TSTP Solution File: COL120-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COL120-1 : 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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:45:59 EDT 2024
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 879
% Syntax : Number of formulae : 1349 ( 557 unt; 0 def)
% Number of atoms : 2514 ( 237 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1934 ( 769 ~; 721 |; 0 &)
% ( 444 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 483 ( 481 usr; 445 prp; 0-3 aty)
% Number of functors : 76 ( 76 usr; 23 con; 0-4 aty)
% Number of variables : 1275 (1275 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3693,plain,
$false,
inference(avatar_sat_refutation,[],[f1377,f1382,f1387,f1392,f1397,f1402,f1407,f1412,f1417,f1422,f1427,f1432,f1437,f1442,f1447,f1452,f1457,f1462,f1467,f1472,f1477,f1482,f1487,f1492,f1497,f1502,f1507,f1512,f1517,f1522,f1527,f1532,f1537,f1542,f1547,f1552,f1557,f1562,f1567,f1572,f1577,f1582,f1587,f1592,f1597,f1602,f1607,f1612,f1617,f1622,f1627,f1632,f1636,f1641,f1646,f1650,f1654,f1659,f1663,f1668,f1672,f1676,f1680,f1684,f1688,f1692,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1732,f1736,f1740,f1744,f1748,f1752,f1756,f1760,f1764,f1768,f1772,f1776,f1780,f1784,f1788,f1792,f1796,f1800,f1804,f1808,f1812,f1816,f1820,f1824,f1828,f1832,f1836,f1840,f1844,f1848,f1852,f1856,f1860,f1864,f1868,f1872,f1876,f1880,f1884,f1888,f1892,f1896,f1900,f1904,f1908,f1912,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1960,f1964,f1968,f1972,f1976,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2008,f2012,f2016,f2020,f2024,f2028,f2032,f2036,f2040,f2044,f2048,f2052,f2056,f2060,f2064,f2068,f2072,f2076,f2080,f2084,f2088,f2092,f2096,f2100,f2104,f2108,f2112,f2116,f2120,f2124,f2128,f2132,f2136,f2140,f2144,f2148,f2152,f2156,f2160,f2164,f2168,f2172,f2176,f2180,f2184,f2188,f2192,f2196,f2200,f2204,f2208,f2212,f2216,f2220,f2224,f2228,f2232,f2236,f2240,f2244,f2248,f2252,f2256,f2260,f2264,f2268,f2272,f2276,f2280,f2284,f2288,f2292,f2296,f2300,f2304,f2308,f2312,f2316,f2320,f2324,f2328,f2332,f2336,f2340,f2344,f2348,f2352,f2356,f2360,f2364,f2368,f2372,f2376,f2380,f2384,f2388,f2392,f2396,f2400,f2404,f2408,f2412,f2416,f2420,f2424,f2428,f2432,f2436,f2440,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2472,f2476,f2480,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2516,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2556,f2867,f2872,f2876,f2880,f2884,f2888,f2892,f2896,f2900,f2904,f2908,f2912,f2916,f2920,f2924,f2928,f2932,f2936,f2940,f2944,f2948,f2953,f2957,f2961,f2965,f2969,f2973,f2977,f2981,f2985,f2989,f2993,f2997,f3001,f3005,f3009,f3013,f3017,f3021,f3025,f3029,f3045,f3053,f3057,f3061,f3067,f3071,f3075,f3079,f3083,f3087,f3091,f3095,f3099,f3103,f3107,f3111,f3115,f3119,f3123,f3127,f3135,f3142,f3146,f3150,f3154,f3158,f3162,f3166,f3170,f3176,f3180,f3184,f3188,f3192,f3196,f3200,f3204,f3208,f3212,f3218,f3222,f3226,f3247,f3251,f3255,f3259,f3263,f3267,f3271,f3275,f3279,f3283,f3287,f3291,f3295,f3299,f3303,f3307,f3311,f3315,f3319,f3323,f3327,f3331,f3335,f3339,f3370,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3412,f3416,f3420,f3424,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3491,f3495,f3499,f3503,f3507,f3511,f3515,f3519,f3523,f3527,f3531,f3541,f3545,f3549,f3553,f3557,f3561,f3565,f3569,f3573,f3577,f3582,f3667,f3671,f3675,f3679,f3683,f3687,f3691,f3692]) ).
fof(f3692,plain,
( ~ spl0_49
| ~ spl0_298
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f3663,f3575,f2926,f1614]) ).
fof(f1614,plain,
( spl0_49
<=> c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2926,plain,
( spl0_298
<=> ! [X41] :
( ~ c_in(c_Pair(v_y,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f3575,plain,
( spl0_436
<=> ! [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_436])]) ).
fof(f3663,plain,
( ~ c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ spl0_298
| ~ spl0_436 ),
inference(resolution,[],[f3576,f2927]) ).
fof(f2927,plain,
( ! [X41] :
( ~ c_in(c_Pair(v_x,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f2926]) ).
fof(f3576,plain,
( ! [X2,X14,X4] : c_in(c_Pair(X4,X4,X2,X2),c_Transitive__Closure_Ortrancl(X14,X2),tc_prod(X2,X2))
| ~ spl0_436 ),
inference(avatar_component_clause,[],[f3575]) ).
fof(f3691,plain,
spl0_444,
inference(avatar_split_clause,[],[f131,f3689]) ).
fof(f3689,plain,
( spl0_444
<=> ! [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_444])]) ).
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_443,
inference(avatar_split_clause,[],[f41,f3685]) ).
fof(f3685,plain,
( spl0_443
<=> ! [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_443])]) ).
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_442,
inference(avatar_split_clause,[],[f40,f3681]) ).
fof(f3681,plain,
( spl0_442
<=> ! [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_442])]) ).
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_441,
inference(avatar_split_clause,[],[f36,f3677]) ).
fof(f3677,plain,
( spl0_441
<=> ! [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_441])]) ).
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_440,
inference(avatar_split_clause,[],[f35,f3673]) ).
fof(f3673,plain,
( spl0_440
<=> ! [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_440])]) ).
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_439,
inference(avatar_split_clause,[],[f34,f3669]) ).
fof(f3669,plain,
( spl0_439
<=> ! [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_439])]) ).
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(f3667,plain,
spl0_438,
inference(avatar_split_clause,[],[f33,f3665]) ).
fof(f3665,plain,
( spl0_438
<=> ! [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_438])]) ).
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(f3582,plain,
( spl0_437
| ~ spl0_64
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f3532,f3368,f1682,f3579]) ).
fof(f3579,plain,
( spl0_437
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f1682,plain,
( spl0_64
<=> ! [X12] : c_Divides_Oop_Advd(X12,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f3368,plain,
( spl0_390
<=> ! [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_390])]) ).
fof(f3532,plain,
( c_0 = c_uminus(c_0,tc_IntDef_Oint)
| ~ spl0_64
| ~ spl0_390 ),
inference(resolution,[],[f3369,f1683]) ).
fof(f1683,plain,
( ! [X12] : c_Divides_Oop_Advd(X12,c_0,tc_IntDef_Oint)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1682]) ).
fof(f3369,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f3368]) ).
fof(f3577,plain,
spl0_436,
inference(avatar_split_clause,[],[f318,f3575]) ).
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(f3573,plain,
spl0_435,
inference(avatar_split_clause,[],[f308,f3571]) ).
fof(f3571,plain,
( spl0_435
<=> ! [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_435])]) ).
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(f3569,plain,
spl0_434,
inference(avatar_split_clause,[],[f307,f3567]) ).
fof(f3567,plain,
( spl0_434
<=> ! [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_434])]) ).
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(f3565,plain,
spl0_433,
inference(avatar_split_clause,[],[f247,f3563]) ).
fof(f3563,plain,
( spl0_433
<=> ! [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_433])]) ).
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(f3561,plain,
spl0_432,
inference(avatar_split_clause,[],[f200,f3559]) ).
fof(f3559,plain,
( spl0_432
<=> ! [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_432])]) ).
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(f3557,plain,
spl0_431,
inference(avatar_split_clause,[],[f199,f3555]) ).
fof(f3555,plain,
( spl0_431
<=> ! [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_431])]) ).
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(f3553,plain,
spl0_430,
inference(avatar_split_clause,[],[f187,f3551]) ).
fof(f3551,plain,
( spl0_430
<=> ! [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_430])]) ).
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(f3549,plain,
spl0_429,
inference(avatar_split_clause,[],[f185,f3547]) ).
fof(f3547,plain,
( spl0_429
<=> ! [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_429])]) ).
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(f3545,plain,
spl0_428,
inference(avatar_split_clause,[],[f179,f3543]) ).
fof(f3543,plain,
( spl0_428
<=> ! [X4,X13,X6,X2] :
( X4 = X6
| c_insert(X4,X13,X2) != c_insert(X6,c_emptyset,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
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(f3541,plain,
spl0_427,
inference(avatar_split_clause,[],[f165,f3539]) ).
fof(f3539,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(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(f3531,plain,
spl0_426,
inference(avatar_split_clause,[],[f164,f3529]) ).
fof(f3529,plain,
( spl0_426
<=> ! [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_426])]) ).
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(f3527,plain,
spl0_425,
inference(avatar_split_clause,[],[f158,f3525]) ).
fof(f3525,plain,
( spl0_425
<=> ! [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_425])]) ).
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(f3523,plain,
spl0_424,
inference(avatar_split_clause,[],[f157,f3521]) ).
fof(f3521,plain,
( spl0_424
<=> ! [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_424])]) ).
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(f3519,plain,
spl0_423,
inference(avatar_split_clause,[],[f154,f3517]) ).
fof(f3517,plain,
( spl0_423
<=> ! [X13,X2,X15] :
( X13 = X15
| c_uminus(X13,tc_set(X2)) != c_uminus(X15,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
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(f3515,plain,
spl0_422,
inference(avatar_split_clause,[],[f149,f3513]) ).
fof(f3513,plain,
( spl0_422
<=> ! [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_422])]) ).
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(f3511,plain,
spl0_421,
inference(avatar_split_clause,[],[f148,f3509]) ).
fof(f3509,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(f3507,plain,
spl0_420,
inference(avatar_split_clause,[],[f147,f3505]) ).
fof(f3505,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(f3503,plain,
spl0_419,
inference(avatar_split_clause,[],[f144,f3501]) ).
fof(f3501,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(f3499,plain,
spl0_418,
inference(avatar_split_clause,[],[f143,f3497]) ).
fof(f3497,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(f3495,plain,
spl0_417,
inference(avatar_split_clause,[],[f142,f3493]) ).
fof(f3493,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(f3491,plain,
( spl0_416
| ~ spl0_319
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3354,f3277,f3011,f3489]) ).
fof(f3489,plain,
( spl0_416
<=> ! [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_416])]) ).
fof(f3011,plain,
( spl0_319
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f3277,plain,
( spl0_374
<=> ! [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_374])]) ).
fof(f3354,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_319
| ~ spl0_374 ),
inference(resolution,[],[f3278,f3012]) ).
fof(f3012,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f3011]) ).
fof(f3278,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_374 ),
inference(avatar_component_clause,[],[f3277]) ).
fof(f3487,plain,
spl0_415,
inference(avatar_split_clause,[],[f139,f3485]) ).
fof(f3485,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(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(f3483,plain,
spl0_414,
inference(avatar_split_clause,[],[f138,f3481]) ).
fof(f3481,plain,
( spl0_414
<=> ! [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_414])]) ).
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(f3479,plain,
spl0_413,
inference(avatar_split_clause,[],[f137,f3477]) ).
fof(f3477,plain,
( spl0_413
<=> ! [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_413])]) ).
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(f3475,plain,
spl0_412,
inference(avatar_split_clause,[],[f134,f3473]) ).
fof(f3473,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(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(f3471,plain,
spl0_411,
inference(avatar_split_clause,[],[f133,f3469]) ).
fof(f3469,plain,
( spl0_411
<=> ! [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_411])]) ).
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(f3467,plain,
spl0_410,
inference(avatar_split_clause,[],[f132,f3465]) ).
fof(f3465,plain,
( spl0_410
<=> ! [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_410])]) ).
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(f3463,plain,
spl0_409,
inference(avatar_split_clause,[],[f88,f3461]) ).
fof(f3461,plain,
( spl0_409
<=> ! [X2,X24,X21,X22] :
( X22 = X24
| c_append(X21,X22,X2) != c_append(X21,X24,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
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(f3459,plain,
spl0_408,
inference(avatar_split_clause,[],[f82,f3457]) ).
fof(f3457,plain,
( spl0_408
<=> ! [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_408])]) ).
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(f3455,plain,
spl0_407,
inference(avatar_split_clause,[],[f81,f3453]) ).
fof(f3453,plain,
( spl0_407
<=> ! [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_407])]) ).
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(f3451,plain,
spl0_406,
inference(avatar_split_clause,[],[f66,f3449]) ).
fof(f3449,plain,
( spl0_406
<=> ! [X2,X24,X21,X22] :
( X22 = X24
| c_append(X22,X21,X2) != c_append(X24,X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
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(f3447,plain,
( spl0_405
| ~ spl0_318
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3353,f3277,f3007,f3445]) ).
fof(f3445,plain,
( spl0_405
<=> ! [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_405])]) ).
fof(f3007,plain,
( spl0_318
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f3353,plain,
( ! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(c_uminus(X0,tc_IntDef_Oint),X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_318
| ~ spl0_374 ),
inference(resolution,[],[f3278,f3008]) ).
fof(f3008,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3007]) ).
fof(f3443,plain,
spl0_404,
inference(avatar_split_clause,[],[f12,f3441]) ).
fof(f3441,plain,
( spl0_404
<=> ! [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_404])]) ).
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(f3439,plain,
spl0_403,
inference(avatar_split_clause,[],[f10,f3437]) ).
fof(f3437,plain,
( spl0_403
<=> ! [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_403])]) ).
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(f3435,plain,
spl0_402,
inference(avatar_split_clause,[],[f8,f3433]) ).
fof(f3433,plain,
( spl0_402
<=> ! [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_402])]) ).
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(f3424,plain,
spl0_401,
inference(avatar_split_clause,[],[f175,f3422]) ).
fof(f3422,plain,
( spl0_401
<=> ! [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_401])]) ).
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(f3420,plain,
spl0_400,
inference(avatar_split_clause,[],[f168,f3418]) ).
fof(f3418,plain,
( spl0_400
<=> ! [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_400])]) ).
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(f3416,plain,
spl0_399,
inference(avatar_split_clause,[],[f167,f3414]) ).
fof(f3414,plain,
( spl0_399
<=> ! [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_399])]) ).
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(f3412,plain,
spl0_398,
inference(avatar_split_clause,[],[f161,f3410]) ).
fof(f3410,plain,
( spl0_398
<=> ! [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_398])]) ).
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(f3408,plain,
spl0_397,
inference(avatar_split_clause,[],[f160,f3406]) ).
fof(f3406,plain,
( spl0_397
<=> ! [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_397])]) ).
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(f3404,plain,
spl0_396,
inference(avatar_split_clause,[],[f153,f3402]) ).
fof(f3402,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(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(f3400,plain,
spl0_395,
inference(avatar_split_clause,[],[f152,f3398]) ).
fof(f3398,plain,
( spl0_395
<=> ! [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_395])]) ).
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(f3396,plain,
( spl0_394
| ~ spl0_293
| ~ spl0_385 ),
inference(avatar_split_clause,[],[f3376,f3321,f2906,f3394]) ).
fof(f3394,plain,
( spl0_394
<=> ! [X0,X1] : ~ c_less(X0,X0,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2906,plain,
( spl0_293
<=> ! [X13,X2] : c_lessequals(X13,X13,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3321,plain,
( spl0_385
<=> ! [X13,X2,X15] :
( ~ c_less(X13,X15,tc_set(X2))
| ~ c_lessequals(X15,X13,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f3376,plain,
( ! [X0,X1] : ~ c_less(X0,X0,tc_set(X1))
| ~ spl0_293
| ~ spl0_385 ),
inference(resolution,[],[f3322,f2907]) ).
fof(f2907,plain,
( ! [X2,X13] : c_lessequals(X13,X13,tc_set(X2))
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f2906]) ).
fof(f3322,plain,
( ! [X2,X15,X13] :
( ~ c_lessequals(X15,X13,tc_set(X2))
| ~ c_less(X13,X15,tc_set(X2)) )
| ~ spl0_385 ),
inference(avatar_component_clause,[],[f3321]) ).
fof(f3392,plain,
spl0_393,
inference(avatar_split_clause,[],[f106,f3390]) ).
fof(f3390,plain,
( spl0_393
<=> ! [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_393])]) ).
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(f3388,plain,
spl0_392,
inference(avatar_split_clause,[],[f105,f3386]) ).
fof(f3386,plain,
( spl0_392
<=> ! [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_392])]) ).
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(f3384,plain,
spl0_391,
inference(avatar_split_clause,[],[f1,f3382]) ).
fof(f3382,plain,
( spl0_391
<=> ! [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_391])]) ).
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(f3370,plain,
( spl0_390
| ~ spl0_309
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3350,f3273,f2971,f3368]) ).
fof(f2971,plain,
( spl0_309
<=> ! [X12] :
( c_0 = X12
| ~ c_Divides_Oop_Advd(c_0,X12,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f3273,plain,
( spl0_373
<=> ! [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_373])]) ).
fof(f3350,plain,
( ! [X0] :
( ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint)
| c_0 = c_uminus(X0,tc_IntDef_Oint) )
| ~ spl0_309
| ~ spl0_373 ),
inference(resolution,[],[f3274,f2972]) ).
fof(f2972,plain,
( ! [X12] :
( ~ c_Divides_Oop_Advd(c_0,X12,tc_IntDef_Oint)
| c_0 = X12 )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f2971]) ).
fof(f3274,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_373 ),
inference(avatar_component_clause,[],[f3273]) ).
fof(f3339,plain,
spl0_389,
inference(avatar_split_clause,[],[f1365,f3337]) ).
fof(f3337,plain,
( spl0_389
<=> ! [X54,X57,X55,X56] :
( X55 = X57
| c_Comb_Ocomb_Oop_A_D_D(X54,X55) != c_Comb_Ocomb_Oop_A_D_D(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f1365,axiom,
! [X56,X54,X57,X55] :
( X55 = X57
| c_Comb_Ocomb_Oop_A_D_D(X54,X55) != c_Comb_Ocomb_Oop_A_D_D(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_1) ).
fof(f3335,plain,
spl0_388,
inference(avatar_split_clause,[],[f1364,f3333]) ).
fof(f3333,plain,
( spl0_388
<=> ! [X55,X54,X56,X57] :
( X54 = X56
| c_Comb_Ocomb_Oop_A_D_D(X54,X55) != c_Comb_Ocomb_Oop_A_D_D(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f1364,axiom,
! [X56,X54,X57,X55] :
( X54 = X56
| c_Comb_Ocomb_Oop_A_D_D(X54,X55) != c_Comb_Ocomb_Oop_A_D_D(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_0) ).
fof(f3331,plain,
spl0_387,
inference(avatar_split_clause,[],[f303,f3329]) ).
fof(f3329,plain,
( spl0_387
<=> ! [X6,X4,X2] :
( X4 = X6
| ~ c_in(X6,c_insert(X4,c_emptyset,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
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(f3327,plain,
spl0_386,
inference(avatar_split_clause,[],[f301,f3325]) ).
fof(f3325,plain,
( spl0_386
<=> ! [X13,X2,X15] :
( ~ c_less(X13,X15,tc_set(X2))
| c_lessequals(X13,X15,tc_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
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(f3323,plain,
spl0_385,
inference(avatar_split_clause,[],[f300,f3321]) ).
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(f3319,plain,
spl0_384,
inference(avatar_split_clause,[],[f126,f3317]) ).
fof(f3317,plain,
( spl0_384
<=> ! [X2,X4] : c_in(c_Pair(X4,X4,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
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(f3315,plain,
spl0_383,
inference(avatar_split_clause,[],[f101,f3313]) ).
fof(f3313,plain,
( spl0_383
<=> ! [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_383])]) ).
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(f3311,plain,
spl0_382,
inference(avatar_split_clause,[],[f100,f3309]) ).
fof(f3309,plain,
( spl0_382
<=> ! [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_382])]) ).
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(f3307,plain,
spl0_381,
inference(avatar_split_clause,[],[f99,f3305]) ).
fof(f3305,plain,
( spl0_381
<=> ! [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_381])]) ).
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(f3303,plain,
spl0_380,
inference(avatar_split_clause,[],[f98,f3301]) ).
fof(f3301,plain,
( spl0_380
<=> ! [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_380])]) ).
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(f3299,plain,
spl0_379,
inference(avatar_split_clause,[],[f87,f3297]) ).
fof(f3297,plain,
( spl0_379
<=> ! [X22,X2,X21] :
( X21 = X22
| c_List_Orev(X21,X2) != c_List_Orev(X22,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
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(f3295,plain,
spl0_378,
inference(avatar_split_clause,[],[f76,f3293]) ).
fof(f3293,plain,
( spl0_378
<=> ! [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_378])]) ).
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(f3291,plain,
spl0_377,
inference(avatar_split_clause,[],[f72,f3289]) ).
fof(f3289,plain,
( spl0_377
<=> ! [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_377])]) ).
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(f3287,plain,
spl0_376,
inference(avatar_split_clause,[],[f71,f3285]) ).
fof(f3285,plain,
( spl0_376
<=> ! [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_376])]) ).
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(f3283,plain,
spl0_375,
inference(avatar_split_clause,[],[f50,f3281]) ).
fof(f3281,plain,
( spl0_375
<=> ! [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_375])]) ).
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(f3279,plain,
spl0_374,
inference(avatar_split_clause,[],[f49,f3277]) ).
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(f3275,plain,
spl0_373,
inference(avatar_split_clause,[],[f46,f3273]) ).
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(f3271,plain,
spl0_372,
inference(avatar_split_clause,[],[f45,f3269]) ).
fof(f3269,plain,
( spl0_372
<=> ! [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_372])]) ).
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(f3267,plain,
spl0_371,
inference(avatar_split_clause,[],[f21,f3265]) ).
fof(f3265,plain,
( spl0_371
<=> ! [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_371])]) ).
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(f3263,plain,
spl0_370,
inference(avatar_split_clause,[],[f20,f3261]) ).
fof(f3261,plain,
( spl0_370
<=> ! [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_370])]) ).
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(f3259,plain,
spl0_369,
inference(avatar_split_clause,[],[f17,f3257]) ).
fof(f3257,plain,
( spl0_369
<=> ! [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_369])]) ).
fof(f17,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_ONumb__not__Scons__iff1_0) ).
fof(f3255,plain,
spl0_368,
inference(avatar_split_clause,[],[f7,f3253]) ).
fof(f3253,plain,
( spl0_368
<=> ! [X4,X2,X3] :
( X3 = X4
| c_Datatype_Ooption_OSome(X3,X2) != c_Datatype_Ooption_OSome(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
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(f3251,plain,
spl0_367,
inference(avatar_split_clause,[],[f4,f3249]) ).
fof(f3249,plain,
( spl0_367
<=> ! [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_367])]) ).
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(f3247,plain,
spl0_366,
inference(avatar_split_clause,[],[f3,f3245]) ).
fof(f3245,plain,
( spl0_366
<=> ! [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_366])]) ).
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(f3226,plain,
spl0_365,
inference(avatar_split_clause,[],[f261,f3224]) ).
fof(f3224,plain,
( spl0_365
<=> ! [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_365])]) ).
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(f3222,plain,
spl0_364,
inference(avatar_split_clause,[],[f260,f3220]) ).
fof(f3220,plain,
( spl0_364
<=> ! [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_364])]) ).
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(f3218,plain,
spl0_363,
inference(avatar_split_clause,[],[f236,f3216]) ).
fof(f3216,plain,
( spl0_363
<=> ! [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_363])]) ).
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(f3212,plain,
spl0_362,
inference(avatar_split_clause,[],[f233,f3210]) ).
fof(f3210,plain,
( spl0_362
<=> ! [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_362])]) ).
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(f3208,plain,
spl0_361,
inference(avatar_split_clause,[],[f232,f3206]) ).
fof(f3206,plain,
( spl0_361
<=> ! [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_361])]) ).
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(f3204,plain,
spl0_360,
inference(avatar_split_clause,[],[f190,f3202]) ).
fof(f3202,plain,
( spl0_360
<=> ! [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_360])]) ).
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(f3200,plain,
spl0_359,
inference(avatar_split_clause,[],[f189,f3198]) ).
fof(f3198,plain,
( spl0_359
<=> ! [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_359])]) ).
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(f3196,plain,
spl0_358,
inference(avatar_split_clause,[],[f186,f3194]) ).
fof(f3194,plain,
( spl0_358
<=> ! [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_358])]) ).
fof(f186,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_OInl__not__Inr__iff1_0) ).
fof(f3192,plain,
spl0_357,
inference(avatar_split_clause,[],[f171,f3190]) ).
fof(f3190,plain,
( spl0_357
<=> ! [X13,X2,X15] :
( c_emptyset = X15
| c_emptyset != c_union(X13,X15,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
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(f3188,plain,
spl0_356,
inference(avatar_split_clause,[],[f170,f3186]) ).
fof(f3186,plain,
( spl0_356
<=> ! [X13,X2,X15] :
( c_emptyset = X13
| c_emptyset != c_union(X13,X15,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
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(f3184,plain,
spl0_355,
inference(avatar_split_clause,[],[f108,f3182]) ).
fof(f3182,plain,
( spl0_355
<=> ! [X18,X12] :
( c_0 = X18
| c_0 != c_plus(X12,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
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(f3180,plain,
spl0_354,
inference(avatar_split_clause,[],[f107,f3178]) ).
fof(f3178,plain,
( spl0_354
<=> ! [X18,X12] :
( c_0 = X12
| c_0 != c_plus(X12,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
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(f3176,plain,
spl0_353,
inference(avatar_split_clause,[],[f73,f3174]) ).
fof(f3174,plain,
( spl0_353
<=> ! [X2,X21] :
( c_List_Olist_ONil = X21
| c_0 != c_Nat_Osize(X21,tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
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(f3170,plain,
spl0_352,
inference(avatar_split_clause,[],[f69,f3168]) ).
fof(f3168,plain,
( spl0_352
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X22
| c_append(X21,X22,X2) != X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
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(f3166,plain,
spl0_351,
inference(avatar_split_clause,[],[f67,f3164]) ).
fof(f3164,plain,
( spl0_351
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X21
| c_append(X21,X22,X2) != X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
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(f3162,plain,
spl0_350,
inference(avatar_split_clause,[],[f64,f3160]) ).
fof(f3160,plain,
( spl0_350
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X22
| c_List_Olist_ONil != c_append(X21,X22,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
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(f3158,plain,
spl0_349,
inference(avatar_split_clause,[],[f63,f3156]) ).
fof(f3156,plain,
( spl0_349
<=> ! [X22,X2,X21] :
( c_List_Olist_ONil = X21
| c_List_Olist_ONil != c_append(X21,X22,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f63,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_Oappend__is__Nil__conv__iff1_0) ).
fof(f3154,plain,
spl0_348,
inference(avatar_split_clause,[],[f27,f3152]) ).
fof(f3152,plain,
( spl0_348
<=> ! [X13,X2,X14] :
( c_emptyset = X13
| c_emptyset != c_Equiv__Relations_Oquotient(X13,X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f27,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__empty__iff1_0) ).
fof(f3150,plain,
spl0_347,
inference(avatar_split_clause,[],[f16,f3148]) ).
fof(f3148,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(f16,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_ONumb__not__Leaf__iff1_0) ).
fof(f3146,plain,
spl0_346,
inference(avatar_split_clause,[],[f11,f3144]) ).
fof(f3144,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(f3142,plain,
( spl0_345
| ~ spl0_309
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f3048,f3011,f2971,f3140]) ).
fof(f3140,plain,
( spl0_345
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f3048,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_309
| ~ spl0_319 ),
inference(resolution,[],[f3012,f2972]) ).
fof(f3135,plain,
( spl0_344
| ~ spl0_309
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3047,f3007,f2971,f3133]) ).
fof(f3133,plain,
( spl0_344
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f3047,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_309
| ~ spl0_318 ),
inference(resolution,[],[f3008,f2972]) ).
fof(f3127,plain,
spl0_343,
inference(avatar_split_clause,[],[f450,f3125]) ).
fof(f3125,plain,
( spl0_343
<=> ! [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_343])]) ).
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(f3123,plain,
spl0_342,
inference(avatar_split_clause,[],[f444,f3121]) ).
fof(f3121,plain,
( spl0_342
<=> ! [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_342])]) ).
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(f3119,plain,
spl0_341,
inference(avatar_split_clause,[],[f394,f3117]) ).
fof(f3117,plain,
( spl0_341
<=> ! [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_341])]) ).
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(f3115,plain,
spl0_340,
inference(avatar_split_clause,[],[f292,f3113]) ).
fof(f3113,plain,
( spl0_340
<=> ! [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_340])]) ).
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(f3111,plain,
spl0_339,
inference(avatar_split_clause,[],[f291,f3109]) ).
fof(f3109,plain,
( spl0_339
<=> ! [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_339])]) ).
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(f3107,plain,
( spl0_338
| ~ spl0_308
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f3046,f3003,f2967,f3105]) ).
fof(f3105,plain,
( spl0_338
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2967,plain,
( spl0_308
<=> ! [X12] :
( c_0 = X12
| ~ c_Divides_Oop_Advd(c_0,X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f3003,plain,
( spl0_317
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f3046,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_nat)
| ~ spl0_308
| ~ spl0_317 ),
inference(resolution,[],[f3004,f2968]) ).
fof(f2968,plain,
( ! [X12] :
( ~ c_Divides_Oop_Advd(c_0,X12,tc_nat)
| c_0 = X12 )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f2967]) ).
fof(f3004,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X12,X9,tc_nat),tc_nat)
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3003]) ).
fof(f3103,plain,
spl0_337,
inference(avatar_split_clause,[],[f290,f3101]) ).
fof(f3101,plain,
( spl0_337
<=> ! [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_337])]) ).
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(f3099,plain,
spl0_336,
inference(avatar_split_clause,[],[f289,f3097]) ).
fof(f3097,plain,
( spl0_336
<=> ! [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_336])]) ).
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(f3095,plain,
spl0_335,
inference(avatar_split_clause,[],[f287,f3093]) ).
fof(f3093,plain,
( spl0_335
<=> ! [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_335])]) ).
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(f3091,plain,
spl0_334,
inference(avatar_split_clause,[],[f286,f3089]) ).
fof(f3089,plain,
( spl0_334
<=> ! [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_334])]) ).
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(f3087,plain,
spl0_333,
inference(avatar_split_clause,[],[f285,f3085]) ).
fof(f3085,plain,
( spl0_333
<=> ! [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_333])]) ).
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(f3083,plain,
spl0_332,
inference(avatar_split_clause,[],[f284,f3081]) ).
fof(f3081,plain,
( spl0_332
<=> ! [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_332])]) ).
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(f3079,plain,
spl0_331,
inference(avatar_split_clause,[],[f235,f3077]) ).
fof(f3077,plain,
( spl0_331
<=> ! [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_331])]) ).
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(f3075,plain,
spl0_330,
inference(avatar_split_clause,[],[f112,f3073]) ).
fof(f3073,plain,
( spl0_330
<=> ! [X18] :
( c_0 = X18
| ~ c_less(X18,c_Suc(c_0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
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(f3071,plain,
spl0_329,
inference(avatar_split_clause,[],[f97,f3069]) ).
fof(f3069,plain,
( spl0_329
<=> ! [X18,X12] :
( X12 = X18
| c_Suc(X12) != c_Suc(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
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(f3067,plain,
spl0_328,
inference(avatar_split_clause,[],[f95,f3065]) ).
fof(f3065,plain,
( spl0_328
<=> ! [X2,X21] :
( c_List_Olist_ONil = X21
| c_emptyset != c_List_Oset(X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f95,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__empty__iff1_0) ).
fof(f3061,plain,
spl0_327,
inference(avatar_split_clause,[],[f85,f3059]) ).
fof(f3059,plain,
( spl0_327
<=> ! [X2,X21] :
( c_List_Olist_ONil = X21
| c_List_Olist_ONil != c_List_Orev(X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
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(f3057,plain,
spl0_326,
inference(avatar_split_clause,[],[f44,f3055]) ).
fof(f3055,plain,
( spl0_326
<=> ! [X18,X12] :
( X12 = X18
| c_IntDef_Oint(X12) != c_IntDef_Oint(X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
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(f3053,plain,
spl0_325,
inference(avatar_split_clause,[],[f2,f3051]) ).
fof(f3051,plain,
( spl0_325
<=> ! [X2,X0] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
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(f3045,plain,
( spl0_324
| ~ spl0_308
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3041,f2999,f2967,f3043]) ).
fof(f3043,plain,
( spl0_324
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2999,plain,
( spl0_316
<=> ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f3041,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_nat)
| ~ spl0_308
| ~ spl0_316 ),
inference(resolution,[],[f3000,f2968]) ).
fof(f3000,plain,
( ! [X9,X12] : c_Divides_Oop_Advd(X9,c_times(X9,X12,tc_nat),tc_nat)
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f2999]) ).
fof(f3029,plain,
spl0_323,
inference(avatar_split_clause,[],[f293,f3027]) ).
fof(f3027,plain,
( spl0_323
<=> ! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
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(f3025,plain,
spl0_322,
inference(avatar_split_clause,[],[f288,f3023]) ).
fof(f3023,plain,
( spl0_322
<=> ! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
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(f3021,plain,
spl0_321,
inference(avatar_split_clause,[],[f259,f3019]) ).
fof(f3019,plain,
( spl0_321
<=> ! [X13,X2] : c_in(c_List_Olist_ONil,c_List_Olists(X13,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
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(f3017,plain,
spl0_320,
inference(avatar_split_clause,[],[f243,f3015]) ).
fof(f3015,plain,
( spl0_320
<=> ! [X2,X21] : c_in(c_List_Oset(X21,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
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(f3013,plain,
spl0_319,
inference(avatar_split_clause,[],[f240,f3011]) ).
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(f3009,plain,
spl0_318,
inference(avatar_split_clause,[],[f239,f3007]) ).
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(f3005,plain,
spl0_317,
inference(avatar_split_clause,[],[f224,f3003]) ).
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(f3001,plain,
spl0_316,
inference(avatar_split_clause,[],[f223,f2999]) ).
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(f2997,plain,
spl0_315,
inference(avatar_split_clause,[],[f176,f2995]) ).
fof(f2995,plain,
( spl0_315
<=> ! [X2,X0,X15] : c_in(X0,c_insert(X0,X15,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
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(f2993,plain,
spl0_314,
inference(avatar_split_clause,[],[f119,f2991]) ).
fof(f2991,plain,
( spl0_314
<=> ! [X32,X31] : ~ c_less(c_plus(X32,X31,tc_nat),X31,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
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(f2989,plain,
spl0_313,
inference(avatar_split_clause,[],[f118,f2987]) ).
fof(f2987,plain,
( spl0_313
<=> ! [X32,X31] : ~ c_less(c_plus(X31,X32,tc_nat),X31,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
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(f2985,plain,
spl0_312,
inference(avatar_split_clause,[],[f116,f2983]) ).
fof(f2983,plain,
( spl0_312
<=> ! [X18] :
( c_0 = X18
| c_less(c_0,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
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(f2981,plain,
spl0_311,
inference(avatar_split_clause,[],[f114,f2979]) ).
fof(f2979,plain,
( spl0_311
<=> ! [X18] :
( c_0 = X18
| ~ c_less(X18,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
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(f2977,plain,
spl0_310,
inference(avatar_split_clause,[],[f110,f2975]) ).
fof(f2975,plain,
( spl0_310
<=> ! [X31] :
( c_0 = X31
| ~ c_lessequals(X31,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
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(f2973,plain,
spl0_309,
inference(avatar_split_clause,[],[f47,f2971]) ).
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(f2969,plain,
spl0_308,
inference(avatar_split_clause,[],[f23,f2967]) ).
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(f2965,plain,
spl0_307,
inference(avatar_split_clause,[],[f266,f2963]) ).
fof(f2963,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(f2961,plain,
spl0_306,
inference(avatar_split_clause,[],[f172,f2959]) ).
fof(f2959,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(f2957,plain,
spl0_305,
inference(avatar_split_clause,[],[f123,f2955]) ).
fof(f2955,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(f2953,plain,
spl0_304,
inference(avatar_split_clause,[],[f109,f2950]) ).
fof(f2950,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(f2948,plain,
spl0_303,
inference(avatar_split_clause,[],[f92,f2946]) ).
fof(f2946,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(f2944,plain,
spl0_302,
inference(avatar_split_clause,[],[f90,f2942]) ).
fof(f2942,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(f2940,plain,
spl0_301,
inference(avatar_split_clause,[],[f80,f2938]) ).
fof(f2938,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(f2936,plain,
spl0_300,
inference(avatar_split_clause,[],[f74,f2934]) ).
fof(f2934,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(f2932,plain,
spl0_299,
inference(avatar_split_clause,[],[f28,f2930]) ).
fof(f2930,plain,
( spl0_299
<=> ! [X2,X14] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X14,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f28,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__empty__iff2_0) ).
fof(f2928,plain,
spl0_298,
inference(avatar_split_clause,[],[f1371,f2926]) ).
fof(f1371,axiom,
! [X41] :
( ~ c_in(c_Pair(v_y,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2924,plain,
spl0_297,
inference(avatar_split_clause,[],[f1363,f2922]) ).
fof(f2922,plain,
( spl0_297
<=> ! [X54,X55] : c_Comb_Ocomb_OS != c_Comb_Ocomb_Oop_A_D_D(X54,X55) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f1363,axiom,
! [X54,X55] : c_Comb_Ocomb_OS != c_Comb_Ocomb_Oop_A_D_D(X54,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__6__iff1_0) ).
fof(f2920,plain,
spl0_296,
inference(avatar_split_clause,[],[f1360,f2918]) ).
fof(f2918,plain,
( spl0_296
<=> ! [X54,X55] : c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X54,X55) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f1360,axiom,
! [X54,X55] : c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X54,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__3__iff1_0) ).
fof(f2916,plain,
spl0_295,
inference(avatar_split_clause,[],[f448,f2914]) ).
fof(f2914,plain,
( spl0_295
<=> ! [X51] :
( ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_set(X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
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(f2912,plain,
spl0_294,
inference(avatar_split_clause,[],[f326,f2910]) ).
fof(f2910,plain,
( spl0_294
<=> ! [X51] :
( ~ class_Finite__Set_Ofinite(X51)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X51)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
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(f2908,plain,
spl0_293,
inference(avatar_split_clause,[],[f310,f2906]) ).
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(f2904,plain,
spl0_292,
inference(avatar_split_clause,[],[f299,f2902]) ).
fof(f2902,plain,
( spl0_292
<=> ! [X13,X2] : c_lessequals(c_emptyset,X13,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
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(f2900,plain,
spl0_291,
inference(avatar_split_clause,[],[f265,f2898]) ).
fof(f2898,plain,
( spl0_291
<=> ! [X18] : c_less(c_0,c_Suc(X18),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
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(f2896,plain,
spl0_290,
inference(avatar_split_clause,[],[f263,f2894]) ).
fof(f2894,plain,
( spl0_290
<=> ! [X18] : c_less(X18,c_Suc(X18),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f263,axiom,
! [X18] : c_less(X18,c_Suc(X18),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f2892,plain,
spl0_289,
inference(avatar_split_clause,[],[f226,f2890]) ).
fof(f2890,plain,
( spl0_289
<=> ! [X2] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
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(f2888,plain,
spl0_288,
inference(avatar_split_clause,[],[f222,f2886]) ).
fof(f2886,plain,
( spl0_288
<=> ! [X9] : c_Divides_Oop_Advd(c_Suc(c_0),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
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(f2884,plain,
spl0_287,
inference(avatar_split_clause,[],[f178,f2882]) ).
fof(f2882,plain,
( spl0_287
<=> ! [X13,X2] : ~ c_less(X13,c_emptyset,tc_set(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
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(f2880,plain,
spl0_286,
inference(avatar_split_clause,[],[f94,f2878]) ).
fof(f2878,plain,
( spl0_286
<=> ! [X2] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f94,axiom,
! [X2] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
fof(f2876,plain,
spl0_285,
inference(avatar_split_clause,[],[f56,f2874]) ).
fof(f2874,plain,
( spl0_285
<=> ! [X2] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
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(f2872,plain,
~ spl0_284,
inference(avatar_split_clause,[],[f43,f2869]) ).
fof(f2869,plain,
( spl0_284
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
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(f2867,plain,
spl0_283,
inference(avatar_split_clause,[],[f6,f2865]) ).
fof(f2865,plain,
( spl0_283
<=> ! [X2,X3] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
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(f2556,plain,
spl0_282,
inference(avatar_split_clause,[],[f1357,f2554]) ).
fof(f2554,plain,
( spl0_282
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
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(f2552,plain,
spl0_281,
inference(avatar_split_clause,[],[f1356,f2550]) ).
fof(f2550,plain,
( spl0_281
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
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(f2548,plain,
spl0_280,
inference(avatar_split_clause,[],[f1355,f2546]) ).
fof(f2546,plain,
( spl0_280
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
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(f2544,plain,
spl0_279,
inference(avatar_split_clause,[],[f1354,f2542]) ).
fof(f2542,plain,
( spl0_279
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
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(f2540,plain,
spl0_278,
inference(avatar_split_clause,[],[f1353,f2538]) ).
fof(f2538,plain,
( spl0_278
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
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(f2536,plain,
spl0_277,
inference(avatar_split_clause,[],[f1352,f2534]) ).
fof(f2534,plain,
( spl0_277
<=> ! [X53] :
( ~ class_Wellfounded__Recursion_Owellorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
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(f2532,plain,
spl0_276,
inference(avatar_split_clause,[],[f1265,f2530]) ).
fof(f2530,plain,
( spl0_276
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
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(f2528,plain,
spl0_275,
inference(avatar_split_clause,[],[f1257,f2526]) ).
fof(f2526,plain,
( spl0_275
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
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(f2524,plain,
spl0_274,
inference(avatar_split_clause,[],[f1256,f2522]) ).
fof(f2522,plain,
( spl0_274
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
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(f2520,plain,
spl0_273,
inference(avatar_split_clause,[],[f1246,f2518]) ).
fof(f2518,plain,
( spl0_273
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
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(f2516,plain,
spl0_272,
inference(avatar_split_clause,[],[f1245,f2514]) ).
fof(f2514,plain,
( spl0_272
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
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(f2512,plain,
spl0_271,
inference(avatar_split_clause,[],[f1244,f2510]) ).
fof(f2510,plain,
( spl0_271
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
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(f2508,plain,
spl0_270,
inference(avatar_split_clause,[],[f1242,f2506]) ).
fof(f2506,plain,
( spl0_270
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
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(f2504,plain,
spl0_269,
inference(avatar_split_clause,[],[f1241,f2502]) ).
fof(f2502,plain,
( spl0_269
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
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(f2500,plain,
spl0_268,
inference(avatar_split_clause,[],[f1240,f2498]) ).
fof(f2498,plain,
( spl0_268
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
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(f2496,plain,
spl0_267,
inference(avatar_split_clause,[],[f1239,f2494]) ).
fof(f2494,plain,
( spl0_267
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
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(f2492,plain,
spl0_266,
inference(avatar_split_clause,[],[f1238,f2490]) ).
fof(f2490,plain,
( spl0_266
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__ring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
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(f2488,plain,
spl0_265,
inference(avatar_split_clause,[],[f1222,f2486]) ).
fof(f2486,plain,
( spl0_265
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
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(f2484,plain,
spl0_264,
inference(avatar_split_clause,[],[f1221,f2482]) ).
fof(f2482,plain,
( spl0_264
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
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(f2480,plain,
spl0_263,
inference(avatar_split_clause,[],[f1220,f2478]) ).
fof(f2478,plain,
( spl0_263
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
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(f2476,plain,
spl0_262,
inference(avatar_split_clause,[],[f1219,f2474]) ).
fof(f2474,plain,
( spl0_262
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
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(f2472,plain,
spl0_261,
inference(avatar_split_clause,[],[f1187,f2470]) ).
fof(f2470,plain,
( spl0_261
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
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(f2468,plain,
spl0_260,
inference(avatar_split_clause,[],[f1178,f2466]) ).
fof(f2466,plain,
( spl0_260
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
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(f2464,plain,
spl0_259,
inference(avatar_split_clause,[],[f1177,f2462]) ).
fof(f2462,plain,
( spl0_259
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
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(f2460,plain,
spl0_258,
inference(avatar_split_clause,[],[f1174,f2458]) ).
fof(f2458,plain,
( spl0_258
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
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(f2456,plain,
spl0_257,
inference(avatar_split_clause,[],[f1164,f2454]) ).
fof(f2454,plain,
( spl0_257
<=> ! [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_257])]) ).
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(f2452,plain,
spl0_256,
inference(avatar_split_clause,[],[f1163,f2450]) ).
fof(f2450,plain,
( spl0_256
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
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(f2448,plain,
spl0_255,
inference(avatar_split_clause,[],[f1160,f2446]) ).
fof(f2446,plain,
( spl0_255
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
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(f2444,plain,
spl0_254,
inference(avatar_split_clause,[],[f1159,f2442]) ).
fof(f2442,plain,
( spl0_254
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
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(f2440,plain,
spl0_253,
inference(avatar_split_clause,[],[f1155,f2438]) ).
fof(f2438,plain,
( spl0_253
<=> ! [X53] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
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(f2436,plain,
spl0_252,
inference(avatar_split_clause,[],[f1153,f2434]) ).
fof(f2434,plain,
( spl0_252
<=> ! [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_252])]) ).
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(f2432,plain,
spl0_251,
inference(avatar_split_clause,[],[f1152,f2430]) ).
fof(f2430,plain,
( spl0_251
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
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(f2428,plain,
spl0_250,
inference(avatar_split_clause,[],[f1145,f2426]) ).
fof(f2426,plain,
( spl0_250
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
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(f2424,plain,
spl0_249,
inference(avatar_split_clause,[],[f1144,f2422]) ).
fof(f2422,plain,
( spl0_249
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
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(f2420,plain,
spl0_248,
inference(avatar_split_clause,[],[f1139,f2418]) ).
fof(f2418,plain,
( spl0_248
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
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(f2416,plain,
spl0_247,
inference(avatar_split_clause,[],[f1138,f2414]) ).
fof(f2414,plain,
( spl0_247
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
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(f2412,plain,
spl0_246,
inference(avatar_split_clause,[],[f1137,f2410]) ).
fof(f2410,plain,
( spl0_246
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
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(f2408,plain,
spl0_245,
inference(avatar_split_clause,[],[f1136,f2406]) ).
fof(f2406,plain,
( spl0_245
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
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(f2404,plain,
spl0_244,
inference(avatar_split_clause,[],[f1135,f2402]) ).
fof(f2402,plain,
( spl0_244
<=> ! [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_244])]) ).
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(f2400,plain,
spl0_243,
inference(avatar_split_clause,[],[f1134,f2398]) ).
fof(f2398,plain,
( spl0_243
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
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(f2396,plain,
spl0_242,
inference(avatar_split_clause,[],[f1133,f2394]) ).
fof(f2394,plain,
( spl0_242
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
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(f2392,plain,
spl0_241,
inference(avatar_split_clause,[],[f1132,f2390]) ).
fof(f2390,plain,
( spl0_241
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
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(f2388,plain,
spl0_240,
inference(avatar_split_clause,[],[f1131,f2386]) ).
fof(f2386,plain,
( spl0_240
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
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(f2384,plain,
spl0_239,
inference(avatar_split_clause,[],[f1122,f2382]) ).
fof(f2382,plain,
( spl0_239
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
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(f2380,plain,
spl0_238,
inference(avatar_split_clause,[],[f1121,f2378]) ).
fof(f2378,plain,
( spl0_238
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
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(f2376,plain,
spl0_237,
inference(avatar_split_clause,[],[f1120,f2374]) ).
fof(f2374,plain,
( spl0_237
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
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(f2372,plain,
spl0_236,
inference(avatar_split_clause,[],[f1119,f2370]) ).
fof(f2370,plain,
( spl0_236
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
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(f2368,plain,
spl0_235,
inference(avatar_split_clause,[],[f1118,f2366]) ).
fof(f2366,plain,
( spl0_235
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
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(f2364,plain,
spl0_234,
inference(avatar_split_clause,[],[f1117,f2362]) ).
fof(f2362,plain,
( spl0_234
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
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(f2360,plain,
spl0_233,
inference(avatar_split_clause,[],[f1116,f2358]) ).
fof(f2358,plain,
( spl0_233
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
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(f2356,plain,
spl0_232,
inference(avatar_split_clause,[],[f1115,f2354]) ).
fof(f2354,plain,
( spl0_232
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
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(f2352,plain,
spl0_231,
inference(avatar_split_clause,[],[f1114,f2350]) ).
fof(f2350,plain,
( spl0_231
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
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(f2348,plain,
spl0_230,
inference(avatar_split_clause,[],[f1113,f2346]) ).
fof(f2346,plain,
( spl0_230
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
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(f2344,plain,
spl0_229,
inference(avatar_split_clause,[],[f1111,f2342]) ).
fof(f2342,plain,
( spl0_229
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
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(f2340,plain,
spl0_228,
inference(avatar_split_clause,[],[f1110,f2338]) ).
fof(f2338,plain,
( spl0_228
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
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(f2336,plain,
spl0_227,
inference(avatar_split_clause,[],[f1109,f2334]) ).
fof(f2334,plain,
( spl0_227
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
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(f2332,plain,
spl0_226,
inference(avatar_split_clause,[],[f1108,f2330]) ).
fof(f2330,plain,
( spl0_226
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
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(f2328,plain,
spl0_225,
inference(avatar_split_clause,[],[f1107,f2326]) ).
fof(f2326,plain,
( spl0_225
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
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(f2324,plain,
spl0_224,
inference(avatar_split_clause,[],[f1106,f2322]) ).
fof(f2322,plain,
( spl0_224
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__semidom(X53)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
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(f2320,plain,
spl0_223,
inference(avatar_split_clause,[],[f1081,f2318]) ).
fof(f2318,plain,
( spl0_223
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
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(f2316,plain,
spl0_222,
inference(avatar_split_clause,[],[f1080,f2314]) ).
fof(f2314,plain,
( spl0_222
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
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(f2312,plain,
spl0_221,
inference(avatar_split_clause,[],[f1079,f2310]) ).
fof(f2310,plain,
( spl0_221
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
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(f2308,plain,
spl0_220,
inference(avatar_split_clause,[],[f1078,f2306]) ).
fof(f2306,plain,
( spl0_220
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
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(f2304,plain,
spl0_219,
inference(avatar_split_clause,[],[f1077,f2302]) ).
fof(f2302,plain,
( spl0_219
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Olordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
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(f2300,plain,
spl0_218,
inference(avatar_split_clause,[],[f1076,f2298]) ).
fof(f2298,plain,
( spl0_218
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
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(f2296,plain,
spl0_217,
inference(avatar_split_clause,[],[f1074,f2294]) ).
fof(f2294,plain,
( spl0_217
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
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(f2292,plain,
spl0_216,
inference(avatar_split_clause,[],[f1073,f2290]) ).
fof(f2290,plain,
( spl0_216
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Oaxclass__abs__if(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
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(f2288,plain,
spl0_215,
inference(avatar_split_clause,[],[f1072,f2286]) ).
fof(f2286,plain,
( spl0_215
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
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(f2284,plain,
spl0_214,
inference(avatar_split_clause,[],[f1071,f2282]) ).
fof(f2282,plain,
( spl0_214
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
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(f2280,plain,
spl0_213,
inference(avatar_split_clause,[],[f1070,f2278]) ).
fof(f2278,plain,
( spl0_213
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
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(f2276,plain,
spl0_212,
inference(avatar_split_clause,[],[f1069,f2274]) ).
fof(f2274,plain,
( spl0_212
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
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(f2272,plain,
spl0_211,
inference(avatar_split_clause,[],[f1068,f2270]) ).
fof(f2270,plain,
( spl0_211
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
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(f2268,plain,
spl0_210,
inference(avatar_split_clause,[],[f1067,f2266]) ).
fof(f2266,plain,
( spl0_210
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
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(f2264,plain,
spl0_209,
inference(avatar_split_clause,[],[f1066,f2262]) ).
fof(f2262,plain,
( spl0_209
<=> ! [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_209])]) ).
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(f2260,plain,
spl0_208,
inference(avatar_split_clause,[],[f1065,f2258]) ).
fof(f2258,plain,
( spl0_208
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
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(f2256,plain,
spl0_207,
inference(avatar_split_clause,[],[f1063,f2254]) ).
fof(f2254,plain,
( spl0_207
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
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(f2252,plain,
spl0_206,
inference(avatar_split_clause,[],[f1062,f2250]) ).
fof(f2250,plain,
( spl0_206
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
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(f2248,plain,
spl0_205,
inference(avatar_split_clause,[],[f1061,f2246]) ).
fof(f2246,plain,
( spl0_205
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
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(f2244,plain,
spl0_204,
inference(avatar_split_clause,[],[f1060,f2242]) ).
fof(f2242,plain,
( spl0_204
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
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(f2240,plain,
spl0_203,
inference(avatar_split_clause,[],[f1059,f2238]) ).
fof(f2238,plain,
( spl0_203
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
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(f2236,plain,
spl0_202,
inference(avatar_split_clause,[],[f1045,f2234]) ).
fof(f2234,plain,
( spl0_202
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__semidom(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
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(f2232,plain,
spl0_201,
inference(avatar_split_clause,[],[f1044,f2230]) ).
fof(f2230,plain,
( spl0_201
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
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(f2228,plain,
spl0_200,
inference(avatar_split_clause,[],[f1043,f2226]) ).
fof(f2226,plain,
( spl0_200
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
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(f2224,plain,
spl0_199,
inference(avatar_split_clause,[],[f1042,f2222]) ).
fof(f2222,plain,
( spl0_199
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
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(f2220,plain,
spl0_198,
inference(avatar_split_clause,[],[f1041,f2218]) ).
fof(f2218,plain,
( spl0_198
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
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(f2216,plain,
spl0_197,
inference(avatar_split_clause,[],[f1040,f2214]) ).
fof(f2214,plain,
( spl0_197
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
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(f2212,plain,
spl0_196,
inference(avatar_split_clause,[],[f1038,f2210]) ).
fof(f2210,plain,
( spl0_196
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
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(f2208,plain,
spl0_195,
inference(avatar_split_clause,[],[f1037,f2206]) ).
fof(f2206,plain,
( spl0_195
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Olordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
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(f2204,plain,
spl0_194,
inference(avatar_split_clause,[],[f1036,f2202]) ).
fof(f2202,plain,
( spl0_194
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__ring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
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(f2200,plain,
spl0_193,
inference(avatar_split_clause,[],[f1035,f2198]) ).
fof(f2198,plain,
( spl0_193
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oaxclass__abs__if(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
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(f2196,plain,
spl0_192,
inference(avatar_split_clause,[],[f1034,f2194]) ).
fof(f2194,plain,
( spl0_192
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
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(f2192,plain,
spl0_191,
inference(avatar_split_clause,[],[f1033,f2190]) ).
fof(f2190,plain,
( spl0_191
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
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(f2188,plain,
spl0_190,
inference(avatar_split_clause,[],[f1032,f2186]) ).
fof(f2186,plain,
( spl0_190
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
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(f2184,plain,
spl0_189,
inference(avatar_split_clause,[],[f1031,f2182]) ).
fof(f2182,plain,
( spl0_189
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
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(f2180,plain,
spl0_188,
inference(avatar_split_clause,[],[f1030,f2178]) ).
fof(f2178,plain,
( spl0_188
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
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(f2176,plain,
spl0_187,
inference(avatar_split_clause,[],[f1029,f2174]) ).
fof(f2174,plain,
( spl0_187
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
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(f2172,plain,
spl0_186,
inference(avatar_split_clause,[],[f1027,f2170]) ).
fof(f2170,plain,
( spl0_186
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
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(f2168,plain,
spl0_185,
inference(avatar_split_clause,[],[f1026,f2166]) ).
fof(f2166,plain,
( spl0_185
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
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(f2164,plain,
spl0_184,
inference(avatar_split_clause,[],[f1025,f2162]) ).
fof(f2162,plain,
( spl0_184
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
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(f2160,plain,
spl0_183,
inference(avatar_split_clause,[],[f1024,f2158]) ).
fof(f2158,plain,
( spl0_183
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
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(f2156,plain,
spl0_182,
inference(avatar_split_clause,[],[f1023,f2154]) ).
fof(f2154,plain,
( spl0_182
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
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(f2152,plain,
spl0_181,
inference(avatar_split_clause,[],[f1022,f2150]) ).
fof(f2150,plain,
( spl0_181
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
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(f2148,plain,
spl0_180,
inference(avatar_split_clause,[],[f1021,f2146]) ).
fof(f2146,plain,
( spl0_180
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
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(f2144,plain,
spl0_179,
inference(avatar_split_clause,[],[f1020,f2142]) ).
fof(f2142,plain,
( spl0_179
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
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(f2140,plain,
spl0_178,
inference(avatar_split_clause,[],[f1019,f2138]) ).
fof(f2138,plain,
( spl0_178
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
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(f2136,plain,
spl0_177,
inference(avatar_split_clause,[],[f1018,f2134]) ).
fof(f2134,plain,
( spl0_177
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__idom(X53)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
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(f2132,plain,
spl0_176,
inference(avatar_split_clause,[],[f925,f2130]) ).
fof(f2130,plain,
( spl0_176
<=> ! [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_176])]) ).
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(f2128,plain,
spl0_175,
inference(avatar_split_clause,[],[f924,f2126]) ).
fof(f2126,plain,
( spl0_175
<=> ! [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_175])]) ).
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(f2124,plain,
spl0_174,
inference(avatar_split_clause,[],[f923,f2122]) ).
fof(f2122,plain,
( spl0_174
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
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(f2120,plain,
spl0_173,
inference(avatar_split_clause,[],[f921,f2118]) ).
fof(f2118,plain,
( spl0_173
<=> ! [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_173])]) ).
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(f2116,plain,
spl0_172,
inference(avatar_split_clause,[],[f920,f2114]) ).
fof(f2114,plain,
( spl0_172
<=> ! [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_172])]) ).
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(f2112,plain,
spl0_171,
inference(avatar_split_clause,[],[f917,f2110]) ).
fof(f2110,plain,
( spl0_171
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
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(f2108,plain,
spl0_170,
inference(avatar_split_clause,[],[f916,f2106]) ).
fof(f2106,plain,
( spl0_170
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
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(f2104,plain,
spl0_169,
inference(avatar_split_clause,[],[f914,f2102]) ).
fof(f2102,plain,
( spl0_169
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
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(f2100,plain,
spl0_168,
inference(avatar_split_clause,[],[f913,f2098]) ).
fof(f2098,plain,
( spl0_168
<=> ! [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_168])]) ).
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(f2096,plain,
spl0_167,
inference(avatar_split_clause,[],[f912,f2094]) ).
fof(f2094,plain,
( spl0_167
<=> ! [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_167])]) ).
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(f2092,plain,
spl0_166,
inference(avatar_split_clause,[],[f911,f2090]) ).
fof(f2090,plain,
( spl0_166
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
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(f2088,plain,
spl0_165,
inference(avatar_split_clause,[],[f910,f2086]) ).
fof(f2086,plain,
( spl0_165
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
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(f2084,plain,
spl0_164,
inference(avatar_split_clause,[],[f909,f2082]) ).
fof(f2082,plain,
( spl0_164
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
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(f2080,plain,
spl0_163,
inference(avatar_split_clause,[],[f908,f2078]) ).
fof(f2078,plain,
( spl0_163
<=> ! [X53] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
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(f2076,plain,
spl0_162,
inference(avatar_split_clause,[],[f907,f2074]) ).
fof(f2074,plain,
( spl0_162
<=> ! [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_162])]) ).
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(f2072,plain,
spl0_161,
inference(avatar_split_clause,[],[f902,f2070]) ).
fof(f2070,plain,
( spl0_161
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
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(f2068,plain,
spl0_160,
inference(avatar_split_clause,[],[f901,f2066]) ).
fof(f2066,plain,
( spl0_160
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
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(f2064,plain,
spl0_159,
inference(avatar_split_clause,[],[f900,f2062]) ).
fof(f2062,plain,
( spl0_159
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__cancel__semiring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
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(f2060,plain,
spl0_158,
inference(avatar_split_clause,[],[f899,f2058]) ).
fof(f2058,plain,
( spl0_158
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
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(f2056,plain,
spl0_157,
inference(avatar_split_clause,[],[f898,f2054]) ).
fof(f2054,plain,
( spl0_157
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
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(f2052,plain,
spl0_156,
inference(avatar_split_clause,[],[f896,f2050]) ).
fof(f2050,plain,
( spl0_156
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__join(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
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(f2048,plain,
spl0_155,
inference(avatar_split_clause,[],[f894,f2046]) ).
fof(f2046,plain,
( spl0_155
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__meet(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
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(f2044,plain,
spl0_154,
inference(avatar_split_clause,[],[f893,f2042]) ).
fof(f2042,plain,
( spl0_154
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
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(f2040,plain,
spl0_153,
inference(avatar_split_clause,[],[f892,f2038]) ).
fof(f2038,plain,
( spl0_153
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
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(f2036,plain,
spl0_152,
inference(avatar_split_clause,[],[f891,f2034]) ).
fof(f2034,plain,
( spl0_152
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
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(f2032,plain,
spl0_151,
inference(avatar_split_clause,[],[f890,f2030]) ).
fof(f2030,plain,
( spl0_151
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
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(f2028,plain,
spl0_150,
inference(avatar_split_clause,[],[f889,f2026]) ).
fof(f2026,plain,
( spl0_150
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Olordered__ab__group__abs(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
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(f2024,plain,
spl0_149,
inference(avatar_split_clause,[],[f884,f2022]) ).
fof(f2022,plain,
( spl0_149
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
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(f2020,plain,
spl0_148,
inference(avatar_split_clause,[],[f875,f2018]) ).
fof(f2018,plain,
( spl0_148
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
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(f2016,plain,
spl0_147,
inference(avatar_split_clause,[],[f874,f2014]) ).
fof(f2014,plain,
( spl0_147
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
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(f2012,plain,
spl0_146,
inference(avatar_split_clause,[],[f872,f2010]) ).
fof(f2010,plain,
( spl0_146
<=> ! [X53] :
( ~ class_Ring__and__Field_Olordered__ring(X53)
| class_Ring__and__Field_Opordered__ring(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
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(f2008,plain,
spl0_145,
inference(avatar_split_clause,[],[f681,f2006]) ).
fof(f2006,plain,
( spl0_145
<=> ! [X53] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
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(f2004,plain,
spl0_144,
inference(avatar_split_clause,[],[f652,f2002]) ).
fof(f2002,plain,
( spl0_144
<=> ! [X53] :
( ~ class_Orderings_Oorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f652,axiom,
! [X53] :
( ~ class_Orderings_Oorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f2000,plain,
spl0_143,
inference(avatar_split_clause,[],[f651,f1998]) ).
fof(f1998,plain,
( spl0_143
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f651,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f1996,plain,
spl0_142,
inference(avatar_split_clause,[],[f650,f1994]) ).
fof(f1994,plain,
( spl0_142
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f650,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f1992,plain,
spl0_141,
inference(avatar_split_clause,[],[f649,f1990]) ).
fof(f1990,plain,
( spl0_141
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
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(f1988,plain,
spl0_140,
inference(avatar_split_clause,[],[f648,f1986]) ).
fof(f1986,plain,
( spl0_140
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
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(f1984,plain,
spl0_139,
inference(avatar_split_clause,[],[f647,f1982]) ).
fof(f1982,plain,
( spl0_139
<=> ! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f647,axiom,
! [X53] :
( ~ class_Orderings_Olinorder(X53)
| class_LOrder_Olorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f1980,plain,
spl0_138,
inference(avatar_split_clause,[],[f639,f1978]) ).
fof(f1978,plain,
( spl0_138
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
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(f1976,plain,
spl0_137,
inference(avatar_split_clause,[],[f638,f1974]) ).
fof(f1974,plain,
( spl0_137
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
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(f1972,plain,
spl0_136,
inference(avatar_split_clause,[],[f637,f1970]) ).
fof(f1970,plain,
( spl0_136
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
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(f1968,plain,
spl0_135,
inference(avatar_split_clause,[],[f631,f1966]) ).
fof(f1966,plain,
( spl0_135
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
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(f1964,plain,
spl0_134,
inference(avatar_split_clause,[],[f630,f1962]) ).
fof(f1962,plain,
( spl0_134
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
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(f1960,plain,
spl0_133,
inference(avatar_split_clause,[],[f629,f1958]) ).
fof(f1958,plain,
( spl0_133
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
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(f1956,plain,
spl0_132,
inference(avatar_split_clause,[],[f628,f1954]) ).
fof(f1954,plain,
( spl0_132
<=> ! [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_132])]) ).
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(f1952,plain,
spl0_131,
inference(avatar_split_clause,[],[f624,f1950]) ).
fof(f1950,plain,
( spl0_131
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
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(f1948,plain,
spl0_130,
inference(avatar_split_clause,[],[f623,f1946]) ).
fof(f1946,plain,
( spl0_130
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
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(f1944,plain,
spl0_129,
inference(avatar_split_clause,[],[f622,f1942]) ).
fof(f1942,plain,
( spl0_129
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
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(f1940,plain,
spl0_128,
inference(avatar_split_clause,[],[f614,f1938]) ).
fof(f1938,plain,
( spl0_128
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
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(f1936,plain,
spl0_127,
inference(avatar_split_clause,[],[f613,f1934]) ).
fof(f1934,plain,
( spl0_127
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
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(f1932,plain,
spl0_126,
inference(avatar_split_clause,[],[f612,f1930]) ).
fof(f1930,plain,
( spl0_126
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
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(f1928,plain,
spl0_125,
inference(avatar_split_clause,[],[f611,f1926]) ).
fof(f1926,plain,
( spl0_125
<=> ! [X53] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
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(f1924,plain,
spl0_124,
inference(avatar_split_clause,[],[f608,f1922]) ).
fof(f1922,plain,
( spl0_124
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Olinorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
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(f1920,plain,
spl0_123,
inference(avatar_split_clause,[],[f602,f1918]) ).
fof(f1918,plain,
( spl0_123
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
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(f1916,plain,
spl0_122,
inference(avatar_split_clause,[],[f601,f1914]) ).
fof(f1914,plain,
( spl0_122
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
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(f1912,plain,
spl0_121,
inference(avatar_split_clause,[],[f600,f1910]) ).
fof(f1910,plain,
( spl0_121
<=> ! [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_121])]) ).
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(f1908,plain,
spl0_120,
inference(avatar_split_clause,[],[f599,f1906]) ).
fof(f1906,plain,
( spl0_120
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
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(f1904,plain,
spl0_119,
inference(avatar_split_clause,[],[f598,f1902]) ).
fof(f1902,plain,
( spl0_119
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
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(f1900,plain,
spl0_118,
inference(avatar_split_clause,[],[f597,f1898]) ).
fof(f1898,plain,
( spl0_118
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
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(f1896,plain,
spl0_117,
inference(avatar_split_clause,[],[f596,f1894]) ).
fof(f1894,plain,
( spl0_117
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
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(f1892,plain,
spl0_116,
inference(avatar_split_clause,[],[f595,f1890]) ).
fof(f1890,plain,
( spl0_116
<=> ! [X53] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
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(f1888,plain,
spl0_115,
inference(avatar_split_clause,[],[f591,f1886]) ).
fof(f1886,plain,
( spl0_115
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
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(f1884,plain,
spl0_114,
inference(avatar_split_clause,[],[f590,f1882]) ).
fof(f1882,plain,
( spl0_114
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
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(f1880,plain,
spl0_113,
inference(avatar_split_clause,[],[f589,f1878]) ).
fof(f1878,plain,
( spl0_113
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
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(f1876,plain,
spl0_112,
inference(avatar_split_clause,[],[f588,f1874]) ).
fof(f1874,plain,
( spl0_112
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
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(f1872,plain,
spl0_111,
inference(avatar_split_clause,[],[f587,f1870]) ).
fof(f1870,plain,
( spl0_111
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
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(f1868,plain,
spl0_110,
inference(avatar_split_clause,[],[f583,f1866]) ).
fof(f1866,plain,
( spl0_110
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
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(f1864,plain,
spl0_109,
inference(avatar_split_clause,[],[f582,f1862]) ).
fof(f1862,plain,
( spl0_109
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
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(f1860,plain,
spl0_108,
inference(avatar_split_clause,[],[f581,f1858]) ).
fof(f1858,plain,
( spl0_108
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
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(f1856,plain,
spl0_107,
inference(avatar_split_clause,[],[f580,f1854]) ).
fof(f1854,plain,
( spl0_107
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
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(f1852,plain,
spl0_106,
inference(avatar_split_clause,[],[f573,f1850]) ).
fof(f1850,plain,
( spl0_106
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
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(f1848,plain,
spl0_105,
inference(avatar_split_clause,[],[f572,f1846]) ).
fof(f1846,plain,
( spl0_105
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
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(f1844,plain,
spl0_104,
inference(avatar_split_clause,[],[f571,f1842]) ).
fof(f1842,plain,
( spl0_104
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
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(f1840,plain,
spl0_103,
inference(avatar_split_clause,[],[f570,f1838]) ).
fof(f1838,plain,
( spl0_103
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
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(f1836,plain,
spl0_102,
inference(avatar_split_clause,[],[f569,f1834]) ).
fof(f1834,plain,
( spl0_102
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
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(f1832,plain,
spl0_101,
inference(avatar_split_clause,[],[f568,f1830]) ).
fof(f1830,plain,
( spl0_101
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
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(f1828,plain,
spl0_100,
inference(avatar_split_clause,[],[f564,f1826]) ).
fof(f1826,plain,
( spl0_100
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
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(f1824,plain,
spl0_99,
inference(avatar_split_clause,[],[f563,f1822]) ).
fof(f1822,plain,
( spl0_99
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
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(f1820,plain,
spl0_98,
inference(avatar_split_clause,[],[f562,f1818]) ).
fof(f1818,plain,
( spl0_98
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
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(f1816,plain,
spl0_97,
inference(avatar_split_clause,[],[f561,f1814]) ).
fof(f1814,plain,
( spl0_97
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
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(f1812,plain,
spl0_96,
inference(avatar_split_clause,[],[f554,f1810]) ).
fof(f1810,plain,
( spl0_96
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
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(f1808,plain,
spl0_95,
inference(avatar_split_clause,[],[f552,f1806]) ).
fof(f1806,plain,
( spl0_95
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
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(f1804,plain,
spl0_94,
inference(avatar_split_clause,[],[f551,f1802]) ).
fof(f1802,plain,
( spl0_94
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
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(f1800,plain,
spl0_93,
inference(avatar_split_clause,[],[f550,f1798]) ).
fof(f1798,plain,
( spl0_93
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
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(f1796,plain,
spl0_92,
inference(avatar_split_clause,[],[f545,f1794]) ).
fof(f1794,plain,
( spl0_92
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
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(f1792,plain,
spl0_91,
inference(avatar_split_clause,[],[f544,f1790]) ).
fof(f1790,plain,
( spl0_91
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
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(f1788,plain,
spl0_90,
inference(avatar_split_clause,[],[f543,f1786]) ).
fof(f1786,plain,
( spl0_90
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
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(f1784,plain,
spl0_89,
inference(avatar_split_clause,[],[f542,f1782]) ).
fof(f1782,plain,
( spl0_89
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
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(f1780,plain,
spl0_88,
inference(avatar_split_clause,[],[f541,f1778]) ).
fof(f1778,plain,
( spl0_88
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
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(f1776,plain,
spl0_87,
inference(avatar_split_clause,[],[f536,f1774]) ).
fof(f1774,plain,
( spl0_87
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
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(f1772,plain,
spl0_86,
inference(avatar_split_clause,[],[f535,f1770]) ).
fof(f1770,plain,
( spl0_86
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X53)
| class_OrderedGroup_Olordered__ab__group(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
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(f1768,plain,
spl0_85,
inference(avatar_split_clause,[],[f534,f1766]) ).
fof(f1766,plain,
( spl0_85
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
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(f1764,plain,
spl0_84,
inference(avatar_split_clause,[],[f533,f1762]) ).
fof(f1762,plain,
( spl0_84
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
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(f1760,plain,
spl0_83,
inference(avatar_split_clause,[],[f532,f1758]) ).
fof(f1758,plain,
( spl0_83
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
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(f1756,plain,
spl0_82,
inference(avatar_split_clause,[],[f531,f1754]) ).
fof(f1754,plain,
( spl0_82
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
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(f1752,plain,
spl0_81,
inference(avatar_split_clause,[],[f530,f1750]) ).
fof(f1750,plain,
( spl0_81
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
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(f1748,plain,
spl0_80,
inference(avatar_split_clause,[],[f526,f1746]) ).
fof(f1746,plain,
( spl0_80
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
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(f1744,plain,
spl0_79,
inference(avatar_split_clause,[],[f525,f1742]) ).
fof(f1742,plain,
( spl0_79
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
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(f1740,plain,
spl0_78,
inference(avatar_split_clause,[],[f524,f1738]) ).
fof(f1738,plain,
( spl0_78
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_LOrder_Olorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
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(f1736,plain,
spl0_77,
inference(avatar_split_clause,[],[f517,f1734]) ).
fof(f1734,plain,
( spl0_77
<=> ! [X53] :
( ~ class_OrderedGroup_Olordered__ab__group(X53)
| class_OrderedGroup_Opordered__ab__group__add(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
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(f1732,plain,
spl0_76,
inference(avatar_split_clause,[],[f458,f1730]) ).
fof(f1730,plain,
( spl0_76
<=> ! [X53] :
( ~ class_LOrder_Omeet__semilorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
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(f1728,plain,
spl0_75,
inference(avatar_split_clause,[],[f457,f1726]) ).
fof(f1726,plain,
( spl0_75
<=> ! [X53] :
( ~ class_LOrder_Omeet__semilorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
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(f1724,plain,
spl0_74,
inference(avatar_split_clause,[],[f456,f1722]) ).
fof(f1722,plain,
( spl0_74
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_LOrder_Ojoin__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
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(f1720,plain,
spl0_73,
inference(avatar_split_clause,[],[f455,f1718]) ).
fof(f1718,plain,
( spl0_73
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f455,axiom,
! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oorder(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f1716,plain,
spl0_72,
inference(avatar_split_clause,[],[f454,f1714]) ).
fof(f1714,plain,
( spl0_72
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f454,axiom,
! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_Orderings_Oord(X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f1712,plain,
spl0_71,
inference(avatar_split_clause,[],[f453,f1710]) ).
fof(f1710,plain,
( spl0_71
<=> ! [X53] :
( ~ class_LOrder_Olorder(X53)
| class_LOrder_Omeet__semilorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
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(f1708,plain,
spl0_70,
inference(avatar_split_clause,[],[f452,f1706]) ).
fof(f1706,plain,
( spl0_70
<=> ! [X53] :
( ~ class_LOrder_Ojoin__semilorder(X53)
| class_Orderings_Oorder(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
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(f1704,plain,
spl0_69,
inference(avatar_split_clause,[],[f451,f1702]) ).
fof(f1702,plain,
( spl0_69
<=> ! [X53] :
( ~ class_LOrder_Ojoin__semilorder(X53)
| class_Orderings_Oord(X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
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(f1700,plain,
spl0_68,
inference(avatar_split_clause,[],[f296,f1698]) ).
fof(f1698,plain,
( spl0_68
<=> ! [X2,X0] : c_in(X0,c_UNIV,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f296,axiom,
! [X2,X0] : c_in(X0,c_UNIV,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f1696,plain,
spl0_67,
inference(avatar_split_clause,[],[f264,f1694]) ).
fof(f1694,plain,
( spl0_67
<=> ! [X18] : ~ c_less(X18,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f264,axiom,
! [X18] : ~ c_less(X18,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f1692,plain,
spl0_66,
inference(avatar_split_clause,[],[f262,f1690]) ).
fof(f1690,plain,
( spl0_66
<=> ! [X18] : c_lessequals(c_0,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f262,axiom,
! [X18] : c_lessequals(c_0,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f1688,plain,
spl0_65,
inference(avatar_split_clause,[],[f238,f1686]) ).
fof(f1686,plain,
( spl0_65
<=> ! [X12] : c_Divides_Oop_Advd(c_1,X12,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
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(f1684,plain,
spl0_64,
inference(avatar_split_clause,[],[f237,f1682]) ).
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(f1680,plain,
spl0_63,
inference(avatar_split_clause,[],[f221,f1678]) ).
fof(f1678,plain,
( spl0_63
<=> ! [X12] : c_Divides_Oop_Advd(X12,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
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(f1676,plain,
spl0_62,
inference(avatar_split_clause,[],[f174,f1674]) ).
fof(f1674,plain,
( spl0_62
<=> ! [X2,X4] : ~ c_in(X4,c_emptyset,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f174,axiom,
! [X2,X4] : ~ c_in(X4,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f1672,plain,
spl0_61,
inference(avatar_split_clause,[],[f120,f1670]) ).
fof(f1670,plain,
( spl0_61
<=> ! [X18] : ~ c_less(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
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(f1668,plain,
spl0_60,
inference(avatar_split_clause,[],[f115,f1665]) ).
fof(f1665,plain,
( spl0_60
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
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(f1663,plain,
spl0_59,
inference(avatar_split_clause,[],[f103,f1661]) ).
fof(f1661,plain,
( spl0_59
<=> ! [X12] : c_0 != c_Suc(X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f103,axiom,
! [X12] : c_0 != c_Suc(X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
fof(f1659,plain,
~ spl0_58,
inference(avatar_split_clause,[],[f1359,f1656]) ).
fof(f1656,plain,
( spl0_58
<=> c_Comb_Ocomb_OK = c_Comb_Ocomb_OS ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1359,axiom,
c_Comb_Ocomb_OK != c_Comb_Ocomb_OS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__2__iff1_0) ).
fof(f1654,plain,
spl0_57,
inference(avatar_split_clause,[],[f447,f1652]) ).
fof(f1652,plain,
( spl0_57
<=> ! [X51] : class_Orderings_Oorder(tc_set(X51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f447,axiom,
! [X51] : class_Orderings_Oorder(tc_set(X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f1650,plain,
spl0_56,
inference(avatar_split_clause,[],[f446,f1648]) ).
fof(f1648,plain,
( spl0_56
<=> ! [X51] : class_Orderings_Oord(tc_set(X51)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f446,axiom,
! [X51] : class_Orderings_Oord(tc_set(X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f1646,plain,
spl0_55,
inference(avatar_split_clause,[],[f324,f1643]) ).
fof(f1643,plain,
( spl0_55
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(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(f1641,plain,
spl0_54,
inference(avatar_split_clause,[],[f322,f1638]) ).
fof(f1638,plain,
( spl0_54
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(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(f1636,plain,
spl0_53,
inference(avatar_split_clause,[],[f321,f1634]) ).
fof(f1634,plain,
( spl0_53
<=> ! [X2] : c_Wellfounded__Recursion_Owf(c_emptyset,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
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(f1632,plain,
~ spl0_52,
inference(avatar_split_clause,[],[f166,f1629]) ).
fof(f1629,plain,
( spl0_52
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f166,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
fof(f1627,plain,
~ spl0_51,
inference(avatar_split_clause,[],[f121,f1624]) ).
fof(f1624,plain,
( spl0_51
<=> c_Numeral_Obit_OB0 = c_Numeral_Obit_OB1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f121,axiom,
c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1__iff1_0) ).
fof(f1622,plain,
~ spl0_50,
inference(avatar_split_clause,[],[f29,f1619]) ).
fof(f1619,plain,
( spl0_50
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f29,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1__iff1_0) ).
fof(f1617,plain,
spl0_49,
inference(avatar_split_clause,[],[f1370,f1614]) ).
fof(f1370,axiom,
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1612,plain,
spl0_48,
inference(avatar_split_clause,[],[f442,f1609]) ).
fof(f1609,plain,
( spl0_48
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f442,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f1607,plain,
spl0_47,
inference(avatar_split_clause,[],[f441,f1604]) ).
fof(f1604,plain,
( spl0_47
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f441,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f1602,plain,
spl0_46,
inference(avatar_split_clause,[],[f440,f1599]) ).
fof(f1599,plain,
( spl0_46
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f440,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f1597,plain,
spl0_45,
inference(avatar_split_clause,[],[f439,f1594]) ).
fof(f1594,plain,
( spl0_45
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f439,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f1592,plain,
spl0_44,
inference(avatar_split_clause,[],[f434,f1589]) ).
fof(f1589,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f434,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f1587,plain,
spl0_43,
inference(avatar_split_clause,[],[f433,f1584]) ).
fof(f1584,plain,
( spl0_43
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f433,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f1582,plain,
spl0_42,
inference(avatar_split_clause,[],[f432,f1579]) ).
fof(f1579,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f432,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f1577,plain,
spl0_41,
inference(avatar_split_clause,[],[f431,f1574]) ).
fof(f1574,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f431,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f1572,plain,
spl0_40,
inference(avatar_split_clause,[],[f430,f1569]) ).
fof(f1569,plain,
( spl0_40
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f430,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f1567,plain,
spl0_39,
inference(avatar_split_clause,[],[f429,f1564]) ).
fof(f1564,plain,
( spl0_39
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f429,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f1562,plain,
spl0_38,
inference(avatar_split_clause,[],[f428,f1559]) ).
fof(f1559,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f428,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f1557,plain,
spl0_37,
inference(avatar_split_clause,[],[f427,f1554]) ).
fof(f1554,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f427,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f1552,plain,
spl0_36,
inference(avatar_split_clause,[],[f426,f1549]) ).
fof(f1549,plain,
( spl0_36
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f426,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f1547,plain,
spl0_35,
inference(avatar_split_clause,[],[f425,f1544]) ).
fof(f1544,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f425,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f1542,plain,
spl0_34,
inference(avatar_split_clause,[],[f424,f1539]) ).
fof(f1539,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f424,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f1537,plain,
spl0_33,
inference(avatar_split_clause,[],[f423,f1534]) ).
fof(f1534,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f423,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f1532,plain,
spl0_32,
inference(avatar_split_clause,[],[f419,f1529]) ).
fof(f1529,plain,
( spl0_32
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f419,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f1527,plain,
spl0_31,
inference(avatar_split_clause,[],[f408,f1524]) ).
fof(f1524,plain,
( spl0_31
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f408,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f1522,plain,
spl0_30,
inference(avatar_split_clause,[],[f393,f1519]) ).
fof(f1519,plain,
( spl0_30
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f393,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f1517,plain,
spl0_29,
inference(avatar_split_clause,[],[f392,f1514]) ).
fof(f1514,plain,
( spl0_29
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f392,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f1512,plain,
spl0_28,
inference(avatar_split_clause,[],[f381,f1509]) ).
fof(f1509,plain,
( spl0_28
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f381,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f1507,plain,
spl0_27,
inference(avatar_split_clause,[],[f379,f1504]) ).
fof(f1504,plain,
( spl0_27
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f379,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f1502,plain,
spl0_26,
inference(avatar_split_clause,[],[f378,f1499]) ).
fof(f1499,plain,
( spl0_26
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f378,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f1497,plain,
spl0_25,
inference(avatar_split_clause,[],[f376,f1494]) ).
fof(f1494,plain,
( spl0_25
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f376,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f1492,plain,
spl0_24,
inference(avatar_split_clause,[],[f375,f1489]) ).
fof(f1489,plain,
( spl0_24
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f375,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f1487,plain,
spl0_23,
inference(avatar_split_clause,[],[f374,f1484]) ).
fof(f1484,plain,
( spl0_23
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f374,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f1482,plain,
spl0_22,
inference(avatar_split_clause,[],[f373,f1479]) ).
fof(f1479,plain,
( spl0_22
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f373,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f1477,plain,
spl0_21,
inference(avatar_split_clause,[],[f372,f1474]) ).
fof(f1474,plain,
( spl0_21
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f372,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f1472,plain,
spl0_20,
inference(avatar_split_clause,[],[f371,f1469]) ).
fof(f1469,plain,
( spl0_20
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f371,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f1467,plain,
spl0_19,
inference(avatar_split_clause,[],[f370,f1464]) ).
fof(f1464,plain,
( spl0_19
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f370,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f1462,plain,
spl0_18,
inference(avatar_split_clause,[],[f369,f1459]) ).
fof(f1459,plain,
( spl0_18
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f369,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f1457,plain,
spl0_17,
inference(avatar_split_clause,[],[f368,f1454]) ).
fof(f1454,plain,
( spl0_17
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f368,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f1452,plain,
spl0_16,
inference(avatar_split_clause,[],[f367,f1449]) ).
fof(f1449,plain,
( spl0_16
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(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(f1447,plain,
spl0_15,
inference(avatar_split_clause,[],[f366,f1444]) ).
fof(f1444,plain,
( spl0_15
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(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(f1442,plain,
spl0_14,
inference(avatar_split_clause,[],[f365,f1439]) ).
fof(f1439,plain,
( spl0_14
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f365,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f1437,plain,
spl0_13,
inference(avatar_split_clause,[],[f364,f1434]) ).
fof(f1434,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f364,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f1432,plain,
spl0_12,
inference(avatar_split_clause,[],[f363,f1429]) ).
fof(f1429,plain,
( spl0_12
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f363,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f1427,plain,
spl0_11,
inference(avatar_split_clause,[],[f362,f1424]) ).
fof(f1424,plain,
( spl0_11
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f362,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f1422,plain,
spl0_10,
inference(avatar_split_clause,[],[f360,f1419]) ).
fof(f1419,plain,
( spl0_10
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f360,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f1417,plain,
spl0_9,
inference(avatar_split_clause,[],[f359,f1414]) ).
fof(f1414,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(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(f1412,plain,
spl0_8,
inference(avatar_split_clause,[],[f358,f1409]) ).
fof(f1409,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f358,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f1407,plain,
spl0_7,
inference(avatar_split_clause,[],[f357,f1404]) ).
fof(f1404,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f357,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f1402,plain,
spl0_6,
inference(avatar_split_clause,[],[f356,f1399]) ).
fof(f1399,plain,
( spl0_6
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f356,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f1397,plain,
spl0_5,
inference(avatar_split_clause,[],[f355,f1394]) ).
fof(f1394,plain,
( spl0_5
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f355,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f1392,plain,
spl0_4,
inference(avatar_split_clause,[],[f354,f1389]) ).
fof(f1389,plain,
( spl0_4
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f354,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f1387,plain,
spl0_3,
inference(avatar_split_clause,[],[f353,f1384]) ).
fof(f1384,plain,
( spl0_3
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f353,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f1382,plain,
spl0_2,
inference(avatar_split_clause,[],[f352,f1379]) ).
fof(f1379,plain,
( spl0_2
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f352,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f1377,plain,
spl0_1,
inference(avatar_split_clause,[],[f1369,f1374]) ).
fof(f1374,plain,
( spl0_1
<=> c_Comb_Odiamond(v_r,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1369,axiom,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL120-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 18:31:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (21451)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (21456)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.40 % (21453)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (21454)WARNING: value z3 for option sas not known
% 0.21/0.40 % (21452)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (21455)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (21454)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.40 % (21457)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40 % (21458)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.42 % (21456)First to succeed.
% 0.21/0.43 % (21456)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21451"
% 0.21/0.43 % (21456)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44 % (21456)------------------------------
% 0.21/0.44 % (21456)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44 % (21456)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (21456)Memory used [KB]: 2559
% 0.21/0.44 % (21456)Time elapsed: 0.033 s
% 0.21/0.44 % (21456)Instructions burned: 95 (million)
% 0.21/0.44 % (21451)Success in time 0.077 s
%------------------------------------------------------------------------------