TSTP Solution File: LCL815-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL815-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:49:57 EDT 2024
% Result : Unsatisfiable 2.68s 0.79s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1015
% Syntax : Number of formulae : 1851 ( 693 unt; 0 def)
% Number of atoms : 4020 ( 894 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 3792 (1623 ~;1636 |; 0 &)
% ( 533 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 568 ( 566 usr; 534 prp; 0-3 aty)
% Number of functors : 60 ( 60 usr; 19 con; 0-5 aty)
% Number of variables : 3275 (3275 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11139,plain,
$false,
inference(avatar_sat_refutation,[],[f1145,f1150,f1155,f1160,f1165,f1170,f1175,f1180,f1185,f1190,f1195,f1200,f1205,f1210,f1215,f1220,f1225,f1230,f1235,f1240,f1245,f1250,f1255,f1260,f1264,f1268,f1272,f1276,f1281,f1286,f1290,f1294,f1298,f1302,f1306,f1312,f1316,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1380,f1384,f1388,f1392,f1396,f1400,f1404,f1408,f1412,f1416,f1420,f1424,f1433,f1437,f1441,f1445,f1449,f1453,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1519,f1524,f1528,f1532,f1536,f1540,f1562,f1567,f1571,f1575,f1579,f1583,f1587,f1591,f1595,f1599,f1603,f1607,f1611,f1615,f1619,f1623,f1627,f1631,f1635,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1676,f1680,f1684,f1688,f1693,f1697,f1701,f1705,f1709,f1733,f1747,f1782,f1788,f1792,f1796,f1800,f1804,f1808,f1812,f1816,f1820,f1826,f1830,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1866,f1870,f1875,f1879,f1883,f1887,f1909,f1954,f1974,f1981,f1987,f1991,f1995,f1999,f2003,f2007,f2020,f2024,f2028,f2032,f2036,f2040,f2044,f2048,f2052,f2056,f2061,f2065,f2069,f2073,f2077,f2081,f2085,f2089,f2093,f2097,f2101,f2105,f2109,f2234,f2302,f2316,f2320,f2324,f2328,f2332,f2336,f2340,f2344,f2348,f2352,f2356,f2360,f2364,f2368,f2372,f2376,f2380,f2384,f2388,f2393,f2397,f2403,f2407,f2411,f2415,f2576,f2633,f2637,f2641,f2645,f2649,f2653,f2657,f2661,f2665,f2669,f2673,f2677,f2681,f2685,f2689,f2693,f2697,f2701,f2705,f2709,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2741,f2745,f2749,f2753,f2757,f2761,f2765,f3132,f3316,f3350,f3354,f3358,f3362,f3366,f3370,f3374,f3378,f3382,f3386,f3390,f3394,f3398,f3402,f3406,f3410,f3414,f3418,f3426,f3430,f3434,f3438,f3442,f3446,f3450,f3454,f3458,f3462,f3466,f3470,f3474,f3478,f3482,f3486,f3490,f3494,f3498,f3502,f3506,f3510,f3514,f3518,f3522,f3526,f3530,f3534,f3538,f3542,f3546,f3564,f3754,f3858,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4350,f4354,f4358,f4362,f4367,f4401,f4405,f4409,f4413,f4417,f4421,f4426,f4472,f4476,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4524,f4581,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5093,f5097,f5101,f5105,f5109,f5113,f5117,f5121,f5125,f5129,f5391,f5469,f5473,f5477,f5481,f5485,f5489,f5493,f5497,f5501,f5505,f5509,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5554,f5558,f5562,f5566,f5570,f5574,f5578,f5854,f6103,f6177,f6181,f6185,f6189,f6195,f6199,f6203,f6207,f6211,f6215,f6219,f6223,f6227,f6231,f6235,f6239,f6243,f6247,f6251,f6256,f6260,f6264,f6268,f6273,f6306,f6310,f6314,f6318,f7078,f7082,f7087,f7148,f7152,f7156,f7160,f7164,f7168,f7172,f7177,f7181,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7632,f7734,f7791,f7795,f7799,f7803,f7808,f7812,f7816,f7820,f7824,f7828,f7832,f7836,f7840,f7844,f7848,f7852,f7881,f7885,f7889,f7893,f7897,f7901,f7905,f7911,f7917,f7921,f7954,f7958,f7962,f7966,f7970,f7974,f7978,f7982,f7986,f7990,f7994,f7998,f8002,f8006,f8102,f8666,f8879,f8883,f9135,f9401,f9441,f9445,f9449,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9501,f9505,f9509,f9513,f9517,f9785,f10022,f10026,f10030,f10034,f10038,f10042,f10046,f10050,f10054,f10058,f10063,f10067,f10071,f10075,f10079,f10083,f10087,f10091,f10095,f10099,f10125,f11106,f11110,f11114,f11118,f11122,f11126,f11130,f11137,f11138]) ).
fof(f11138,plain,
( ~ spl0_525
| spl0_161
| ~ spl0_524 ),
inference(avatar_split_clause,[],[f11095,f10097,f1984,f10122]) ).
fof(f10122,plain,
( spl0_525
<=> c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f1984,plain,
( spl0_161
<=> c_Type_Otypings(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Orderings_Obot__class_Obot(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f10097,plain,
( spl0_524
<=> ! [X28,X88,X51,X57,X22] :
( ~ c_Type_Otypings(X28,X51,X88)
| c_Type_Otypings(c_Type_Oshift(X28,X22,X57,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X22),X51,tc_Lambda_OdB,tc_Lambda_OdB),X88) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f11095,plain,
( ~ c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____)
| spl0_161
| ~ spl0_524 ),
inference(resolution,[],[f10098,f1986]) ).
fof(f1986,plain,
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Orderings_Obot__class_Obot(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____)
| spl0_161 ),
inference(avatar_component_clause,[],[f1984]) ).
fof(f10098,plain,
( ! [X51,X28,X57,X88,X22] :
( c_Type_Otypings(c_Type_Oshift(X28,X22,X57,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X22),X51,tc_Lambda_OdB,tc_Lambda_OdB),X88)
| ~ c_Type_Otypings(X28,X51,X88) )
| ~ spl0_524 ),
inference(avatar_component_clause,[],[f10097]) ).
fof(f11137,plain,
spl0_533,
inference(avatar_split_clause,[],[f864,f11135]) ).
fof(f11135,plain,
( spl0_533
<=> ! [X11,X9,X0,X10,X22] : c_List_Olist_OCons(X9,c_List_Olist__update(X11,X22,X10,X0),X0) = c_List_Olist__update(c_List_Olist_OCons(X9,X11,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat)),X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f864,plain,
! [X10,X0,X11,X9,X22] : c_List_Olist_OCons(X9,c_List_Olist__update(X11,X22,X10,X0),X0) = c_List_Olist__update(c_List_Olist_OCons(X9,X11,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat)),X10,X0),
inference(definition_unfolding,[],[f645,f5]) ).
fof(f5,axiom,
! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f645,axiom,
! [X10,X0,X11,X9,X22] : c_List_Olist__update(c_List_Olist_OCons(X9,X11,X0),c_Suc(X22),X10,X0) = c_List_Olist_OCons(X9,c_List_Olist__update(X11,X22,X10,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
fof(f11130,plain,
spl0_532,
inference(avatar_split_clause,[],[f752,f11128]) ).
fof(f11128,plain,
( spl0_532
<=> ! [X25,X5,X26] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25)),X5) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X26),X5)),hAPP(hAPP(c_Lambda_Olift,X25),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f752,axiom,
! [X26,X5,X25] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25)),X5) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X26),X5)),hAPP(hAPP(c_Lambda_Olift,X25),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
fof(f11126,plain,
spl0_531,
inference(avatar_split_clause,[],[f463,f11124]) ).
fof(f11124,plain,
( spl0_531
<=> ! [X37,X45,X0,X71,X33,X46,X72] : c_Fun_Ocomp(X37,c_Fun_Ocomp(X45,X71,X72,X46,X0),X46,X33,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X37,X45,X46,X33,X72),X71,X72,X33,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f463,axiom,
! [X72,X46,X71,X0,X37,X45,X33] : c_Fun_Ocomp(X37,c_Fun_Ocomp(X45,X71,X72,X46,X0),X46,X33,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X37,X45,X46,X33,X72),X71,X72,X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f11122,plain,
spl0_530,
inference(avatar_split_clause,[],[f298,f11120]) ).
fof(f11120,plain,
( spl0_530
<=> ! [X2,X5,X3] :
( ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f298,axiom,
! [X2,X3,X5] :
( ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
fof(f11118,plain,
spl0_529,
inference(avatar_split_clause,[],[f245,f11116]) ).
fof(f11116,plain,
( spl0_529
<=> ! [X13,X22,X5] :
( ~ c_lessequals(X5,X13,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X22),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X13,X5,tc_nat)),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f245,axiom,
! [X5,X22,X13] :
( ~ c_lessequals(X5,X13,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X22),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X13,X5,tc_nat)),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
fof(f11114,plain,
spl0_528,
inference(avatar_split_clause,[],[f244,f11112]) ).
fof(f11112,plain,
( spl0_528
<=> ! [X13,X22,X5] :
( ~ c_lessequals(X5,X13,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X13),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X13,X5,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f244,axiom,
! [X5,X22,X13] :
( ~ c_lessequals(X5,X13,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X13),X5,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Ominus__class_Ominus(X13,X5,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
fof(f11110,plain,
spl0_527,
inference(avatar_split_clause,[],[f117,f11108]) ).
fof(f11108,plain,
( spl0_527
<=> ! [X2,X5,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f117,axiom,
! [X2,X3,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f11106,plain,
spl0_526,
inference(avatar_split_clause,[],[f116,f11104]) ).
fof(f11104,plain,
( spl0_526
<=> ! [X9,X10,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f116,axiom,
! [X10,X9,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f10125,plain,
spl0_525,
inference(avatar_split_clause,[],[f872,f10122]) ).
fof(f872,plain,
c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(definition_unfolding,[],[f785,f756]) ).
fof(f756,axiom,
v_i____ = v_n____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
fof(f785,axiom,
c_Type_Otypings(v_e____,c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f10099,plain,
spl0_524,
inference(avatar_split_clause,[],[f783,f10097]) ).
fof(f783,axiom,
! [X51,X28,X88,X57,X22] :
( ~ c_Type_Otypings(X28,X51,X88)
| c_Type_Otypings(c_Type_Oshift(X28,X22,X57,tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X22),X51,tc_Lambda_OdB,tc_Lambda_OdB),X88) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__types_0) ).
fof(f10095,plain,
spl0_523,
inference(avatar_split_clause,[],[f770,f10093]) ).
fof(f10093,plain,
( spl0_523
<=> ! [X57,X22,X29,X25,X32,X89] :
( ~ c_Type_Otyping(X89,X32,X57)
| ~ c_Type_Otyping(c_Type_Oshift(X89,X22,X57,tc_Type_Otype),X25,X29)
| c_Type_Otyping(X89,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X32),X22),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f770,axiom,
! [X29,X57,X89,X22,X25,X32] :
( ~ c_Type_Otyping(X89,X32,X57)
| ~ c_Type_Otyping(c_Type_Oshift(X89,X22,X57,tc_Type_Otype),X25,X29)
| c_Type_Otyping(X89,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X32),X22),X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
fof(f10091,plain,
spl0_522,
inference(avatar_split_clause,[],[f629,f10089]) ).
fof(f10089,plain,
( spl0_522
<=> ! [X35,X11,X0,X9,X74,X22] :
( X22 = X74
| c_List_Olist__update(c_List_Olist__update(X11,X22,X9,X0),X74,X35,X0) = c_List_Olist__update(c_List_Olist__update(X11,X74,X35,X0),X22,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f629,axiom,
! [X0,X11,X9,X22,X35,X74] :
( X22 = X74
| c_List_Olist__update(c_List_Olist__update(X11,X22,X9,X0),X74,X35,X0) = c_List_Olist__update(c_List_Olist__update(X11,X74,X35,X0),X22,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
fof(f10087,plain,
spl0_521,
inference(avatar_split_clause,[],[f611,f10085]) ).
fof(f10085,plain,
( spl0_521
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f611,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f10083,plain,
spl0_520,
inference(avatar_split_clause,[],[f585,f10081]) ).
fof(f10081,plain,
( spl0_520
<=> ! [X10,X9,X11,X0,X12] : c_List_Olist__update(c_List_Oappend(X11,c_List_Olist_OCons(X9,X12,X0),X0),c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X10,X0) = c_List_Oappend(X11,c_List_Olist_OCons(X10,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f585,axiom,
! [X10,X0,X11,X9,X12] : c_List_Olist__update(c_List_Oappend(X11,c_List_Olist_OCons(X9,X12,X0),X0),c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X10,X0) = c_List_Oappend(X11,c_List_Olist_OCons(X10,X12,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
fof(f10079,plain,
spl0_519,
inference(avatar_split_clause,[],[f473,f10077]) ).
fof(f10077,plain,
( spl0_519
<=> ! [X2,X5,X3] :
( ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f473,axiom,
! [X2,X3,X5] :
( ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
fof(f10075,plain,
spl0_518,
inference(avatar_split_clause,[],[f401,f10073]) ).
fof(f10073,plain,
( spl0_518
<=> ! [X13,X5,X27,X22] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X27,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X27),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f401,axiom,
! [X27,X22,X5,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X27,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X27),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f10071,plain,
spl0_517,
inference(avatar_split_clause,[],[f303,f10069]) ).
fof(f10069,plain,
( spl0_517
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f303,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f10067,plain,
spl0_516,
inference(avatar_split_clause,[],[f302,f10065]) ).
fof(f10065,plain,
( spl0_516
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f302,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f10063,plain,
spl0_515,
inference(avatar_split_clause,[],[f293,f10061]) ).
fof(f10061,plain,
( spl0_515
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f293,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f10058,plain,
spl0_514,
inference(avatar_split_clause,[],[f269,f10056]) ).
fof(f10056,plain,
( spl0_514
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f269,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f10054,plain,
spl0_513,
inference(avatar_split_clause,[],[f240,f10052]) ).
fof(f10052,plain,
( spl0_513
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f240,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f10050,plain,
spl0_512,
inference(avatar_split_clause,[],[f239,f10048]) ).
fof(f10048,plain,
( spl0_512
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f239,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f10046,plain,
spl0_511,
inference(avatar_split_clause,[],[f159,f10044]) ).
fof(f10044,plain,
( spl0_511
<=> ! [X2,X5,X3] :
( ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f159,axiom,
! [X2,X3,X5] :
( ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X5,tc_nat),c_HOL_Ominus__class_Ominus(X2,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
fof(f10042,plain,
spl0_510,
inference(avatar_split_clause,[],[f154,f10040]) ).
fof(f10040,plain,
( spl0_510
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f154,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f10038,plain,
spl0_509,
inference(avatar_split_clause,[],[f107,f10036]) ).
fof(f10036,plain,
( spl0_509
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f107,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f10034,plain,
spl0_508,
inference(avatar_split_clause,[],[f94,f10032]) ).
fof(f10032,plain,
( spl0_508
<=> ! [X13,X5,X27,X22] :
( ~ c_lessequals(X22,X13,tc_nat)
| ~ c_lessequals(X5,X27,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X27),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f94,axiom,
! [X27,X22,X5,X13] :
( ~ c_lessequals(X22,X13,tc_nat)
| ~ c_lessequals(X5,X27,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X27),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
fof(f10030,plain,
spl0_507,
inference(avatar_split_clause,[],[f56,f10028]) ).
fof(f10028,plain,
( spl0_507
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X6,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f56,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X6,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f10026,plain,
spl0_506,
inference(avatar_split_clause,[],[f55,f10024]) ).
fof(f10024,plain,
( spl0_506
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f55,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f10022,plain,
spl0_505,
inference(avatar_split_clause,[],[f12,f10020]) ).
fof(f10020,plain,
( spl0_505
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f12,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f9785,plain,
( spl0_504
| ~ spl0_53
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f4370,f4365,f1378,f9783]) ).
fof(f9783,plain,
( spl0_504
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f1378,plain,
( spl0_53
<=> ! [X2,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f4365,plain,
( spl0_318
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Omax(X3,X2,tc_nat) = X3
| ~ c_lessequals(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f4370,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_53
| ~ spl0_318 ),
inference(resolution,[],[f4366,f1379]) ).
fof(f1379,plain,
( ! [X2,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1378]) ).
fof(f4366,plain,
( ! [X2,X3] :
( ~ c_lessequals(X2,X3,tc_nat)
| c_Orderings_Oord__class_Omax(X3,X2,tc_nat) = X3 )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f4365]) ).
fof(f9517,plain,
spl0_503,
inference(avatar_split_clause,[],[f930,f9515]) ).
fof(f9515,plain,
( spl0_503
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f930,plain,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X0),X0) ),
inference(definition_unfolding,[],[f414,f5]) ).
fof(f414,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_Suc(X2),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
fof(f9513,plain,
spl0_502,
inference(avatar_split_clause,[],[f877,f9511]) ).
fof(f9511,plain,
( spl0_502
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_Oof__nat(X3,X0)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f877,plain,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_Oof__nat(X3,X0)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
inference(definition_unfolding,[],[f170,f5]) ).
fof(f170,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X3),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_Oof__nat(X3,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
fof(f9509,plain,
( spl0_501
| ~ spl0_226
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f4141,f3512,f2663,f9507]) ).
fof(f9507,plain,
( spl0_501
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2663,plain,
( spl0_226
<=> ! [X2,X5,X3] :
( c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f3512,plain,
( spl0_295
<=> ! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f4141,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) )
| ~ spl0_226
| ~ spl0_295 ),
inference(resolution,[],[f3513,f2664]) ).
fof(f2664,plain,
( ! [X2,X3,X5] :
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5),X2,tc_nat)
| c_lessequals(X5,X2,tc_nat) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2663]) ).
fof(f3513,plain,
( ! [X2,X3] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat)
| c_lessequals(X3,X2,tc_nat) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3512]) ).
fof(f9505,plain,
spl0_500,
inference(avatar_split_clause,[],[f861,f9503]) ).
fof(f9503,plain,
( spl0_500
<=> ! [X11,X0,X9,X2] : c_List_Olist_OCons(X9,c_List_Otake(X2,X11,X0),X0) = c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(X9,X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f861,plain,
! [X2,X0,X11,X9] : c_List_Olist_OCons(X9,c_List_Otake(X2,X11,X0),X0) = c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(X9,X11,X0),X0),
inference(definition_unfolding,[],[f83,f5]) ).
fof(f83,axiom,
! [X2,X0,X11,X9] : c_List_Otake(c_Suc(X2),c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Olist_OCons(X9,c_List_Otake(X2,X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
fof(f9501,plain,
spl0_499,
inference(avatar_split_clause,[],[f749,f9499]) ).
fof(f9499,plain,
( spl0_499
<=> ! [X37,X33,X11,X0,X12,X1] : c_List_Ofoldr(X37,c_List_Oappend(X11,X12,X33),X1,X33,X0) = c_List_Ofoldr(X37,X11,c_List_Ofoldr(X37,X12,X1,X33,X0),X33,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f749,axiom,
! [X0,X11,X1,X37,X12,X33] : c_List_Ofoldr(X37,c_List_Oappend(X11,X12,X33),X1,X33,X0) = c_List_Ofoldr(X37,X11,c_List_Ofoldr(X37,X12,X1,X33,X0),X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
fof(f9497,plain,
spl0_498,
inference(avatar_split_clause,[],[f726,f9495]) ).
fof(f9495,plain,
( spl0_498
<=> ! [X37,X10,X11,X0,X5,X33] : c_List_Omap(X37,c_List_Olist__update(X11,X5,X10,X33),X33,X0) = c_List_Olist__update(c_List_Omap(X37,X11,X33,X0),X5,hAPP(X37,X10),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f726,axiom,
! [X10,X0,X11,X37,X5,X33] : c_List_Omap(X37,c_List_Olist__update(X11,X5,X10,X33),X33,X0) = c_List_Olist__update(c_List_Omap(X37,X11,X33,X0),X5,hAPP(X37,X10),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).
fof(f9493,plain,
spl0_497,
inference(avatar_split_clause,[],[f710,f9491]) ).
fof(f9491,plain,
( spl0_497
<=> ! [X37,X33,X11,X0,X12] : c_List_Omap(X37,c_List_Oappend(X11,X12,X33),X33,X0) = c_List_Oappend(c_List_Omap(X37,X11,X33,X0),c_List_Omap(X37,X12,X33,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f710,axiom,
! [X0,X11,X37,X12,X33] : c_List_Omap(X37,c_List_Oappend(X11,X12,X33),X33,X0) = c_List_Oappend(c_List_Omap(X37,X11,X33,X0),c_List_Omap(X37,X12,X33,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
fof(f9489,plain,
spl0_496,
inference(avatar_split_clause,[],[f646,f9487]) ).
fof(f9487,plain,
( spl0_496
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0)),c_Nat_Osemiring__1__class_Oof__nat(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f646,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0)),c_Nat_Osemiring__1__class_Oof__nat(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
fof(f9485,plain,
spl0_495,
inference(avatar_split_clause,[],[f634,f9483]) ).
fof(f9483,plain,
( spl0_495
<=> ! [X11,X0,X9,X2] : c_List_Oappend(c_List_Oreplicate(X2,X9,X0),c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Olist_OCons(X9,c_List_Oappend(c_List_Oreplicate(X2,X9,X0),X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f634,axiom,
! [X2,X0,X11,X9] : c_List_Oappend(c_List_Oreplicate(X2,X9,X0),c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Olist_OCons(X9,c_List_Oappend(c_List_Oreplicate(X2,X9,X0),X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
fof(f9481,plain,
spl0_494,
inference(avatar_split_clause,[],[f529,f9479]) ).
fof(f9479,plain,
( spl0_494
<=> ! [X10,X9,X0,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X6,X0)
| c_lessequals(c_Power_Opower__class_Opower(X6,X9,X0),c_Power_Opower__class_Opower(X6,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f529,axiom,
! [X10,X0,X6,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X6,X0)
| c_lessequals(c_Power_Opower__class_Opower(X6,X9,X0),c_Power_Opower__class_Opower(X6,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
fof(f9477,plain,
spl0_493,
inference(avatar_split_clause,[],[f527,f9475]) ).
fof(f9475,plain,
( spl0_493
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f527,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
fof(f9473,plain,
spl0_492,
inference(avatar_split_clause,[],[f484,f9471]) ).
fof(f9471,plain,
( spl0_492
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f484,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
fof(f9469,plain,
spl0_491,
inference(avatar_split_clause,[],[f483,f9467]) ).
fof(f9467,plain,
( spl0_491
<=> ! [X0,X23,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f483,axiom,
! [X2,X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X23,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X23,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
fof(f9465,plain,
( spl0_490
| ~ spl0_221
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f4123,f3504,f2643,f9463]) ).
fof(f9463,plain,
( spl0_490
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2643,plain,
( spl0_221
<=> ! [X13,X22,X3] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f3504,plain,
( spl0_293
<=> ! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f4123,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
| ~ spl0_221
| ~ spl0_293 ),
inference(resolution,[],[f3505,f2644]) ).
fof(f2644,plain,
( ! [X3,X22,X13] :
( c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2643]) ).
fof(f3505,plain,
( ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_lessequals(X3,X2,tc_nat) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3504]) ).
fof(f9461,plain,
spl0_489,
inference(avatar_split_clause,[],[f249,f9459]) ).
fof(f9459,plain,
( spl0_489
<=> ! [X13,X22,X5] :
( ~ c_lessequals(X5,X13,tc_nat)
| c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f249,axiom,
! [X5,X22,X13] :
( ~ c_lessequals(X5,X13,tc_nat)
| c_HOL_Ominus__class_Ominus(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
fof(f9457,plain,
spl0_488,
inference(avatar_split_clause,[],[f236,f9455]) ).
fof(f9455,plain,
( spl0_488
<=> ! [X0,X11,X14] :
( c_List_Otake(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X14,X0) != X11
| c_List_Oappend(X11,c_List_Odrop(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X14,X0),X0) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f236,axiom,
! [X0,X11,X14] :
( c_List_Otake(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X14,X0) != X11
| c_List_Oappend(X11,c_List_Odrop(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X14,X0),X0) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
fof(f9453,plain,
spl0_487,
inference(avatar_split_clause,[],[f209,f9451]) ).
fof(f9451,plain,
( spl0_487
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f209,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f9449,plain,
spl0_486,
inference(avatar_split_clause,[],[f162,f9447]) ).
fof(f9447,plain,
( spl0_486
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f162,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f9445,plain,
spl0_485,
inference(avatar_split_clause,[],[f155,f9443]) ).
fof(f9443,plain,
( spl0_485
<=> ! [X0,X23,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,X23,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f155,axiom,
! [X2,X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,X23,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X23,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
fof(f9441,plain,
spl0_484,
inference(avatar_split_clause,[],[f75,f9439]) ).
fof(f9439,plain,
( spl0_484
<=> ! [X3,X5,X27,X2] :
( ~ c_HOL_Oord__class_Oless(X5,X27,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X27) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f75,axiom,
! [X2,X3,X27,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X27,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X27) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f9401,plain,
( spl0_483
| ~ spl0_226
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f4099,f3500,f2663,f9399]) ).
fof(f9399,plain,
( spl0_483
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f3500,plain,
( spl0_292
<=> ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f4099,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) )
| ~ spl0_226
| ~ spl0_292 ),
inference(resolution,[],[f3501,f2664]) ).
fof(f3501,plain,
( ! [X2,X3] :
( c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3500]) ).
fof(f9135,plain,
( spl0_482
| ~ spl0_221
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4081,f3496,f2643,f9133]) ).
fof(f9133,plain,
( spl0_482
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f3496,plain,
( spl0_291
<=> ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f4081,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
| ~ spl0_221
| ~ spl0_291 ),
inference(resolution,[],[f3497,f2644]) ).
fof(f3497,plain,
( ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3496]) ).
fof(f8883,plain,
( spl0_481
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_461 ),
inference(avatar_split_clause,[],[f7913,f7909,f6249,f1686,f1534,f8881]) ).
fof(f8881,plain,
( spl0_481
<=> ! [X10,X11,X0,X12,X9] :
( c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0) != c_List_Oappend(X11,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X9,X0),X0)
| X9 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f1534,plain,
( spl0_90
<=> ! [X9,X0] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1686,plain,
( spl0_123
<=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f6249,plain,
( spl0_407
<=> ! [X9,X0,X2] : c_List_Olist_OCons(X9,c_List_Oreplicate(X2,X9,X0),X0) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f7909,plain,
( spl0_461
<=> ! [X10,X11,X0,X12,X9] :
( X9 = X10
| c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f7913,plain,
( ! [X10,X0,X11,X9,X12] :
( c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0) != c_List_Oappend(X11,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X9,X0),X0)
| X9 = X10 )
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_461 ),
inference(forward_demodulation,[],[f7912,f6924]) ).
fof(f6924,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407 ),
inference(forward_demodulation,[],[f6894,f1687]) ).
fof(f1687,plain,
( ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X2) = X2
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f6894,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X0,X1)
| ~ spl0_90
| ~ spl0_407 ),
inference(superposition,[],[f6250,f1535]) ).
fof(f1535,plain,
( ! [X0,X9] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X9,X0)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1534]) ).
fof(f6250,plain,
( ! [X2,X0,X9] : c_List_Olist_OCons(X9,c_List_Oreplicate(X2,X9,X0),X0) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X9,X0)
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f6249]) ).
fof(f7912,plain,
( ! [X10,X0,X11,X9,X12] :
( c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0)
| X9 = X10 )
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_461 ),
inference(forward_demodulation,[],[f7910,f6924]) ).
fof(f7910,plain,
( ! [X10,X0,X11,X9,X12] :
( X9 = X10
| c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_461 ),
inference(avatar_component_clause,[],[f7909]) ).
fof(f8879,plain,
( spl0_480
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_460 ),
inference(avatar_split_clause,[],[f7907,f7903,f6249,f1686,f1534,f8877]) ).
fof(f8877,plain,
( spl0_480
<=> ! [X10,X11,X0,X12,X9] :
( c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0) != c_List_Oappend(X11,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X9,X0),X0)
| X11 = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f7903,plain,
( spl0_460
<=> ! [X10,X9,X11,X0,X12] :
( X11 = X12
| c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f7907,plain,
( ! [X10,X0,X11,X9,X12] :
( c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0) != c_List_Oappend(X11,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X9,X0),X0)
| X11 = X12 )
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_460 ),
inference(forward_demodulation,[],[f7906,f6924]) ).
fof(f7906,plain,
( ! [X10,X0,X11,X9,X12] :
( c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0)
| X11 = X12 )
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_460 ),
inference(forward_demodulation,[],[f7904,f6924]) ).
fof(f7904,plain,
( ! [X10,X0,X11,X9,X12] :
( X11 = X12
| c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_460 ),
inference(avatar_component_clause,[],[f7903]) ).
fof(f8666,plain,
( spl0_479
| ~ spl0_185
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3727,f3388,f2091,f8664]) ).
fof(f8664,plain,
( spl0_479
<=> ! [X0] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Orderings_Oord__class_Omax(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2091,plain,
( spl0_185
<=> ! [X9] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f3388,plain,
( spl0_264
<=> ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),X3) = c_Orderings_Oord__class_Omax(X2,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f3727,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Orderings_Oord__class_Omax(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)
| ~ spl0_185
| ~ spl0_264 ),
inference(superposition,[],[f2092,f3389]) ).
fof(f3389,plain,
( ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),X3) = c_Orderings_Oord__class_Omax(X2,X3,tc_nat)
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f3388]) ).
fof(f2092,plain,
( ! [X9] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f2091]) ).
fof(f8102,plain,
( spl0_478
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_441 ),
inference(avatar_split_clause,[],[f7804,f7801,f6249,f1686,f1534,f8100]) ).
fof(f8100,plain,
( spl0_478
<=> ! [X10,X11,X0,X12] :
( c_List_Oappend(c_List_Orev(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0) = X11
| c_List_Orev(X11,X0) != c_List_Olist_OCons(X10,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f7801,plain,
( spl0_441
<=> ! [X10,X11,X0,X12] :
( c_List_Orev(X11,X0) != c_List_Olist_OCons(X10,X12,X0)
| c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f7804,plain,
( ! [X10,X0,X11,X12] :
( c_List_Oappend(c_List_Orev(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X10,X0),X0) = X11
| c_List_Orev(X11,X0) != c_List_Olist_OCons(X10,X12,X0) )
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_441 ),
inference(forward_demodulation,[],[f7802,f6924]) ).
fof(f7802,plain,
( ! [X10,X0,X11,X12] :
( c_List_Orev(X11,X0) != c_List_Olist_OCons(X10,X12,X0)
| c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) = X11 )
| ~ spl0_441 ),
inference(avatar_component_clause,[],[f7801]) ).
fof(f8006,plain,
spl0_477,
inference(avatar_split_clause,[],[f1139,f8004]) ).
fof(f8004,plain,
( spl0_477
<=> ! [X2,X0] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f1139,plain,
! [X2,X0] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
inference(forward_demodulation,[],[f761,f689]) ).
fof(f689,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__nat__def_0) ).
fof(f761,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f8002,plain,
spl0_476,
inference(avatar_split_clause,[],[f1135,f8000]) ).
fof(f8000,plain,
( spl0_476
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f1135,plain,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
inference(forward_demodulation,[],[f287,f689]) ).
fof(f287,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
fof(f7998,plain,
spl0_475,
inference(avatar_split_clause,[],[f1133,f7996]) ).
fof(f7996,plain,
( spl0_475
<=> ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f1133,plain,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f1132,f689]) ).
fof(f1132,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(forward_demodulation,[],[f1131,f689]) ).
fof(f1131,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
inference(forward_demodulation,[],[f125,f689]) ).
fof(f125,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f7994,plain,
( spl0_474
| ~ spl0_304
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f7402,f4340,f3562,f7992]) ).
fof(f7992,plain,
( spl0_474
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) != c_Orderings_Oord__class_Omax(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f3562,plain,
( spl0_304
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f4340,plain,
( spl0_312
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) != c_Orderings_Oord__class_Omax(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f7402,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) != c_Orderings_Oord__class_Omax(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_304
| ~ spl0_312 ),
inference(superposition,[],[f4341,f3563]) ).
fof(f3563,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat)
| ~ spl0_304 ),
inference(avatar_component_clause,[],[f3562]) ).
fof(f4341,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) != c_Orderings_Oord__class_Omax(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f4340]) ).
fof(f7990,plain,
spl0_473,
inference(avatar_split_clause,[],[f1114,f7988]) ).
fof(f7988,plain,
( spl0_473
<=> ! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__Nat__Xnat__Xinduct__1(X16)),c_HOL_Oone__class_Oone(tc_nat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f1114,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__Nat__Xnat__Xinduct__1(X16)),c_HOL_Oone__class_Oone(tc_nat)))) ),
inference(forward_demodulation,[],[f949,f689]) ).
fof(f949,plain,
! [X16,X17] :
( hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__Nat__Xnat__Xinduct__1(X16)),c_HOL_Oone__class_Oone(tc_nat)))) ),
inference(definition_unfolding,[],[f23,f5]) ).
fof(f23,axiom,
! [X16,X17] :
( hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X16,c_Suc(v_sko__Nat__Xnat__Xinduct__1(X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_1) ).
fof(f7986,plain,
spl0_472,
inference(avatar_split_clause,[],[f1113,f7984]) ).
fof(f7984,plain,
( spl0_472
<=> ! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__List__Xupt__Xinduct__1(X16)),c_HOL_Oone__class_Oone(tc_nat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f1113,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__List__Xupt__Xinduct__1(X16)),c_HOL_Oone__class_Oone(tc_nat)))) ),
inference(forward_demodulation,[],[f948,f689]) ).
fof(f948,plain,
! [X16,X17] :
( hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_sko__List__Xupt__Xinduct__1(X16)),c_HOL_Oone__class_Oone(tc_nat)))) ),
inference(definition_unfolding,[],[f57,f5]) ).
fof(f57,axiom,
! [X16,X17] :
( hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X16,c_Suc(v_sko__List__Xupt__Xinduct__1(X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_1) ).
fof(f7982,plain,
spl0_471,
inference(avatar_split_clause,[],[f1045,f7980]) ).
fof(f7980,plain,
( spl0_471
<=> ! [X11,X0,X9,X2] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_List_Odrop(X2,c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f1045,plain,
! [X2,X0,X11,X9] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_List_Odrop(X2,c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X11,X0) ),
inference(forward_demodulation,[],[f487,f689]) ).
fof(f487,axiom,
! [X2,X0,X11,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_List_Odrop(X2,c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).
fof(f7978,plain,
spl0_470,
inference(avatar_split_clause,[],[f1006,f7976]) ).
fof(f7976,plain,
( spl0_470
<=> ! [X9,X0,X5,X2] : c_List_Oappend(c_List_Oreplicate(X2,X9,X0),c_List_Oreplicate(X5,X9,X0),X0) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f1006,plain,
! [X2,X0,X9,X5] : c_List_Oappend(c_List_Oreplicate(X2,X9,X0),c_List_Oreplicate(X5,X9,X0),X0) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),X9,X0),
inference(forward_demodulation,[],[f390,f448]) ).
fof(f448,axiom,
! [X2,X3,X0,X9] : c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X9,X0) = c_List_Oappend(c_List_Oreplicate(X2,X9,X0),c_List_Oreplicate(X3,X9,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__add_0) ).
fof(f390,axiom,
! [X2,X0,X9,X5] : c_List_Oappend(c_List_Oreplicate(X2,X9,X0),c_List_Oreplicate(X5,X9,X0),X0) = c_List_Oappend(c_List_Oreplicate(X5,X9,X0),c_List_Oreplicate(X2,X9,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
fof(f7974,plain,
spl0_469,
inference(avatar_split_clause,[],[f920,f7972]) ).
fof(f7972,plain,
( spl0_469
<=> ! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f920,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f538,f5,f5]) ).
fof(f538,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f7970,plain,
spl0_468,
inference(avatar_split_clause,[],[f914,f7968]) ).
fof(f7968,plain,
( spl0_468
<=> ! [X2,X3] :
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f914,plain,
! [X2,X3] :
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f673,f5,f5]) ).
fof(f673,axiom,
! [X2,X3] :
( c_lessequals(X2,X3,tc_nat)
| ~ c_lessequals(c_Suc(X2),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f7966,plain,
spl0_467,
inference(avatar_split_clause,[],[f890,f7964]) ).
fof(f7964,plain,
( spl0_467
<=> ! [X70,X2] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X70,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X70,tc_Lambda_OdB),c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f890,plain,
! [X2,X70] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X70,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X70,tc_Lambda_OdB),c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(definition_unfolding,[],[f402,f737]) ).
fof(f737,axiom,
! [X0,X11,X1,X37,X33] : c_List_Ofoldl(X37,X1,X11,X0,X33) = c_List_Ofoldr(c_COMBC(X37,X0,X33,X0),c_List_Orev(X11,X33),X1,X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).
fof(f402,axiom,
! [X2,X70] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X70,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X70,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
fof(f7962,plain,
spl0_466,
inference(avatar_split_clause,[],[f878,f7960]) ).
fof(f7960,plain,
( spl0_466
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Ofoldr(c_COMBC(c_HOL_Oplus__class_Oplus(X0),X0,X0,X0),c_List_Orev(X11,X0),c_HOL_Ozero__class_Ozero(X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f878,plain,
! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Ofoldr(c_COMBC(c_HOL_Oplus__class_Oplus(X0),X0,X0,X0),c_List_Orev(X11,X0),c_HOL_Ozero__class_Ozero(X0),X0,X0) ),
inference(definition_unfolding,[],[f102,f737]) ).
fof(f102,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0),X11,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
fof(f7958,plain,
spl0_465,
inference(avatar_split_clause,[],[f853,f7956]) ).
fof(f7956,plain,
( spl0_465
<=> ! [X2,X50,X25,X26] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X25) != c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X50,tc_Lambda_OdB),c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f853,plain,
! [X50,X2,X26,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X25) != c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X50,tc_Lambda_OdB),c_Lambda_OdB_OVar(X2),tc_Lambda_OdB,tc_Lambda_OdB),
inference(definition_unfolding,[],[f513,f737]) ).
fof(f513,axiom,
! [X50,X2,X26,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X25) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X2),X50,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f7954,plain,
spl0_464,
inference(avatar_split_clause,[],[f748,f7952]) ).
fof(f7952,plain,
( spl0_464
<=> ! [X37,X9,X11,X0,X33,X1] : c_List_Ofoldr(X37,c_List_Olist_OCons(X9,X11,X33),X1,X33,X0) = hAPP(hAPP(X37,X9),c_List_Ofoldr(X37,X11,X1,X33,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f748,axiom,
! [X0,X11,X1,X37,X9,X33] : c_List_Ofoldr(X37,c_List_Olist_OCons(X9,X11,X33),X1,X33,X0) = hAPP(hAPP(X37,X9),c_List_Ofoldr(X37,X11,X1,X33,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
fof(f7921,plain,
spl0_463,
inference(avatar_split_clause,[],[f720,f7919]) ).
fof(f7919,plain,
( spl0_463
<=> ! [X37,X11,X45,X0,X33,X46] : c_List_Omap(X37,c_List_Omap(X45,X11,X46,X33),X33,X0) = c_List_Omap(c_Fun_Ocomp(X37,X45,X33,X0,X46),X11,X46,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f720,axiom,
! [X46,X11,X0,X37,X45,X33] : c_List_Omap(X37,c_List_Omap(X45,X11,X46,X33),X33,X0) = c_List_Omap(c_Fun_Ocomp(X37,X45,X33,X0,X46),X11,X46,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__map_0) ).
fof(f7917,plain,
spl0_462,
inference(avatar_split_clause,[],[f711,f7915]) ).
fof(f7915,plain,
( spl0_462
<=> ! [X37,X33,X11,X0,X12] :
( c_Nat_Osize__class_Osize(X11,tc_List_Olist(X33)) = c_Nat_Osize__class_Osize(X12,tc_List_Olist(X33))
| c_List_Omap(X37,X11,X33,X0) != c_List_Omap(X37,X12,X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f711,axiom,
! [X0,X11,X37,X12,X33] :
( c_Nat_Osize__class_Osize(X11,tc_List_Olist(X33)) = c_Nat_Osize__class_Osize(X12,tc_List_Olist(X33))
| c_List_Omap(X37,X11,X33,X0) != c_List_Omap(X37,X12,X33,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
fof(f7911,plain,
spl0_461,
inference(avatar_split_clause,[],[f656,f7909]) ).
fof(f656,axiom,
! [X10,X0,X11,X9,X12] :
( X9 = X10
| c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
fof(f7905,plain,
spl0_460,
inference(avatar_split_clause,[],[f655,f7903]) ).
fof(f655,axiom,
! [X10,X0,X11,X9,X12] :
( X11 = X12
| c_List_Oappend(X11,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X12,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
fof(f7901,plain,
spl0_459,
inference(avatar_split_clause,[],[f603,f7899]) ).
fof(f7899,plain,
( spl0_459
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f603,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f7897,plain,
spl0_458,
inference(avatar_split_clause,[],[f602,f7895]) ).
fof(f7895,plain,
( spl0_458
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f602,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f7893,plain,
spl0_457,
inference(avatar_split_clause,[],[f601,f7891]) ).
fof(f7891,plain,
( spl0_457
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f601,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f7889,plain,
spl0_456,
inference(avatar_split_clause,[],[f600,f7887]) ).
fof(f7887,plain,
( spl0_456
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f600,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f7885,plain,
spl0_455,
inference(avatar_split_clause,[],[f599,f7883]) ).
fof(f7883,plain,
( spl0_455
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f599,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f7881,plain,
spl0_454,
inference(avatar_split_clause,[],[f598,f7879]) ).
fof(f7879,plain,
( spl0_454
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f598,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f7852,plain,
spl0_453,
inference(avatar_split_clause,[],[f485,f7850]) ).
fof(f7850,plain,
( spl0_453
<=> ! [X2,X5,X25,X26] : c_Lambda_Oliftn(X2,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25),X5) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X2,X26,X5)),c_Lambda_Oliftn(X2,X25,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f485,axiom,
! [X2,X26,X5,X25] : c_Lambda_Oliftn(X2,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25),X5) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X2,X26,X5)),c_Lambda_Oliftn(X2,X25,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
fof(f7848,plain,
spl0_452,
inference(avatar_split_clause,[],[f475,f7846]) ).
fof(f7846,plain,
( spl0_452
<=> ! [X0,X6,X1,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f475,axiom,
! [X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f7844,plain,
spl0_451,
inference(avatar_split_clause,[],[f448,f7842]) ).
fof(f7842,plain,
( spl0_451
<=> ! [X3,X0,X9,X2] : c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X9,X0) = c_List_Oappend(c_List_Oreplicate(X2,X9,X0),c_List_Oreplicate(X3,X9,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f7840,plain,
spl0_450,
inference(avatar_split_clause,[],[f429,f7838]) ).
fof(f7838,plain,
( spl0_450
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f429,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f7836,plain,
spl0_449,
inference(avatar_split_clause,[],[f428,f7834]) ).
fof(f7834,plain,
( spl0_449
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f428,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f7832,plain,
spl0_448,
inference(avatar_split_clause,[],[f427,f7830]) ).
fof(f7830,plain,
( spl0_448
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X6,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f427,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X6,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f7828,plain,
spl0_447,
inference(avatar_split_clause,[],[f426,f7826]) ).
fof(f7826,plain,
( spl0_447
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f426,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X6),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f7824,plain,
spl0_446,
inference(avatar_split_clause,[],[f425,f7822]) ).
fof(f7822,plain,
( spl0_446
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X6,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f425,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X6,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f7820,plain,
spl0_445,
inference(avatar_split_clause,[],[f424,f7818]) ).
fof(f7818,plain,
( spl0_445
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f424,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X7),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f7816,plain,
spl0_444,
inference(avatar_split_clause,[],[f411,f7814]) ).
fof(f7814,plain,
( spl0_444
<=> ! [X57,X29,X58,X25,X26] :
( ~ c_Type_Otyping(X58,X25,X29)
| ~ c_Type_Otyping(X58,X26,hAPP(hAPP(c_Type_Otype_OFun,X29),X57))
| c_Type_Otyping(X58,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25),X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f411,axiom,
! [X58,X29,X57,X26,X25] :
( ~ c_Type_Otyping(X58,X25,X29)
| ~ c_Type_Otyping(X58,X26,hAPP(hAPP(c_Type_Otype_OFun,X29),X57))
| c_Type_Otyping(X58,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25),X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
fof(f7812,plain,
( spl0_443
| ~ spl0_304
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f7401,f3752,f3562,f7810]) ).
fof(f7810,plain,
( spl0_443
<=> ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f3752,plain,
( spl0_305
<=> ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f7401,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X0,tc_nat),tc_nat)
| ~ spl0_304
| ~ spl0_305 ),
inference(superposition,[],[f3753,f3563]) ).
fof(f3753,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f3752]) ).
fof(f7808,plain,
spl0_442,
inference(avatar_split_clause,[],[f267,f7806]) ).
fof(f7806,plain,
( spl0_442
<=> ! [X11,X0,X12] : c_Nat_Osize__class_Osize(c_List_Oappend(X11,X12,X0),tc_List_Olist(X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0))),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f267,axiom,
! [X0,X11,X12] : c_Nat_Osize__class_Osize(c_List_Oappend(X11,X12,X0),tc_List_Olist(X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0))),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__append_0) ).
fof(f7803,plain,
spl0_441,
inference(avatar_split_clause,[],[f179,f7801]) ).
fof(f179,axiom,
! [X10,X0,X11,X12] :
( c_List_Orev(X11,X0) != c_List_Olist_OCons(X10,X12,X0)
| c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
fof(f7799,plain,
spl0_440,
inference(avatar_split_clause,[],[f166,f7797]) ).
fof(f7797,plain,
( spl0_440
<=> ! [X2,X5,X3] :
( X2 = X3
| ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X5,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f166,axiom,
! [X2,X3,X5] :
( X2 = X3
| ~ c_lessequals(X5,X3,tc_nat)
| ~ c_lessequals(X5,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X5,tc_nat) != c_HOL_Ominus__class_Ominus(X2,X5,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
fof(f7795,plain,
spl0_439,
inference(avatar_split_clause,[],[f127,f7793]) ).
fof(f7793,plain,
( spl0_439
<=> ! [X11,X0,X3,X2] : c_List_Otake(X2,c_List_Odrop(X3,X11,X0),X0) = c_List_Odrop(X3,c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f127,axiom,
! [X2,X3,X0,X11] : c_List_Otake(X2,c_List_Odrop(X3,X11,X0),X0) = c_List_Odrop(X3,c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__drop_0) ).
fof(f7791,plain,
spl0_438,
inference(avatar_split_clause,[],[f35,f7789]) ).
fof(f7789,plain,
( spl0_438
<=> ! [X13,X22,X5] :
( ~ c_lessequals(X5,X13,tc_nat)
| ~ c_lessequals(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f35,axiom,
! [X5,X22,X13] :
( ~ c_lessequals(X5,X13,tc_nat)
| ~ c_lessequals(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
fof(f7734,plain,
( spl0_437
| ~ spl0_304
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f7400,f3856,f3562,f7732]) ).
fof(f7732,plain,
( spl0_437
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X0,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f3856,plain,
( spl0_306
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f7400,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X0,tc_nat),X1,tc_nat)
| ~ spl0_304
| ~ spl0_306 ),
inference(superposition,[],[f3857,f3563]) ).
fof(f3857,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f3856]) ).
fof(f7632,plain,
( spl0_436
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f7173,f7170,f6249,f1686,f1534,f7630]) ).
fof(f7630,plain,
( spl0_436
<=> ! [X22,X9,X0] : c_List_Olist_OCons(X9,c_List_Oreplicate(X22,X9,X0),X0) = c_List_Oappend(c_List_Oreplicate(X22,X9,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X9,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f7170,plain,
( spl0_426
<=> ! [X22,X9,X0] : c_List_Oappend(c_List_Oreplicate(X22,X9,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) = c_List_Olist_OCons(X9,c_List_Oreplicate(X22,X9,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f7173,plain,
( ! [X0,X9,X22] : c_List_Olist_OCons(X9,c_List_Oreplicate(X22,X9,X0),X0) = c_List_Oappend(c_List_Oreplicate(X22,X9,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X9,X0),X0)
| ~ spl0_90
| ~ spl0_123
| ~ spl0_407
| ~ spl0_426 ),
inference(forward_demodulation,[],[f7171,f6924]) ).
fof(f7171,plain,
( ! [X0,X9,X22] : c_List_Oappend(c_List_Oreplicate(X22,X9,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) = c_List_Olist_OCons(X9,c_List_Oreplicate(X22,X9,X0),X0)
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f7170]) ).
fof(f7252,plain,
spl0_435,
inference(avatar_split_clause,[],[f1018,f7250]) ).
fof(f7250,plain,
( spl0_435
<=> ! [X51] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Orderings_Obot__class_Obot(tc_nat)),X51,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X51,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f1018,plain,
! [X51] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Orderings_Obot__class_Obot(tc_nat)),X51,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X51,tc_Lambda_OdB) ),
inference(forward_demodulation,[],[f772,f689]) ).
fof(f772,axiom,
! [X51] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X51,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),X51,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
fof(f7248,plain,
spl0_434,
inference(avatar_split_clause,[],[f955,f7246]) ).
fof(f7246,plain,
( spl0_434
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f955,plain,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f104,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f7244,plain,
spl0_433,
inference(avatar_split_clause,[],[f910,f7242]) ).
fof(f7242,plain,
( spl0_433
<=> ! [X50,X3,X26] :
( c_Lambda_OdB_OVar(X3) = X26
| c_Lambda_OdB_OVar(X3) != c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X50,tc_Lambda_OdB),X26,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f910,plain,
! [X50,X3,X26] :
( c_Lambda_OdB_OVar(X3) = X26
| c_Lambda_OdB_OVar(X3) != c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X50,tc_Lambda_OdB),X26,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition_unfolding,[],[f252,f737]) ).
fof(f252,axiom,
! [X50,X3,X26] :
( c_Lambda_OdB_OVar(X3) = X26
| c_Lambda_OdB_OVar(X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X50,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
fof(f7240,plain,
spl0_432,
inference(avatar_split_clause,[],[f908,f7238]) ).
fof(f7238,plain,
( spl0_432
<=> ! [X49,X50,X26] :
( c_Lambda_OdB_OAbs(X49) = X26
| c_Lambda_OdB_OAbs(X49) != c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X50,tc_Lambda_OdB),X26,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f908,plain,
! [X50,X49,X26] :
( c_Lambda_OdB_OAbs(X49) = X26
| c_Lambda_OdB_OAbs(X49) != c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X50,tc_Lambda_OdB),X26,tc_Lambda_OdB,tc_Lambda_OdB) ),
inference(definition_unfolding,[],[f292,f737]) ).
fof(f292,axiom,
! [X50,X49,X26] :
( c_Lambda_OdB_OAbs(X49) = X26
| c_Lambda_OdB_OAbs(X49) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X50,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
fof(f7236,plain,
spl0_431,
inference(avatar_split_clause,[],[f856,f7234]) ).
fof(f7234,plain,
( spl0_431
<=> ! [X25,X5,X2] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X2,X25,X5)),X5) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X25,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f856,plain,
! [X2,X5,X25] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X2,X25,X5)),X5) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X25,X5),
inference(definition_unfolding,[],[f187,f5]) ).
fof(f187,axiom,
! [X2,X5,X25] : c_Lambda_Oliftn(c_Suc(X2),X25,X5) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X2,X25,X5)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
fof(f7232,plain,
spl0_430,
inference(avatar_split_clause,[],[f723,f7230]) ).
fof(f7230,plain,
( spl0_430
<=> ! [X37,X11,X9,X0,X33] : c_List_Omap(X37,c_List_Olist_OCons(X9,X11,X33),X33,X0) = c_List_Olist_OCons(hAPP(X37,X9),c_List_Omap(X37,X11,X33,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f723,axiom,
! [X0,X11,X37,X9,X33] : c_List_Omap(X37,c_List_Olist_OCons(X9,X11,X33),X33,X0) = c_List_Olist_OCons(hAPP(X37,X9),c_List_Omap(X37,X11,X33,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
fof(f7228,plain,
spl0_429,
inference(avatar_split_clause,[],[f671,f7226]) ).
fof(f7226,plain,
( spl0_429
<=> ! [X5,X26] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X26)),X5) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f671,axiom,
! [X26,X5] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X26)),X5) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
fof(f7181,plain,
spl0_428,
inference(avatar_split_clause,[],[f652,f7179]) ).
fof(f7179,plain,
( spl0_428
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(c_List_Oappend(X11,X12,X0),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_List_Olistsum(X11,X0)),c_List_Olistsum(X12,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f652,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(c_List_Oappend(X11,X12,X0),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_List_Olistsum(X11,X0)),c_List_Olistsum(X12,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__append_0) ).
fof(f7177,plain,
spl0_427,
inference(avatar_split_clause,[],[f545,f7175]) ).
fof(f7175,plain,
( spl0_427
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f545,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f7172,plain,
spl0_426,
inference(avatar_split_clause,[],[f519,f7170]) ).
fof(f519,axiom,
! [X0,X9,X22] : c_List_Oappend(c_List_Oreplicate(X22,X9,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) = c_List_Olist_OCons(X9,c_List_Oreplicate(X22,X9,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
fof(f7168,plain,
spl0_425,
inference(avatar_split_clause,[],[f464,f7166]) ).
fof(f7166,plain,
( spl0_425
<=> ! [X13,X22,X32] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X32),X22) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f464,axiom,
! [X22,X32,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X32),X22) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__gt_0) ).
fof(f7164,plain,
spl0_424,
inference(avatar_split_clause,[],[f454,f7162]) ).
fof(f7162,plain,
( spl0_424
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X2 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X2,X0) != c_Power_Opower__class_Opower(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f454,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X2 = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X2,X0) != c_Power_Opower__class_Opower(X1,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f7160,plain,
spl0_423,
inference(avatar_split_clause,[],[f438,f7158]) ).
fof(f7158,plain,
( spl0_423
<=> ! [X28,X13,X0,X29,X22] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| hAPP(c_Type_Oshift(X28,X22,X29,X0),X13) = hAPP(X28,c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f438,axiom,
! [X28,X29,X0,X22,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| hAPP(c_Type_Oshift(X28,X22,X29,X0),X13) = hAPP(X28,c_HOL_Ominus__class_Ominus(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__lt_0) ).
fof(f7156,plain,
spl0_422,
inference(avatar_split_clause,[],[f175,f7154]) ).
fof(f7154,plain,
( spl0_422
<=> ! [X2,X5,X3] : c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f175,axiom,
! [X2,X3,X5] : c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f7152,plain,
spl0_421,
inference(avatar_split_clause,[],[f174,f7150]) ).
fof(f7150,plain,
( spl0_421
<=> ! [X2,X5,X3] : c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f174,axiom,
! [X2,X3,X5] : c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f7148,plain,
spl0_420,
inference(avatar_split_clause,[],[f141,f7146]) ).
fof(f7146,plain,
( spl0_420
<=> ! [X22,X0,X11] : c_List_Orev(c_List_Odrop(X22,X11,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X22,tc_nat),c_List_Orev(X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f141,axiom,
! [X0,X11,X22] : c_List_Orev(c_List_Odrop(X22,X11,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X22,tc_nat),c_List_Orev(X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__drop_0) ).
fof(f7087,plain,
( spl0_419
| ~ spl0_38
| ~ spl0_366
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f7083,f7080,f5495,f1318,f7085]) ).
fof(f7085,plain,
( spl0_419
<=> ! [X22,X5] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X22)),X5) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OVar(X22),c_Orderings_Obot__class_Obot(tc_nat))
| c_HOL_Oord__class_Oless(X22,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f1318,plain,
( spl0_38
<=> ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f5495,plain,
( spl0_366
<=> ! [X22,X2,X5] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X22),X5) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f7080,plain,
( spl0_418
<=> ! [X22,X5] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X22)),X5) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f7083,plain,
( ! [X22,X5] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X22)),X5) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OVar(X22),c_Orderings_Obot__class_Obot(tc_nat))
| c_HOL_Oord__class_Oless(X22,X5,tc_nat) )
| ~ spl0_38
| ~ spl0_366
| ~ spl0_418 ),
inference(forward_demodulation,[],[f7081,f5794]) ).
fof(f5794,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_38
| ~ spl0_366 ),
inference(resolution,[],[f5496,f1319]) ).
fof(f1319,plain,
( ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f5496,plain,
( ! [X2,X22,X5] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X22),X5) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X2)) )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f5495]) ).
fof(f7081,plain,
( ! [X22,X5] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X22)),X5) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat))) )
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f7080]) ).
fof(f7082,plain,
spl0_418,
inference(avatar_split_clause,[],[f137,f7080]) ).
fof(f137,axiom,
! [X22,X5] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X22)),X5) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
fof(f7078,plain,
spl0_417,
inference(avatar_split_clause,[],[f136,f7076]) ).
fof(f7076,plain,
( spl0_417
<=> ! [X22,X0,X11] : c_List_Orev(c_List_Otake(X22,X11,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X22,tc_nat),c_List_Orev(X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f136,axiom,
! [X0,X11,X22] : c_List_Orev(c_List_Otake(X22,X11,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X22,tc_nat),c_List_Orev(X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__take_0) ).
fof(f6318,plain,
spl0_416,
inference(avatar_split_clause,[],[f1136,f6316]) ).
fof(f6316,plain,
( spl0_416
<=> ! [X9,X16,X2] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X9))
| hBOOL(hAPP(X16,X2))
| ~ c_HOL_Oord__class_Oless(X9,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f1136,plain,
! [X2,X9,X16] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X9))
| hBOOL(hAPP(X16,X2))
| ~ c_HOL_Oord__class_Oless(X9,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16),tc_nat) ),
inference(forward_demodulation,[],[f31,f689]) ).
fof(f31,axiom,
! [X2,X9,X16] :
( hBOOL(hAPP(X16,X9))
| hBOOL(hAPP(X16,X2))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X9,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_2) ).
fof(f6314,plain,
spl0_415,
inference(avatar_split_clause,[],[f1079,f6312]) ).
fof(f6312,plain,
( spl0_415
<=> ! [X2,X5,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X5,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f1079,plain,
! [X2,X3,X5] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X5,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5),tc_nat) ),
inference(forward_demodulation,[],[f11,f689]) ).
fof(f11,axiom,
! [X2,X3,X5] :
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lem0_0) ).
fof(f6310,plain,
spl0_414,
inference(avatar_split_clause,[],[f1069,f6308]) ).
fof(f6308,plain,
( spl0_414
<=> ! [X57,X29,X58,X25] :
( ~ c_Type_Otyping(c_Type_Oshift(X58,c_Orderings_Obot__class_Obot(tc_nat),X29,tc_Type_Otype),X25,X57)
| c_Type_Otyping(X58,c_Lambda_OdB_OAbs(X25),hAPP(hAPP(c_Type_Otype_OFun,X29),X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f1069,plain,
! [X58,X29,X57,X25] :
( ~ c_Type_Otyping(c_Type_Oshift(X58,c_Orderings_Obot__class_Obot(tc_nat),X29,tc_Type_Otype),X25,X57)
| c_Type_Otyping(X58,c_Lambda_OdB_OAbs(X25),hAPP(hAPP(c_Type_Otype_OFun,X29),X57)) ),
inference(forward_demodulation,[],[f759,f689]) ).
fof(f759,axiom,
! [X58,X29,X57,X25] :
( ~ c_Type_Otyping(c_Type_Oshift(X58,c_HOL_Ozero__class_Ozero(tc_nat),X29,tc_Type_Otype),X25,X57)
| c_Type_Otyping(X58,c_Lambda_OdB_OAbs(X25),hAPP(hAPP(c_Type_Otype_OFun,X29),X57)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
fof(f6306,plain,
( spl0_413
| ~ spl0_40
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2982,f2675,f1326,f6304]) ).
fof(f6304,plain,
( spl0_413
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f1326,plain,
( spl0_40
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f2675,plain,
( spl0_229
<=> ! [X9,X0,X6,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X6,X0)
| c_HOL_Oord__class_Oless(X9,c_Orderings_Oord__class_Omax(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2982,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_40
| ~ spl0_229 ),
inference(duplicate_literal_removal,[],[f2965]) ).
fof(f2965,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_40
| ~ spl0_229 ),
inference(resolution,[],[f2676,f1327]) ).
fof(f1327,plain,
( ! [X0,X9] :
( ~ c_HOL_Oord__class_Oless(X9,X9,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f2676,plain,
( ! [X0,X1,X6,X9] :
( c_HOL_Oord__class_Oless(X9,c_Orderings_Oord__class_Omax(X1,X6,X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,X6,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2675]) ).
fof(f6273,plain,
( spl0_412
| ~ spl0_222
| ~ spl0_264
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f6269,f6266,f3388,f2647,f6271]) ).
fof(f6271,plain,
( spl0_412
<=> ! [X2] :
( c_Orderings_Oord__class_Omax(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2647,plain,
( spl0_222
<=> ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f6266,plain,
( spl0_411
<=> ! [X2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f6269,plain,
( ! [X2] :
( c_Orderings_Oord__class_Omax(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) )
| ~ spl0_222
| ~ spl0_264
| ~ spl0_411 ),
inference(forward_demodulation,[],[f6267,f3705]) ).
fof(f3705,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))
| ~ spl0_222
| ~ spl0_264 ),
inference(superposition,[],[f3389,f2648]) ).
fof(f2648,plain,
( ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2647]) ).
fof(f6267,plain,
( ! [X2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f6266]) ).
fof(f6268,plain,
spl0_411,
inference(avatar_split_clause,[],[f1055,f6266]) ).
fof(f1055,plain,
! [X2] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f1054,f74]) ).
fof(f74,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f1054,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
inference(forward_demodulation,[],[f922,f689]) ).
fof(f922,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2 ),
inference(definition_unfolding,[],[f395,f5]) ).
fof(f395,axiom,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
fof(f6264,plain,
spl0_410,
inference(avatar_split_clause,[],[f938,f6262]) ).
fof(f6262,plain,
( spl0_410
<=> ! [X13,X22,X5] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X5,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat)),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f938,plain,
! [X22,X5,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X5,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat)),X5,tc_nat) ),
inference(definition_unfolding,[],[f423,f5]) ).
fof(f423,axiom,
! [X22,X5,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X5,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X22),X5,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f6260,plain,
spl0_409,
inference(avatar_split_clause,[],[f929,f6258]) ).
fof(f6258,plain,
( spl0_409
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f929,plain,
! [X2,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
inference(definition_unfolding,[],[f27,f5]) ).
fof(f27,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f6256,plain,
spl0_408,
inference(avatar_split_clause,[],[f866,f6253]) ).
fof(f6253,plain,
( spl0_408
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f866,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(definition_unfolding,[],[f757,f756]) ).
fof(f757,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_headT_0) ).
fof(f6251,plain,
spl0_407,
inference(avatar_split_clause,[],[f852,f6249]) ).
fof(f852,plain,
! [X2,X0,X9] : c_List_Olist_OCons(X9,c_List_Oreplicate(X2,X9,X0),X0) = c_List_Oreplicate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X9,X0),
inference(definition_unfolding,[],[f128,f5]) ).
fof(f128,axiom,
! [X2,X0,X9] : c_List_Oreplicate(c_Suc(X2),X9,X0) = c_List_Olist_OCons(X9,c_List_Oreplicate(X2,X9,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
fof(f6247,plain,
spl0_406,
inference(avatar_split_clause,[],[f850,f6245]) ).
fof(f6245,plain,
( spl0_406
<=> ! [X9,X0,X30] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X9,X30,X0),tc_List_Olist(X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0))),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f850,plain,
! [X0,X9,X30] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X9,X30,X0),tc_List_Olist(X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0))),c_HOL_Oone__class_Oone(tc_nat)),
inference(definition_unfolding,[],[f96,f5]) ).
fof(f96,axiom,
! [X0,X9,X30] : c_Suc(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X9,X30,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
fof(f6243,plain,
spl0_405,
inference(avatar_split_clause,[],[f849,f6241]) ).
fof(f6241,plain,
( spl0_405
<=> ! [X11,X0,X9,X2] : c_List_Odrop(X2,X11,X0) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(X9,X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f849,plain,
! [X2,X0,X11,X9] : c_List_Odrop(X2,X11,X0) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(X9,X11,X0),X0),
inference(definition_unfolding,[],[f173,f5]) ).
fof(f173,axiom,
! [X2,X0,X11,X9] : c_List_Odrop(X2,X11,X0) = c_List_Odrop(c_Suc(X2),c_List_Olist_OCons(X9,X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
fof(f6239,plain,
spl0_404,
inference(avatar_split_clause,[],[f733,f6237]) ).
fof(f6237,plain,
( spl0_404
<=> ! [X22,X25,X49,X26] :
( ~ c_Lambda_Obeta(X49,X26)
| c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X49),X25),X22),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X25),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f733,axiom,
! [X49,X26,X22,X25] :
( ~ c_Lambda_Obeta(X49,X26)
| c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,X49),X25),X22),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X25),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
fof(f6235,plain,
( spl0_403
| ~ spl0_40
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2960,f2671,f1326,f6233]) ).
fof(f6233,plain,
( spl0_403
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2671,plain,
( spl0_228
<=> ! [X9,X0,X6,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| c_HOL_Oord__class_Oless(X9,c_Orderings_Oord__class_Omax(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2960,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_40
| ~ spl0_228 ),
inference(duplicate_literal_removal,[],[f2943]) ).
fof(f2943,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_40
| ~ spl0_228 ),
inference(resolution,[],[f2672,f1327]) ).
fof(f2672,plain,
( ! [X0,X1,X6,X9] :
( c_HOL_Oord__class_Oless(X9,c_Orderings_Oord__class_Omax(X1,X6,X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2671]) ).
fof(f6231,plain,
spl0_402,
inference(avatar_split_clause,[],[f708,f6229]) ).
fof(f6229,plain,
( spl0_402
<=> ! [X0,X11,X37] :
( c_List_Omap(X37,X11,X0,X0) = X11
| c_List_Osko__List__Xmap__idI__1__1(X37,X11,X0) != hAPP(X37,c_List_Osko__List__Xmap__idI__1__1(X37,X11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f708,axiom,
! [X0,X11,X37] :
( c_List_Omap(X37,X11,X0,X0) = X11
| c_List_Osko__List__Xmap__idI__1__1(X37,X11,X0) != hAPP(X37,c_List_Osko__List__Xmap__idI__1__1(X37,X11,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__idI_1) ).
fof(f6227,plain,
spl0_401,
inference(avatar_split_clause,[],[f606,f6225]) ).
fof(f6225,plain,
( spl0_401
<=> ! [X2,X5,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f606,axiom,
! [X2,X3,X5] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f6223,plain,
spl0_400,
inference(avatar_split_clause,[],[f605,f6221]) ).
fof(f6221,plain,
( spl0_400
<=> ! [X2,X5,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f605,axiom,
! [X2,X3,X5] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f6219,plain,
spl0_399,
inference(avatar_split_clause,[],[f604,f6217]) ).
fof(f6217,plain,
( spl0_399
<=> ! [X13,X22,X5] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f604,axiom,
! [X22,X5,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f6215,plain,
spl0_398,
inference(avatar_split_clause,[],[f432,f6213]) ).
fof(f6213,plain,
( spl0_398
<=> ! [X2,X5,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f432,axiom,
! [X2,X3,X5] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
fof(f6211,plain,
spl0_397,
inference(avatar_split_clause,[],[f431,f6209]) ).
fof(f6209,plain,
( spl0_397
<=> ! [X2,X5,X3] :
( c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f431,axiom,
! [X2,X3,X5] :
( c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
fof(f6207,plain,
spl0_396,
inference(avatar_split_clause,[],[f430,f6205]) ).
fof(f6205,plain,
( spl0_396
<=> ! [X13,X22,X5] :
( ~ c_lessequals(X22,X13,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f430,axiom,
! [X22,X5,X13] :
( ~ c_lessequals(X22,X13,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
fof(f6203,plain,
spl0_395,
inference(avatar_split_clause,[],[f317,f6201]) ).
fof(f6201,plain,
( spl0_395
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f317,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f6199,plain,
spl0_394,
inference(avatar_split_clause,[],[f316,f6197]) ).
fof(f6197,plain,
( spl0_394
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f316,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f6195,plain,
spl0_393,
inference(avatar_split_clause,[],[f315,f6193]) ).
fof(f6193,plain,
( spl0_393
<=> ! [X0,X6,X1,X7] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f315,axiom,
! [X0,X1,X6,X7] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f6189,plain,
spl0_392,
inference(avatar_split_clause,[],[f307,f6187]) ).
fof(f6187,plain,
( spl0_392
<=> ! [X6,X1,X7] :
( ~ c_lessequals(X7,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f307,axiom,
! [X1,X6,X7] :
( ~ c_lessequals(X7,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X7,tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
fof(f6185,plain,
spl0_391,
inference(avatar_split_clause,[],[f106,f6183]) ).
fof(f6183,plain,
( spl0_391
<=> ! [X11,X0,X3,X2] : c_List_Odrop(X2,c_List_Otake(X3,X11,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_List_Odrop(X2,X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f106,axiom,
! [X2,X3,X0,X11] : c_List_Odrop(X2,c_List_Otake(X3,X11,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_List_Odrop(X2,X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__take_0) ).
fof(f6181,plain,
spl0_390,
inference(avatar_split_clause,[],[f87,f6179]) ).
fof(f6179,plain,
( spl0_390
<=> ! [X22,X5,X26] :
( X5 = X22
| c_HOL_Oord__class_Oless(X5,X22,tc_nat)
| c_Lambda_OdB_OVar(X22) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X22)),X26),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f87,axiom,
! [X26,X5,X22] :
( X5 = X22
| c_HOL_Oord__class_Oless(X5,X22,tc_nat)
| c_Lambda_OdB_OVar(X22) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X22)),X26),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
fof(f6177,plain,
spl0_389,
inference(avatar_split_clause,[],[f79,f6175]) ).
fof(f6175,plain,
( spl0_389
<=> ! [X2,X27,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X27,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X27,X2,tc_nat),c_HOL_Ominus__class_Ominus(X27,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f79,axiom,
! [X2,X3,X27] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X27,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X27,X2,tc_nat),c_HOL_Ominus__class_Ominus(X27,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f6103,plain,
( spl0_388
| ~ spl0_34
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f5860,f5503,f1300,f6101]) ).
fof(f6101,plain,
( spl0_388
<=> ! [X2,X0,X1,X3] : c_Lambda_OdB_OVar(X3) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f1300,plain,
( spl0_34
<=> ! [X48,X17] : c_Lambda_OdB_OVar(X17) != c_Lambda_OdB_OAbs(X48) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f5503,plain,
( spl0_368
<=> ! [X2,X5,X26] : c_Lambda_Oliftn(X2,c_Lambda_OdB_OAbs(X26),X5) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X2,X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f5860,plain,
( ! [X2,X3,X0,X1] : c_Lambda_OdB_OVar(X3) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2)
| ~ spl0_34
| ~ spl0_368 ),
inference(superposition,[],[f1301,f5504]) ).
fof(f5504,plain,
( ! [X2,X26,X5] : c_Lambda_Oliftn(X2,c_Lambda_OdB_OAbs(X26),X5) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X2,X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f5503]) ).
fof(f1301,plain,
( ! [X48,X17] : c_Lambda_OdB_OVar(X17) != c_Lambda_OdB_OAbs(X48)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1300]) ).
fof(f5854,plain,
( spl0_387
| ~ spl0_122
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2881,f2655,f1682,f5852]) ).
fof(f5852,plain,
( spl0_387
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f1682,plain,
( spl0_122
<=> ! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Orderings_Obot__class_Obot(tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f2655,plain,
( spl0_224
<=> ! [X13,X22,X3] :
( ~ c_lessequals(X22,X13,tc_nat)
| c_lessequals(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2881,plain,
( ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) )
| ~ spl0_122
| ~ spl0_224 ),
inference(superposition,[],[f2656,f1683]) ).
fof(f1683,plain,
( ! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Orderings_Obot__class_Obot(tc_nat)) = X3
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1682]) ).
fof(f2656,plain,
( ! [X3,X22,X13] :
( c_lessequals(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat)
| ~ c_lessequals(X22,X13,tc_nat) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2655]) ).
fof(f5578,plain,
spl0_386,
inference(avatar_split_clause,[],[f1124,f5576]) ).
fof(f5576,plain,
( spl0_386
<=> ! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_HOL_Oone__class_Oone(tc_nat) = X2
| c_HOL_Oone__class_Oone(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f1124,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_HOL_Oone__class_Oone(tc_nat) = X2
| c_HOL_Oone__class_Oone(tc_nat) = X3 ),
inference(forward_demodulation,[],[f1123,f976]) ).
fof(f976,plain,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X2) = X2,
inference(forward_demodulation,[],[f701,f689]) ).
fof(f701,axiom,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f1123,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Oone__class_Oone(tc_nat) = X2
| c_HOL_Oone__class_Oone(tc_nat) = X3 ),
inference(forward_demodulation,[],[f1122,f689]) ).
fof(f1122,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) = X2
| c_HOL_Oone__class_Oone(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1121,f976]) ).
fof(f1121,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
| c_HOL_Oone__class_Oone(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1120,f689]) ).
fof(f1120,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1119,f976]) ).
fof(f1119,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f950,f689]) ).
fof(f950,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f207,f5,f5,f5]) ).
fof(f207,axiom,
! [X2,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
fof(f5574,plain,
spl0_385,
inference(avatar_split_clause,[],[f1118,f5572]) ).
fof(f5572,plain,
( spl0_385
<=> ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f1118,plain,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat) ),
inference(forward_demodulation,[],[f1117,f689]) ).
fof(f1117,plain,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat) ),
inference(forward_demodulation,[],[f647,f689]) ).
fof(f647,axiom,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f5570,plain,
( spl0_384
| ~ spl0_121
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2832,f2647,f1678,f5568]) ).
fof(f5568,plain,
( spl0_384
<=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f1678,plain,
( spl0_121
<=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f2832,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) != X0
| ~ spl0_121
| ~ spl0_222 ),
inference(superposition,[],[f1679,f2648]) ).
fof(f1679,plain,
( ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) != X2
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1678]) ).
fof(f5566,plain,
spl0_383,
inference(avatar_split_clause,[],[f1099,f5564]) ).
fof(f5564,plain,
( spl0_383
<=> ! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_HOL_Oone__class_Oone(tc_nat) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f1099,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_HOL_Oone__class_Oone(tc_nat) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1098,f976]) ).
fof(f1098,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Oone__class_Oone(tc_nat) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1097,f689]) ).
fof(f1097,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1096,f976]) ).
fof(f1096,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1095,f689]) ).
fof(f1095,plain,
! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f944,f689]) ).
fof(f944,plain,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f363,f5,f5]) ).
fof(f363,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
fof(f5562,plain,
spl0_382,
inference(avatar_split_clause,[],[f1094,f5560]) ).
fof(f5560,plain,
( spl0_382
<=> ! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f1094,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X3 ),
inference(forward_demodulation,[],[f1093,f976]) ).
fof(f1093,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X3 ),
inference(forward_demodulation,[],[f1092,f689]) ).
fof(f1092,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1091,f976]) ).
fof(f1091,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1090,f689]) ).
fof(f1090,plain,
! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f943,f689]) ).
fof(f943,plain,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f169,f5,f5]) ).
fof(f169,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
fof(f5558,plain,
spl0_381,
inference(avatar_split_clause,[],[f1084,f5556]) ).
fof(f5556,plain,
( spl0_381
<=> ! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_Orderings_Obot__class_Obot(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f1084,plain,
! [X2,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2)
| c_Orderings_Obot__class_Obot(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1083,f976]) ).
fof(f1083,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))
| c_Orderings_Obot__class_Obot(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1082,f689]) ).
fof(f1082,plain,
! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X3
| c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f1081,f689]) ).
fof(f1081,plain,
! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f941,f689]) ).
fof(f941,plain,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f208,f5]) ).
fof(f208,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
fof(f5554,plain,
spl0_380,
inference(avatar_split_clause,[],[f1076,f5552]) ).
fof(f5552,plain,
( spl0_380
<=> ! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f1076,plain,
! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| X2 = X3 ),
inference(forward_demodulation,[],[f1075,f689]) ).
fof(f1075,plain,
! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| X2 = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
inference(forward_demodulation,[],[f575,f689]) ).
fof(f575,axiom,
! [X2,X3] :
( X2 = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f5550,plain,
spl0_379,
inference(avatar_split_clause,[],[f932,f5548]) ).
fof(f5548,plain,
( spl0_379
<=> ! [X2,X3] :
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f932,plain,
! [X2,X3] :
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f242,f5]) ).
fof(f242,axiom,
! [X2,X3] :
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
fof(f5546,plain,
spl0_378,
inference(avatar_split_clause,[],[f931,f5544]) ).
fof(f5544,plain,
( spl0_378
<=> ! [X2,X3] :
( X2 = X3
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f931,plain,
! [X2,X3] :
( X2 = X3
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f631,f5]) ).
fof(f631,axiom,
! [X2,X3] :
( X2 = X3
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f5542,plain,
spl0_377,
inference(avatar_split_clause,[],[f718,f5540]) ).
fof(f5540,plain,
( spl0_377
<=> ! [X37,X11,X0,X33,X2] : c_List_Otake(X2,c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Otake(X2,X11,X33),X33,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f718,axiom,
! [X2,X0,X11,X37,X33] : c_List_Otake(X2,c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Otake(X2,X11,X33),X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__map_0) ).
fof(f5538,plain,
spl0_376,
inference(avatar_split_clause,[],[f715,f5536]) ).
fof(f5536,plain,
( spl0_376
<=> ! [X37,X11,X0,X33,X2] : c_List_Orotate(X2,c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Orotate(X2,X11,X33),X33,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f715,axiom,
! [X2,X0,X11,X37,X33] : c_List_Orotate(X2,c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Orotate(X2,X11,X33),X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__map_0) ).
fof(f5534,plain,
spl0_375,
inference(avatar_split_clause,[],[f707,f5532]) ).
fof(f5532,plain,
( spl0_375
<=> ! [X37,X11,X0,X33,X2] : c_List_Odrop(X2,c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Odrop(X2,X11,X33),X33,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f707,axiom,
! [X2,X0,X11,X37,X33] : c_List_Odrop(X2,c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Odrop(X2,X11,X33),X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__map_0) ).
fof(f5530,plain,
spl0_374,
inference(avatar_split_clause,[],[f530,f5528]) ).
fof(f5528,plain,
( spl0_374
<=> ! [X11,X0,X3,X2] : c_List_Orotate(X3,c_List_Orotate(X2,X11,X0),X0) = c_List_Orotate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f530,axiom,
! [X2,X3,X0,X11] : c_List_Orotate(X3,c_List_Orotate(X2,X11,X0),X0) = c_List_Orotate(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).
fof(f5526,plain,
( spl0_373
| ~ spl0_49
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2432,f2322,f1362,f5524]) ).
fof(f5524,plain,
( spl0_373
<=> ! [X0,X1] : c_List_Otake(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f1362,plain,
( spl0_49
<=> ! [X0,X11] : c_List_Oappend(X11,c_List_Olist_ONil(X0),X0) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2322,plain,
( spl0_194
<=> ! [X12,X0,X11] : c_List_Otake(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),c_List_Oappend(X11,X12,X0),X0) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f2432,plain,
( ! [X0,X1] : c_List_Otake(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) = X0
| ~ spl0_49
| ~ spl0_194 ),
inference(superposition,[],[f2323,f1363]) ).
fof(f1363,plain,
( ! [X0,X11] : c_List_Oappend(X11,c_List_Olist_ONil(X0),X0) = X11
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1362]) ).
fof(f2323,plain,
( ! [X0,X11,X12] : c_List_Otake(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),c_List_Oappend(X11,X12,X0),X0) = X11
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2322]) ).
fof(f5522,plain,
spl0_372,
inference(avatar_split_clause,[],[f510,f5520]) ).
fof(f5520,plain,
( spl0_372
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X10,X15,X0),X0) = c_Orderings_Oord__class_Omax(X10,c_Orderings_Oord__class_Omax(X9,X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f510,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X10,X15,X0),X0) = c_Orderings_Oord__class_Omax(X10,c_Orderings_Oord__class_Omax(X9,X15,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
fof(f5518,plain,
spl0_371,
inference(avatar_split_clause,[],[f509,f5516]) ).
fof(f5516,plain,
( spl0_371
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) = c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X10,X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f509,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) = c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X10,X15,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
fof(f5514,plain,
spl0_370,
inference(avatar_split_clause,[],[f446,f5512]) ).
fof(f5512,plain,
( spl0_370
<=> ! [X11,X0,X3,X2] : c_List_Odrop(X2,c_List_Odrop(X3,X11,X0),X0) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f446,axiom,
! [X2,X3,X0,X11] : c_List_Odrop(X2,c_List_Odrop(X3,X11,X0),X0) = c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__drop_0) ).
fof(f5509,plain,
spl0_369,
inference(avatar_split_clause,[],[f372,f5507]) ).
fof(f5507,plain,
( spl0_369
<=> ! [X0,X12,X10] : c_List_Olist_OCons(X10,X12,X0) = c_List_Orev(c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f372,axiom,
! [X10,X0,X12] : c_List_Olist_OCons(X10,X12,X0) = c_List_Orev(c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
fof(f5505,plain,
spl0_368,
inference(avatar_split_clause,[],[f277,f5503]) ).
fof(f277,axiom,
! [X2,X26,X5] : c_Lambda_Oliftn(X2,c_Lambda_OdB_OAbs(X26),X5) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X2,X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X5),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
fof(f5501,plain,
spl0_367,
inference(avatar_split_clause,[],[f276,f5499]) ).
fof(f5499,plain,
( spl0_367
<=> ! [X9,X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(c_List_Olist_OCons(X9,X11,X0),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_List_Olistsum(X11,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f276,axiom,
! [X0,X11,X9] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(c_List_Olist_OCons(X9,X11,X0),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_List_Olistsum(X11,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
fof(f5497,plain,
spl0_366,
inference(avatar_split_clause,[],[f265,f5495]) ).
fof(f265,axiom,
! [X2,X22,X5] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X22),X5) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
fof(f5493,plain,
spl0_365,
inference(avatar_split_clause,[],[f222,f5491]) ).
fof(f5491,plain,
( spl0_365
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X15,X9,X0)
| c_HOL_Oord__class_Oless(X15,X10,X0)
| ~ c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f222,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X15,X9,X0)
| c_HOL_Oord__class_Oless(X15,X10,X0)
| ~ c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
fof(f5489,plain,
spl0_364,
inference(avatar_split_clause,[],[f167,f5487]) ).
fof(f5487,plain,
( spl0_364
<=> ! [X9,X0,X11] : c_List_Orev(c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Oappend(c_List_Orev(X11,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f167,axiom,
! [X0,X11,X9] : c_List_Orev(c_List_Olist_OCons(X9,X11,X0),X0) = c_List_Oappend(c_List_Orev(X11,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
fof(f5485,plain,
spl0_363,
inference(avatar_split_clause,[],[f161,f5483]) ).
fof(f5483,plain,
( spl0_363
<=> ! [X13,X22,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X13,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f161,axiom,
! [X22,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X13,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X5),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f5481,plain,
( spl0_362
| ~ spl0_62
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2293,f2107,f1414,f5479]) ).
fof(f5479,plain,
( spl0_362
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(tc_nat) != X0
| c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f1414,plain,
( spl0_62
<=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f2107,plain,
( spl0_189
<=> ! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_lessequals(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2293,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_nat) != X0
| c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) )
| ~ spl0_62
| ~ spl0_189 ),
inference(superposition,[],[f2108,f1415]) ).
fof(f1415,plain,
( ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X3
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1414]) ).
fof(f2108,plain,
( ! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_lessequals(X3,X2,tc_nat) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2107]) ).
fof(f5477,plain,
spl0_361,
inference(avatar_split_clause,[],[f84,f5475]) ).
fof(f5475,plain,
( spl0_361
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X15,X9,X0)
| c_lessequals(X15,X10,X0)
| ~ c_lessequals(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f84,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X15,X9,X0)
| c_lessequals(X15,X10,X0)
| ~ c_lessequals(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
fof(f5473,plain,
spl0_360,
inference(avatar_split_clause,[],[f38,f5471]) ).
fof(f5471,plain,
( spl0_360
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X15,X9,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X10,X15,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f38,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X15,X9,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X10,X15,X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
fof(f5469,plain,
spl0_359,
inference(avatar_split_clause,[],[f19,f5467]) ).
fof(f5467,plain,
( spl0_359
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X15,X0)
| ~ c_HOL_Oord__class_Oless(X10,X15,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f19,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X15,X0)
| ~ c_HOL_Oord__class_Oless(X10,X15,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
fof(f5391,plain,
( spl0_358
| ~ spl0_11
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2207,f2034,f1192,f5389]) ).
fof(f5389,plain,
( spl0_358
<=> ! [X0] : c_List_Olistsum(X0,tc_nat) = c_List_Olistsum(c_List_Orev(X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f1192,plain,
( spl0_11
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f2034,plain,
( spl0_171
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Olistsum(c_List_Orev(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f2207,plain,
( ! [X0] : c_List_Olistsum(X0,tc_nat) = c_List_Olistsum(c_List_Orev(X0,tc_nat),tc_nat)
| ~ spl0_11
| ~ spl0_171 ),
inference(resolution,[],[f2035,f1194]) ).
fof(f1194,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f2035,plain,
( ! [X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Olistsum(c_List_Orev(X11,X0),X0) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f2034]) ).
fof(f5129,plain,
spl0_357,
inference(avatar_split_clause,[],[f1137,f5127]) ).
fof(f5127,plain,
( spl0_357
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f1137,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0) ),
inference(forward_demodulation,[],[f763,f689]) ).
fof(f763,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f5125,plain,
spl0_356,
inference(avatar_split_clause,[],[f1134,f5123]) ).
fof(f5123,plain,
( spl0_356
<=> ! [X2,X0] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f1134,plain,
! [X2,X0] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
inference(forward_demodulation,[],[f762,f689]) ).
fof(f762,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f5121,plain,
spl0_355,
inference(avatar_split_clause,[],[f1080,f5119]) ).
fof(f5119,plain,
( spl0_355
<=> ! [X6,X16,X1] :
( hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat)
| ~ hBOOL(hAPP(X16,c_HOL_Ominus__class_Ominus(X1,X6,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f1080,plain,
! [X1,X6,X16] :
( hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat)
| ~ hBOOL(hAPP(X16,c_HOL_Ominus__class_Ominus(X1,X6,tc_nat))) ),
inference(forward_demodulation,[],[f627,f689]) ).
fof(f627,axiom,
! [X1,X6,X16] :
( ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat)
| hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X16,c_HOL_Ominus__class_Ominus(X1,X6,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
fof(f5117,plain,
spl0_354,
inference(avatar_split_clause,[],[f1073,f5115]) ).
fof(f5115,plain,
( spl0_354
<=> ! [X2,X10,X0,X9,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X3
| X9 = X10
| c_List_Oreplicate(X3,X9,X0) != c_List_Oreplicate(X2,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f1073,plain,
! [X2,X3,X10,X0,X9] :
( c_Orderings_Obot__class_Obot(tc_nat) = X3
| X9 = X10
| c_List_Oreplicate(X3,X9,X0) != c_List_Oreplicate(X2,X10,X0) ),
inference(forward_demodulation,[],[f699,f689]) ).
fof(f699,axiom,
! [X2,X3,X10,X0,X9] :
( X9 = X10
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Oreplicate(X3,X9,X0) != c_List_Oreplicate(X2,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
fof(f5113,plain,
spl0_353,
inference(avatar_split_clause,[],[f1059,f5111]) ).
fof(f5111,plain,
( spl0_353
<=> ! [X22,X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X22,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f1059,plain,
! [X2,X22] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X22,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f1058,f855]) ).
fof(f855,plain,
! [X2,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f367,f5]) ).
fof(f367,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(X3,c_Suc(X2),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
fof(f1058,plain,
! [X2,X22] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f924,f689]) ).
fof(f924,plain,
! [X2,X22] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),X2,tc_nat) ),
inference(definition_unfolding,[],[f654,f5]) ).
fof(f654,axiom,
! [X2,X22] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,c_Suc(X22),tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f5109,plain,
spl0_352,
inference(avatar_split_clause,[],[f771,f5107]) ).
fof(f5107,plain,
( spl0_352
<=> ! [X28,X57,X22,X29,X25] :
( ~ c_Type_Otyping(X28,X25,X29)
| c_Type_Otyping(c_Type_Oshift(X28,X22,X57,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X25),X22),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f771,axiom,
! [X28,X29,X57,X22,X25] :
( ~ c_Type_Otyping(X28,X25,X29)
| c_Type_Otyping(c_Type_Oshift(X28,X22,X57,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X25),X22),X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
fof(f5105,plain,
spl0_351,
inference(avatar_split_clause,[],[f740,f5103]) ).
fof(f5103,plain,
( spl0_351
<=> ! [X9,X84,X29,X16] :
( hBOOL(hAPP(X16,X84))
| hBOOL(hAPP(X16,X29))
| c_Type_Osko__Type__Xtype__induct__1__1(X16) != hAPP(hAPP(c_Type_Otype_OFun,X84),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f740,axiom,
! [X29,X9,X16,X84] :
( hBOOL(hAPP(X16,X84))
| hBOOL(hAPP(X16,X29))
| c_Type_Osko__Type__Xtype__induct__1__1(X16) != hAPP(hAPP(c_Type_Otype_OFun,X84),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_0) ).
fof(f5101,plain,
spl0_350,
inference(avatar_split_clause,[],[f739,f5099]) ).
fof(f5099,plain,
( spl0_350
<=> ! [X82,X29,X16,X83] :
( hBOOL(hAPP(X16,X83))
| hBOOL(hAPP(X16,X29))
| c_Type_Osko__Type__Xtype__induct__1__1(X16) != hAPP(hAPP(c_Type_Otype_OFun,X82),X83) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f739,axiom,
! [X82,X83,X29,X16] :
( hBOOL(hAPP(X16,X83))
| hBOOL(hAPP(X16,X29))
| c_Type_Osko__Type__Xtype__induct__1__1(X16) != hAPP(hAPP(c_Type_Otype_OFun,X82),X83) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_1) ).
fof(f5097,plain,
spl0_349,
inference(avatar_split_clause,[],[f595,f5095]) ).
fof(f5095,plain,
( spl0_349
<=> ! [X13,X22,X5] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f595,axiom,
! [X22,X5,X13] :
( c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f5093,plain,
spl0_348,
inference(avatar_split_clause,[],[f594,f5091]) ).
fof(f5091,plain,
( spl0_348
<=> ! [X13,X22,X5] :
( ~ c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f594,axiom,
! [X22,X5,X13] :
( ~ c_HOL_Oord__class_Oless(X22,c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),X13,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f5059,plain,
spl0_347,
inference(avatar_split_clause,[],[f320,f5057]) ).
fof(f5057,plain,
( spl0_347
<=> ! [X2,X5,X3] :
( ~ c_lessequals(X5,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f320,axiom,
! [X2,X3,X5] :
( ~ c_lessequals(X5,X2,tc_nat)
| c_lessequals(X3,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
fof(f5055,plain,
spl0_346,
inference(avatar_split_clause,[],[f312,f5053]) ).
fof(f5053,plain,
( spl0_346
<=> ! [X2,X5,X3] :
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f312,axiom,
! [X2,X3,X5] :
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f5051,plain,
spl0_345,
inference(avatar_split_clause,[],[f311,f5049]) ).
fof(f5049,plain,
( spl0_345
<=> ! [X9,X10,X15] :
( X10 = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f311,axiom,
! [X10,X9,X15] :
( X10 = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
fof(f5047,plain,
spl0_344,
inference(avatar_split_clause,[],[f301,f5045]) ).
fof(f5045,plain,
( spl0_344
<=> ! [X59,X33,X0,X5] : c_List_Omap(c_COMBK(X5,X0,X33),X59,X33,X0) = c_List_Oreplicate(c_Nat_Osize__class_Osize(X59,tc_List_Olist(X33)),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f301,axiom,
! [X0,X59,X5,X33] : c_List_Omap(c_COMBK(X5,X0,X33),X59,X33,X0) = c_List_Oreplicate(c_Nat_Osize__class_Osize(X59,tc_List_Olist(X33)),X5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate__const_0) ).
fof(f5043,plain,
spl0_343,
inference(avatar_split_clause,[],[f220,f5041]) ).
fof(f5041,plain,
( spl0_343
<=> ! [X22,X5,X13] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),X22,tc_nat)
| ~ c_lessequals(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f220,axiom,
! [X5,X22,X13] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),X22,tc_nat)
| ~ c_lessequals(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
fof(f5039,plain,
spl0_342,
inference(avatar_split_clause,[],[f219,f5037]) ).
fof(f5037,plain,
( spl0_342
<=> ! [X22,X5,X13] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),X22,tc_nat)
| c_lessequals(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f219,axiom,
! [X5,X22,X13] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X13,X5,tc_nat),X22,tc_nat)
| c_lessequals(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
fof(f5035,plain,
spl0_341,
inference(avatar_split_clause,[],[f93,f5033]) ).
fof(f5033,plain,
( spl0_341
<=> ! [X9,X0,X11] :
( c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = X11
| c_List_Orev(X11,X0) != c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f93,axiom,
! [X0,X11,X9] :
( c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = X11
| c_List_Orev(X11,X0) != c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
fof(f4581,plain,
( spl0_340
| ~ spl0_295
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f4166,f3516,f3512,f4579]) ).
fof(f4579,plain,
( spl0_340
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f3516,plain,
( spl0_296
<=> ! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f4166,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_295
| ~ spl0_296 ),
inference(resolution,[],[f3517,f3513]) ).
fof(f3517,plain,
( ! [X2,X3] :
( ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3516]) ).
fof(f4524,plain,
spl0_339,
inference(avatar_split_clause,[],[f1116,f4522]) ).
fof(f4522,plain,
( spl0_339
<=> ! [X2,X16] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16),tc_nat)
| ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f1116,plain,
! [X2,X16] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16),tc_nat)
| ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X2)) ),
inference(forward_demodulation,[],[f1115,f689]) ).
fof(f1115,plain,
! [X2,X16] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X2))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16),tc_nat) ),
inference(forward_demodulation,[],[f150,f689]) ).
fof(f150,axiom,
! [X2,X16] :
( hBOOL(hAPP(X16,X2))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_0) ).
fof(f4520,plain,
spl0_338,
inference(avatar_split_clause,[],[f1089,f4518]) ).
fof(f4518,plain,
( spl0_338
<=> ! [X2,X0,X11] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Otake(X2,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f1089,plain,
! [X2,X0,X11] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Otake(X2,X11,X0) ),
inference(forward_demodulation,[],[f300,f689]) ).
fof(f300,axiom,
! [X2,X0,X11] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Otake(X2,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
fof(f4516,plain,
spl0_337,
inference(avatar_split_clause,[],[f1015,f4514]) ).
fof(f4514,plain,
( spl0_337
<=> ! [X0,X11,X33] :
( c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Oreplicate(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X33)),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Omonoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f1015,plain,
! [X0,X11,X33] :
( c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Oreplicate(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X33)),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Omonoid__add(X0) ),
inference(forward_demodulation,[],[f704,f301]) ).
fof(f704,axiom,
! [X0,X11,X33] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Omap(c_COMBK(c_HOL_Ozero__class_Ozero(X0),X0,X33),X11,X33,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__0_0) ).
fof(f4512,plain,
spl0_336,
inference(avatar_split_clause,[],[f998,f4510]) ).
fof(f4510,plain,
( spl0_336
<=> ! [X25,X26] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X25),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X25),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f998,plain,
! [X26,X25] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X25),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X25),c_Orderings_Obot__class_Obot(tc_nat))),
inference(forward_demodulation,[],[f266,f689]) ).
fof(f266,axiom,
! [X26,X25] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X25),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X25),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f4508,plain,
spl0_335,
inference(avatar_split_clause,[],[f980,f4506]) ).
fof(f4506,plain,
( spl0_335
<=> ! [X22,X3] : c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X22)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f980,plain,
! [X3,X22] : c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X22)),tc_nat),
inference(forward_demodulation,[],[f842,f839]) ).
fof(f839,plain,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X2),
inference(definition_unfolding,[],[f6,f5]) ).
fof(f6,axiom,
! [X2] : c_Suc(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
fof(f842,plain,
! [X3,X22] : c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X22)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f33,f5]) ).
fof(f33,axiom,
! [X3,X22] : c_HOL_Oord__class_Oless(X22,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X22)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f4504,plain,
spl0_334,
inference(avatar_split_clause,[],[f978,f4502]) ).
fof(f4502,plain,
( spl0_334
<=> ! [X22,X3] : c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X3)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f978,plain,
! [X3,X22] : c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X3)),tc_nat),
inference(forward_demodulation,[],[f840,f839]) ).
fof(f840,plain,
! [X3,X22] : c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X3)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f32,f5]) ).
fof(f32,axiom,
! [X3,X22] : c_HOL_Oord__class_Oless(X22,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X3)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
fof(f4500,plain,
spl0_333,
inference(avatar_split_clause,[],[f814,f4498]) ).
fof(f4498,plain,
( spl0_333
<=> ! [X33,X34,X0,X16,X46,X90] : hAPP(hAPP(c_COMBC(X16,X33,X46,X0),X34),X90) = hAPP(hAPP(X16,X90),X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f814,axiom,
! [X46,X0,X90,X16,X34,X33] : hAPP(hAPP(c_COMBC(X16,X33,X46,X0),X34),X90) = hAPP(hAPP(X16,X90),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
fof(f4496,plain,
( spl0_332
| ~ spl0_220
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4082,f3496,f2639,f4494]) ).
fof(f4494,plain,
( spl0_332
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2639,plain,
( spl0_220
<=> ! [X13,X22,X3] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f4082,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_220
| ~ spl0_291 ),
inference(resolution,[],[f3497,f2640]) ).
fof(f2640,plain,
( ! [X3,X22,X13] :
( c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2639]) ).
fof(f4492,plain,
spl0_331,
inference(avatar_split_clause,[],[f754,f4490]) ).
fof(f4490,plain,
( spl0_331
<=> ! [X28,X0,X13,X29,X22] :
( ~ c_HOL_Oord__class_Oless(X13,X22,tc_nat)
| hAPP(c_Type_Oshift(X28,X22,X29,X0),X13) = hAPP(X28,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f754,axiom,
! [X28,X29,X0,X22,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X22,tc_nat)
| hAPP(c_Type_Oshift(X28,X22,X29,X0),X13) = hAPP(X28,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
fof(f4488,plain,
spl0_330,
inference(avatar_split_clause,[],[f742,f4486]) ).
fof(f4486,plain,
( spl0_330
<=> ! [X55,X0,X85,X56,X86] : hAPP(hAPP(X56,X85),X86) = c_Type_Otype_Otype__case(X55,X56,hAPP(hAPP(c_Type_Otype_OFun,X85),X86),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f742,axiom,
! [X0,X56,X86,X55,X85] : hAPP(hAPP(X56,X85),X86) = c_Type_Otype_Otype__case(X55,X56,hAPP(hAPP(c_Type_Otype_OFun,X85),X86),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
fof(f4484,plain,
spl0_329,
inference(avatar_split_clause,[],[f716,f4482]) ).
fof(f4482,plain,
( spl0_329
<=> ! [X37,X11,X0,X33] : c_List_Orev(c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Orev(X11,X33),X33,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f716,axiom,
! [X0,X11,X37,X33] : c_List_Orev(c_List_Omap(X37,X11,X33,X0),X0) = c_List_Omap(X37,c_List_Orev(X11,X33),X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).
fof(f4480,plain,
spl0_328,
inference(avatar_split_clause,[],[f713,f4478]) ).
fof(f4478,plain,
( spl0_328
<=> ! [X37,X33,X0,X9,X2] : c_List_Omap(X37,c_List_Oreplicate(X2,X9,X33),X33,X0) = c_List_Oreplicate(X2,hAPP(X37,X9),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f713,axiom,
! [X2,X0,X37,X9,X33] : c_List_Omap(X37,c_List_Oreplicate(X2,X9,X33),X33,X0) = c_List_Oreplicate(X2,hAPP(X37,X9),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).
fof(f4476,plain,
spl0_327,
inference(avatar_split_clause,[],[f678,f4474]) ).
fof(f4474,plain,
( spl0_327
<=> ! [X11,X51,X0,X9] : c_List_Oappend(X11,c_List_Oappend(X9,X51,X0),X0) = c_List_Oappend(c_List_Oappend(X11,X9,X0),X51,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f678,axiom,
! [X51,X0,X11,X9] : c_List_Oappend(X11,c_List_Oappend(X9,X51,X0),X0) = c_List_Oappend(c_List_Oappend(X11,X9,X0),X51,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
fof(f4472,plain,
spl0_326,
inference(avatar_split_clause,[],[f672,f4470]) ).
fof(f4470,plain,
( spl0_326
<=> ! [X10,X11,X0,X9,X22] : c_List_Olist__update(X11,X22,X10,X0) = c_List_Olist__update(c_List_Olist__update(X11,X22,X9,X0),X22,X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f672,axiom,
! [X10,X0,X11,X9,X22] : c_List_Olist__update(X11,X22,X10,X0) = c_List_Olist__update(c_List_Olist__update(X11,X22,X9,X0),X22,X10,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
fof(f4426,plain,
( spl0_325
| ~ spl0_222
| ~ spl0_264
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4422,f4419,f3388,f2647,f4424]) ).
fof(f4424,plain,
( spl0_325
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Omax(X3,X2,tc_nat) = X3
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f4419,plain,
( spl0_324
<=> ! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f4422,plain,
( ! [X2,X3] :
( c_Orderings_Oord__class_Omax(X3,X2,tc_nat) = X3
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) )
| ~ spl0_222
| ~ spl0_264
| ~ spl0_324 ),
inference(forward_demodulation,[],[f4420,f3705]) ).
fof(f4420,plain,
( ! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3 )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f4419]) ).
fof(f4421,plain,
spl0_324,
inference(avatar_split_clause,[],[f653,f4419]) ).
fof(f653,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f4417,plain,
spl0_323,
inference(avatar_split_clause,[],[f525,f4415]) ).
fof(f4415,plain,
( spl0_323
<=> ! [X12,X0,X11] : c_List_Orev(c_List_Oappend(X11,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Orev(X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f525,axiom,
! [X0,X11,X12] : c_List_Orev(c_List_Oappend(X11,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Orev(X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
fof(f4413,plain,
( spl0_322
| ~ spl0_290
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f4080,f3496,f3492,f4411]) ).
fof(f4411,plain,
( spl0_322
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f3492,plain,
( spl0_290
<=> ! [X2,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f4080,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_290
| ~ spl0_291 ),
inference(resolution,[],[f3497,f3493]) ).
fof(f3493,plain,
( ! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) )
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3492]) ).
fof(f4409,plain,
spl0_321,
inference(avatar_split_clause,[],[f478,f4407]) ).
fof(f4407,plain,
( spl0_321
<=> ! [X13,X22,X49] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X49))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X49),c_Lambda_OdB_OVar(X22)),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f478,axiom,
! [X49,X22,X13] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X49))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X49),c_Lambda_OdB_OVar(X22)),X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
fof(f4405,plain,
spl0_320,
inference(avatar_split_clause,[],[f476,f4403]) ).
fof(f4403,plain,
( spl0_320
<=> ! [X22,X32,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X22,tc_nat)
| c_Lambda_OdB_OVar(X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X32),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f476,axiom,
! [X22,X32,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X22,tc_nat)
| c_Lambda_OdB_OVar(X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X32),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
fof(f4401,plain,
spl0_319,
inference(avatar_split_clause,[],[f462,f4399]) ).
fof(f4399,plain,
( spl0_319
<=> ! [X11,X0,X12,X8] :
( ~ c_List_Olistsp(X8,X11,X0)
| ~ c_List_Olistsp(X8,X12,X0)
| c_List_Olistsp(X8,c_List_Oappend(X11,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f462,axiom,
! [X0,X11,X8,X12] :
( ~ c_List_Olistsp(X8,X11,X0)
| ~ c_List_Olistsp(X8,X12,X0)
| c_List_Olistsp(X8,c_List_Oappend(X11,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
fof(f4367,plain,
( spl0_318
| ~ spl0_222
| ~ spl0_264
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4363,f4360,f3388,f2647,f4365]) ).
fof(f4360,plain,
( spl0_317
<=> ! [X2,X3] :
( ~ c_lessequals(X2,X3,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f4363,plain,
( ! [X2,X3] :
( c_Orderings_Oord__class_Omax(X3,X2,tc_nat) = X3
| ~ c_lessequals(X2,X3,tc_nat) )
| ~ spl0_222
| ~ spl0_264
| ~ spl0_317 ),
inference(forward_demodulation,[],[f4361,f3705]) ).
fof(f4361,plain,
( ! [X2,X3] :
( ~ c_lessequals(X2,X3,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3 )
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f4360]) ).
fof(f4362,plain,
spl0_317,
inference(avatar_split_clause,[],[f436,f4360]) ).
fof(f436,axiom,
! [X2,X3] :
( ~ c_lessequals(X2,X3,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
fof(f4358,plain,
spl0_316,
inference(avatar_split_clause,[],[f384,f4356]) ).
fof(f4356,plain,
( spl0_316
<=> ! [X5,X0,X9,X22] : c_List_Odrop(X22,c_List_Oreplicate(X5,X9,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X5,X22,tc_nat),X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f384,axiom,
! [X0,X9,X22,X5] : c_List_Odrop(X22,c_List_Oreplicate(X5,X9,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X5,X22,tc_nat),X9,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
fof(f4354,plain,
spl0_315,
inference(avatar_split_clause,[],[f319,f4352]) ).
fof(f4352,plain,
( spl0_315
<=> ! [X60,X0,X14,X9] : c_List_Olist_OCons(X9,c_List_Oappend(X60,X14,X0),X0) = c_List_Oappend(c_List_Olist_OCons(X9,X60,X0),X14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f319,axiom,
! [X0,X9,X14,X60] : c_List_Olist_OCons(X9,c_List_Oappend(X60,X14,X0),X0) = c_List_Oappend(c_List_Olist_OCons(X9,X60,X0),X14,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
fof(f4350,plain,
spl0_314,
inference(avatar_split_clause,[],[f299,f4348]) ).
fof(f4348,plain,
( spl0_314
<=> ! [X13,X22,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X13,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X5,tc_nat),X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f299,axiom,
! [X22,X5,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X13,tc_nat),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X22,X5,tc_nat),X13,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f4346,plain,
spl0_313,
inference(avatar_split_clause,[],[f268,f4344]) ).
fof(f4344,plain,
( spl0_313
<=> ! [X2,X0,X11] : c_Nat_Osize__class_Osize(c_List_Odrop(X2,X11,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f268,axiom,
! [X2,X0,X11] : c_Nat_Osize__class_Osize(c_List_Odrop(X2,X11,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__drop_0) ).
fof(f4342,plain,
( spl0_312
| ~ spl0_158
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3728,f3388,f1952,f4340]) ).
fof(f1952,plain,
( spl0_158
<=> ! [X24] : c_Orderings_Obot__class_Obot(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f3728,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) != c_Orderings_Oord__class_Omax(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_158
| ~ spl0_264 ),
inference(superposition,[],[f1953,f3389]) ).
fof(f1953,plain,
( ! [X24] : c_Orderings_Obot__class_Obot(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1952]) ).
fof(f4338,plain,
spl0_311,
inference(avatar_split_clause,[],[f221,f4336]) ).
fof(f4336,plain,
( spl0_311
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f221,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f4334,plain,
spl0_310,
inference(avatar_split_clause,[],[f73,f4332]) ).
fof(f4332,plain,
( spl0_310
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f73,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X6),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f4330,plain,
spl0_309,
inference(avatar_split_clause,[],[f72,f4328]) ).
fof(f4328,plain,
( spl0_309
<=> ! [X0,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f72,axiom,
! [X0,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X7),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f4326,plain,
spl0_308,
inference(avatar_split_clause,[],[f26,f4324]) ).
fof(f4324,plain,
( spl0_308
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f4322,plain,
spl0_307,
inference(avatar_split_clause,[],[f22,f4320]) ).
fof(f4320,plain,
( spl0_307
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f3858,plain,
( spl0_306
| ~ spl0_116
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3710,f3388,f1657,f3856]) ).
fof(f1657,plain,
( spl0_116
<=> ! [X22,X13] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X22),X22,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f3710,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_116
| ~ spl0_264 ),
inference(superposition,[],[f1658,f3389]) ).
fof(f1658,plain,
( ! [X22,X13] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X22),X22,tc_nat)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1657]) ).
fof(f3754,plain,
( spl0_305
| ~ spl0_101
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3707,f3388,f1597,f3752]) ).
fof(f1597,plain,
( spl0_101
<=> ! [X2,X3] : c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f3707,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_101
| ~ spl0_264 ),
inference(superposition,[],[f1598,f3389]) ).
fof(f1598,plain,
( ! [X2,X3] : c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat)
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f3564,plain,
( spl0_304
| ~ spl0_21
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2161,f2026,f1242,f3562]) ).
fof(f1242,plain,
( spl0_21
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f2026,plain,
( spl0_169
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = c_Orderings_Oord__class_Omax(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f2161,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat)
| ~ spl0_21
| ~ spl0_169 ),
inference(resolution,[],[f2027,f1244]) ).
fof(f1244,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f2027,plain,
( ! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = c_Orderings_Oord__class_Omax(X10,X9,X0) )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f2026]) ).
fof(f3546,plain,
spl0_303,
inference(avatar_split_clause,[],[f1112,f3544]) ).
fof(f3544,plain,
( spl0_303
<=> ! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| hBOOL(hAPP(X16,v_sko__List__Xupt__Xinduct__1(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f1112,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| hBOOL(hAPP(X16,v_sko__List__Xupt__Xinduct__1(X16))) ),
inference(forward_demodulation,[],[f690,f689]) ).
fof(f690,axiom,
! [X16,X17] :
( hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X16,v_sko__List__Xupt__Xinduct__1(X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
fof(f3542,plain,
spl0_302,
inference(avatar_split_clause,[],[f1111,f3540]) ).
fof(f3540,plain,
( spl0_302
<=> ! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| hBOOL(hAPP(X16,v_sko__Nat__Xnat__Xinduct__1(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f1111,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X17))
| hBOOL(hAPP(X16,v_sko__Nat__Xnat__Xinduct__1(X16))) ),
inference(forward_demodulation,[],[f686,f689]) ).
fof(f686,axiom,
! [X16,X17] :
( hBOOL(hAPP(X16,X17))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X16,v_sko__Nat__Xnat__Xinduct__1(X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
fof(f3538,plain,
spl0_301,
inference(avatar_split_clause,[],[f1110,f3536]) ).
fof(f3536,plain,
( spl0_301
<=> ! [X2,X16] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X2))
| ~ hBOOL(hAPP(X16,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f1110,plain,
! [X2,X16] :
( ~ hBOOL(hAPP(X16,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X16,X2))
| ~ hBOOL(hAPP(X16,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16))) ),
inference(forward_demodulation,[],[f693,f689]) ).
fof(f693,axiom,
! [X2,X16] :
( hBOOL(hAPP(X16,X2))
| ~ hBOOL(hAPP(X16,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X16,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_1) ).
fof(f3534,plain,
spl0_300,
inference(avatar_split_clause,[],[f1072,f3532]) ).
fof(f3532,plain,
( spl0_300
<=> ! [X2,X0] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f1072,plain,
! [X2,X0] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
inference(forward_demodulation,[],[f453,f689]) ).
fof(f453,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f3530,plain,
spl0_299,
inference(avatar_split_clause,[],[f1071,f3528]) ).
fof(f3528,plain,
( spl0_299
<=> ! [X2,X0] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f1071,plain,
! [X2,X0] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
inference(forward_demodulation,[],[f452,f689]) ).
fof(f452,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f3526,plain,
spl0_298,
inference(avatar_split_clause,[],[f996,f3524]) ).
fof(f3524,plain,
( spl0_298
<=> ! [X10,X11,X0,X9] : c_List_Olist_OCons(X10,X11,X0) = c_List_Olist__update(c_List_Olist_OCons(X9,X11,X0),c_Orderings_Obot__class_Obot(tc_nat),X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f996,plain,
! [X10,X0,X11,X9] : c_List_Olist_OCons(X10,X11,X0) = c_List_Olist__update(c_List_Olist_OCons(X9,X11,X0),c_Orderings_Obot__class_Obot(tc_nat),X10,X0),
inference(forward_demodulation,[],[f494,f689]) ).
fof(f494,axiom,
! [X10,X0,X11,X9] : c_List_Olist__update(c_List_Olist_OCons(X9,X11,X0),c_HOL_Ozero__class_Ozero(tc_nat),X10,X0) = c_List_Olist_OCons(X10,X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
fof(f3522,plain,
spl0_297,
inference(avatar_split_clause,[],[f918,f3520]) ).
fof(f3520,plain,
( spl0_297
<=> ! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f918,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f500,f5]) ).
fof(f500,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f3518,plain,
spl0_296,
inference(avatar_split_clause,[],[f915,f3516]) ).
fof(f915,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ),
inference(definition_unfolding,[],[f60,f5]) ).
fof(f60,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_lessequals(c_Suc(X3),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
fof(f3514,plain,
spl0_295,
inference(avatar_split_clause,[],[f913,f3512]) ).
fof(f913,plain,
! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat) ),
inference(definition_unfolding,[],[f310,f5]) ).
fof(f310,axiom,
! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| c_lessequals(c_Suc(X2),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f3510,plain,
( spl0_294
| ~ spl0_59
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2139,f2018,f1402,f3508]) ).
fof(f3508,plain,
( spl0_294
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f1402,plain,
( spl0_59
<=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f2018,plain,
( spl0_167
<=> ! [X13,X2,X5] :
( ~ c_HOL_Oord__class_Oless(X13,X5,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X2,tc_nat),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f2139,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_59
| ~ spl0_167 ),
inference(superposition,[],[f2019,f1403]) ).
fof(f1403,plain,
( ! [X3] : c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f2019,plain,
( ! [X2,X5,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X2,tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X5,tc_nat) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f2018]) ).
fof(f3506,plain,
spl0_293,
inference(avatar_split_clause,[],[f912,f3504]) ).
fof(f912,plain,
! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f100,f5]) ).
fof(f100,axiom,
! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f3502,plain,
spl0_292,
inference(avatar_split_clause,[],[f900,f3500]) ).
fof(f900,plain,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat) ),
inference(definition_unfolding,[],[f61,f5]) ).
fof(f61,axiom,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_lessequals(c_Suc(X2),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
fof(f3498,plain,
spl0_291,
inference(avatar_split_clause,[],[f899,f3496]) ).
fof(f899,plain,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f499,f5]) ).
fof(f499,axiom,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f3494,plain,
spl0_290,
inference(avatar_split_clause,[],[f894,f3492]) ).
fof(f894,plain,
! [X2,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f99,f5]) ).
fof(f99,axiom,
! [X2,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f3490,plain,
spl0_289,
inference(avatar_split_clause,[],[f891,f3488]) ).
fof(f3488,plain,
( spl0_289
<=> ! [X2,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f891,plain,
! [X2,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X3,tc_nat) ),
inference(definition_unfolding,[],[f309,f5]) ).
fof(f309,axiom,
! [X2,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(c_Suc(X2),X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f3486,plain,
spl0_288,
inference(avatar_split_clause,[],[f780,f3484]) ).
fof(f3484,plain,
( spl0_288
<=> ! [X86,X85,X81,X80] :
( X81 = X86
| hAPP(hAPP(c_Type_Otype_OFun,X80),X81) != hAPP(hAPP(c_Type_Otype_OFun,X85),X86) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f780,axiom,
! [X80,X81,X86,X85] :
( X81 = X86
| hAPP(hAPP(c_Type_Otype_OFun,X80),X81) != hAPP(hAPP(c_Type_Otype_OFun,X85),X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
fof(f3482,plain,
spl0_287,
inference(avatar_split_clause,[],[f779,f3480]) ).
fof(f3480,plain,
( spl0_287
<=> ! [X81,X85,X80,X86] :
( X80 = X85
| hAPP(hAPP(c_Type_Otype_OFun,X80),X81) != hAPP(hAPP(c_Type_Otype_OFun,X85),X86) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f779,axiom,
! [X80,X81,X86,X85] :
( X80 = X85
| hAPP(hAPP(c_Type_Otype_OFun,X80),X81) != hAPP(hAPP(c_Type_Otype_OFun,X85),X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
fof(f3478,plain,
spl0_286,
inference(avatar_split_clause,[],[f753,f3476]) ).
fof(f3476,plain,
( spl0_286
<=> ! [X49,X22,X26] :
( ~ c_Lambda_Obeta(X49,X26)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X49),X22),hAPP(hAPP(c_Lambda_Olift,X26),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f753,axiom,
! [X49,X26,X22] :
( ~ c_Lambda_Obeta(X49,X26)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X49),X22),hAPP(hAPP(c_Lambda_Olift,X26),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
fof(f3474,plain,
spl0_285,
inference(avatar_split_clause,[],[f728,f3472]) ).
fof(f3472,plain,
( spl0_285
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X0),X11,c_HOL_Ozero__class_Ozero(X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f728,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X0),X11,c_HOL_Ozero__class_Ozero(X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
fof(f3470,plain,
spl0_284,
inference(avatar_split_clause,[],[f619,f3468]) ).
fof(f3468,plain,
( spl0_284
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X15,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f619,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X15,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f3466,plain,
spl0_283,
inference(avatar_split_clause,[],[f618,f3464]) ).
fof(f3464,plain,
( spl0_283
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X15,X0)
| c_HOL_Oord__class_Oless(X9,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f618,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X15,X0)
| c_HOL_Oord__class_Oless(X9,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3462,plain,
spl0_282,
inference(avatar_split_clause,[],[f612,f3460]) ).
fof(f3460,plain,
( spl0_282
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(X10,X15,X0)
| c_lessequals(X9,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f612,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(X10,X15,X0)
| c_lessequals(X9,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3458,plain,
spl0_281,
inference(avatar_split_clause,[],[f610,f3456]) ).
fof(f3456,plain,
( spl0_281
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X15,X10,X0)
| c_HOL_Oord__class_Oless(X15,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f610,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X15,X10,X0)
| c_HOL_Oord__class_Oless(X15,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3454,plain,
spl0_280,
inference(avatar_split_clause,[],[f609,f3452]) ).
fof(f3452,plain,
( spl0_280
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X15,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f609,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X15,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3450,plain,
spl0_279,
inference(avatar_split_clause,[],[f608,f3448]) ).
fof(f3448,plain,
( spl0_279
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X15,X10,X0)
| c_lessequals(X15,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f608,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X15,X10,X0)
| c_lessequals(X15,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3446,plain,
spl0_278,
inference(avatar_split_clause,[],[f518,f3444]) ).
fof(f3444,plain,
( spl0_278
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f518,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = c_Orderings_Oord__class_Omax(X9,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f3442,plain,
spl0_277,
inference(avatar_split_clause,[],[f511,f3440]) ).
fof(f3440,plain,
( spl0_277
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f511,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f3438,plain,
spl0_276,
inference(avatar_split_clause,[],[f434,f3436]) ).
fof(f3436,plain,
( spl0_276
<=> ! [X11,X0,X9,X22] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X22,tc_nat)
| c_List_Olist__update(X11,X22,X9,X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f434,axiom,
! [X0,X11,X9,X22] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X22,tc_nat)
| c_List_Olist__update(X11,X22,X9,X0) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
fof(f3434,plain,
spl0_275,
inference(avatar_split_clause,[],[f420,f3432]) ).
fof(f3432,plain,
( spl0_275
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f420,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f3430,plain,
spl0_274,
inference(avatar_split_clause,[],[f419,f3428]) ).
fof(f3428,plain,
( spl0_274
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f419,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f3426,plain,
( ~ spl0_272
| spl0_273
| ~ spl0_97
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1761,f1686,f1581,f3424,f3420]) ).
fof(f3420,plain,
( spl0_272
<=> hBOOL(c_Type_Osko__Type__Xtype__induct__1__1(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f3424,plain,
( spl0_273
<=> ! [X0] : hBOOL(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f1581,plain,
( spl0_97
<=> ! [X29,X16] :
( hBOOL(hAPP(X16,X29))
| ~ hBOOL(hAPP(X16,c_Type_Osko__Type__Xtype__induct__1__1(X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1761,plain,
( ! [X0] :
( hBOOL(X0)
| ~ hBOOL(c_Type_Osko__Type__Xtype__induct__1__1(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))) )
| ~ spl0_97
| ~ spl0_123 ),
inference(forward_demodulation,[],[f1760,f1687]) ).
fof(f1760,plain,
( ! [X0] :
( ~ hBOOL(c_Type_Osko__Type__Xtype__induct__1__1(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat))))
| hBOOL(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0)) )
| ~ spl0_97
| ~ spl0_123 ),
inference(superposition,[],[f1582,f1687]) ).
fof(f1582,plain,
( ! [X29,X16] :
( ~ hBOOL(hAPP(X16,c_Type_Osko__Type__Xtype__induct__1__1(X16)))
| hBOOL(hAPP(X16,X29)) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1581]) ).
fof(f3418,plain,
spl0_271,
inference(avatar_split_clause,[],[f399,f3416]) ).
fof(f3416,plain,
( spl0_271
<=> ! [X54,X53,X69,X68] :
( X53 = X68
| hAPP(hAPP(c_Lambda_OdB_OApp,X53),X54) != hAPP(hAPP(c_Lambda_OdB_OApp,X68),X69) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f399,axiom,
! [X68,X54,X69,X53] :
( X53 = X68
| hAPP(hAPP(c_Lambda_OdB_OApp,X53),X54) != hAPP(hAPP(c_Lambda_OdB_OApp,X68),X69) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f3414,plain,
spl0_270,
inference(avatar_split_clause,[],[f398,f3412]) ).
fof(f3412,plain,
( spl0_270
<=> ! [X54,X69,X68,X53] :
( X54 = X69
| hAPP(hAPP(c_Lambda_OdB_OApp,X53),X54) != hAPP(hAPP(c_Lambda_OdB_OApp,X68),X69) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f398,axiom,
! [X54,X68,X69,X53] :
( X54 = X69
| hAPP(hAPP(c_Lambda_OdB_OApp,X53),X54) != hAPP(hAPP(c_Lambda_OdB_OApp,X68),X69) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f3410,plain,
spl0_269,
inference(avatar_split_clause,[],[f379,f3408]) ).
fof(f3408,plain,
( spl0_269
<=> ! [X2,X0,X11] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat)
| c_List_Olist_ONil(X0) = c_List_Odrop(X2,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f379,axiom,
! [X2,X0,X11] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat)
| c_List_Olist_ONil(X0) = c_List_Odrop(X2,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__all_0) ).
fof(f3406,plain,
spl0_268,
inference(avatar_split_clause,[],[f378,f3404]) ).
fof(f3404,plain,
( spl0_268
<=> ! [X2,X0,X11] :
( c_List_Olist_ONil(X0) != c_List_Odrop(X2,X11,X0)
| c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f378,axiom,
! [X2,X0,X11] :
( c_List_Olist_ONil(X0) != c_List_Odrop(X2,X11,X0)
| c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
fof(f3402,plain,
spl0_267,
inference(avatar_split_clause,[],[f371,f3400]) ).
fof(f3400,plain,
( spl0_267
<=> ! [X25,X32,X26] :
( ~ c_Lambda_Obeta(X26,X25)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X26),X32),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f371,axiom,
! [X26,X25,X32] :
( ~ c_Lambda_Obeta(X26,X25)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X26),X32),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
fof(f3398,plain,
spl0_266,
inference(avatar_split_clause,[],[f370,f3396]) ).
fof(f3396,plain,
( spl0_266
<=> ! [X25,X32,X26] :
( ~ c_Lambda_Obeta(X26,X25)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X32),X26),hAPP(hAPP(c_Lambda_OdB_OApp,X32),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f370,axiom,
! [X26,X25,X32] :
( ~ c_Lambda_Obeta(X26,X25)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X32),X26),hAPP(hAPP(c_Lambda_OdB_OApp,X32),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
fof(f3394,plain,
spl0_265,
inference(avatar_split_clause,[],[f288,f3392]) ).
fof(f3392,plain,
( spl0_265
<=> ! [X2,X0,X11] :
( c_List_Orotate(X2,X11,X0) = X11
| ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f288,axiom,
! [X2,X0,X11] :
( c_List_Orotate(X2,X11,X0) = X11
| ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__length01_0) ).
fof(f3390,plain,
spl0_264,
inference(avatar_split_clause,[],[f273,f3388]) ).
fof(f273,axiom,
! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat)),X3) = c_Orderings_Oord__class_Omax(X2,X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
fof(f3386,plain,
spl0_263,
inference(avatar_split_clause,[],[f258,f3384]) ).
fof(f3384,plain,
( spl0_263
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f258,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3382,plain,
spl0_262,
inference(avatar_split_clause,[],[f191,f3380]) ).
fof(f3380,plain,
( spl0_262
<=> ! [X6,X47,X0,X33,X46,X1] : hAPP(X1,hAPP(X6,X47)) = hAPP(c_Fun_Ocomp(X1,X6,X46,X33,X0),X47) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f191,axiom,
! [X46,X0,X1,X47,X6,X33] : hAPP(X1,hAPP(X6,X47)) = hAPP(c_Fun_Ocomp(X1,X6,X46,X33,X0),X47),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f3378,plain,
( spl0_261
| ~ spl0_54
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1759,f1686,f1382,f3376]) ).
fof(f3376,plain,
( spl0_261
<=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Lambda_OdB_OVar(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1382,plain,
( spl0_54
<=> ! [X9,X58] : c_Type_Otyping(X58,c_Lambda_OdB_OVar(X9),hAPP(X58,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1759,plain,
( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Lambda_OdB_OVar(X0),X0)
| ~ spl0_54
| ~ spl0_123 ),
inference(superposition,[],[f1383,f1687]) ).
fof(f1383,plain,
( ! [X58,X9] : c_Type_Otyping(X58,c_Lambda_OdB_OVar(X9),hAPP(X58,X9))
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1382]) ).
fof(f3374,plain,
spl0_260,
inference(avatar_split_clause,[],[f157,f3372]) ).
fof(f3372,plain,
( spl0_260
<=> ! [X2,X27,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X27,tc_nat),c_HOL_Ominus__class_Ominus(X2,X27,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f157,axiom,
! [X2,X3,X27] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X27,tc_nat),c_HOL_Ominus__class_Ominus(X2,X27,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f3370,plain,
spl0_259,
inference(avatar_split_clause,[],[f156,f3368]) ).
fof(f3368,plain,
( spl0_259
<=> ! [X2,X27,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X27,X2,tc_nat),c_HOL_Ominus__class_Ominus(X27,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f156,axiom,
! [X2,X3,X27] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X27,X2,tc_nat),c_HOL_Ominus__class_Ominus(X27,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f3366,plain,
spl0_258,
inference(avatar_split_clause,[],[f110,f3364]) ).
fof(f3364,plain,
( spl0_258
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X15,X10,X0)
| c_HOL_Oord__class_Oless(X15,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f110,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X15,X10,X0)
| c_HOL_Oord__class_Oless(X15,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3362,plain,
spl0_257,
inference(avatar_split_clause,[],[f109,f3360]) ).
fof(f3360,plain,
( spl0_257
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X15,X0)
| c_HOL_Oord__class_Oless(X9,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f109,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X15,X0)
| c_HOL_Oord__class_Oless(X9,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f3358,plain,
spl0_256,
inference(avatar_split_clause,[],[f92,f3356]) ).
fof(f3356,plain,
( spl0_256
<=> ! [X9,X0,X11] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X9,X11,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f92,axiom,
! [X0,X11,X9] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X9,X11,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
fof(f3354,plain,
spl0_255,
inference(avatar_split_clause,[],[f8,f3352]) ).
fof(f3352,plain,
( spl0_255
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f8,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
fof(f3350,plain,
spl0_254,
inference(avatar_split_clause,[],[f7,f3348]) ).
fof(f3348,plain,
( spl0_254
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f7,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X3,X2,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
fof(f3316,plain,
( spl0_253
| ~ spl0_54
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1753,f1682,f1382,f3314]) ).
fof(f3314,plain,
( spl0_253
<=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_Orderings_Obot__class_Obot(tc_nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1753,plain,
( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_Orderings_Obot__class_Obot(tc_nat)),X0)
| ~ spl0_54
| ~ spl0_122 ),
inference(superposition,[],[f1383,f1683]) ).
fof(f3132,plain,
( spl0_252
| ~ spl0_54
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1748,f1669,f1382,f3130]) ).
fof(f3130,plain,
( spl0_252
<=> ! [X2,X0,X1,X3] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1669,plain,
( spl0_119
<=> ! [X29,X9,X0,X28] : hAPP(c_Type_Oshift(X28,X9,X29,X0),X9) = X29 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1748,plain,
( ! [X2,X3,X0,X1] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2)
| ~ spl0_54
| ~ spl0_119 ),
inference(superposition,[],[f1383,f1670]) ).
fof(f1670,plain,
( ! [X28,X29,X0,X9] : hAPP(c_Type_Oshift(X28,X9,X29,X0),X9) = X29
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f2765,plain,
spl0_251,
inference(avatar_split_clause,[],[f1044,f2763]) ).
fof(f2763,plain,
( spl0_251
<=> ! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1044,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1043,f689]) ).
fof(f1043,plain,
! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(forward_demodulation,[],[f577,f689]) ).
fof(f577,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f2761,plain,
spl0_250,
inference(avatar_split_clause,[],[f1042,f2759]) ).
fof(f2759,plain,
( spl0_250
<=> ! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1042,plain,
! [X2,X3] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X3 ),
inference(forward_demodulation,[],[f1041,f689]) ).
fof(f1041,plain,
! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
inference(forward_demodulation,[],[f578,f689]) ).
fof(f578,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f2757,plain,
spl0_249,
inference(avatar_split_clause,[],[f837,f2755]) ).
fof(f2755,plain,
( spl0_249
<=> ! [X2,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f837,plain,
! [X2,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f105,f5]) ).
fof(f105,axiom,
! [X2,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_Suc(X3),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f2753,plain,
spl0_248,
inference(avatar_split_clause,[],[f784,f2751]) ).
fof(f2751,plain,
( spl0_248
<=> ! [X25,X5,X26] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X25),X5)),X26),X5) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f784,axiom,
! [X26,X5,X25] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X25),X5)),X26),X5) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f2749,plain,
spl0_247,
inference(avatar_split_clause,[],[f714,f2747]) ).
fof(f2747,plain,
( spl0_247
<=> ! [X37,X11,X0,X33] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X33)) = c_Nat_Osize__class_Osize(c_List_Omap(X37,X11,X33,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f714,axiom,
! [X0,X11,X37,X33] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X33)) = c_Nat_Osize__class_Osize(c_List_Omap(X37,X11,X33,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).
fof(f2745,plain,
spl0_246,
inference(avatar_split_clause,[],[f669,f2743]) ).
fof(f2743,plain,
( spl0_246
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f669,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f2741,plain,
spl0_245,
inference(avatar_split_clause,[],[f665,f2739]) ).
fof(f2739,plain,
( spl0_245
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Oorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f665,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
fof(f2737,plain,
spl0_244,
inference(avatar_split_clause,[],[f507,f2735]) ).
fof(f2735,plain,
( spl0_244
<=> ! [X22,X25] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X25),c_Lambda_OdB_OVar(X22)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f507,axiom,
! [X22,X25] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X25),c_Lambda_OdB_OVar(X22)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
fof(f2733,plain,
spl0_243,
inference(avatar_split_clause,[],[f505,f2731]) ).
fof(f2731,plain,
( spl0_243
<=> ! [X9,X0] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f505,axiom,
! [X0,X9] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
fof(f2729,plain,
spl0_242,
inference(avatar_split_clause,[],[f496,f2727]) ).
fof(f2727,plain,
( spl0_242
<=> ! [X11,X0,X9,X22] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X11,X22,X9,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f496,axiom,
! [X0,X11,X9,X22] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X11,X22,X9,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
fof(f2725,plain,
spl0_241,
inference(avatar_split_clause,[],[f490,f2723]) ).
fof(f2723,plain,
( spl0_241
<=> ! [X22,X5] :
( ~ c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| c_Lambda_OdB_OVar(X22) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X22)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f490,axiom,
! [X22,X5] :
( ~ c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| c_Lambda_OdB_OVar(X22) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X22)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f2721,plain,
( spl0_240
| ~ spl0_24
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1969,f1881,f1257,f2719]) ).
fof(f2719,plain,
( spl0_240
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1257,plain,
( spl0_24
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1881,plain,
( spl0_155
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Power_Opower(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1969,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_24
| ~ spl0_155 ),
inference(resolution,[],[f1882,f1259]) ).
fof(f1259,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f1257]) ).
fof(f1882,plain,
( ! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_Orderings_Obot__class_Obot(tc_nat),X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1881]) ).
fof(f2717,plain,
spl0_239,
inference(avatar_split_clause,[],[f489,f2715]) ).
fof(f2715,plain,
( spl0_239
<=> ! [X22,X2] :
( ~ c_lessequals(X22,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X22,tc_nat),tc_nat) = X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f489,axiom,
! [X2,X22] :
( ~ c_lessequals(X22,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X2,X22,tc_nat),tc_nat) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f2713,plain,
spl0_238,
inference(avatar_split_clause,[],[f392,f2711]) ).
fof(f2711,plain,
( spl0_238
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f392,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f2709,plain,
spl0_237,
inference(avatar_split_clause,[],[f389,f2707]) ).
fof(f2707,plain,
( spl0_237
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Oorder(X0)
| X9 = X10
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f389,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| X9 = X10
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f2705,plain,
spl0_236,
inference(avatar_split_clause,[],[f285,f2703]) ).
fof(f2703,plain,
( spl0_236
<=> ! [X9,X0,X10,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X10,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f285,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X10,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f2701,plain,
spl0_235,
inference(avatar_split_clause,[],[f231,f2699]) ).
fof(f2699,plain,
( spl0_235
<=> ! [X9,X0,X12] : ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X9,X12,X0),tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f231,axiom,
! [X0,X9,X12] : ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X9,X12,X0),tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
fof(f2697,plain,
spl0_234,
inference(avatar_split_clause,[],[f214,f2695]) ).
fof(f2695,plain,
( spl0_234
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X15,X9,X0)
| c_lessequals(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f214,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X15,X9,X0)
| c_lessequals(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
fof(f2693,plain,
spl0_233,
inference(avatar_split_clause,[],[f213,f2691]) ).
fof(f2691,plain,
( spl0_233
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X15,X10,X0)
| c_lessequals(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f213,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X15,X10,X0)
| c_lessequals(X15,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
fof(f2689,plain,
spl0_232,
inference(avatar_split_clause,[],[f212,f2687]) ).
fof(f2687,plain,
( spl0_232
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X15,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f212,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X15,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
fof(f2685,plain,
spl0_231,
inference(avatar_split_clause,[],[f211,f2683]) ).
fof(f2683,plain,
( spl0_231
<=> ! [X9,X0,X10,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X15,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f211,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X15,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
fof(f2681,plain,
spl0_230,
inference(avatar_split_clause,[],[f184,f2679]) ).
fof(f2679,plain,
( spl0_230
<=> ! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X9,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f184,axiom,
! [X10,X0,X9,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X9,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X9,X10,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f2677,plain,
spl0_229,
inference(avatar_split_clause,[],[f181,f2675]) ).
fof(f181,axiom,
! [X0,X1,X6,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X6,X0)
| c_HOL_Oord__class_Oless(X9,c_Orderings_Oord__class_Omax(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
fof(f2673,plain,
spl0_228,
inference(avatar_split_clause,[],[f180,f2671]) ).
fof(f180,axiom,
! [X0,X1,X6,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| c_HOL_Oord__class_Oless(X9,c_Orderings_Oord__class_Omax(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
fof(f2669,plain,
spl0_227,
inference(avatar_split_clause,[],[f133,f2667]) ).
fof(f2667,plain,
( spl0_227
<=> ! [X2,X5,X3] :
( c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f133,axiom,
! [X2,X3,X5] :
( c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f2665,plain,
spl0_226,
inference(avatar_split_clause,[],[f132,f2663]) ).
fof(f132,axiom,
! [X2,X3,X5] :
( c_lessequals(X5,X2,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f2661,plain,
spl0_225,
inference(avatar_split_clause,[],[f131,f2659]) ).
fof(f2659,plain,
( spl0_225
<=> ! [X13,X22,X3] :
( ~ c_lessequals(X22,X13,tc_nat)
| c_lessequals(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f131,axiom,
! [X3,X22,X13] :
( ~ c_lessequals(X22,X13,tc_nat)
| c_lessequals(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X3),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
fof(f2657,plain,
spl0_224,
inference(avatar_split_clause,[],[f130,f2655]) ).
fof(f130,axiom,
! [X3,X22,X13] :
( ~ c_lessequals(X22,X13,tc_nat)
| c_lessequals(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
fof(f2653,plain,
spl0_223,
inference(avatar_split_clause,[],[f98,f2651]) ).
fof(f2651,plain,
( spl0_223
<=> ! [X2,X0,X11] :
( c_List_Otake(X2,X11,X0) = X11
| ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f98,axiom,
! [X2,X0,X11] :
( c_List_Otake(X2,X11,X0) = X11
| ~ c_lessequals(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
fof(f2649,plain,
spl0_222,
inference(avatar_split_clause,[],[f74,f2647]) ).
fof(f2645,plain,
spl0_221,
inference(avatar_split_clause,[],[f67,f2643]) ).
fof(f67,axiom,
! [X3,X22,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f2641,plain,
spl0_220,
inference(avatar_split_clause,[],[f66,f2639]) ).
fof(f66,axiom,
! [X3,X22,X13] :
( ~ c_HOL_Oord__class_Oless(X22,X13,tc_nat)
| c_HOL_Oord__class_Oless(X22,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X3),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
fof(f2637,plain,
( spl0_219
| ~ spl0_85
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2579,f2390,f1512,f2635]) ).
fof(f2635,plain,
( spl0_219
<=> ! [X0] : v_T____ != c_Type_Otype_OAtom(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1512,plain,
( spl0_85
<=> ! [X80,X81,X17] : c_Type_Otype_OAtom(X17) != hAPP(hAPP(c_Type_Otype_OFun,X80),X81) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f2390,plain,
( spl0_211
<=> v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2579,plain,
( ! [X0] : v_T____ != c_Type_Otype_OAtom(X0)
| ~ spl0_85
| ~ spl0_211 ),
inference(superposition,[],[f1513,f2392]) ).
fof(f2392,plain,
( v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2390]) ).
fof(f1513,plain,
( ! [X80,X81,X17] : c_Type_Otype_OAtom(X17) != hAPP(hAPP(c_Type_Otype_OFun,X80),X81)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f2633,plain,
spl0_218,
inference(avatar_split_clause,[],[f65,f2631]) ).
fof(f2631,plain,
( spl0_218
<=> ! [X22,X5,X13] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X13),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f65,axiom,
! [X22,X5,X13] :
( c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X13),X5,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f2576,plain,
( spl0_217
| ~ spl0_17
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1889,f1790,f1222,f2574]) ).
fof(f2574,plain,
( spl0_217
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1222,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1790,plain,
( spl0_133
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1889,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_17
| ~ spl0_133 ),
inference(resolution,[],[f1791,f1224]) ).
fof(f1224,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f1222]) ).
fof(f1791,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X2,X0) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1790]) ).
fof(f2415,plain,
spl0_216,
inference(avatar_split_clause,[],[f1053,f2413]) ).
fof(f2413,plain,
( spl0_216
<=> ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1053,plain,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(forward_demodulation,[],[f638,f689]) ).
fof(f638,axiom,
! [X2,X3] :
( c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2411,plain,
spl0_215,
inference(avatar_split_clause,[],[f1049,f2409]) ).
fof(f2409,plain,
( spl0_215
<=> ! [X0,X11] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),tc_nat)
| c_List_Olist_ONil(X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1049,plain,
! [X0,X11] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),tc_nat)
| c_List_Olist_ONil(X0) = X11 ),
inference(forward_demodulation,[],[f323,f689]) ).
fof(f323,axiom,
! [X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
fof(f2407,plain,
spl0_214,
inference(avatar_split_clause,[],[f1039,f2405]) ).
fof(f2405,plain,
( spl0_214
<=> ! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1039,plain,
! [X2,X3] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != X3 ),
inference(forward_demodulation,[],[f582,f689]) ).
fof(f582,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f2403,plain,
spl0_213,
inference(avatar_split_clause,[],[f1027,f2401]) ).
fof(f2401,plain,
( spl0_213
<=> ! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1027,plain,
! [X2,X3] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
inference(forward_demodulation,[],[f639,f689]) ).
fof(f639,axiom,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2397,plain,
spl0_212,
inference(avatar_split_clause,[],[f985,f2395]) ).
fof(f2395,plain,
( spl0_212
<=> ! [X2,X3] : c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f985,plain,
! [X2,X3] : c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f160,f689]) ).
fof(f160,axiom,
! [X2,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f2393,plain,
spl0_211,
inference(avatar_split_clause,[],[f773,f2390]) ).
fof(f773,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
fof(f2388,plain,
spl0_210,
inference(avatar_split_clause,[],[f751,f2386]) ).
fof(f2386,plain,
( spl0_210
<=> ! [X22,X25] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X25),X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f751,axiom,
! [X22,X25] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X25),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f2384,plain,
spl0_209,
inference(avatar_split_clause,[],[f706,f2382]) ).
fof(f2382,plain,
( spl0_209
<=> ! [X37,X11,X0,X33] :
( c_List_Olist_ONil(X33) = X11
| c_List_Olist_ONil(X0) != c_List_Omap(X37,X11,X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f706,axiom,
! [X0,X11,X37,X33] :
( c_List_Olist_ONil(X33) = X11
| c_List_Olist_ONil(X0) != c_List_Omap(X37,X11,X33,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
fof(f2380,plain,
spl0_208,
inference(avatar_split_clause,[],[f622,f2378]) ).
fof(f2378,plain,
( spl0_208
<=> ! [X61,X4,X0,X62,X1] :
( X4 = X62
| c_List_Olist_OCons(X1,X4,X0) != c_List_Olist_OCons(X61,X62,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f622,axiom,
! [X0,X1,X62,X4,X61] :
( X4 = X62
| c_List_Olist_OCons(X1,X4,X0) != c_List_Olist_OCons(X61,X62,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
fof(f2376,plain,
spl0_207,
inference(avatar_split_clause,[],[f621,f2374]) ).
fof(f2374,plain,
( spl0_207
<=> ! [X61,X4,X0,X62,X1] :
( X1 = X61
| c_List_Olist_OCons(X1,X4,X0) != c_List_Olist_OCons(X61,X62,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f621,axiom,
! [X0,X1,X62,X4,X61] :
( X1 = X61
| c_List_Olist_OCons(X1,X4,X0) != c_List_Olist_OCons(X61,X62,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
fof(f2372,plain,
spl0_206,
inference(avatar_split_clause,[],[f614,f2370]) ).
fof(f2370,plain,
( spl0_206
<=> ! [X13,X22,X5] :
( ~ c_lessequals(X22,X13,tc_nat)
| ~ c_lessequals(X13,X5,tc_nat)
| c_lessequals(X22,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f614,axiom,
! [X22,X5,X13] :
( ~ c_lessequals(X22,X13,tc_nat)
| ~ c_lessequals(X13,X5,tc_nat)
| c_lessequals(X22,X5,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2368,plain,
spl0_205,
inference(avatar_split_clause,[],[f544,f2366]) ).
fof(f2366,plain,
( spl0_205
<=> ! [X11,X9,X0,X5] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Olist__update(X11,X5,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f544,axiom,
! [X0,X11,X9,X5] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Olist__update(X11,X5,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
fof(f2364,plain,
spl0_204,
inference(avatar_split_clause,[],[f443,f2362]) ).
fof(f2362,plain,
( spl0_204
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f443,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Oone__class_Oone(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f2360,plain,
spl0_203,
inference(avatar_split_clause,[],[f377,f2358]) ).
fof(f2358,plain,
( spl0_203
<=> ! [X22,X2,X5] :
( ~ c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| c_Lambda_OdB_OVar(X22) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X22),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f377,axiom,
! [X2,X22,X5] :
( ~ c_HOL_Oord__class_Oless(X22,X5,tc_nat)
| c_Lambda_OdB_OVar(X22) = c_Lambda_Oliftn(X2,c_Lambda_OdB_OVar(X22),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
fof(f2356,plain,
( spl0_202
| ~ spl0_29
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f2237,f2079,f1278,f2354]) ).
fof(f2354,plain,
( spl0_202
<=> ! [X0] :
( ~ c_Lambda_Obeta(v_u____,X0)
| c_Type_Otyping(v_e____,X0,v_T____) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1278,plain,
( spl0_29
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f2079,plain,
( spl0_182
<=> ! [X29,X73,X25,X28] :
( ~ c_Lambda_Obeta(X25,X73)
| ~ c_Type_Otyping(X28,X25,X29)
| c_Type_Otyping(X28,X73,X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2237,plain,
( ! [X0] :
( ~ c_Lambda_Obeta(v_u____,X0)
| c_Type_Otyping(v_e____,X0,v_T____) )
| ~ spl0_29
| ~ spl0_182 ),
inference(resolution,[],[f2080,f1280]) ).
fof(f1280,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1278]) ).
fof(f2080,plain,
( ! [X28,X29,X73,X25] :
( ~ c_Type_Otyping(X28,X25,X29)
| ~ c_Lambda_Obeta(X25,X73)
| c_Type_Otyping(X28,X73,X29) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2079]) ).
fof(f2352,plain,
spl0_201,
inference(avatar_split_clause,[],[f365,f2350]) ).
fof(f2350,plain,
( spl0_201
<=> ! [X2,X0,X11] : c_List_Oappend(c_List_Otake(X2,X11,X0),c_List_Odrop(X2,X11,X0),X0) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f365,axiom,
! [X2,X0,X11] : c_List_Oappend(c_List_Otake(X2,X11,X0),c_List_Odrop(X2,X11,X0),X0) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
fof(f2348,plain,
spl0_200,
inference(avatar_split_clause,[],[f297,f2346]) ).
fof(f2346,plain,
( spl0_200
<=> ! [X11,X0,X12] : c_List_Odrop(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),c_List_Oappend(X11,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f297,axiom,
! [X0,X11,X12] : c_List_Odrop(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),c_List_Oappend(X11,X12,X0),X0) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
fof(f2344,plain,
spl0_199,
inference(avatar_split_clause,[],[f255,f2342]) ).
fof(f2342,plain,
( spl0_199
<=> ! [X2,X0,X11] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate(X2,X11,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f255,axiom,
! [X2,X0,X11] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate(X2,X11,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rotate_0) ).
fof(f2340,plain,
spl0_198,
inference(avatar_split_clause,[],[f113,f2338]) ).
fof(f2338,plain,
( spl0_198
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X9,X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f113,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X9,X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2336,plain,
spl0_197,
inference(avatar_split_clause,[],[f112,f2334]) ).
fof(f2334,plain,
( spl0_197
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X10,X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) != X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f112,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X10,X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) != X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2332,plain,
spl0_196,
inference(avatar_split_clause,[],[f111,f2330]) ).
fof(f2330,plain,
( spl0_196
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X10,X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f111,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X10,X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2328,plain,
spl0_195,
inference(avatar_split_clause,[],[f80,f2326]) ).
fof(f2326,plain,
( spl0_195
<=> ! [X2,X0,X3] :
( ~ class_Nat_Osemiring__char__0(X0)
| X2 = X3
| c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f80,axiom,
! [X2,X3,X0] :
( ~ class_Nat_Osemiring__char__0(X0)
| X2 = X3
| c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f2324,plain,
spl0_194,
inference(avatar_split_clause,[],[f54,f2322]) ).
fof(f54,axiom,
! [X0,X11,X12] : c_List_Otake(c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)),c_List_Oappend(X11,X12,X0),X0) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
fof(f2320,plain,
spl0_193,
inference(avatar_split_clause,[],[f18,f2318]) ).
fof(f2318,plain,
( spl0_193
<=> ! [X11,X0,X14,X12] :
( X12 = X14
| c_List_Oappend(X11,X12,X0) != c_List_Oappend(X11,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f18,axiom,
! [X0,X11,X14,X12] :
( X12 = X14
| c_List_Oappend(X11,X12,X0) != c_List_Oappend(X11,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
fof(f2316,plain,
spl0_192,
inference(avatar_split_clause,[],[f17,f2314]) ).
fof(f2314,plain,
( spl0_192
<=> ! [X11,X0,X14,X12] :
( X12 = X14
| c_List_Oappend(X12,X11,X0) != c_List_Oappend(X14,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f17,axiom,
! [X0,X11,X14,X12] :
( X12 = X14
| c_List_Oappend(X12,X11,X0) != c_List_Oappend(X14,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
fof(f2302,plain,
spl0_191,
inference(avatar_split_clause,[],[f14,f2300]) ).
fof(f2300,plain,
( spl0_191
<=> ! [X10,X9,X0,X3,X2] :
( X2 = X3
| c_List_Oreplicate(X3,X9,X0) != c_List_Oreplicate(X2,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f14,axiom,
! [X2,X3,X10,X0,X9] :
( X2 = X3
| c_List_Oreplicate(X3,X9,X0) != c_List_Oreplicate(X2,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
fof(f2234,plain,
( spl0_190
| ~ spl0_25
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2125,f2018,f1262,f2232]) ).
fof(f2232,plain,
( spl0_190
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1262,plain,
( spl0_25
<=> ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f2125,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_25
| ~ spl0_167 ),
inference(resolution,[],[f2019,f1263]) ).
fof(f1263,plain,
( ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f2109,plain,
spl0_189,
inference(avatar_split_clause,[],[f1052,f2107]) ).
fof(f1052,plain,
! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_lessequals(X3,X2,tc_nat) ),
inference(forward_demodulation,[],[f20,f689]) ).
fof(f20,axiom,
! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f2105,plain,
spl0_188,
inference(avatar_split_clause,[],[f1048,f2103]) ).
fof(f2103,plain,
( spl0_188
<=> ! [X0,X11] :
( c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) != c_Orderings_Obot__class_Obot(tc_nat)
| c_List_Olist_ONil(X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1048,plain,
! [X0,X11] :
( c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) != c_Orderings_Obot__class_Obot(tc_nat)
| c_List_Olist_ONil(X0) = X11 ),
inference(forward_demodulation,[],[f468,f689]) ).
fof(f468,axiom,
! [X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
fof(f2101,plain,
spl0_187,
inference(avatar_split_clause,[],[f1037,f2099]) ).
fof(f2099,plain,
( spl0_187
<=> ! [X2,X0,X9] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X2,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1037,plain,
! [X2,X0,X9] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X2,X9,X0) ),
inference(forward_demodulation,[],[f467,f689]) ).
fof(f467,axiom,
! [X2,X0,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X2,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
fof(f2097,plain,
spl0_186,
inference(avatar_split_clause,[],[f1019,f2095]) ).
fof(f2095,plain,
( spl0_186
<=> ! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1019,plain,
! [X2,X3] :
( c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_lessequals(X3,X2,tc_nat) ),
inference(forward_demodulation,[],[f21,f689]) ).
fof(f21,axiom,
! [X2,X3] :
( ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f2093,plain,
spl0_185,
inference(avatar_split_clause,[],[f959,f2091]) ).
fof(f959,plain,
! [X9] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(forward_demodulation,[],[f830,f689]) ).
fof(f830,plain,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f177,f5]) ).
fof(f177,axiom,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X9),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f2089,plain,
spl0_184,
inference(avatar_split_clause,[],[f663,f2087]) ).
fof(f2087,plain,
( spl0_184
<=> ! [X2,X3] :
( X2 = X3
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f663,axiom,
! [X2,X3] :
( X2 = X3
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
fof(f2085,plain,
spl0_183,
inference(avatar_split_clause,[],[f643,f2083]) ).
fof(f2083,plain,
( spl0_183
<=> ! [X0,X11] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X11,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f643,axiom,
! [X0,X11] : c_Nat_Osize__class_Osize(X11,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X11,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
fof(f2081,plain,
spl0_182,
inference(avatar_split_clause,[],[f625,f2079]) ).
fof(f625,axiom,
! [X28,X73,X29,X25] :
( ~ c_Lambda_Obeta(X25,X73)
| ~ c_Type_Otyping(X28,X25,X29)
| c_Type_Otyping(X28,X73,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f2077,plain,
spl0_181,
inference(avatar_split_clause,[],[f567,f2075]) ).
fof(f2075,plain,
( spl0_181
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f567,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f2073,plain,
spl0_180,
inference(avatar_split_clause,[],[f566,f2071]) ).
fof(f2071,plain,
( spl0_180
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f566,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2069,plain,
spl0_179,
inference(avatar_split_clause,[],[f565,f2067]) ).
fof(f2067,plain,
( spl0_179
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f565,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2065,plain,
spl0_178,
inference(avatar_split_clause,[],[f564,f2063]) ).
fof(f2063,plain,
( spl0_178
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f564,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f2061,plain,
( spl0_177
| ~ spl0_14
| ~ spl0_36
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1763,f1695,f1309,f1207,f2058]) ).
fof(f2058,plain,
( spl0_177
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1207,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1309,plain,
( spl0_36
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1695,plain,
( spl0_125
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1763,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_36
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1762,f1311]) ).
fof(f1311,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1309]) ).
fof(f1762,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_125 ),
inference(resolution,[],[f1696,f1209]) ).
fof(f1209,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1696,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X0) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1695]) ).
fof(f2056,plain,
spl0_176,
inference(avatar_split_clause,[],[f563,f2054]) ).
fof(f2054,plain,
( spl0_176
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f563,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2052,plain,
spl0_175,
inference(avatar_split_clause,[],[f561,f2050]) ).
fof(f2050,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f561,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f2048,plain,
spl0_174,
inference(avatar_split_clause,[],[f523,f2046]) ).
fof(f2046,plain,
( spl0_174
<=> ! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f523,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3),X2,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f2044,plain,
spl0_173,
inference(avatar_split_clause,[],[f522,f2042]) ).
fof(f2042,plain,
( spl0_173
<=> ! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X2,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f522,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),X2,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f2040,plain,
spl0_172,
inference(avatar_split_clause,[],[f477,f2038]) ).
fof(f2038,plain,
( spl0_172
<=> ! [X2,X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Orotate(X2,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f477,axiom,
! [X2,X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Orotate(X2,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
fof(f2036,plain,
spl0_171,
inference(avatar_split_clause,[],[f461,f2034]) ).
fof(f461,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_List_Olistsum(X11,X0) = c_List_Olistsum(c_List_Orev(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__rev_0) ).
fof(f2032,plain,
spl0_170,
inference(avatar_split_clause,[],[f385,f2030]) ).
fof(f2030,plain,
( spl0_170
<=> ! [X9,X10] :
( X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f385,axiom,
! [X10,X9] :
( X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f2028,plain,
spl0_169,
inference(avatar_split_clause,[],[f375,f2026]) ).
fof(f375,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X10,X0) = c_Orderings_Oord__class_Omax(X10,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f2024,plain,
spl0_168,
inference(avatar_split_clause,[],[f281,f2022]) ).
fof(f2022,plain,
( spl0_168
<=> ! [X2,X3] :
( X2 = X3
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f281,axiom,
! [X2,X3] :
( X2 = X3
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f2020,plain,
spl0_167,
inference(avatar_split_clause,[],[f251,f2018]) ).
fof(f251,axiom,
! [X2,X5,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X5,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X2,tc_nat),X5,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f2007,plain,
spl0_166,
inference(avatar_split_clause,[],[f233,f2005]) ).
fof(f2005,plain,
( spl0_166
<=> ! [X12,X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Oappend(X11,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f233,axiom,
! [X0,X11,X12] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Oappend(X11,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
fof(f2003,plain,
spl0_165,
inference(avatar_split_clause,[],[f229,f2001]) ).
fof(f2001,plain,
( spl0_165
<=> ! [X11,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(X11,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f229,axiom,
! [X0,X11,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(X11,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
fof(f1999,plain,
spl0_164,
inference(avatar_split_clause,[],[f86,f1997]) ).
fof(f1997,plain,
( spl0_164
<=> ! [X11,X0,X12,X8] :
( c_List_Olistsp(X8,X11,X0)
| ~ c_List_Olistsp(X8,c_List_Oappend(X11,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f86,axiom,
! [X0,X11,X8,X12] :
( c_List_Olistsp(X8,X11,X0)
| ~ c_List_Olistsp(X8,c_List_Oappend(X11,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
fof(f1995,plain,
spl0_163,
inference(avatar_split_clause,[],[f85,f1993]) ).
fof(f1993,plain,
( spl0_163
<=> ! [X11,X0,X12,X8] :
( c_List_Olistsp(X8,X12,X0)
| ~ c_List_Olistsp(X8,c_List_Oappend(X11,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f85,axiom,
! [X0,X11,X8,X12] :
( c_List_Olistsp(X8,X12,X0)
| ~ c_List_Olistsp(X8,c_List_Oappend(X11,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
fof(f1991,plain,
spl0_162,
inference(avatar_split_clause,[],[f78,f1989]) ).
fof(f1989,plain,
( spl0_162
<=> ! [X9,X0,X2] : c_List_Oreplicate(X2,X9,X0) = c_List_Orev(c_List_Oreplicate(X2,X9,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f78,axiom,
! [X2,X0,X9] : c_List_Oreplicate(X2,X9,X0) = c_List_Orev(c_List_Oreplicate(X2,X9,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
fof(f1987,plain,
( ~ spl0_161
| ~ spl0_36
| spl0_160 ),
inference(avatar_split_clause,[],[f1982,f1978,f1309,f1984]) ).
fof(f1978,plain,
( spl0_160
<=> c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1982,plain,
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Orderings_Obot__class_Obot(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____)
| ~ spl0_36
| spl0_160 ),
inference(forward_demodulation,[],[f1980,f1311]) ).
fof(f1980,plain,
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____)
| spl0_160 ),
inference(avatar_component_clause,[],[f1978]) ).
fof(f1981,plain,
~ spl0_160,
inference(avatar_split_clause,[],[f819,f1978]) ).
fof(f819,plain,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_n____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(definition_unfolding,[],[f786,f756]) ).
fof(f786,axiom,
~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1974,plain,
( spl0_159
| ~ spl0_123
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1968,f1877,f1686,f1971]) ).
fof(f1971,plain,
( spl0_159
<=> c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1877,plain,
( spl0_154
<=> ! [X2] : c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1968,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_123
| ~ spl0_154 ),
inference(superposition,[],[f1878,f1687]) ).
fof(f1878,plain,
( ! [X2] : c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f1954,plain,
( spl0_158
| ~ spl0_36
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1871,f1868,f1309,f1952]) ).
fof(f1868,plain,
( spl0_152
<=> ! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1871,plain,
( ! [X24] : c_Orderings_Obot__class_Obot(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_36
| ~ spl0_152 ),
inference(forward_demodulation,[],[f1869,f1311]) ).
fof(f1869,plain,
( ! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1868]) ).
fof(f1909,plain,
( spl0_157
| ~ spl0_40
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1901,f1794,f1326,f1907]) ).
fof(f1907,plain,
( spl0_157
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1794,plain,
( spl0_134
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1901,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_40
| ~ spl0_134 ),
inference(duplicate_literal_removal,[],[f1895]) ).
fof(f1895,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_40
| ~ spl0_134 ),
inference(resolution,[],[f1795,f1327]) ).
fof(f1795,plain,
( ! [X10,X0,X9] :
( c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X10,X9,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1794]) ).
fof(f1887,plain,
spl0_156,
inference(avatar_split_clause,[],[f1017,f1885]) ).
fof(f1885,plain,
( spl0_156
<=> ! [X9,X0] :
( c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X9,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1017,plain,
! [X0,X9] :
( c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X9,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(forward_demodulation,[],[f457,f689]) ).
fof(f457,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X9,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f1883,plain,
spl0_155,
inference(avatar_split_clause,[],[f1014,f1881]) ).
fof(f1014,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Power_Opower(X0) ),
inference(forward_demodulation,[],[f456,f689]) ).
fof(f456,axiom,
! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f1879,plain,
spl0_154,
inference(avatar_split_clause,[],[f827,f1877]) ).
fof(f827,plain,
! [X2] : c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f421,f5]) ).
fof(f421,axiom,
! [X2] : c_HOL_Oord__class_Oless(X2,c_Suc(X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f1875,plain,
spl0_153,
inference(avatar_split_clause,[],[f826,f1873]) ).
fof(f1873,plain,
( spl0_153
<=> ! [X2] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f826,plain,
! [X2] : ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)),X2,tc_nat),
inference(definition_unfolding,[],[f472,f5]) ).
fof(f472,axiom,
! [X2] : ~ c_lessequals(c_Suc(X2),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1870,plain,
spl0_152,
inference(avatar_split_clause,[],[f822,f1868]) ).
fof(f822,plain,
! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X24),c_HOL_Oone__class_Oone(tc_nat)),
inference(definition_unfolding,[],[f584,f5]) ).
fof(f584,axiom,
! [X24] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f1866,plain,
spl0_151,
inference(avatar_split_clause,[],[f732,f1864]) ).
fof(f1864,plain,
( spl0_151
<=> ! [X5,X32] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X5)),X32),X5) = X32 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f732,axiom,
! [X5,X32] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X5)),X32),X5) = X32,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f1862,plain,
spl0_150,
inference(avatar_split_clause,[],[f709,f1860]) ).
fof(f1860,plain,
( spl0_150
<=> ! [X0,X11,X37,X33] :
( c_List_Odistinct(X11,X33)
| ~ c_List_Odistinct(c_List_Omap(X37,X11,X33,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f709,axiom,
! [X0,X11,X37,X33] :
( c_List_Odistinct(X11,X33)
| ~ c_List_Odistinct(c_List_Omap(X37,X11,X33,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__map_0) ).
fof(f1858,plain,
spl0_149,
inference(avatar_split_clause,[],[f684,f1856]) ).
fof(f1856,plain,
( spl0_149
<=> ! [X6,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f684,axiom,
! [X0,X1,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f1854,plain,
spl0_148,
inference(avatar_split_clause,[],[f682,f1852]) ).
fof(f1852,plain,
( spl0_148
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f682,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1850,plain,
spl0_147,
inference(avatar_split_clause,[],[f680,f1848]) ).
fof(f1848,plain,
( spl0_147
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f680,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1846,plain,
spl0_146,
inference(avatar_split_clause,[],[f679,f1844]) ).
fof(f1844,plain,
( spl0_146
<=> ! [X6,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f679,axiom,
! [X0,X1,X6] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1842,plain,
spl0_145,
inference(avatar_split_clause,[],[f591,f1840]) ).
fof(f1840,plain,
( spl0_145
<=> ! [X12,X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_List_Oappend(X11,X12,X0) != X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f591,axiom,
! [X0,X11,X12] :
( c_List_Olist_ONil(X0) = X11
| c_List_Oappend(X11,X12,X0) != X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
fof(f1838,plain,
spl0_144,
inference(avatar_split_clause,[],[f589,f1836]) ).
fof(f1836,plain,
( spl0_144
<=> ! [X11,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(X11,X12,X0) != X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f589,axiom,
! [X0,X11,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(X11,X12,X0) != X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
fof(f1834,plain,
spl0_143,
inference(avatar_split_clause,[],[f531,f1832]) ).
fof(f1832,plain,
( spl0_143
<=> ! [X55,X0,X56,X17] : hAPP(X55,X17) = c_Type_Otype_Otype__case(X55,X56,c_Type_Otype_OAtom(X17),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f531,axiom,
! [X0,X56,X55,X17] : hAPP(X55,X17) = c_Type_Otype_Otype__case(X55,X56,c_Type_Otype_OAtom(X17),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
fof(f1830,plain,
spl0_142,
inference(avatar_split_clause,[],[f469,f1828]) ).
fof(f1828,plain,
( spl0_142
<=> ! [X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Orev(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f469,axiom,
! [X0,X11] :
( c_List_Olist_ONil(X0) = X11
| c_List_Olist_ONil(X0) != c_List_Orev(X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
fof(f1826,plain,
spl0_141,
inference(avatar_split_clause,[],[f451,f1824]) ).
fof(f1824,plain,
( spl0_141
<=> ! [X11,X0,X12] :
( X11 = X12
| c_List_Orev(X11,X0) != c_List_Orev(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f451,axiom,
! [X0,X11,X12] :
( X11 = X12
| c_List_Orev(X11,X0) != c_List_Orev(X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
fof(f1820,plain,
spl0_140,
inference(avatar_split_clause,[],[f406,f1818]) ).
fof(f1818,plain,
( spl0_140
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f406,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1816,plain,
spl0_139,
inference(avatar_split_clause,[],[f405,f1814]) ).
fof(f1814,plain,
( spl0_139
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f405,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1812,plain,
spl0_138,
inference(avatar_split_clause,[],[f360,f1810]) ).
fof(f1810,plain,
( spl0_138
<=> ! [X9,X0,X11] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X9,X11,X0),X0) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f360,axiom,
! [X0,X11,X9] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X9,X11,X0),X0) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
fof(f1808,plain,
spl0_137,
inference(avatar_split_clause,[],[f253,f1806]) ).
fof(f1806,plain,
( spl0_137
<=> ! [X17,X55,X0,X56] : c_Type_Otype_Otype__rec(X55,X56,c_Type_Otype_OAtom(X17),X0) = hAPP(X55,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f253,axiom,
! [X0,X56,X55,X17] : c_Type_Otype_Otype__rec(X55,X56,c_Type_Otype_OAtom(X17),X0) = hAPP(X55,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
fof(f1804,plain,
spl0_136,
inference(avatar_split_clause,[],[f149,f1802]) ).
fof(f1802,plain,
( spl0_136
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f149,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1800,plain,
spl0_135,
inference(avatar_split_clause,[],[f147,f1798]) ).
fof(f1798,plain,
( spl0_135
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f147,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1796,plain,
spl0_134,
inference(avatar_split_clause,[],[f146,f1794]) ).
fof(f146,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f1792,plain,
spl0_133,
inference(avatar_split_clause,[],[f138,f1790]) ).
fof(f138,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1788,plain,
spl0_132,
inference(avatar_split_clause,[],[f82,f1786]) ).
fof(f1786,plain,
( spl0_132
<=> ! [X29,X22,X28] :
( ~ c_Type_Otyping(X28,c_Lambda_OdB_OVar(X22),X29)
| hAPP(X28,X22) = X29 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f82,axiom,
! [X28,X29,X22] :
( ~ c_Type_Otyping(X28,c_Lambda_OdB_OVar(X22),X29)
| hAPP(X28,X22) = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f1782,plain,
( spl0_131
| ~ spl0_18
| ~ spl0_36
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1728,f1605,f1309,f1227,f1779]) ).
fof(f1779,plain,
( spl0_131
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1227,plain,
( spl0_18
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1605,plain,
( spl0_103
<=> ! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1728,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat)
| ~ spl0_18
| ~ spl0_36
| ~ spl0_103 ),
inference(forward_demodulation,[],[f1727,f1311]) ).
fof(f1727,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat)
| ~ spl0_18
| ~ spl0_103 ),
inference(resolution,[],[f1606,f1229]) ).
fof(f1229,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f1606,plain,
( ! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1605]) ).
fof(f1747,plain,
( spl0_130
| ~ spl0_9
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1725,f1589,f1182,f1745]) ).
fof(f1745,plain,
( spl0_130
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1182,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1589,plain,
( spl0_99
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X9,c_HOL_Oone__class_Oone(tc_nat),X0) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1725,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_9
| ~ spl0_99 ),
inference(resolution,[],[f1590,f1184]) ).
fof(f1184,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f1590,plain,
( ! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X9,c_HOL_Oone__class_Oone(tc_nat),X0) = X9 )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1589]) ).
fof(f1733,plain,
( spl0_129
| ~ spl0_14
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1724,f1585,f1207,f1730]) ).
fof(f1730,plain,
( spl0_129
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1585,plain,
( spl0_98
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1724,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_98 ),
inference(resolution,[],[f1586,f1209]) ).
fof(f1586,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1585]) ).
fof(f1709,plain,
spl0_128,
inference(avatar_split_clause,[],[f1036,f1707]) ).
fof(f1707,plain,
( spl0_128
<=> ! [X2] :
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1036,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1035,f974]) ).
fof(f974,plain,
! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Orderings_Obot__class_Obot(tc_nat)) = X3,
inference(forward_demodulation,[],[f702,f689]) ).
fof(f702,axiom,
! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Ozero__class_Ozero(tc_nat)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f1035,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Orderings_Obot__class_Obot(tc_nat)),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1034,f689]) ).
fof(f1034,plain,
! [X2] :
( ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1033,f74]) ).
fof(f1033,plain,
! [X2] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(forward_demodulation,[],[f906,f689]) ).
fof(f906,plain,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f3,f5]) ).
fof(f3,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1705,plain,
spl0_127,
inference(avatar_split_clause,[],[f1032,f1703]) ).
fof(f1703,plain,
( spl0_127
<=> ! [X2] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1032,plain,
! [X2] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1031,f689]) ).
fof(f1031,plain,
! [X2] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
inference(forward_demodulation,[],[f572,f689]) ).
fof(f572,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1701,plain,
spl0_126,
inference(avatar_split_clause,[],[f1030,f1699]) ).
fof(f1699,plain,
( spl0_126
<=> ! [X2] :
( ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1030,plain,
! [X2] :
( ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
inference(forward_demodulation,[],[f1029,f689]) ).
fof(f1029,plain,
! [X2] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f576,f689]) ).
fof(f576,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1697,plain,
spl0_125,
inference(avatar_split_clause,[],[f1013,f1695]) ).
fof(f1013,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Osemiring__1(X0) ),
inference(forward_demodulation,[],[f764,f689]) ).
fof(f764,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1693,plain,
spl0_124,
inference(avatar_split_clause,[],[f1001,f1690]) ).
fof(f1690,plain,
( spl0_124
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1001,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_T____),
inference(forward_demodulation,[],[f865,f773]) ).
fof(f865,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(definition_unfolding,[],[f765,f756]) ).
fof(f765,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_varT_0) ).
fof(f1688,plain,
spl0_123,
inference(avatar_split_clause,[],[f976,f1686]) ).
fof(f1684,plain,
spl0_122,
inference(avatar_split_clause,[],[f974,f1682]) ).
fof(f1680,plain,
spl0_121,
inference(avatar_split_clause,[],[f820,f1678]) ).
fof(f820,plain,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Oone__class_Oone(tc_nat)) != X2,
inference(definition_unfolding,[],[f596,f5]) ).
fof(f596,axiom,
! [X2] : c_Suc(X2) != X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f1676,plain,
( ~ spl0_8
| ~ spl0_120
| ~ spl0_36
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1546,f1468,f1309,f1673,f1177]) ).
fof(f1177,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1673,plain,
( spl0_120
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1468,plain,
( spl0_74
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1546,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_36
| ~ spl0_74 ),
inference(superposition,[],[f1469,f1311]) ).
fof(f1469,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1468]) ).
fof(f1671,plain,
spl0_119,
inference(avatar_split_clause,[],[f781,f1669]) ).
fof(f781,axiom,
! [X28,X29,X0,X9] : hAPP(c_Type_Oshift(X28,X9,X29,X0),X9) = X29,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f1667,plain,
spl0_118,
inference(avatar_split_clause,[],[f750,f1665]) ).
fof(f1665,plain,
( spl0_118
<=> ! [X0,X1,X37,X33] : c_List_Ofoldr(X37,c_List_Olist_ONil(X33),X1,X33,X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f750,axiom,
! [X0,X1,X37,X33] : c_List_Ofoldr(X37,c_List_Olist_ONil(X33),X1,X33,X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
fof(f1663,plain,
spl0_117,
inference(avatar_split_clause,[],[f719,f1661]) ).
fof(f1661,plain,
( spl0_117
<=> ! [X0,X37,X33] : c_List_Olist_ONil(X0) = c_List_Omap(X37,c_List_Olist_ONil(X33),X33,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f719,axiom,
! [X0,X37,X33] : c_List_Olist_ONil(X0) = c_List_Omap(X37,c_List_Olist_ONil(X33),X33,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
fof(f1659,plain,
spl0_116,
inference(avatar_split_clause,[],[f587,f1657]) ).
fof(f587,axiom,
! [X22,X13] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X22),X22,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1655,plain,
spl0_115,
inference(avatar_split_clause,[],[f586,f1653]) ).
fof(f1653,plain,
( spl0_115
<=> ! [X22,X13] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X13),X22,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f586,axiom,
! [X22,X13] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X22),X13),X22,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1651,plain,
spl0_114,
inference(avatar_split_clause,[],[f533,f1649]) ).
fof(f1649,plain,
( spl0_114
<=> ! [X9,X0,X11] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Olist_OCons(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f533,axiom,
! [X0,X11,X9] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Olist_OCons(X9,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I2_J_1) ).
fof(f1647,plain,
spl0_113,
inference(avatar_split_clause,[],[f516,f1645]) ).
fof(f1645,plain,
( spl0_113
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f516,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
fof(f1643,plain,
spl0_112,
inference(avatar_split_clause,[],[f514,f1641]) ).
fof(f1641,plain,
( spl0_112
<=> ! [X22,X0,X11] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Otake(X22,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f514,axiom,
! [X0,X11,X22] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Otake(X22,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__take_0) ).
fof(f1639,plain,
spl0_111,
inference(avatar_split_clause,[],[f466,f1637]) ).
fof(f1637,plain,
( spl0_111
<=> ! [X2,X0,X9] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X2,X9,X0),tc_List_Olist(X0)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f466,axiom,
! [X2,X0,X9] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X2,X9,X0),tc_List_Olist(X0)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
fof(f1635,plain,
spl0_110,
inference(avatar_split_clause,[],[f459,f1633]) ).
fof(f1633,plain,
( spl0_110
<=> ! [X2,X0,X11] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Orotate(X2,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f459,axiom,
! [X2,X0,X11] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Orotate(X2,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_1) ).
fof(f1631,plain,
( spl0_109
| ~ spl0_54
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1542,f1439,f1382,f1629]) ).
fof(f1629,plain,
( spl0_109
<=> ! [X0,X3,X2,X1] : c_Type_Otyping(c_COMBK(X0,X1,X2),c_Lambda_OdB_OVar(X3),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1439,plain,
( spl0_67
<=> ! [X33,X34,X0,X16] : hAPP(c_COMBK(X16,X0,X33),X34) = X16 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1542,plain,
( ! [X2,X3,X0,X1] : c_Type_Otyping(c_COMBK(X0,X1,X2),c_Lambda_OdB_OVar(X3),X0)
| ~ spl0_54
| ~ spl0_67 ),
inference(superposition,[],[f1383,f1440]) ).
fof(f1440,plain,
( ! [X0,X16,X34,X33] : hAPP(c_COMBK(X16,X0,X33),X34) = X16
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f1627,plain,
spl0_108,
inference(avatar_split_clause,[],[f458,f1625]) ).
fof(f1625,plain,
( spl0_108
<=> ! [X2,X0,X11] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Orotate(X2,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f458,axiom,
! [X2,X0,X11] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Orotate(X2,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rotate_0) ).
fof(f1623,plain,
spl0_107,
inference(avatar_split_clause,[],[f381,f1621]) ).
fof(f1621,plain,
( spl0_107
<=> ! [X22,X0,X11] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Odrop(X22,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f381,axiom,
! [X0,X11,X22] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Odrop(X22,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__drop_0) ).
fof(f1619,plain,
spl0_106,
inference(avatar_split_clause,[],[f373,f1617]) ).
fof(f1617,plain,
( spl0_106
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f373,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1615,plain,
spl0_105,
inference(avatar_split_clause,[],[f368,f1613]) ).
fof(f1613,plain,
( spl0_105
<=> ! [X49] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X49))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X49))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f368,axiom,
! [X49] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X49))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f1611,plain,
spl0_104,
inference(avatar_split_clause,[],[f306,f1609]) ).
fof(f1609,plain,
( spl0_104
<=> ! [X22,X0,X47] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X22,X47,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f306,axiom,
! [X0,X47,X22] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X22,X47,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
fof(f1607,plain,
spl0_103,
inference(avatar_split_clause,[],[f286,f1605]) ).
fof(f286,axiom,
! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
fof(f1603,plain,
spl0_102,
inference(avatar_split_clause,[],[f272,f1601]) ).
fof(f1601,plain,
( spl0_102
<=> ! [X9,X3] : c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X9),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f272,axiom,
! [X3,X9] : c_lessequals(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X9),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
fof(f1599,plain,
spl0_101,
inference(avatar_split_clause,[],[f271,f1597]) ).
fof(f271,axiom,
! [X2,X3] : c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f1595,plain,
spl0_100,
inference(avatar_split_clause,[],[f201,f1593]) ).
fof(f1593,plain,
( spl0_100
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f201,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
fof(f1591,plain,
spl0_99,
inference(avatar_split_clause,[],[f200,f1589]) ).
fof(f200,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X9,c_HOL_Oone__class_Oone(tc_nat),X0) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1587,plain,
spl0_98,
inference(avatar_split_clause,[],[f163,f1585]) ).
fof(f163,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
fof(f1583,plain,
spl0_97,
inference(avatar_split_clause,[],[f152,f1581]) ).
fof(f152,axiom,
! [X29,X16] :
( hBOOL(hAPP(X16,X29))
| ~ hBOOL(hAPP(X16,c_Type_Osko__Type__Xtype__induct__1__1(X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_2) ).
fof(f1579,plain,
spl0_96,
inference(avatar_split_clause,[],[f49,f1577]) ).
fof(f1577,plain,
( spl0_96
<=> ! [X11,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(X11,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f49,axiom,
! [X0,X11,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(X11,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_1) ).
fof(f1575,plain,
spl0_95,
inference(avatar_split_clause,[],[f48,f1573]) ).
fof(f1573,plain,
( spl0_95
<=> ! [X12,X0,X11] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Oappend(X11,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f48,axiom,
! [X0,X11,X12] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Oappend(X11,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__append_0) ).
fof(f1571,plain,
spl0_94,
inference(avatar_split_clause,[],[f41,f1569]) ).
fof(f1569,plain,
( spl0_94
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f41,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1567,plain,
spl0_93,
inference(avatar_split_clause,[],[f40,f1565]) ).
fof(f1565,plain,
( spl0_93
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f40,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,c_Orderings_Oord__class_Omax(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1562,plain,
( spl0_92
| ~ spl0_21
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f1552,f1480,f1242,f1560]) ).
fof(f1560,plain,
( spl0_92
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1480,plain,
( spl0_77
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X9,X0) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1552,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_21
| ~ spl0_77 ),
inference(resolution,[],[f1481,f1244]) ).
fof(f1481,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X9,X0) = X9 )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f1540,plain,
spl0_91,
inference(avatar_split_clause,[],[f971,f1538]) ).
fof(f1538,plain,
( spl0_91
<=> ! [X0,X11] : c_List_Olist_ONil(X0) = c_List_Otake(c_Orderings_Obot__class_Obot(tc_nat),X11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f971,plain,
! [X0,X11] : c_List_Olist_ONil(X0) = c_List_Otake(c_Orderings_Obot__class_Obot(tc_nat),X11,X0),
inference(forward_demodulation,[],[f449,f689]) ).
fof(f449,axiom,
! [X0,X11] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__0_0) ).
fof(f1536,plain,
spl0_90,
inference(avatar_split_clause,[],[f969,f1534]) ).
fof(f969,plain,
! [X0,X9] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X9,X0),
inference(forward_demodulation,[],[f256,f689]) ).
fof(f256,axiom,
! [X0,X9] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X9,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
fof(f1532,plain,
spl0_89,
inference(avatar_split_clause,[],[f968,f1530]) ).
fof(f1530,plain,
( spl0_89
<=> ! [X0] : c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f968,plain,
! [X0] : c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f235,f689]) ).
fof(f235,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
fof(f1528,plain,
spl0_88,
inference(avatar_split_clause,[],[f967,f1526]) ).
fof(f1526,plain,
( spl0_88
<=> ! [X2] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f967,plain,
! [X2] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat),
inference(forward_demodulation,[],[f692,f689]) ).
fof(f692,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1524,plain,
spl0_87,
inference(avatar_split_clause,[],[f836,f1521]) ).
fof(f1521,plain,
( spl0_87
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f836,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(definition_unfolding,[],[f734,f756]) ).
fof(f734,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argT_0) ).
fof(f1519,plain,
spl0_86,
inference(avatar_split_clause,[],[f835,f1516]) ).
fof(f1516,plain,
( spl0_86
<=> c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f835,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
inference(definition_unfolding,[],[f778,f756]) ).
fof(f778,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).
fof(f1514,plain,
spl0_85,
inference(avatar_split_clause,[],[f738,f1512]) ).
fof(f738,axiom,
! [X80,X81,X17] : c_Type_Otype_OAtom(X17) != hAPP(hAPP(c_Type_Otype_OFun,X80),X81),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
fof(f1510,plain,
spl0_84,
inference(avatar_split_clause,[],[f681,f1508]) ).
fof(f1508,plain,
( spl0_84
<=> ! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f681,axiom,
! [X2,X3] :
( c_lessequals(X3,X2,tc_nat)
| c_lessequals(X2,X3,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1506,plain,
spl0_83,
inference(avatar_split_clause,[],[f632,f1504]) ).
fof(f1504,plain,
( spl0_83
<=> ! [X48,X69,X68] : c_Lambda_OdB_OAbs(X48) != hAPP(hAPP(c_Lambda_OdB_OApp,X68),X69) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f632,axiom,
! [X48,X68,X69] : c_Lambda_OdB_OAbs(X48) != hAPP(hAPP(c_Lambda_OdB_OApp,X68),X69),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f1502,plain,
spl0_82,
inference(avatar_split_clause,[],[f630,f1500]) ).
fof(f1500,plain,
( spl0_82
<=> ! [X17,X24] :
( X17 = X24
| c_Lambda_OdB_OVar(X17) != c_Lambda_OdB_OVar(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f630,axiom,
! [X17,X24] :
( X17 = X24
| c_Lambda_OdB_OVar(X17) != c_Lambda_OdB_OVar(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f1498,plain,
spl0_81,
inference(avatar_split_clause,[],[f517,f1496]) ).
fof(f1496,plain,
( spl0_81
<=> ! [X25,X26] :
( ~ c_Lambda_Obeta(X26,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X26),c_Lambda_OdB_OAbs(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f517,axiom,
! [X26,X25] :
( ~ c_Lambda_Obeta(X26,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X26),c_Lambda_OdB_OAbs(X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f1494,plain,
spl0_80,
inference(avatar_split_clause,[],[f491,f1492]) ).
fof(f1492,plain,
( spl0_80
<=> ! [X2,X0] : c_List_Olist_ONil(X0) = c_List_Orotate(X2,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f491,axiom,
! [X2,X0] : c_List_Olist_ONil(X0) = c_List_Orotate(X2,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
fof(f1490,plain,
spl0_79,
inference(avatar_split_clause,[],[f433,f1488]) ).
fof(f1488,plain,
( spl0_79
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f433,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1486,plain,
spl0_78,
inference(avatar_split_clause,[],[f404,f1484]) ).
fof(f1484,plain,
( spl0_78
<=> ! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_lessequals(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f404,axiom,
! [X2,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| c_lessequals(X3,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
fof(f1482,plain,
spl0_77,
inference(avatar_split_clause,[],[f397,f1480]) ).
fof(f397,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X9,X9,X0) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1478,plain,
spl0_76,
inference(avatar_split_clause,[],[f383,f1476]) ).
fof(f1476,plain,
( spl0_76
<=> ! [X0,X11] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Orev(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f383,axiom,
! [X0,X11] :
( c_List_Odistinct(X11,X0)
| ~ c_List_Odistinct(c_List_Orev(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_0) ).
fof(f1474,plain,
spl0_75,
inference(avatar_split_clause,[],[f382,f1472]) ).
fof(f1472,plain,
( spl0_75
<=> ! [X0,X11] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Orev(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f382,axiom,
! [X0,X11] :
( ~ c_List_Odistinct(X11,X0)
| c_List_Odistinct(c_List_Orev(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct__rev_1) ).
fof(f1470,plain,
spl0_74,
inference(avatar_split_clause,[],[f275,f1468]) ).
fof(f275,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1466,plain,
spl0_73,
inference(avatar_split_clause,[],[f246,f1464]) ).
fof(f1464,plain,
( spl0_73
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f246,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1462,plain,
spl0_72,
inference(avatar_split_clause,[],[f238,f1460]) ).
fof(f1460,plain,
( spl0_72
<=> ! [X54,X53,X17] : c_Lambda_OdB_OVar(X17) != hAPP(hAPP(c_Lambda_OdB_OApp,X53),X54) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f238,axiom,
! [X54,X17,X53] : c_Lambda_OdB_OVar(X17) != hAPP(hAPP(c_Lambda_OdB_OApp,X53),X54),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f1458,plain,
( ~ spl0_12
| ~ spl0_71
| ~ spl0_36
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f1426,f1394,f1309,f1455,f1197]) ).
fof(f1197,plain,
( spl0_12
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1455,plain,
( spl0_71
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1394,plain,
( spl0_57
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1426,plain,
( c_HOL_Oone__class_Oone(tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_nat)
| ~ spl0_36
| ~ spl0_57 ),
inference(superposition,[],[f1395,f1311]) ).
fof(f1395,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1394]) ).
fof(f1453,plain,
spl0_70,
inference(avatar_split_clause,[],[f230,f1451]) ).
fof(f1451,plain,
( spl0_70
<=> ! [X52,X48] :
( X48 = X52
| c_Lambda_OdB_OAbs(X48) != c_Lambda_OdB_OAbs(X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f230,axiom,
! [X48,X52] :
( X48 = X52
| c_Lambda_OdB_OAbs(X48) != c_Lambda_OdB_OAbs(X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f1449,plain,
spl0_69,
inference(avatar_split_clause,[],[f226,f1447]) ).
fof(f1447,plain,
( spl0_69
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f226,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1445,plain,
spl0_68,
inference(avatar_split_clause,[],[f185,f1443]) ).
fof(f1443,plain,
( spl0_68
<=> ! [X2,X0] : c_List_Olist_ONil(X0) = c_List_Odrop(X2,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f185,axiom,
! [X2,X0] : c_List_Olist_ONil(X0) = c_List_Odrop(X2,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
fof(f1441,plain,
spl0_67,
inference(avatar_split_clause,[],[f140,f1439]) ).
fof(f140,axiom,
! [X0,X16,X34,X33] : hAPP(c_COMBK(X16,X0,X33),X34) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f1437,plain,
spl0_66,
inference(avatar_split_clause,[],[f58,f1435]) ).
fof(f1435,plain,
( spl0_66
<=> ! [X17,X24] :
( X17 = X24
| c_Type_Otype_OAtom(X17) != c_Type_Otype_OAtom(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f58,axiom,
! [X17,X24] :
( X17 = X24
| c_Type_Otype_OAtom(X17) != c_Type_Otype_OAtom(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
fof(f1433,plain,
spl0_65,
inference(avatar_split_clause,[],[f24,f1431]) ).
fof(f1431,plain,
( spl0_65
<=> ! [X2,X0] : c_List_Olist_ONil(X0) = c_List_Otake(X2,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f24,axiom,
! [X2,X0] : c_List_Olist_ONil(X0) = c_List_Otake(X2,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
fof(f1424,plain,
spl0_64,
inference(avatar_split_clause,[],[f966,f1422]) ).
fof(f1422,plain,
( spl0_64
<=> ! [X0,X11] : c_List_Odrop(c_Orderings_Obot__class_Obot(tc_nat),X11,X0) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f966,plain,
! [X0,X11] : c_List_Odrop(c_Orderings_Obot__class_Obot(tc_nat),X11,X0) = X11,
inference(forward_demodulation,[],[f691,f689]) ).
fof(f691,axiom,
! [X0,X11] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X11,X0) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
fof(f1420,plain,
spl0_63,
inference(avatar_split_clause,[],[f965,f1418]) ).
fof(f1418,plain,
( spl0_63
<=> ! [X25,X5] : c_Lambda_Oliftn(c_Orderings_Obot__class_Obot(tc_nat),X25,X5) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f965,plain,
! [X5,X25] : c_Lambda_Oliftn(c_Orderings_Obot__class_Obot(tc_nat),X25,X5) = X25,
inference(forward_demodulation,[],[f571,f689]) ).
fof(f571,axiom,
! [X5,X25] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X5) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
fof(f1416,plain,
spl0_62,
inference(avatar_split_clause,[],[f964,f1414]) ).
fof(f964,plain,
! [X3] : c_HOL_Ominus__class_Ominus(X3,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f579,f689]) ).
fof(f579,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1412,plain,
spl0_61,
inference(avatar_split_clause,[],[f963,f1410]) ).
fof(f1410,plain,
( spl0_61
<=> ! [X2] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f963,plain,
! [X2] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) = X2,
inference(forward_demodulation,[],[f698,f689]) ).
fof(f698,axiom,
! [X2] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
fof(f1408,plain,
spl0_60,
inference(avatar_split_clause,[],[f962,f1406]) ).
fof(f1406,plain,
( spl0_60
<=> ! [X2] : c_Orderings_Oord__class_Omax(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f962,plain,
! [X2] : c_Orderings_Oord__class_Omax(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X2,
inference(forward_demodulation,[],[f697,f689]) ).
fof(f697,axiom,
! [X2] : c_Orderings_Oord__class_Omax(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
fof(f1404,plain,
spl0_59,
inference(avatar_split_clause,[],[f961,f1402]) ).
fof(f961,plain,
! [X3] : c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f580,f689]) ).
fof(f580,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1400,plain,
spl0_58,
inference(avatar_split_clause,[],[f817,f1398]) ).
fof(f1398,plain,
( spl0_58
<=> ! [X93,X0,X94] :
( X93 = X94
| ~ c_fequal(X93,X94,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f817,axiom,
! [X0,X94,X93] :
( X93 = X94
| ~ c_fequal(X93,X94,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1396,plain,
spl0_57,
inference(avatar_split_clause,[],[f547,f1394]) ).
fof(f547,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1392,plain,
spl0_56,
inference(avatar_split_clause,[],[f520,f1390]) ).
fof(f1390,plain,
( spl0_56
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f520,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
fof(f1388,plain,
spl0_55,
inference(avatar_split_clause,[],[f322,f1386]) ).
fof(f1386,plain,
( spl0_55
<=> ! [X61,X0,X62] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X61,X62,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f322,axiom,
! [X0,X62,X61] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X61,X62,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
fof(f1384,plain,
spl0_54,
inference(avatar_split_clause,[],[f291,f1382]) ).
fof(f291,axiom,
! [X58,X9] : c_Type_Otyping(X58,c_Lambda_OdB_OVar(X9),hAPP(X58,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f1380,plain,
spl0_53,
inference(avatar_split_clause,[],[f290,f1378]) ).
fof(f290,axiom,
! [X2,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1376,plain,
spl0_52,
inference(avatar_split_clause,[],[f51,f1374]) ).
fof(f1374,plain,
( spl0_52
<=> ! [X0,X12] : c_List_Orev(c_List_Orev(X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f51,axiom,
! [X0,X12] : c_List_Orev(c_List_Orev(X12,X0),X0) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
fof(f1372,plain,
spl0_51,
inference(avatar_split_clause,[],[f47,f1370]) ).
fof(f1370,plain,
( spl0_51
<=> ! [X9,X0] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f47,axiom,
! [X0,X9] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1368,plain,
spl0_50,
inference(avatar_split_clause,[],[f46,f1366]) ).
fof(f1366,plain,
( spl0_50
<=> ! [X0,X12] : c_List_Oappend(c_List_Olist_ONil(X0),X12,X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f46,axiom,
! [X0,X12] : c_List_Oappend(c_List_Olist_ONil(X0),X12,X0) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
fof(f1364,plain,
spl0_49,
inference(avatar_split_clause,[],[f44,f1362]) ).
fof(f44,axiom,
! [X0,X11] : c_List_Oappend(X11,c_List_Olist_ONil(X0),X0) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
fof(f1360,plain,
spl0_48,
inference(avatar_split_clause,[],[f957,f1358]) ).
fof(f1358,plain,
( spl0_48
<=> ! [X7] : c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osize__class_Osize(X7,tc_String_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f957,plain,
! [X7] : c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osize__class_Osize(X7,tc_String_Ochar),
inference(forward_demodulation,[],[f695,f689]) ).
fof(f695,axiom,
! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(X7,tc_String_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_size__char_0) ).
fof(f1356,plain,
spl0_47,
inference(avatar_split_clause,[],[f789,f1354]) ).
fof(f1354,plain,
( spl0_47
<=> ! [X92,X91] :
( ~ class_Orderings_Obot(X92)
| class_Orderings_Obot(tc_fun(X91,X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f789,axiom,
! [X91,X92] :
( ~ class_Orderings_Obot(X92)
| class_Orderings_Obot(tc_fun(X91,X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1352,plain,
spl0_46,
inference(avatar_split_clause,[],[f788,f1350]) ).
fof(f1350,plain,
( spl0_46
<=> ! [X92,X91] :
( ~ class_Orderings_Oorder(X92)
| class_Orderings_Oorder(tc_fun(X91,X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f788,axiom,
! [X91,X92] :
( ~ class_Orderings_Oorder(X92)
| class_Orderings_Oorder(tc_fun(X91,X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1348,plain,
spl0_45,
inference(avatar_split_clause,[],[f787,f1346]) ).
fof(f1346,plain,
( spl0_45
<=> ! [X92,X91] :
( ~ class_Orderings_Opreorder(X92)
| class_Orderings_Opreorder(tc_fun(X91,X92)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f787,axiom,
! [X91,X92] :
( ~ class_Orderings_Opreorder(X92)
| class_Orderings_Opreorder(tc_fun(X91,X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1344,plain,
spl0_44,
inference(avatar_split_clause,[],[f617,f1342]) ).
fof(f1342,plain,
( spl0_44
<=> ! [X9,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f617,axiom,
! [X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1340,plain,
spl0_43,
inference(avatar_split_clause,[],[f616,f1338]) ).
fof(f1338,plain,
( spl0_43
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f616,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1336,plain,
spl0_42,
inference(avatar_split_clause,[],[f492,f1334]) ).
fof(f1334,plain,
( spl0_42
<=> ! [X25,X0,X9] : c_List_Olist_OCons(X9,X25,X0) != X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f492,axiom,
! [X0,X9,X25] : c_List_Olist_OCons(X9,X25,X0) != X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f1332,plain,
spl0_41,
inference(avatar_split_clause,[],[f263,f1330]) ).
fof(f1330,plain,
( spl0_41
<=> ! [X9,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f263,axiom,
! [X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1328,plain,
spl0_40,
inference(avatar_split_clause,[],[f262,f1326]) ).
fof(f262,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1324,plain,
spl0_39,
inference(avatar_split_clause,[],[f261,f1322]) ).
fof(f1322,plain,
( spl0_39
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f261,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1320,plain,
( spl0_38
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1307,f1304,f1318]) ).
fof(f1304,plain,
( spl0_35
<=> ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1307,plain,
( ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1305,f689]) ).
fof(f1305,plain,
( ! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f1316,plain,
spl0_37,
inference(avatar_split_clause,[],[f956,f1314]) ).
fof(f1314,plain,
( spl0_37
<=> ! [X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f956,plain,
! [X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat),
inference(forward_demodulation,[],[f694,f689]) ).
fof(f694,axiom,
! [X2] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1312,plain,
spl0_36,
inference(avatar_split_clause,[],[f689,f1309]) ).
fof(f1306,plain,
spl0_35,
inference(avatar_split_clause,[],[f688,f1304]) ).
fof(f688,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f1302,plain,
spl0_34,
inference(avatar_split_clause,[],[f199,f1300]) ).
fof(f199,axiom,
! [X48,X17] : c_Lambda_OdB_OVar(X17) != c_Lambda_OdB_OAbs(X48),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f1298,plain,
spl0_33,
inference(avatar_split_clause,[],[f188,f1296]) ).
fof(f1296,plain,
( spl0_33
<=> ! [X2] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f188,axiom,
! [X2] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
fof(f1294,plain,
spl0_32,
inference(avatar_split_clause,[],[f13,f1292]) ).
fof(f1292,plain,
( spl0_32
<=> ! [X0,X8] : c_List_Olistsp(X8,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f13,axiom,
! [X0,X8] : c_List_Olistsp(X8,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
fof(f1290,plain,
spl0_31,
inference(avatar_split_clause,[],[f816,f1288]) ).
fof(f1288,plain,
( spl0_31
<=> ! [X9,X0] : c_fequal(X9,X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f816,axiom,
! [X0,X9] : c_fequal(X9,X9,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1286,plain,
spl0_30,
inference(avatar_split_clause,[],[f760,f1283]) ).
fof(f1283,plain,
( spl0_30
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f760,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
fof(f1281,plain,
spl0_29,
inference(avatar_split_clause,[],[f758,f1278]) ).
fof(f758,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
fof(f1276,plain,
spl0_28,
inference(avatar_split_clause,[],[f615,f1274]) ).
fof(f1274,plain,
( spl0_28
<=> ! [X9] : c_lessequals(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f615,axiom,
! [X9] : c_lessequals(X9,X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f1272,plain,
spl0_27,
inference(avatar_split_clause,[],[f415,f1270]) ).
fof(f1270,plain,
( spl0_27
<=> ! [X22,X25] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X22),X25) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f415,axiom,
! [X22,X25] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X22),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f1268,plain,
spl0_26,
inference(avatar_split_clause,[],[f412,f1266]) ).
fof(f1266,plain,
( spl0_26
<=> ! [X0] : c_List_Odistinct(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f412,axiom,
! [X0] : c_List_Odistinct(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distinct_Osimps_I1_J_0) ).
fof(f1264,plain,
spl0_25,
inference(avatar_split_clause,[],[f259,f1262]) ).
fof(f259,axiom,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1260,plain,
spl0_24,
inference(avatar_split_clause,[],[f813,f1257]) ).
fof(f813,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1255,plain,
spl0_23,
inference(avatar_split_clause,[],[f812,f1252]) ).
fof(f1252,plain,
( spl0_23
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f812,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1250,plain,
spl0_22,
inference(avatar_split_clause,[],[f811,f1247]) ).
fof(f1247,plain,
( spl0_22
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f811,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1245,plain,
spl0_21,
inference(avatar_split_clause,[],[f810,f1242]) ).
fof(f810,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1240,plain,
spl0_20,
inference(avatar_split_clause,[],[f809,f1237]) ).
fof(f1237,plain,
( spl0_20
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f809,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1235,plain,
spl0_19,
inference(avatar_split_clause,[],[f808,f1232]) ).
fof(f1232,plain,
( spl0_19
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f808,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f1230,plain,
spl0_18,
inference(avatar_split_clause,[],[f807,f1227]) ).
fof(f807,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1225,plain,
spl0_17,
inference(avatar_split_clause,[],[f806,f1222]) ).
fof(f806,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1220,plain,
spl0_16,
inference(avatar_split_clause,[],[f805,f1217]) ).
fof(f1217,plain,
( spl0_16
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f805,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1215,plain,
spl0_15,
inference(avatar_split_clause,[],[f804,f1212]) ).
fof(f1212,plain,
( spl0_15
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f804,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1210,plain,
spl0_14,
inference(avatar_split_clause,[],[f803,f1207]) ).
fof(f803,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1205,plain,
spl0_13,
inference(avatar_split_clause,[],[f802,f1202]) ).
fof(f1202,plain,
( spl0_13
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f802,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(f1200,plain,
spl0_12,
inference(avatar_split_clause,[],[f801,f1197]) ).
fof(f801,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1195,plain,
spl0_11,
inference(avatar_split_clause,[],[f800,f1192]) ).
fof(f800,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1190,plain,
spl0_10,
inference(avatar_split_clause,[],[f799,f1187]) ).
fof(f1187,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f799,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1185,plain,
spl0_9,
inference(avatar_split_clause,[],[f798,f1182]) ).
fof(f798,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1180,plain,
spl0_8,
inference(avatar_split_clause,[],[f797,f1177]) ).
fof(f797,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1175,plain,
spl0_7,
inference(avatar_split_clause,[],[f796,f1172]) ).
fof(f1172,plain,
( spl0_7
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f796,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1170,plain,
spl0_6,
inference(avatar_split_clause,[],[f795,f1167]) ).
fof(f1167,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f795,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1165,plain,
spl0_5,
inference(avatar_split_clause,[],[f794,f1162]) ).
fof(f1162,plain,
( spl0_5
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f794,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1160,plain,
spl0_4,
inference(avatar_split_clause,[],[f793,f1157]) ).
fof(f1157,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f793,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1155,plain,
spl0_3,
inference(avatar_split_clause,[],[f792,f1152]) ).
fof(f1152,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f792,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1150,plain,
spl0_2,
inference(avatar_split_clause,[],[f791,f1147]) ).
fof(f1147,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f791,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1145,plain,
spl0_1,
inference(avatar_split_clause,[],[f790,f1142]) ).
fof(f1142,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f790,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL815-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 22:51:25 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (4074)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (4096)WARNING: value z3 for option sas not known
% 0.22/0.42 % (4094)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.42 % (4095)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.42 % (4096)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.42 % (4098)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.42 % (4097)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.42 % (4099)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.42 % (4100)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.57 TRYING [1]
% 1.38/0.58 TRYING [2]
% 2.68/0.77 % (4098)First to succeed.
% 2.68/0.79 % (4098)Refutation found. Thanks to Tanya!
% 2.68/0.79 % SZS status Unsatisfiable for theBenchmark
% 2.68/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/0.80 % (4098)------------------------------
% 2.68/0.80 % (4098)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.68/0.80 % (4098)Termination reason: Refutation
% 2.68/0.80
% 2.68/0.80 % (4098)Memory used [KB]: 7005
% 2.68/0.80 % (4098)Time elapsed: 0.366 s
% 2.68/0.80 % (4098)Instructions burned: 913 (million)
% 2.68/0.80 % (4098)------------------------------
% 2.68/0.80 % (4098)------------------------------
% 2.68/0.80 % (4074)Success in time 0.41 s
%------------------------------------------------------------------------------