2080]) ).
fof(f2080,plain,
( spl0_164
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f902,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f2078,plain,
spl0_163,
inference(avatar_split_clause,[],[f901,f2076]) ).
fof(f2076,plain,
( spl0_163
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f901,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f2074,plain,
spl0_162,
inference(avatar_split_clause,[],[f900,f2072]) ).
fof(f2072,plain,
( spl0_162
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f900,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f2070,plain,
spl0_161,
inference(avatar_split_clause,[],[f899,f2068]) ).
fof(f2068,plain,
( spl0_161
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f899,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f2066,plain,
spl0_160,
inference(avatar_split_clause,[],[f898,f2064]) ).
fof(f2064,plain,
( spl0_160
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f898,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f2062,plain,
spl0_159,
inference(avatar_split_clause,[],[f896,f2060]) ).
fof(f2060,plain,
( spl0_159
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f896,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f2058,plain,
spl0_158,
inference(avatar_split_clause,[],[f894,f2056]) ).
fof(f2056,plain,
( spl0_158
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f894,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f2054,plain,
spl0_157,
inference(avatar_split_clause,[],[f893,f2052]) ).
fof(f2052,plain,
( spl0_157
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f893,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f2050,plain,
spl0_156,
inference(avatar_split_clause,[],[f892,f2048]) ).
fof(f2048,plain,
( spl0_156
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f892,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f2046,plain,
spl0_155,
inference(avatar_split_clause,[],[f891,f2044]) ).
fof(f2044,plain,
( spl0_155
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f891,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f2042,plain,
spl0_154,
inference(avatar_split_clause,[],[f890,f2040]) ).
fof(f2040,plain,
( spl0_154
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f890,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f2038,plain,
spl0_153,
inference(avatar_split_clause,[],[f889,f2036]) ).
fof(f2036,plain,
( spl0_153
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f889,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f2034,plain,
spl0_152,
inference(avatar_split_clause,[],[f884,f2032]) ).
fof(f2032,plain,
( spl0_152
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f884,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f2030,plain,
spl0_151,
inference(avatar_split_clause,[],[f875,f2028]) ).
fof(f2028,plain,
( spl0_151
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f875,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f2026,plain,
spl0_150,
inference(avatar_split_clause,[],[f874,f2024]) ).
fof(f2024,plain,
( spl0_150
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f874,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f2022,plain,
spl0_149,
inference(avatar_split_clause,[],[f872,f2020]) ).
fof(f2020,plain,
( spl0_149
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f872,axiom,
! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__ring(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f2018,plain,
spl0_148,
inference(avatar_split_clause,[],[f681,f2016]) ).
fof(f2016,plain,
( spl0_148
<=> ! [X53] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f681,axiom,
! [X53] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f2014,plain,
spl0_147,
inference(avatar_split_clause,[],[f652,f2012]) ).
fof(f2012,plain,
( spl0_147
<=> ! [X53] :
( ~ class_Orderings_Oorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f652,axiom,
! [X53] :
( ~ class_Orderings_Oorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f2010,plain,
spl0_146,
inference(avatar_split_clause,[],[f651,f2008]) ).
fof(f2008,plain,
( spl0_146
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f651,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f2006,plain,
spl0_145,
inference(avatar_split_clause,[],[f650,f2004]) ).
fof(f2004,plain,
( spl0_145
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f650,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f2002,plain,
spl0_144,
inference(avatar_split_clause,[],[f649,f2000]) ).
fof(f2000,plain,
( spl0_144
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f649,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f1998,plain,
spl0_143,
inference(avatar_split_clause,[],[f648,f1996]) ).
fof(f1996,plain,
( spl0_143
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f648,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f1994,plain,
spl0_142,
inference(avatar_split_clause,[],[f647,f1992]) ).
fof(f1992,plain,
( spl0_142
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f647,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f1990,plain,
spl0_141,
inference(avatar_split_clause,[],[f639,f1988]) ).
fof(f1988,plain,
( spl0_141
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f639,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f1986,plain,
spl0_140,
inference(avatar_split_clause,[],[f638,f1984]) ).
fof(f1984,plain,
( spl0_140
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f638,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f1982,plain,
spl0_139,
inference(avatar_split_clause,[],[f637,f1980]) ).
fof(f1980,plain,
( spl0_139
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f637,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f1978,plain,
spl0_138,
inference(avatar_split_clause,[],[f631,f1976]) ).
fof(f1976,plain,
( spl0_138
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f631,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f1974,plain,
spl0_137,
inference(avatar_split_clause,[],[f630,f1972]) ).
fof(f1972,plain,
( spl0_137
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f630,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f1970,plain,
spl0_136,
inference(avatar_split_clause,[],[f629,f1968]) ).
fof(f1968,plain,
( spl0_136
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f629,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f1966,plain,
spl0_135,
inference(avatar_split_clause,[],[f628,f1964]) ).
fof(f1964,plain,
( spl0_135
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f628,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f1962,plain,
spl0_134,
inference(avatar_split_clause,[],[f624,f1960]) ).
fof(f1960,plain,
( spl0_134
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f624,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f1958,plain,
spl0_133,
inference(avatar_split_clause,[],[f623,f1956]) ).
fof(f1956,plain,
( spl0_133
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f623,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f1954,plain,
spl0_132,
inference(avatar_split_clause,[],[f622,f1952]) ).
fof(f1952,plain,
( spl0_132
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f622,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f1950,plain,
spl0_131,
inference(avatar_split_clause,[],[f614,f1948]) ).
fof(f1948,plain,
( spl0_131
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f614,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f1946,plain,
spl0_130,
inference(avatar_split_clause,[],[f613,f1944]) ).
fof(f1944,plain,
( spl0_130
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f613,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f1942,plain,
spl0_129,
inference(avatar_split_clause,[],[f612,f1940]) ).
fof(f1940,plain,
( spl0_129
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f612,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f1938,plain,
spl0_128,
inference(avatar_split_clause,[],[f611,f1936]) ).
fof(f1936,plain,
( spl0_128
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f611,axiom,
! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f1934,plain,
spl0_127,
inference(avatar_split_clause,[],[f608,f1932]) ).
fof(f1932,plain,
( spl0_127
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f608,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Olinorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f1930,plain,
spl0_126,
inference(avatar_split_clause,[],[f602,f1928]) ).
fof(f1928,plain,
( spl0_126
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f602,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f1926,plain,
spl0_125,
inference(avatar_split_clause,[],[f601,f1924]) ).
fof(f1924,plain,
( spl0_125
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f601,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f1922,plain,
spl0_124,
inference(avatar_split_clause,[],[f600,f1920]) ).
fof(f1920,plain,
( spl0_124
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f600,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f1918,plain,
spl0_123,
inference(avatar_split_clause,[],[f599,f1916]) ).
fof(f1916,plain,
( spl0_123
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f599,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f1914,plain,
spl0_122,
inference(avatar_split_clause,[],[f598,f1912]) ).
fof(f1912,plain,
( spl0_122
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f598,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f1910,plain,
spl0_121,
inference(avatar_split_clause,[],[f597,f1908]) ).
fof(f1908,plain,
( spl0_121
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f597,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f1906,plain,
spl0_120,
inference(avatar_split_clause,[],[f596,f1904]) ).
fof(f1904,plain,
( spl0_120
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f596,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f1902,plain,
spl0_119,
inference(avatar_split_clause,[],[f595,f1900]) ).
fof(f1900,plain,
( spl0_119
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f595,axiom,
! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f1898,plain,
spl0_118,
inference(avatar_split_clause,[],[f591,f1896]) ).
fof(f1896,plain,
( spl0_118
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f591,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f1894,plain,
spl0_117,
inference(avatar_split_clause,[],[f590,f1892]) ).
fof(f1892,plain,
( spl0_117
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f590,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f1890,plain,
spl0_116,
inference(avatar_split_clause,[],[f589,f1888]) ).
fof(f1888,plain,
( spl0_116
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f589,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f1886,plain,
spl0_115,
inference(avatar_split_clause,[],[f588,f1884]) ).
fof(f1884,plain,
( spl0_115
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f588,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f1882,plain,
spl0_114,
inference(avatar_split_clause,[],[f587,f1880]) ).
fof(f1880,plain,
( spl0_114
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f587,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f1878,plain,
spl0_113,
inference(avatar_split_clause,[],[f583,f1876]) ).
fof(f1876,plain,
( spl0_113
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f583,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f1874,plain,
spl0_112,
inference(avatar_split_clause,[],[f582,f1872]) ).
fof(f1872,plain,
( spl0_112
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f582,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f1870,plain,
spl0_111,
inference(avatar_split_clause,[],[f581,f1868]) ).
fof(f1868,plain,
( spl0_111
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f581,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f1866,plain,
spl0_110,
inference(avatar_split_clause,[],[f580,f1864]) ).
fof(f1864,plain,
( spl0_110
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f580,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f1862,plain,
spl0_109,
inference(avatar_split_clause,[],[f573,f1860]) ).
fof(f1860,plain,
( spl0_109
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f573,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f1858,plain,
spl0_108,
inference(avatar_split_clause,[],[f572,f1856]) ).
fof(f1856,plain,
( spl0_108
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f572,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f1854,plain,
spl0_107,
inference(avatar_split_clause,[],[f571,f1852]) ).
fof(f1852,plain,
( spl0_107
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f571,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f1850,plain,
spl0_106,
inference(avatar_split_clause,[],[f570,f1848]) ).
fof(f1848,plain,
( spl0_106
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f570,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f1846,plain,
spl0_105,
inference(avatar_split_clause,[],[f569,f1844]) ).
fof(f1844,plain,
( spl0_105
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f569,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f1842,plain,
spl0_104,
inference(avatar_split_clause,[],[f568,f1840]) ).
fof(f1840,plain,
( spl0_104
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f568,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f1838,plain,
spl0_103,
inference(avatar_split_clause,[],[f564,f1836]) ).
fof(f1836,plain,
( spl0_103
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f564,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f1834,plain,
spl0_102,
inference(avatar_split_clause,[],[f563,f1832]) ).
fof(f1832,plain,
( spl0_102
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f563,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f1830,plain,
spl0_101,
inference(avatar_split_clause,[],[f562,f1828]) ).
fof(f1828,plain,
( spl0_101
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f562,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f1826,plain,
spl0_100,
inference(avatar_split_clause,[],[f561,f1824]) ).
fof(f1824,plain,
( spl0_100
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f561,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f1822,plain,
spl0_99,
inference(avatar_split_clause,[],[f554,f1820]) ).
fof(f1820,plain,
( spl0_99
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f554,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f1818,plain,
spl0_98,
inference(avatar_split_clause,[],[f552,f1816]) ).
fof(f1816,plain,
( spl0_98
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f552,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f1814,plain,
spl0_97,
inference(avatar_split_clause,[],[f551,f1812]) ).
fof(f1812,plain,
( spl0_97
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f551,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f1810,plain,
spl0_96,
inference(avatar_split_clause,[],[f550,f1808]) ).
fof(f1808,plain,
( spl0_96
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f550,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f1806,plain,
spl0_95,
inference(avatar_split_clause,[],[f545,f1804]) ).
fof(f1804,plain,
( spl0_95
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f545,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f1802,plain,
spl0_94,
inference(avatar_split_clause,[],[f544,f1800]) ).
fof(f1800,plain,
( spl0_94
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f544,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f1798,plain,
spl0_93,
inference(avatar_split_clause,[],[f543,f1796]) ).
fof(f1796,plain,
( spl0_93
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f543,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f1794,plain,
spl0_92,
inference(avatar_split_clause,[],[f542,f1792]) ).
fof(f1792,plain,
( spl0_92
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f542,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f1790,plain,
spl0_91,
inference(avatar_split_clause,[],[f541,f1788]) ).
fof(f1788,plain,
( spl0_91
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f541,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f1786,plain,
spl0_90,
inference(avatar_split_clause,[],[f536,f1784]) ).
fof(f1784,plain,
( spl0_90
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f536,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f1782,plain,
spl0_89,
inference(avatar_split_clause,[],[f535,f1780]) ).
fof(f1780,plain,
( spl0_89
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f535,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f1778,plain,
spl0_88,
inference(avatar_split_clause,[],[f534,f1776]) ).
fof(f1776,plain,
( spl0_88
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f534,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f1774,plain,
spl0_87,
inference(avatar_split_clause,[],[f533,f1772]) ).
fof(f1772,plain,
( spl0_87
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f533,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f1770,plain,
spl0_86,
inference(avatar_split_clause,[],[f532,f1768]) ).
fof(f1768,plain,
( spl0_86
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f532,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f1766,plain,
spl0_85,
inference(avatar_split_clause,[],[f531,f1764]) ).
fof(f1764,plain,
( spl0_85
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f531,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f1762,plain,
spl0_84,
inference(avatar_split_clause,[],[f530,f1760]) ).
fof(f1760,plain,
( spl0_84
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f530,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f1758,plain,
spl0_83,
inference(avatar_split_clause,[],[f526,f1756]) ).
fof(f1756,plain,
( spl0_83
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f526,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f1754,plain,
spl0_82,
inference(avatar_split_clause,[],[f525,f1752]) ).
fof(f1752,plain,
( spl0_82
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f525,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f1750,plain,
spl0_81,
inference(avatar_split_clause,[],[f524,f1748]) ).
fof(f1748,plain,
( spl0_81
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f524,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f1746,plain,
spl0_80,
inference(avatar_split_clause,[],[f517,f1744]) ).
fof(f1744,plain,
( spl0_80
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f517,axiom,
! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f1742,plain,
spl0_79,
inference(avatar_split_clause,[],[f458,f1740]) ).
fof(f1740,plain,
( spl0_79
<=> ! [X53] :
( ~ class_LOrder_Omeet__semilorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f458,axiom,
! [X53] :
( ~ class_LOrder_Omeet__semilorder(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f1738,plain,
spl0_78,
inference(avatar_split_clause,[],[f457,f1736]) ).
fof(f1736,plain,
( spl0_78
<=> ! [X53] :
( ~ class_LOrder_Omeet__semilorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f457,axiom,
! [X53] :
( ~ class_LOrder_Omeet__semilorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f1734,plain,
spl0_77,
inference(avatar_split_clause,[],[f456,f1732]) ).
fof(f1732,plain,
( spl0_77
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f456,axiom,
! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f1730,plain,
spl0_76,
inference(avatar_split_clause,[],[f455,f1728]) ).
fof(f1728,plain,
( spl0_76
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f455,axiom,
! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f1726,plain,
spl0_75,
inference(avatar_split_clause,[],[f454,f1724]) ).
fof(f1724,plain,
( spl0_75
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f454,axiom,
! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f1722,plain,
spl0_74,
inference(avatar_split_clause,[],[f453,f1720]) ).
fof(f1720,plain,
( spl0_74
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f453,axiom,
! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_LOrder_Omeet__semilorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f1718,plain,
spl0_73,
inference(avatar_split_clause,[],[f452,f1716]) ).
fof(f1716,plain,
( spl0_73
<=> ! [X53] :
( ~ class_LOrder_Ojoin__semilorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f452,axiom,
! [X53] :
( ~ class_LOrder_Ojoin__semilorder(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f1714,plain,
spl0_72,
inference(avatar_split_clause,[],[f451,f1712]) ).
fof(f1712,plain,
( spl0_72
<=> ! [X53] :
( ~ class_LOrder_Ojoin__semilorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f451,axiom,
! [X53] :
( ~ class_LOrder_Ojoin__semilorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f1710,plain,
spl0_71,
inference(avatar_split_clause,[],[f296,f1708]) ).
fof(f296,axiom,
! [X2,X0] : c_in(X0,c_UNIV,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f1706,plain,
spl0_70,
inference(avatar_split_clause,[],[f264,f1704]) ).
fof(f1704,plain,
( spl0_70
<=> ! [X18] : ~ c_less(X18,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f264,axiom,
! [X18] : ~ c_less(X18,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f1702,plain,
spl0_69,
inference(avatar_split_clause,[],[f262,f1700]) ).
fof(f1700,plain,
( spl0_69
<=> ! [X18] : c_lessequals(c_0,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f262,axiom,
! [X18] : c_lessequals(c_0,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f1698,plain,
spl0_68,
inference(avatar_split_clause,[],[f238,f1696]) ).
fof(f1696,plain,
( spl0_68
<=> ! [X12] : c_Divides_Oop_Advd(c_1,X12,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f238,axiom,
! [X12] : c_Divides_Oop_Advd(c_1,X12,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f1694,plain,
spl0_67,
inference(avatar_split_clause,[],[f237,f1692]) ).
fof(f1692,plain,
( spl0_67
<=> ! [X12] : c_Divides_Oop_Advd(X12,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f237,axiom,
! [X12] : c_Divides_Oop_Advd(X12,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f1690,plain,
spl0_66,
inference(avatar_split_clause,[],[f221,f1688]) ).
fof(f1688,plain,
( spl0_66
<=> ! [X12] : c_Divides_Oop_Advd(X12,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f221,axiom,
! [X12] : c_Divides_Oop_Advd(X12,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f1686,plain,
spl0_65,
inference(avatar_split_clause,[],[f174,f1684]) ).
fof(f1684,plain,
( spl0_65
<=> ! [X2,X4] : ~ c_in(X4,c_emptyset,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f174,axiom,
! [X2,X4] : ~ c_in(X4,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f1682,plain,
spl0_64,
inference(avatar_split_clause,[],[f120,f1680]) ).
fof(f1680,plain,
( spl0_64
<=> ! [X18] : ~ c_less(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f120,axiom,
! [X18] : ~ c_less(X18,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
fof(f1678,plain,
spl0_63,
inference(avatar_split_clause,[],[f115,f1675]) ).
fof(f1675,plain,
( spl0_63
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f115,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one__iff2_0) ).
fof(f1673,plain,
spl0_62,
inference(avatar_split_clause,[],[f103,f1671]) ).
fof(f1671,plain,
( spl0_62
<=> ! [X12] : c_0 != c_Suc(X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f103,axiom,
! [X12] : c_0 != c_Suc(X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
fof(f1669,plain,
( spl0_60
| spl0_61 ),
inference(avatar_split_clause,[],[f1366,f1666,f1662]) ).
fof(f1366,axiom,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1660,plain,
spl0_59,
inference(avatar_split_clause,[],[f447,f1658]) ).
fof(f1658,plain,
( spl0_59
<=> ! [X51] : class_Orderings_Oorder(tc_set(X51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f447,axiom,
! [X51] : class_Orderings_Oorder(tc_set(X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f1656,plain,
spl0_58,
inference(avatar_split_clause,[],[f446,f1654]) ).
fof(f1654,plain,
( spl0_58
<=> ! [X51] : class_Orderings_Oord(tc_set(X51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f446,axiom,
! [X51] : class_Orderings_Oord(tc_set(X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f1652,plain,
spl0_57,
inference(avatar_split_clause,[],[f324,f1649]) ).
fof(f1649,plain,
( spl0_57
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f324,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(f1647,plain,
spl0_56,
inference(avatar_split_clause,[],[f322,f1644]) ).
fof(f1644,plain,
( spl0_56
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f322,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(f1642,plain,
spl0_55,
inference(avatar_split_clause,[],[f321,f1640]) ).
fof(f1640,plain,
( spl0_55
<=> ! [X2] : c_Wellfounded__Recursion_Owf(c_emptyset,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f321,axiom,
! [X2] : c_Wellfounded__Recursion_Owf(c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f1638,plain,
~ spl0_54,
inference(avatar_split_clause,[],[f166,f1635]) ).
fof(f1635,plain,
( spl0_54
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f166,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
fof(f1633,plain,
~ spl0_53,
inference(avatar_split_clause,[],[f122,f1630]) ).
fof(f1630,plain,
( spl0_53
<=> c_Numeral_Obit_OB0 = c_Numeral_Obit_OB1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f122,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2__iff1_0) ).
fof(f1628,plain,
~ spl0_52,
inference(avatar_split_clause,[],[f30,f1625]) ).
fof(f1625,plain,
( spl0_52
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f30,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2__iff1_0) ).
fof(f1623,plain,
~ spl0_51,
inference(avatar_split_clause,[],[f1365,f1620]) ).
fof(f1365,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1618,plain,
~ spl0_50,
inference(avatar_split_clause,[],[f1364,f1615]) ).
fof(f1364,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1613,plain,
spl0_49,
inference(avatar_split_clause,[],[f442,f1610]) ).
fof(f1610,plain,
( spl0_49
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f442,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f1608,plain,
spl0_48,
inference(avatar_split_clause,[],[f441,f1605]) ).
fof(f1605,plain,
( spl0_48
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f441,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f1603,plain,
spl0_47,
inference(avatar_split_clause,[],[f440,f1600]) ).
fof(f1600,plain,
( spl0_47
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f440,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f1598,plain,
spl0_46,
inference(avatar_split_clause,[],[f439,f1595]) ).
fof(f1595,plain,
( spl0_46
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f439,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f1593,plain,
spl0_45,
inference(avatar_split_clause,[],[f434,f1590]) ).
fof(f1590,plain,
( spl0_45
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f434,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f1588,plain,
spl0_44,
inference(avatar_split_clause,[],[f433,f1585]) ).
fof(f1585,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f433,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f1583,plain,
spl0_43,
inference(avatar_split_clause,[],[f432,f1580]) ).
fof(f1580,plain,
( spl0_43
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f432,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f1578,plain,
spl0_42,
inference(avatar_split_clause,[],[f431,f1575]) ).
fof(f1575,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f431,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f1573,plain,
spl0_41,
inference(avatar_split_clause,[],[f430,f1570]) ).
fof(f1570,plain,
( spl0_41
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f430,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f1568,plain,
spl0_40,
inference(avatar_split_clause,[],[f429,f1565]) ).
fof(f1565,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f429,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f1563,plain,
spl0_39,
inference(avatar_split_clause,[],[f428,f1560]) ).
fof(f1560,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f428,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f1558,plain,
spl0_38,
inference(avatar_split_clause,[],[f427,f1555]) ).
fof(f1555,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f427,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f1553,plain,
spl0_37,
inference(avatar_split_clause,[],[f426,f1550]) ).
fof(f1550,plain,
( spl0_37
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f426,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f1548,plain,
spl0_36,
inference(avatar_split_clause,[],[f425,f1545]) ).
fof(f1545,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f425,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f1543,plain,
spl0_35,
inference(avatar_split_clause,[],[f424,f1540]) ).
fof(f1540,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f424,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f1538,plain,
spl0_34,
inference(avatar_split_clause,[],[f423,f1535]) ).
fof(f1535,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f423,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f1533,plain,
spl0_33,
inference(avatar_split_clause,[],[f419,f1530]) ).
fof(f1530,plain,
( spl0_33
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f419,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f1528,plain,
spl0_32,
inference(avatar_split_clause,[],[f408,f1525]) ).
fof(f1525,plain,
( spl0_32
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f408,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f1523,plain,
spl0_31,
inference(avatar_split_clause,[],[f393,f1520]) ).
fof(f1520,plain,
( spl0_31
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f393,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f1518,plain,
spl0_30,
inference(avatar_split_clause,[],[f392,f1515]) ).
fof(f1515,plain,
( spl0_30
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f392,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f1513,plain,
spl0_29,
inference(avatar_split_clause,[],[f381,f1510]) ).
fof(f1510,plain,
( spl0_29
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f381,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f1508,plain,
spl0_28,
inference(avatar_split_clause,[],[f379,f1505]) ).
fof(f1505,plain,
( spl0_28
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f379,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f1503,plain,
spl0_27,
inference(avatar_split_clause,[],[f378,f1500]) ).
fof(f1500,plain,
( spl0_27
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f378,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f1498,plain,
spl0_26,
inference(avatar_split_clause,[],[f376,f1495]) ).
fof(f1495,plain,
( spl0_26
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f376,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f1493,plain,
spl0_25,
inference(avatar_split_clause,[],[f375,f1490]) ).
fof(f1490,plain,
( spl0_25
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f375,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f1488,plain,
spl0_24,
inference(avatar_split_clause,[],[f374,f1485]) ).
fof(f1485,plain,
( spl0_24
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f374,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f1483,plain,
spl0_23,
inference(avatar_split_clause,[],[f373,f1480]) ).
fof(f1480,plain,
( spl0_23
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f373,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f1478,plain,
spl0_22,
inference(avatar_split_clause,[],[f372,f1475]) ).
fof(f1475,plain,
( spl0_22
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f372,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f1473,plain,
spl0_21,
inference(avatar_split_clause,[],[f371,f1470]) ).
fof(f1470,plain,
( spl0_21
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f371,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f1468,plain,
spl0_20,
inference(avatar_split_clause,[],[f370,f1465]) ).
fof(f1465,plain,
( spl0_20
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f370,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f1463,plain,
spl0_19,
inference(avatar_split_clause,[],[f369,f1460]) ).
fof(f1460,plain,
( spl0_19
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f369,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f1458,plain,
spl0_18,
inference(avatar_split_clause,[],[f368,f1455]) ).
fof(f1455,plain,
( spl0_18
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f368,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f1453,plain,
spl0_17,
inference(avatar_split_clause,[],[f367,f1450]) ).
fof(f1450,plain,
( spl0_17
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f367,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f1448,plain,
spl0_16,
inference(avatar_split_clause,[],[f366,f1445]) ).
fof(f1445,plain,
( spl0_16
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f366,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f1443,plain,
spl0_15,
inference(avatar_split_clause,[],[f365,f1440]) ).
fof(f1440,plain,
( spl0_15
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f365,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f1438,plain,
spl0_14,
inference(avatar_split_clause,[],[f364,f1435]) ).
fof(f1435,plain,
( spl0_14
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f364,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f1433,plain,
spl0_13,
inference(avatar_split_clause,[],[f363,f1430]) ).
fof(f1430,plain,
( spl0_13
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f363,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f1428,plain,
spl0_12,
inference(avatar_split_clause,[],[f362,f1425]) ).
fof(f1425,plain,
( spl0_12
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f362,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f1423,plain,
spl0_11,
inference(avatar_split_clause,[],[f360,f1420]) ).
fof(f1420,plain,
( spl0_11
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f360,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f1418,plain,
spl0_10,
inference(avatar_split_clause,[],[f359,f1415]) ).
fof(f1415,plain,
( spl0_10
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f359,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f1413,plain,
spl0_9,
inference(avatar_split_clause,[],[f358,f1410]) ).
fof(f1410,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f358,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f1408,plain,
spl0_8,
inference(avatar_split_clause,[],[f357,f1405]) ).
fof(f1405,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f357,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f1403,plain,
spl0_7,
inference(avatar_split_clause,[],[f356,f1400]) ).
fof(f1400,plain,
( spl0_7
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f356,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f1398,plain,
spl0_6,
inference(avatar_split_clause,[],[f355,f1395]) ).
fof(f1395,plain,
( spl0_6
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f355,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f1393,plain,
spl0_5,
inference(avatar_split_clause,[],[f354,f1390]) ).
fof(f1390,plain,
( spl0_5
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f354,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f1388,plain,
spl0_4,
inference(avatar_split_clause,[],[f353,f1385]) ).
fof(f1385,plain,
( spl0_4
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f353,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f1383,plain,
spl0_3,
inference(avatar_split_clause,[],[f352,f1380]) ).
fof(f1380,plain,
( spl0_3
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f352,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f1378,plain,
spl0_2,
inference(avatar_split_clause,[],[f1363,f1375]) ).
fof(f1363,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1373,plain,
spl0_1,
inference(avatar_split_clause,[],[f1362,f1370]) ).
fof(f1370,plain,
( spl0_1
<=> c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1362,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET851-1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 16:45:53 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (4278)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41 % (4281)WARNING: value z3 for option sas not known
% 0.23/0.41 % (4279)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.41 % (4282)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.41 % (4281)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)
% 0.23/0.41 % (4280)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.41 % (4283)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)
% 0.23/0.41 % (4284)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)
% 0.23/0.41 % (4285)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)
% 0.23/0.46 % (4283)First to succeed.
% 0.23/0.47 TRYING [1]
% 0.23/0.48 % (4283)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4278"
% 0.23/0.48 TRYING [2]
% 0.23/0.48 % (4283)Refutation found. Thanks to Tanya!
% 0.23/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.50 % (4283)------------------------------
% 0.23/0.50 % (4283)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.23/0.50 % (4283)Termination reason: Refutation
% 0.23/0.50
% 0.23/0.50 % (4283)Memory used [KB]: 2789
% 0.23/0.50 % (4283)Time elapsed: 0.073 s
% 0.23/0.50 % (4283)Instructions burned: 118 (million)
% 0.23/0.50 % (4278)Success in time 0.13 s
%------------------------------------------------------------------------------