TSTP Solution File: LCL848-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL848-1 : 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 13:51:41 EDT 2024
% Result : Unsatisfiable 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 691
% Syntax : Number of formulae : 1108 ( 480 unt; 0 def)
% Number of atoms : 2163 ( 420 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1769 ( 714 ~; 698 |; 0 &)
% ( 357 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 402 ( 400 usr; 358 prp; 0-4 aty)
% Number of functors : 49 ( 49 usr; 11 con; 0-5 aty)
% Number of variables : 1459 (1459 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3924,plain,
$false,
inference(avatar_sat_refutation,[],[f744,f749,f754,f759,f764,f769,f774,f779,f784,f789,f794,f799,f804,f809,f814,f819,f824,f829,f834,f839,f844,f849,f854,f859,f864,f869,f874,f879,f884,f889,f894,f899,f904,f909,f914,f919,f924,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f979,f984,f989,f994,f999,f1004,f1009,f1014,f1019,f1024,f1029,f1034,f1039,f1043,f1047,f1051,f1056,f1061,f1065,f1070,f1074,f1078,f1082,f1086,f1090,f1094,f1098,f1102,f1106,f1110,f1114,f1118,f1122,f1126,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1174,f1178,f1182,f1186,f1190,f1194,f1198,f1202,f1206,f1210,f1214,f1218,f1222,f1226,f1234,f1238,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1270,f1274,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1341,f1351,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1401,f1405,f1409,f1414,f1418,f1422,f1426,f1430,f1434,f1438,f1442,f1446,f1450,f1455,f1459,f1463,f1467,f1471,f1475,f1541,f1567,f1575,f1579,f1583,f1587,f1591,f1596,f1600,f1604,f1608,f1612,f1616,f1620,f1624,f1628,f1632,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1835,f1872,f1876,f1880,f1892,f1896,f1900,f1904,f1908,f1912,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1952,f1956,f1960,f1964,f1968,f1972,f1976,f1980,f1984,f1988,f1992,f1996,f2000,f2004,f2008,f2046,f2198,f2209,f2213,f2217,f2221,f2225,f2229,f2233,f2237,f2241,f2245,f2249,f2253,f2257,f2261,f2265,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2309,f2313,f2317,f2321,f2325,f2360,f2426,f2507,f2511,f2515,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2549,f2553,f2557,f2561,f2565,f2569,f2573,f2577,f2581,f2585,f2589,f2593,f2597,f2601,f2606,f2610,f2614,f2618,f2622,f2626,f2630,f2634,f2638,f2642,f2646,f2651,f2655,f2659,f2663,f2667,f2671,f2675,f2680,f2722,f2834,f3137,f3141,f3145,f3149,f3155,f3159,f3163,f3167,f3171,f3175,f3179,f3183,f3187,f3191,f3199,f3203,f3207,f3211,f3215,f3219,f3223,f3227,f3231,f3235,f3243,f3247,f3251,f3255,f3259,f3263,f3267,f3271,f3275,f3279,f3283,f3287,f3291,f3295,f3299,f3303,f3307,f3311,f3315,f3319,f3323,f3510,f3687,f3910,f3914,f3918,f3922,f3923]) ).
fof(f3923,plain,
( ~ spl0_303
| spl0_67
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3902,f3313,f1067,f2677]) ).
fof(f2677,plain,
( spl0_303
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f1067,plain,
( spl0_67
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f3313,plain,
( spl0_348
<=> ! [X0,X35] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X35,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X35,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f3902,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
| spl0_67
| ~ spl0_348 ),
inference(resolution,[],[f3314,f1069]) ).
fof(f1069,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| spl0_67 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f3314,plain,
( ! [X0,X35] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X35,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X35,tc_Lambda_OdB) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f3313]) ).
fof(f3922,plain,
spl0_357,
inference(avatar_split_clause,[],[f157,f3920]) ).
fof(f3920,plain,
( spl0_357
<=> ! [X13,X0,X2,X7] :
( c_in(X7,c_List_Oset(X13,X2),X2)
| ~ c_in(X7,c_List_Oset(c_List_Otake(X0,X13,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f157,axiom,
! [X2,X0,X7,X13] :
( c_in(X7,c_List_Oset(X13,X2),X2)
| ~ c_in(X7,c_List_Oset(c_List_Otake(X0,X13,X2),X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__takeD_0) ).
fof(f3918,plain,
spl0_356,
inference(avatar_split_clause,[],[f146,f3916]) ).
fof(f3916,plain,
( spl0_356
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f146,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X3,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f3914,plain,
spl0_355,
inference(avatar_split_clause,[],[f61,f3912]) ).
fof(f3912,plain,
( spl0_355
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f61,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X3,X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X3,X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f3910,plain,
spl0_354,
inference(avatar_split_clause,[],[f55,f3908]) ).
fof(f3908,plain,
( spl0_354
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X1),X0,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f55,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X1),X0,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
fof(f3687,plain,
( ~ spl0_352
| spl0_353
| ~ spl0_72
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3638,f3201,f1088,f3685,f3681]) ).
fof(f3681,plain,
( spl0_352
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f3685,plain,
( spl0_353
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f1088,plain,
( spl0_72
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f3201,plain,
( spl0_321
<=> ! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f3638,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_72
| ~ spl0_321 ),
inference(resolution,[],[f3202,f1089]) ).
fof(f1089,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f3202,plain,
( ! [X2,X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3201]) ).
fof(f3510,plain,
( spl0_351
| ~ spl0_133
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1788,f1677,f1355,f3508]) ).
fof(f3508,plain,
( spl0_351
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f1355,plain,
( spl0_133
<=> ! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1677,plain,
( spl0_190
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1788,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_133
| ~ spl0_190 ),
inference(resolution,[],[f1678,f1356]) ).
fof(f1356,plain,
( ! [X0,X1] :
( c_lessequals(X1,c_Suc(X0),tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1355]) ).
fof(f1678,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1677]) ).
fof(f3323,plain,
spl0_350,
inference(avatar_split_clause,[],[f640,f3321]) ).
fof(f3321,plain,
( spl0_350
<=> ! [X70,X55,X71,X56] :
( X56 = X71
| hAPP(hAPP(c_Lambda_OdB_OApp,X55),X56) != hAPP(hAPP(c_Lambda_OdB_OApp,X70),X71) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f640,axiom,
! [X70,X71,X56,X55] :
( X56 = X71
| hAPP(hAPP(c_Lambda_OdB_OApp,X55),X56) != hAPP(hAPP(c_Lambda_OdB_OApp,X70),X71) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f3319,plain,
spl0_349,
inference(avatar_split_clause,[],[f639,f3317]) ).
fof(f3317,plain,
( spl0_349
<=> ! [X55,X71,X56,X70] :
( X55 = X70
| hAPP(hAPP(c_Lambda_OdB_OApp,X55),X56) != hAPP(hAPP(c_Lambda_OdB_OApp,X70),X71) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f639,axiom,
! [X70,X71,X56,X55] :
( X55 = X70
| hAPP(hAPP(c_Lambda_OdB_OApp,X55),X56) != hAPP(hAPP(c_Lambda_OdB_OApp,X70),X71) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f3315,plain,
spl0_348,
inference(avatar_split_clause,[],[f627,f3313]) ).
fof(f627,axiom,
! [X0,X35] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X35,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X35,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
fof(f3311,plain,
spl0_347,
inference(avatar_split_clause,[],[f621,f3309]) ).
fof(f3309,plain,
( spl0_347
<=> ! [X36,X0,X52,X42] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X42)),X52) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X36,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f621,axiom,
! [X0,X36,X52,X42] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X42)),X52) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X36,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f3307,plain,
spl0_346,
inference(avatar_split_clause,[],[f602,f3305]) ).
fof(f3305,plain,
( spl0_346
<=> ! [X13,X2,X7] :
( c_List_Olist_ONil(X2) = X13
| c_List_Olast(X13,X2) = c_List_Olast(c_List_Olist_OCons(X7,X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f602,axiom,
! [X2,X7,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Olast(X13,X2) = c_List_Olast(c_List_Olist_OCons(X7,X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
fof(f3303,plain,
spl0_345,
inference(avatar_split_clause,[],[f599,f3301]) ).
fof(f3301,plain,
( spl0_345
<=> ! [X28,X13,X2,X7] :
( hBOOL(hAPP(X28,X7))
| c_List_Olist_ONil(X2) = c_List_OtakeWhile(X28,c_List_Olist_OCons(X7,X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f599,axiom,
! [X2,X28,X7,X13] :
( hBOOL(hAPP(X28,X7))
| c_List_Olist_ONil(X2) = c_List_OtakeWhile(X28,c_List_Olist_OCons(X7,X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).
fof(f3299,plain,
spl0_344,
inference(avatar_split_clause,[],[f578,f3297]) ).
fof(f3297,plain,
( spl0_344
<=> ! [X13,X2,X9,X7] : c_List_Olist__update(c_List_Olist_OCons(X7,X13,X2),c_HOL_Ozero__class_Ozero(tc_nat),X9,X2) = c_List_Olist_OCons(X9,X13,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f578,axiom,
! [X2,X9,X7,X13] : c_List_Olist__update(c_List_Olist_OCons(X7,X13,X2),c_HOL_Ozero__class_Ozero(tc_nat),X9,X2) = c_List_Olist_OCons(X9,X13,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
fof(f3295,plain,
spl0_343,
inference(avatar_split_clause,[],[f539,f3293]) ).
fof(f3293,plain,
( spl0_343
<=> ! [X61,X60,X62,X52] :
( ~ c_Type_Otyping(X60,X52,X62)
| c_Type_Otyping(X60,X61,X62)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X52),X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f539,axiom,
! [X62,X52,X60,X61] :
( ~ c_Type_Otyping(X60,X52,X62)
| c_Type_Otyping(X60,X61,X62)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X52),X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f3291,plain,
spl0_342,
inference(avatar_split_clause,[],[f520,f3289]) ).
fof(f3289,plain,
( spl0_342
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f520,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f3287,plain,
spl0_341,
inference(avatar_split_clause,[],[f519,f3285]) ).
fof(f3285,plain,
( spl0_341
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f519,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f3283,plain,
spl0_340,
inference(avatar_split_clause,[],[f517,f3281]) ).
fof(f3281,plain,
( spl0_340
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f517,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f3279,plain,
spl0_339,
inference(avatar_split_clause,[],[f516,f3277]) ).
fof(f3277,plain,
( spl0_339
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f516,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f3275,plain,
spl0_338,
inference(avatar_split_clause,[],[f500,f3273]) ).
fof(f3273,plain,
( spl0_338
<=> ! [X13,X2,X21] :
( c_List_Olist_ONil(X2) = X21
| c_List_Olast(c_List_Oappend(X13,X21,X2),X2) = c_List_Olast(X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f500,axiom,
! [X2,X21,X13] :
( c_List_Olist_ONil(X2) = X21
| c_List_Olast(c_List_Oappend(X13,X21,X2),X2) = c_List_Olast(X21,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
fof(f3271,plain,
spl0_337,
inference(avatar_split_clause,[],[f441,f3269]) ).
fof(f3269,plain,
( spl0_337
<=> ! [X13,X2] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_List_Olistsum(X13,X2) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X13,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f441,axiom,
! [X2,X13] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_List_Olistsum(X13,X2) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X13,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
fof(f3267,plain,
spl0_336,
inference(avatar_split_clause,[],[f360,f3265]) ).
fof(f3265,plain,
( spl0_336
<=> ! [X52,X42] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X42),X52))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X42)),c_Lambda_OdB_OAbs(X52))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f360,axiom,
! [X52,X42] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X42),X52))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X42)),c_Lambda_OdB_OAbs(X52))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f3263,plain,
spl0_335,
inference(avatar_split_clause,[],[f356,f3261]) ).
fof(f3261,plain,
( spl0_335
<=> ! [X13,X2,X7] :
( ~ c_in(X7,c_List_Oset(X13,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f356,axiom,
! [X2,X7,X13] :
( ~ c_in(X7,c_List_Oset(X13,X2),X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__pos__if__in__set_0) ).
fof(f3259,plain,
spl0_334,
inference(avatar_split_clause,[],[f323,f3257]) ).
fof(f3257,plain,
( spl0_334
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X8,X2)
| c_HOL_Oord__class_Oless(X7,X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f323,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X8,X2)
| c_HOL_Oord__class_Oless(X7,X8,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f3255,plain,
spl0_333,
inference(avatar_split_clause,[],[f322,f3253]) ).
fof(f3253,plain,
( spl0_333
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(X8,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f322,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(X8,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3251,plain,
spl0_332,
inference(avatar_split_clause,[],[f307,f3249]) ).
fof(f3249,plain,
( spl0_332
<=> ! [X2,X44,X43,X28,X29,X45] : hAPP(c_COMBC(X28,X43,X29,X44,X2),X45) = hAPP(hAPP(X28,X45),X43) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f307,axiom,
! [X2,X28,X29,X44,X45,X43] : hAPP(c_COMBC(X28,X43,X29,X44,X2),X45) = hAPP(hAPP(X28,X45),X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f3247,plain,
spl0_331,
inference(avatar_split_clause,[],[f305,f3245]) ).
fof(f3245,plain,
( spl0_331
<=> ! [X2,X9,X7] :
( ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2)
| X7 = X9
| c_Int_Onumber__class_Onumber__of(X7,X2) != c_Int_Onumber__class_Onumber__of(X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f305,axiom,
! [X2,X9,X7] :
( ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2)
| X7 = X9
| c_Int_Onumber__class_Onumber__of(X7,X2) != c_Int_Onumber__class_Onumber__of(X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f3243,plain,
spl0_330,
inference(avatar_split_clause,[],[f271,f3241]) ).
fof(f3241,plain,
( spl0_330
<=> ! [X13,X2,X0] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X0,tc_nat)
| c_List_Olist_ONil(X2) = c_List_Odrop(X0,X13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f271,axiom,
! [X2,X0,X13] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X0,tc_nat)
| c_List_Olist_ONil(X2) = c_List_Odrop(X0,X13,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__all_0) ).
fof(f3235,plain,
spl0_329,
inference(avatar_split_clause,[],[f270,f3233]) ).
fof(f3233,plain,
( spl0_329
<=> ! [X13,X2,X0] :
( c_List_Olist_ONil(X2) != c_List_Odrop(X0,X13,X2)
| c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f270,axiom,
! [X2,X0,X13] :
( c_List_Olist_ONil(X2) != c_List_Odrop(X0,X13,X2)
| c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
fof(f3231,plain,
spl0_328,
inference(avatar_split_clause,[],[f253,f3229]) ).
fof(f3229,plain,
( spl0_328
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_HOL_Oone__class_Oone(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f253,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_HOL_Oone__class_Oone(X2)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f3227,plain,
spl0_327,
inference(avatar_split_clause,[],[f223,f3225]) ).
fof(f3225,plain,
( spl0_327
<=> ! [X2,X9,X7] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| X7 = X9
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f223,axiom,
! [X2,X9,X7] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| X7 = X9
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f3223,plain,
spl0_326,
inference(avatar_split_clause,[],[f189,f3221]) ).
fof(f3221,plain,
( spl0_326
<=> ! [X7,X9,X25,X2] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X9 = X25
| c_HOL_Ominus__class_Ominus(X25,X9,X2) != c_HOL_Ominus__class_Ominus(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f189,axiom,
! [X2,X9,X7,X25] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X9 = X25
| c_HOL_Ominus__class_Ominus(X25,X9,X2) != c_HOL_Ominus__class_Ominus(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
fof(f3219,plain,
spl0_325,
inference(avatar_split_clause,[],[f179,f3217]) ).
fof(f3217,plain,
( spl0_325
<=> ! [X13,X2,X7] :
( c_in(X7,c_List_Oset(X13,X2),X2)
| ~ c_in(X7,c_List_Oset(c_List_Obutlast(X13,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f179,axiom,
! [X2,X7,X13] :
( c_in(X7,c_List_Oset(X13,X2),X2)
| ~ c_in(X7,c_List_Oset(c_List_Obutlast(X13,X2),X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).
fof(f3215,plain,
spl0_324,
inference(avatar_split_clause,[],[f177,f3213]) ).
fof(f3213,plain,
( spl0_324
<=> ! [X13,X10,X2,X7] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X10,tc_nat)
| c_List_Olist__update(X13,X10,X7,X2) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f177,axiom,
! [X2,X10,X7,X13] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X10,tc_nat)
| c_List_Olist__update(X13,X10,X7,X2) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
fof(f3211,plain,
spl0_323,
inference(avatar_split_clause,[],[f164,f3209]) ).
fof(f3209,plain,
( spl0_323
<=> ! [X31,X13,X2,X7] :
( ~ c_List_Olistsp(X31,X13,X2)
| hBOOL(hAPP(X31,X7))
| ~ c_in(X7,c_List_Oset(X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f164,axiom,
! [X31,X2,X7,X13] :
( ~ c_List_Olistsp(X31,X13,X2)
| hBOOL(hAPP(X31,X7))
| ~ c_in(X7,c_List_Oset(X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_0) ).
fof(f3207,plain,
spl0_322,
inference(avatar_split_clause,[],[f155,f3205]) ).
fof(f3205,plain,
( spl0_322
<=> ! [X13,X2,X21] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(c_List_Oappend(X13,X21,X2),X2) = c_List_Ohd(X13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f155,axiom,
! [X2,X21,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(c_List_Oappend(X13,X21,X2),X2) = c_List_Ohd(X13,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
fof(f3203,plain,
spl0_321,
inference(avatar_split_clause,[],[f116,f3201]) ).
fof(f116,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f3199,plain,
spl0_320,
inference(avatar_split_clause,[],[f115,f3197]) ).
fof(f3197,plain,
( spl0_320
<=> ! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f115,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f3191,plain,
spl0_319,
inference(avatar_split_clause,[],[f89,f3189]) ).
fof(f3189,plain,
( spl0_319
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f89,axiom,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
fof(f3187,plain,
spl0_318,
inference(avatar_split_clause,[],[f86,f3185]) ).
fof(f3185,plain,
( spl0_318
<=> ! [X0,X1,X16] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X16,tc_nat),c_HOL_Ominus__class_Ominus(X0,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f86,axiom,
! [X0,X1,X16] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X16,tc_nat),c_HOL_Ominus__class_Ominus(X0,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f3183,plain,
spl0_317,
inference(avatar_split_clause,[],[f85,f3181]) ).
fof(f3181,plain,
( spl0_317
<=> ! [X0,X1,X16] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X16,X0,tc_nat),c_HOL_Ominus__class_Ominus(X16,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f85,axiom,
! [X0,X1,X16] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X16,X0,tc_nat),c_HOL_Ominus__class_Ominus(X16,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f3179,plain,
spl0_316,
inference(avatar_split_clause,[],[f65,f3177]) ).
fof(f3177,plain,
( spl0_316
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f65,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
fof(f3175,plain,
spl0_315,
inference(avatar_split_clause,[],[f64,f3173]) ).
fof(f3173,plain,
( spl0_315
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f64,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
fof(f3171,plain,
spl0_314,
inference(avatar_split_clause,[],[f45,f3169]) ).
fof(f3169,plain,
( spl0_314
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X7,X9,X2)
| c_lessequals(X9,X7,X2)
| c_HOL_Oord__class_Oless(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f45,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X7,X9,X2)
| c_lessequals(X9,X7,X2)
| c_HOL_Oord__class_Oless(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3167,plain,
spl0_313,
inference(avatar_split_clause,[],[f38,f3165]) ).
fof(f3165,plain,
( spl0_313
<=> ! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X3,X4,X2)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f38,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X3,X4,X2)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f3163,plain,
spl0_312,
inference(avatar_split_clause,[],[f37,f3161]) ).
fof(f3161,plain,
( spl0_312
<=> ! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X3,X4,X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f37,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X3,X4,X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f3159,plain,
spl0_311,
inference(avatar_split_clause,[],[f13,f3157]) ).
fof(f3157,plain,
( spl0_311
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(X8,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f13,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(X8,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3155,plain,
spl0_310,
inference(avatar_split_clause,[],[f12,f3153]) ).
fof(f3153,plain,
( spl0_310
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X8,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2)
| c_HOL_Oord__class_Oless(X8,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f12,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X8,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2)
| c_HOL_Oord__class_Oless(X8,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3149,plain,
spl0_309,
inference(avatar_split_clause,[],[f11,f3147]) ).
fof(f3147,plain,
( spl0_309
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(X8,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f11,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(X8,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3145,plain,
spl0_308,
inference(avatar_split_clause,[],[f10,f3143]) ).
fof(f3143,plain,
( spl0_308
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X7,X9,X2)
| ~ c_lessequals(X9,X8,X2)
| c_lessequals(X7,X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f10,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X7,X9,X2)
| ~ c_lessequals(X9,X8,X2)
| c_lessequals(X7,X8,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3141,plain,
spl0_307,
inference(avatar_split_clause,[],[f4,f3139]) ).
fof(f3139,plain,
( spl0_307
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X7,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X8,X2)
| c_HOL_Oord__class_Oless(X7,X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f4,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X7,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X8,X2)
| c_HOL_Oord__class_Oless(X7,X8,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3137,plain,
spl0_306,
inference(avatar_split_clause,[],[f3,f3135]) ).
fof(f3135,plain,
( spl0_306
<=> ! [X7,X8,X9,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X9,X8,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| c_HOL_Oord__class_Oless(X7,X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f3,axiom,
! [X2,X8,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X9,X8,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| c_HOL_Oord__class_Oless(X7,X8,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f2834,plain,
( spl0_305
| ~ spl0_49
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1571,f1461,f981,f2831]) ).
fof(f2831,plain,
( spl0_305
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_List_Olistsum(c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f981,plain,
( spl0_49
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1461,plain,
( spl0_159
<=> ! [X2] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_List_Olistsum(c_List_Olist_ONil(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1571,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_List_Olistsum(c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_49
| ~ spl0_159 ),
inference(resolution,[],[f1462,f983]) ).
fof(f983,plain,
( class_OrderedGroup_Omonoid__add(tc_Int_Oint)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f1462,plain,
( ! [X2] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_List_Olistsum(c_List_Olist_ONil(X2),X2) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1461]) ).
fof(f2722,plain,
( spl0_304
| ~ spl0_18
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1570,f1461,f826,f2719]) ).
fof(f2719,plain,
( spl0_304
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f826,plain,
( spl0_18
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1570,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat)
| ~ spl0_18
| ~ spl0_159 ),
inference(resolution,[],[f1462,f828]) ).
fof(f828,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f2680,plain,
spl0_303,
inference(avatar_split_clause,[],[f658,f2677]) ).
fof(f658,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f2675,plain,
spl0_302,
inference(avatar_split_clause,[],[f656,f2673]) ).
fof(f2673,plain,
( spl0_302
<=> ! [X52,X10] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X52))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X52),c_Lambda_OdB_OVar(X10)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f656,axiom,
! [X10,X52] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X52))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X52),c_Lambda_OdB_OVar(X10)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
fof(f2671,plain,
spl0_301,
inference(avatar_split_clause,[],[f655,f2669]) ).
fof(f2669,plain,
( spl0_301
<=> ! [X36,X1,X42] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X36
| c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f655,axiom,
! [X36,X1,X42] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X36
| c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
fof(f2667,plain,
spl0_300,
inference(avatar_split_clause,[],[f641,f2665]) ).
fof(f2665,plain,
( spl0_300
<=> ! [X36,X1,X42] :
( c_Lambda_OdB_OVar(X1) = X42
| c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f641,axiom,
! [X36,X1,X42] :
( c_Lambda_OdB_OVar(X1) = X42
| c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
fof(f2663,plain,
spl0_299,
inference(avatar_split_clause,[],[f625,f2661]) ).
fof(f2661,plain,
( spl0_299
<=> ! [X36,X18,X42] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X36
| c_Lambda_OdB_OAbs(X18) != c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f625,axiom,
! [X36,X18,X42] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X36
| c_Lambda_OdB_OAbs(X18) != c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
fof(f2659,plain,
spl0_298,
inference(avatar_split_clause,[],[f616,f2657]) ).
fof(f2657,plain,
( spl0_298
<=> ! [X11,X10] :
( ~ c_HOL_Oord__class_Oless(X10,X11,tc_nat)
| c_Lambda_OdB_OVar(X10) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X10)),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f616,axiom,
! [X10,X11] :
( ~ c_HOL_Oord__class_Oless(X10,X11,tc_nat)
| c_Lambda_OdB_OVar(X10) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X10)),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f2655,plain,
spl0_297,
inference(avatar_split_clause,[],[f609,f2653]) ).
fof(f2653,plain,
( spl0_297
<=> ! [X18,X36,X42] :
( c_Lambda_OdB_OAbs(X18) = X42
| c_Lambda_OdB_OAbs(X18) != c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f609,axiom,
! [X36,X18,X42] :
( c_Lambda_OdB_OAbs(X18) = X42
| c_Lambda_OdB_OAbs(X18) != c_List_Ofoldl(c_Lambda_OdB_OApp,X42,X36,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
fof(f2651,plain,
( spl0_296
| ~ spl0_44
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1569,f1457,f956,f2648]) ).
fof(f2648,plain,
( spl0_296
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f956,plain,
( spl0_44
<=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1457,plain,
( spl0_158
<=> ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1569,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_44
| ~ spl0_158 ),
inference(resolution,[],[f1458,f958]) ).
fof(f958,plain,
( class_Ring__and__Field_Osemiring__1(tc_Int_Oint)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f1458,plain,
( ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f2646,plain,
spl0_295,
inference(avatar_split_clause,[],[f601,f2644]) ).
fof(f2644,plain,
( spl0_295
<=> ! [X2,X7] : c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f601,axiom,
! [X2,X7] : c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
fof(f2642,plain,
spl0_294,
inference(avatar_split_clause,[],[f564,f2640]) ).
fof(f2640,plain,
( spl0_294
<=> ! [X52,X11,X42] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X52),X11)),X42),X11) = X52 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f564,axiom,
! [X11,X52,X42] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X52),X11)),X42),X11) = X52,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f2638,plain,
spl0_293,
inference(avatar_split_clause,[],[f506,f2636]) ).
fof(f2636,plain,
( spl0_293
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X2)
| c_HOL_Oord__class_Oless(X9,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f506,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X2)
| c_HOL_Oord__class_Oless(X9,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f2634,plain,
spl0_292,
inference(avatar_split_clause,[],[f505,f2632]) ).
fof(f2632,plain,
( spl0_292
<=> ! [X2,X9,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X2)
| c_HOL_Oord__class_Oless(X9,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f505,axiom,
! [X2,X9,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,X2)
| c_HOL_Oord__class_Oless(X9,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f2630,plain,
spl0_291,
inference(avatar_split_clause,[],[f493,f2628]) ).
fof(f2628,plain,
( spl0_291
<=> ! [X0,X10,X2,X7] :
( ~ c_HOL_Oord__class_Oless(X10,X0,tc_nat)
| c_List_Onth(c_List_Oreplicate(X0,X7,X2),X10,X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f493,axiom,
! [X2,X10,X0,X7] :
( ~ c_HOL_Oord__class_Oless(X10,X0,tc_nat)
| c_List_Onth(c_List_Oreplicate(X0,X7,X2),X10,X2) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__replicate_0) ).
fof(f2626,plain,
spl0_290,
inference(avatar_split_clause,[],[f471,f2624]) ).
fof(f2624,plain,
( spl0_290
<=> ! [X29,X2,X22,X13] : c_Nat_Osize__class_Osize(c_List_Omap(X22,X13,X29,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X13,tc_List_Olist(X29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f471,axiom,
! [X2,X29,X22,X13] : c_Nat_Osize__class_Osize(c_List_Omap(X22,X13,X29,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X13,tc_List_Olist(X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).
fof(f2622,plain,
spl0_289,
inference(avatar_split_clause,[],[f371,f2620]) ).
fof(f2620,plain,
( spl0_289
<=> ! [X2,X7] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X7),c_HOL_Ozero__class_Ozero(X2)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f371,axiom,
! [X2,X7] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X7),c_HOL_Ozero__class_Ozero(X2)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2618,plain,
spl0_288,
inference(avatar_split_clause,[],[f368,f2616]) ).
fof(f2616,plain,
( spl0_288
<=> ! [X2] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),c_HOL_Ozero__class_Ozero(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f368,axiom,
! [X2] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),c_HOL_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2614,plain,
spl0_287,
inference(avatar_split_clause,[],[f365,f2612]) ).
fof(f2612,plain,
( spl0_287
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_HOL_Ozero__class_Ozero(X2) = X3
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X3,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f365,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_HOL_Ozero__class_Ozero(X2) = X3
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X3,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f2610,plain,
spl0_286,
inference(avatar_split_clause,[],[f294,f2608]) ).
fof(f2608,plain,
( spl0_286
<=> ! [X13,X2,X0] : c_List_Obutlast(c_List_Odrop(X0,X13,X2),X2) = c_List_Odrop(X0,c_List_Obutlast(X13,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f294,axiom,
! [X2,X0,X13] : c_List_Obutlast(c_List_Odrop(X0,X13,X2),X2) = c_List_Odrop(X0,c_List_Obutlast(X13,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
fof(f2606,plain,
( spl0_285
| ~ spl0_14
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1568,f1457,f806,f2603]) ).
fof(f2603,plain,
( spl0_285
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f806,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1568,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_158 ),
inference(resolution,[],[f1458,f808]) ).
fof(f808,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f2601,plain,
spl0_284,
inference(avatar_split_clause,[],[f289,f2599]) ).
fof(f2599,plain,
( spl0_284
<=> ! [X13,X10,X2,X7] : c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X13,X10,X7,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f289,axiom,
! [X2,X10,X7,X13] : c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X13,X10,X7,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
fof(f2597,plain,
spl0_283,
inference(avatar_split_clause,[],[f284,f2595]) ).
fof(f2595,plain,
( spl0_283
<=> ! [X13,X2] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(X13,X2) = c_List_Olast(c_List_Orev(X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f284,axiom,
! [X2,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(X13,X2) = c_List_Olast(c_List_Orev(X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__rev_0) ).
fof(f2593,plain,
spl0_282,
inference(avatar_split_clause,[],[f283,f2591]) ).
fof(f2591,plain,
( spl0_282
<=> ! [X13,X2] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(c_List_Orev(X13,X2),X2) = c_List_Olast(X13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f283,axiom,
! [X2,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(c_List_Orev(X13,X2),X2) = c_List_Olast(X13,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__rev_0) ).
fof(f2589,plain,
spl0_281,
inference(avatar_split_clause,[],[f267,f2587]) ).
fof(f2587,plain,
( spl0_281
<=> ! [X13,X2] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(X13,X2) = c_List_Onth(X13,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f267,axiom,
! [X2,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Ohd(X13,X2) = c_List_Onth(X13,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__conv__nth_0) ).
fof(f2585,plain,
spl0_280,
inference(avatar_split_clause,[],[f209,f2583]) ).
fof(f2583,plain,
( spl0_280
<=> ! [X2,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X4,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f209,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4),X4,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2581,plain,
spl0_279,
inference(avatar_split_clause,[],[f203,f2579]) ).
fof(f2579,plain,
( spl0_279
<=> ! [X0,X1] :
( c_Suc(X0) = X1
| c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f203,axiom,
! [X0,X1] :
( c_Suc(X0) = X1
| c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
fof(f2577,plain,
spl0_278,
inference(avatar_split_clause,[],[f202,f2575]) ).
fof(f2575,plain,
( spl0_278
<=> ! [X0,X10] :
( ~ c_lessequals(X10,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X10,tc_nat),tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f202,axiom,
! [X10,X0] :
( ~ c_lessequals(X10,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X10,tc_nat),tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f2573,plain,
spl0_277,
inference(avatar_split_clause,[],[f197,f2571]) ).
fof(f2571,plain,
( spl0_277
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_Suc(X1) = X0
| c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f197,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_Suc(X1) = X0
| c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f2569,plain,
spl0_276,
inference(avatar_split_clause,[],[f178,f2567]) ).
fof(f2567,plain,
( spl0_276
<=> ! [X13,X2,X28] : c_lessequals(c_Nat_Osize__class_Osize(c_List_OtakeWhile(X28,X13,X2),tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f178,axiom,
! [X2,X28,X13] : c_lessequals(c_Nat_Osize__class_Osize(c_List_OtakeWhile(X28,X13,X2),tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__takeWhile__le_0) ).
fof(f2565,plain,
spl0_275,
inference(avatar_split_clause,[],[f176,f2563]) ).
fof(f2563,plain,
( spl0_275
<=> ! [X2,X0,X7] : c_List_Oreplicate(c_Suc(X0),X7,X2) = c_List_Olist_OCons(X7,c_List_Oreplicate(X0,X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f176,axiom,
! [X2,X0,X7] : c_List_Oreplicate(c_Suc(X0),X7,X2) = c_List_Olist_OCons(X7,c_List_Oreplicate(X0,X7,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
fof(f2561,plain,
spl0_274,
inference(avatar_split_clause,[],[f170,f2559]) ).
fof(f2559,plain,
( spl0_274
<=> ! [X13,X2,X0] :
( c_List_Otake(X0,X13,X2) = X13
| ~ c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f170,axiom,
! [X2,X0,X13] :
( c_List_Otake(X0,X13,X2) = X13
| ~ c_lessequals(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
fof(f2557,plain,
spl0_273,
inference(avatar_split_clause,[],[f169,f2555]) ).
fof(f2555,plain,
( spl0_273
<=> ! [X13,X0,X2,X7] : c_List_Odrop(X0,X13,X2) = c_List_Odrop(c_Suc(X0),c_List_Olist_OCons(X7,X13,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f169,axiom,
! [X2,X0,X7,X13] : c_List_Odrop(X0,X13,X2) = c_List_Odrop(c_Suc(X0),c_List_Olist_OCons(X7,X13,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
fof(f2553,plain,
spl0_272,
inference(avatar_split_clause,[],[f161,f2551]) ).
fof(f2551,plain,
( spl0_272
<=> ! [X28,X13,X2,X7] :
( hBOOL(hAPP(X28,X7))
| ~ c_in(X7,c_List_Oset(c_List_OtakeWhile(X28,X13,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f161,axiom,
! [X2,X28,X7,X13] :
( hBOOL(hAPP(X28,X7))
| ~ c_in(X7,c_List_Oset(c_List_OtakeWhile(X28,X13,X2),X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).
fof(f2549,plain,
spl0_271,
inference(avatar_split_clause,[],[f159,f2547]) ).
fof(f2547,plain,
( spl0_271
<=> ! [X13,X2,X0,X7] : c_List_Onth(c_List_Olist_OCons(X7,X13,X2),c_Suc(X0),X2) = c_List_Onth(X13,X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f159,axiom,
! [X2,X0,X7,X13] : c_List_Onth(c_List_Olist_OCons(X7,X13,X2),c_Suc(X0),X2) = c_List_Onth(X13,X0,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons__Suc_0) ).
fof(f2544,plain,
spl0_270,
inference(avatar_split_clause,[],[f152,f2542]) ).
fof(f2542,plain,
( spl0_270
<=> ! [X2,X21,X7] : ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X7,X21,X2),tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X21,tc_List_Olist(X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f152,axiom,
! [X2,X21,X7] : ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X7,X21,X2),tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X21,tc_List_Olist(X2)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
fof(f2540,plain,
spl0_269,
inference(avatar_split_clause,[],[f150,f2538]) ).
fof(f2538,plain,
( spl0_269
<=> ! [X2,X7,X25] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X7,X25,X2),tc_List_Olist(X2)) = c_Suc(c_Nat_Osize__class_Osize(X25,tc_List_Olist(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f150,axiom,
! [X2,X7,X25] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X7,X25,X2),tc_List_Olist(X2)) = c_Suc(c_Nat_Osize__class_Osize(X25,tc_List_Olist(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
fof(f2536,plain,
spl0_268,
inference(avatar_split_clause,[],[f147,f2534]) ).
fof(f2534,plain,
( spl0_268
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Suc(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f147,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),c_Suc(X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f2532,plain,
spl0_267,
inference(avatar_split_clause,[],[f105,f2530]) ).
fof(f2530,plain,
( spl0_267
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| X7 = X9
| ~ c_lessequals(X7,X9,X2)
| c_HOL_Oord__class_Oless(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f105,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| X7 = X9
| ~ c_lessequals(X7,X9,X2)
| c_HOL_Oord__class_Oless(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f2528,plain,
spl0_266,
inference(avatar_split_clause,[],[f95,f2526]) ).
fof(f2526,plain,
( spl0_266
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| X3 = X4
| ~ c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f95,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| X3 = X4
| ~ c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
fof(f2524,plain,
spl0_265,
inference(avatar_split_clause,[],[f94,f2522]) ).
fof(f2522,plain,
( spl0_265
<=> ! [X0,X10] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(X10),tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f94,axiom,
! [X10,X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(X10),tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f2520,plain,
( ~ spl0_264
| spl0_260
| ~ spl0_115
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2416,f2243,f1264,f2424,f2517]) ).
fof(f2517,plain,
( spl0_264
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2424,plain,
( spl0_260
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1264,plain,
( spl0_115
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f2243,plain,
( spl0_237
<=> ! [X2,X3,X4] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2416,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_115
| ~ spl0_237 ),
inference(trivial_inequality_removal,[],[f2414]) ).
fof(f2414,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_115
| ~ spl0_237 ),
inference(superposition,[],[f2244,f1265]) ).
fof(f1265,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f2244,plain,
( ! [X2,X3,X4] :
( c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X3,X4,X2)
| X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X2) )
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2243]) ).
fof(f2515,plain,
spl0_263,
inference(avatar_split_clause,[],[f66,f2513]) ).
fof(f2513,plain,
( spl0_263
<=> ! [X2,X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ominus__class_Ominus(X3,X4,X2)),X4) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f66,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ominus__class_Ominus(X3,X4,X2)),X4) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2511,plain,
spl0_262,
inference(avatar_split_clause,[],[f41,f2509]) ).
fof(f2509,plain,
( spl0_262
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| X7 = X9
| ~ c_lessequals(X7,X9,X2)
| ~ c_lessequals(X9,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f41,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| X7 = X9
| ~ c_lessequals(X7,X9,X2)
| ~ c_lessequals(X9,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f2507,plain,
spl0_261,
inference(avatar_split_clause,[],[f29,f2505]) ).
fof(f2505,plain,
( spl0_261
<=> ! [X11,X12,X10] :
( ~ c_HOL_Oord__class_Oless(X10,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X10),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f29,axiom,
! [X10,X11,X12] :
( ~ c_HOL_Oord__class_Oless(X10,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X10),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f2426,plain,
( ~ spl0_259
| spl0_260
| ~ spl0_115
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2411,f2239,f1264,f2424,f2420]) ).
fof(f2420,plain,
( spl0_259
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2239,plain,
( spl0_236
<=> ! [X2,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2411,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_115
| ~ spl0_236 ),
inference(trivial_inequality_removal,[],[f2409]) ).
fof(f2409,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_115
| ~ spl0_236 ),
inference(superposition,[],[f2240,f1265]) ).
fof(f2240,plain,
( ! [X2,X3,X4] :
( c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X3,X4,X2)
| X3 = X4
| ~ class_OrderedGroup_Ogroup__add(X2) )
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2239]) ).
fof(f2360,plain,
( spl0_258
| ~ spl0_50
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1543,f1420,f986,f2358]) ).
fof(f2358,plain,
( spl0_258
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f986,plain,
( spl0_50
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1420,plain,
( spl0_149
<=> ! [X2,X7] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1543,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
| ~ spl0_50
| ~ spl0_149 ),
inference(resolution,[],[f1421,f988]) ).
fof(f988,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f1421,plain,
( ! [X2,X7] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X7,X7,X2) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1420]) ).
fof(f2325,plain,
spl0_257,
inference(avatar_split_clause,[],[f643,f2323]) ).
fof(f2323,plain,
( spl0_257
<=> ! [X52,X10] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X52))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X52),X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f643,axiom,
! [X10,X52] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X52))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X52),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f2321,plain,
spl0_256,
inference(avatar_split_clause,[],[f636,f2319]) ).
fof(f2319,plain,
( spl0_256
<=> ! [X67,X3,X69,X2,X68] :
( X3 = X68
| c_List_Olist_OCons(X3,X67,X2) != c_List_Olist_OCons(X68,X69,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f636,axiom,
! [X2,X3,X68,X69,X67] :
( X3 = X68
| c_List_Olist_OCons(X3,X67,X2) != c_List_Olist_OCons(X68,X69,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
fof(f2317,plain,
spl0_255,
inference(avatar_split_clause,[],[f635,f2315]) ).
fof(f2315,plain,
( spl0_255
<=> ! [X67,X3,X69,X2,X68] :
( X67 = X69
| c_List_Olist_OCons(X3,X67,X2) != c_List_Olist_OCons(X68,X69,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f635,axiom,
! [X2,X3,X68,X69,X67] :
( X67 = X69
| c_List_Olist_OCons(X3,X67,X2) != c_List_Olist_OCons(X68,X69,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
fof(f2313,plain,
spl0_254,
inference(avatar_split_clause,[],[f478,f2311]) ).
fof(f2311,plain,
( spl0_254
<=> ! [X2,X0,X1] :
( ~ class_Nat_Osemiring__char__0(X2)
| X0 = X1
| c_Nat_Osemiring__1__class_Oof__nat(X1,X2) != c_Nat_Osemiring__1__class_Oof__nat(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f478,axiom,
! [X2,X0,X1] :
( ~ class_Nat_Osemiring__char__0(X2)
| X0 = X1
| c_Nat_Osemiring__1__class_Oof__nat(X1,X2) != c_Nat_Osemiring__1__class_Oof__nat(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f2309,plain,
spl0_253,
inference(avatar_split_clause,[],[f470,f2307]) ).
fof(f2307,plain,
( spl0_253
<=> ! [X13,X2,X21] : c_List_Otake(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),c_List_Oappend(X13,X21,X2),X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f470,axiom,
! [X2,X21,X13] : c_List_Otake(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),c_List_Oappend(X13,X21,X2),X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
fof(f2305,plain,
spl0_252,
inference(avatar_split_clause,[],[f461,f2303]) ).
fof(f2303,plain,
( spl0_252
<=> ! [X32,X13,X21,X2] :
( X21 = X32
| c_List_Oappend(X13,X21,X2) != c_List_Oappend(X13,X32,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f461,axiom,
! [X2,X21,X32,X13] :
( X21 = X32
| c_List_Oappend(X13,X21,X2) != c_List_Oappend(X13,X32,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
fof(f2301,plain,
spl0_251,
inference(avatar_split_clause,[],[f460,f2299]) ).
fof(f2299,plain,
( spl0_251
<=> ! [X32,X13,X21,X2] :
( X21 = X32
| c_List_Oappend(X21,X13,X2) != c_List_Oappend(X32,X13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f460,axiom,
! [X2,X21,X32,X13] :
( X21 = X32
| c_List_Oappend(X21,X13,X2) != c_List_Oappend(X32,X13,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
fof(f2297,plain,
spl0_250,
inference(avatar_split_clause,[],[f459,f2295]) ).
fof(f2295,plain,
( spl0_250
<=> ! [X0,X7,X9,X2,X1] :
( X0 = X1
| c_List_Oreplicate(X0,X9,X2) != c_List_Oreplicate(X1,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f459,axiom,
! [X2,X0,X1,X9,X7] :
( X0 = X1
| c_List_Oreplicate(X0,X9,X2) != c_List_Oreplicate(X1,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
fof(f2293,plain,
( spl0_249
| ~ spl0_50
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1542,f1416,f986,f2291]) ).
fof(f2291,plain,
( spl0_249
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f1416,plain,
( spl0_148
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1542,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_50
| ~ spl0_148 ),
inference(resolution,[],[f1417,f988]) ).
fof(f1417,plain,
( ! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f2289,plain,
spl0_248,
inference(avatar_split_clause,[],[f440,f2287]) ).
fof(f2287,plain,
( spl0_248
<=> ! [X11,X13,X2,X7] :
( c_List_Olist_ONil(X2) = X13
| c_List_Olist_ONil(X2) != c_List_Olist__update(X13,X11,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f440,axiom,
! [X2,X11,X7,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Olist_ONil(X2) != c_List_Olist__update(X13,X11,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
fof(f2285,plain,
spl0_247,
inference(avatar_split_clause,[],[f406,f2283]) ).
fof(f2283,plain,
( spl0_247
<=> ! [X13,X29,X22,X2] :
( c_List_Olist_ONil(X29) = X13
| c_List_Omap(X22,X13,X29,X2) != c_List_Olist_ONil(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f406,axiom,
! [X2,X29,X22,X13] :
( c_List_Olist_ONil(X29) = X13
| c_List_Omap(X22,X13,X29,X2) != c_List_Olist_ONil(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
fof(f2281,plain,
spl0_246,
inference(avatar_split_clause,[],[f400,f2279]) ).
fof(f2279,plain,
( spl0_246
<=> ! [X13,X2,X7] : c_List_Obutlast(c_List_Oappend(X13,c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2),X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f400,axiom,
! [X2,X7,X13] : c_List_Obutlast(c_List_Oappend(X13,c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2),X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
fof(f2277,plain,
spl0_245,
inference(avatar_split_clause,[],[f399,f2275]) ).
fof(f2275,plain,
( spl0_245
<=> ! [X13,X2,X7] : c_List_Olast(c_List_Oappend(X13,c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f399,axiom,
! [X2,X7,X13] : c_List_Olast(c_List_Oappend(X13,c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2),X2) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
fof(f2273,plain,
spl0_244,
inference(avatar_split_clause,[],[f397,f2271]) ).
fof(f2271,plain,
( spl0_244
<=> ! [X13,X2] :
( c_List_Olist_ONil(X2) = X13
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f397,axiom,
! [X2,X13] :
( c_List_Olist_ONil(X2) = X13
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
fof(f2269,plain,
spl0_243,
inference(avatar_split_clause,[],[f301,f2267]) ).
fof(f2267,plain,
( spl0_243
<=> ! [X13,X2,X21] : c_List_Odrop(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),c_List_Oappend(X13,X21,X2),X2) = X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f301,axiom,
! [X2,X21,X13] : c_List_Odrop(c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)),c_List_Oappend(X13,X21,X2),X2) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
fof(f2265,plain,
spl0_242,
inference(avatar_split_clause,[],[f295,f2263]) ).
fof(f2263,plain,
( spl0_242
<=> ! [X13,X2,X0] : c_List_Oappend(c_List_Otake(X0,X13,X2),c_List_Odrop(X0,X13,X2),X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f295,axiom,
! [X2,X0,X13] : c_List_Oappend(c_List_Otake(X0,X13,X2),c_List_Odrop(X0,X13,X2),X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
fof(f2261,plain,
spl0_241,
inference(avatar_split_clause,[],[f293,f2259]) ).
fof(f2259,plain,
( spl0_241
<=> ! [X2,X0,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Olast(c_List_Oreplicate(X0,X7,X2),X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f293,axiom,
! [X2,X0,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Olast(c_List_Oreplicate(X0,X7,X2),X2) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__replicate_0) ).
fof(f2257,plain,
spl0_240,
inference(avatar_split_clause,[],[f280,f2255]) ).
fof(f2255,plain,
( spl0_240
<=> ! [X41,X2] :
( c_List_Olist_ONil(X2) = X41
| c_in(c_List_Olast(X41,X2),c_List_Oset(X41,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f280,axiom,
! [X2,X41] :
( c_List_Olist_ONil(X2) = X41
| c_in(c_List_Olast(X41,X2),c_List_Oset(X41,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__in__set_0) ).
fof(f2253,plain,
spl0_239,
inference(avatar_split_clause,[],[f257,f2251]) ).
fof(f2251,plain,
( spl0_239
<=> ! [X34,X7,X25,X2] : c_in(X7,c_List_Oset(c_List_Oappend(X25,c_List_Olist_OCons(X7,X34,X2),X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f257,axiom,
! [X2,X7,X34,X25] : c_in(X7,c_List_Oset(c_List_Oappend(X25,c_List_Olist_OCons(X7,X34,X2),X2),X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).
fof(f2249,plain,
( spl0_238
| ~ spl0_111
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1527,f1407,f1248,f2247]) ).
fof(f2247,plain,
( spl0_238
<=> ! [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_238])]) ).
fof(f1248,plain,
( spl0_111
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1407,plain,
( spl0_146
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1527,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_111
| ~ spl0_146 ),
inference(resolution,[],[f1408,f1249]) ).
fof(f1249,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_Suc(X1),tc_nat)
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f1408,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f2245,plain,
spl0_237,
inference(avatar_split_clause,[],[f225,f2243]) ).
fof(f225,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f2241,plain,
spl0_236,
inference(avatar_split_clause,[],[f224,f2239]) ).
fof(f224,axiom,
! [X2,X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f2237,plain,
spl0_235,
inference(avatar_split_clause,[],[f208,f2235]) ).
fof(f2235,plain,
( spl0_235
<=> ! [X13,X2] :
( c_List_Olist_ONil(X2) = X13
| c_in(c_List_Ohd(X13,X2),c_List_Oset(X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f208,axiom,
! [X2,X13] :
( c_List_Olist_ONil(X2) = X13
| c_in(c_List_Ohd(X13,X2),c_List_Oset(X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__in__set_0) ).
fof(f2233,plain,
spl0_234,
inference(avatar_split_clause,[],[f175,f2231]) ).
fof(f2231,plain,
( spl0_234
<=> ! [X2,X0,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Ohd(c_List_Oreplicate(X0,X7,X2),X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f175,axiom,
! [X2,X0,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Ohd(c_List_Oreplicate(X0,X7,X2),X2) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__replicate_0) ).
fof(f2229,plain,
spl0_233,
inference(avatar_split_clause,[],[f165,f2227]) ).
fof(f2227,plain,
( spl0_233
<=> ! [X0,X9,X2,X7] :
( X7 = X9
| ~ c_in(X7,c_List_Oset(c_List_Oreplicate(X0,X9,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f165,axiom,
! [X2,X0,X9,X7] :
( X7 = X9
| ~ c_in(X7,c_List_Oset(c_List_Oreplicate(X0,X9,X2),X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).
fof(f2225,plain,
spl0_232,
inference(avatar_split_clause,[],[f143,f2223]) ).
fof(f2223,plain,
( spl0_232
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f143,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2221,plain,
spl0_231,
inference(avatar_split_clause,[],[f142,f2219]) ).
fof(f2219,plain,
( spl0_231
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f142,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2217,plain,
spl0_230,
inference(avatar_split_clause,[],[f131,f2215]) ).
fof(f2215,plain,
( spl0_230
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Oone__class_Oone(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f131,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Oone__class_Oone(X2)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f2213,plain,
spl0_229,
inference(avatar_split_clause,[],[f49,f2211]) ).
fof(f2211,plain,
( spl0_229
<=> ! [X0,X1] :
( X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f49,axiom,
! [X0,X1] :
( X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
fof(f2209,plain,
spl0_228,
inference(avatar_split_clause,[],[f8,f2207]) ).
fof(f2207,plain,
( spl0_228
<=> ! [X11,X12,X10] :
( ~ c_lessequals(X10,X12,tc_nat)
| ~ c_lessequals(X12,X11,tc_nat)
| c_lessequals(X10,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f8,axiom,
! [X10,X11,X12] :
( ~ c_lessequals(X10,X12,tc_nat)
| ~ c_lessequals(X12,X11,tc_nat)
| c_lessequals(X10,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2198,plain,
spl0_227,
inference(avatar_split_clause,[],[f1,f2196]) ).
fof(f2196,plain,
( spl0_227
<=> ! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f2046,plain,
( spl0_226
| ~ spl0_142
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1634,f1565,f1391,f2044]) ).
fof(f2044,plain,
( spl0_226
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1391,plain,
( spl0_142
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1565,plain,
( spl0_164
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1634,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_142
| ~ spl0_164 ),
inference(resolution,[],[f1566,f1392]) ).
fof(f1392,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1391]) ).
fof(f1566,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1565]) ).
fof(f2008,plain,
spl0_225,
inference(avatar_split_clause,[],[f582,f2006]) ).
fof(f2006,plain,
( spl0_225
<=> ! [X2,X0,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Olist_ONil(X2) != c_List_Oreplicate(X0,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f582,axiom,
! [X2,X0,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Olist_ONil(X2) != c_List_Oreplicate(X0,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
fof(f2004,plain,
spl0_224,
inference(avatar_split_clause,[],[f581,f2002]) ).
fof(f2002,plain,
( spl0_224
<=> ! [X13,X2] :
( c_List_Olist_ONil(X2) = X13
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f581,axiom,
! [X2,X13] :
( c_List_Olist_ONil(X2) = X13
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
fof(f2000,plain,
spl0_223,
inference(avatar_split_clause,[],[f559,f1998]) ).
fof(f1998,plain,
( spl0_223
<=> ! [X48,X14,X50,X49,X2] : hAPP(X48,X14) = c_Lambda_OdB_OdB__case(X48,X49,X50,c_Lambda_OdB_OVar(X14),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f559,axiom,
! [X50,X2,X48,X49,X14] : hAPP(X48,X14) = c_Lambda_OdB_OdB__case(X48,X49,X50,c_Lambda_OdB_OVar(X14),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
fof(f1996,plain,
spl0_222,
inference(avatar_split_clause,[],[f545,f1994]) ).
fof(f1994,plain,
( spl0_222
<=> ! [X13,X2] : c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orev(X13,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f545,axiom,
! [X2,X13] : c_Nat_Osize__class_Osize(X13,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orev(X13,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
fof(f1992,plain,
spl0_221,
inference(avatar_split_clause,[],[f541,f1990]) ).
fof(f1990,plain,
( spl0_221
<=> ! [X13,X2,X21] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(X21,X2)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X13,X21,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f541,axiom,
! [X2,X21,X13] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(X21,X2)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X13,X21,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
fof(f1988,plain,
spl0_220,
inference(avatar_split_clause,[],[f540,f1986]) ).
fof(f1986,plain,
( spl0_220
<=> ! [X13,X2,X21] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(X13,X2)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X13,X21,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f540,axiom,
! [X2,X21,X13] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(X13,X2)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X13,X21,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
fof(f1984,plain,
spl0_219,
inference(avatar_split_clause,[],[f522,f1982]) ).
fof(f1982,plain,
( spl0_219
<=> ! [X13,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_List_Olistsum(X13,X2) = c_List_Olistsum(c_List_Orev(X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f522,axiom,
! [X2,X13] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_List_Olistsum(X13,X2) = c_List_Olistsum(c_List_Orev(X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__rev_0) ).
fof(f1980,plain,
spl0_218,
inference(avatar_split_clause,[],[f509,f1978]) ).
fof(f1978,plain,
( spl0_218
<=> ! [X9,X7] :
( X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f509,axiom,
! [X9,X7] :
( X7 = X9
| c_HOL_Oord__class_Oless(X7,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f1976,plain,
( spl0_217
| ~ spl0_131
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1491,f1359,f1339,f1974]) ).
fof(f1974,plain,
( spl0_217
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1339,plain,
( spl0_131
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1359,plain,
( spl0_134
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1491,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_131
| ~ spl0_134 ),
inference(resolution,[],[f1340,f1360]) ).
fof(f1360,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X1),X0,tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f1340,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f1972,plain,
spl0_216,
inference(avatar_split_clause,[],[f477,f1970]) ).
fof(f1970,plain,
( spl0_216
<=> ! [X2,X0,X7] : c_List_Oreplicate(X0,X7,X2) = c_List_Orev(c_List_Oreplicate(X0,X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f477,axiom,
! [X2,X0,X7] : c_List_Oreplicate(X0,X7,X2) = c_List_Orev(c_List_Oreplicate(X0,X7,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
fof(f1968,plain,
spl0_215,
inference(avatar_split_clause,[],[f462,f1966]) ).
fof(f1966,plain,
( spl0_215
<=> ! [X13,X2,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X13,X2)
| c_List_Olinorder__class_Osorted(c_List_Otake(X0,X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f462,axiom,
! [X2,X0,X13] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X13,X2)
| c_List_Olinorder__class_Osorted(c_List_Otake(X0,X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__take_0) ).
fof(f1964,plain,
spl0_214,
inference(avatar_split_clause,[],[f420,f1962]) ).
fof(f1962,plain,
( spl0_214
<=> ! [X13,X2,X21] :
( c_List_Olist_ONil(X2) = X13
| c_List_Oappend(X13,X21,X2) != c_List_Olist_ONil(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f420,axiom,
! [X2,X21,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Oappend(X13,X21,X2) != c_List_Olist_ONil(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
fof(f1960,plain,
spl0_213,
inference(avatar_split_clause,[],[f417,f1958]) ).
fof(f1958,plain,
( spl0_213
<=> ! [X13,X2,X21] :
( c_List_Olist_ONil(X2) = X21
| c_List_Oappend(X13,X21,X2) != c_List_Olist_ONil(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f417,axiom,
! [X2,X21,X13] :
( c_List_Olist_ONil(X2) = X21
| c_List_Oappend(X13,X21,X2) != c_List_Olist_ONil(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
fof(f1956,plain,
spl0_212,
inference(avatar_split_clause,[],[f395,f1954]) ).
fof(f1954,plain,
( spl0_212
<=> ! [X13,X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(X13,X2)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X7,X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f395,axiom,
! [X2,X7,X13] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(X13,X2)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X7,X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
fof(f1952,plain,
spl0_211,
inference(avatar_split_clause,[],[f376,f1950]) ).
fof(f1950,plain,
( spl0_211
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f376,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1948,plain,
spl0_210,
inference(avatar_split_clause,[],[f375,f1946]) ).
fof(f1946,plain,
( spl0_210
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f375,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1944,plain,
spl0_209,
inference(avatar_split_clause,[],[f374,f1942]) ).
fof(f1942,plain,
( spl0_209
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f374,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1940,plain,
spl0_208,
inference(avatar_split_clause,[],[f373,f1938]) ).
fof(f1938,plain,
( spl0_208
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f373,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1936,plain,
spl0_207,
inference(avatar_split_clause,[],[f372,f1934]) ).
fof(f1934,plain,
( spl0_207
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f372,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1932,plain,
( spl0_206
| ~ spl0_131
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1490,f1371,f1339,f1930]) ).
fof(f1930,plain,
( spl0_206
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1371,plain,
( spl0_137
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1490,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_131
| ~ spl0_137 ),
inference(resolution,[],[f1340,f1372]) ).
fof(f1372,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f1928,plain,
spl0_205,
inference(avatar_split_clause,[],[f370,f1926]) ).
fof(f1926,plain,
( spl0_205
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f370,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1924,plain,
spl0_204,
inference(avatar_split_clause,[],[f329,f1922]) ).
fof(f1922,plain,
( spl0_204
<=> ! [X48,X51,X50,X49,X2] : c_Lambda_OdB_OdB__case(X48,X49,X50,c_Lambda_OdB_OAbs(X51),X2) = hAPP(X50,X51) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f329,axiom,
! [X50,X2,X51,X48,X49] : c_Lambda_OdB_OdB__case(X48,X49,X50,c_Lambda_OdB_OAbs(X51),X2) = hAPP(X50,X51),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
fof(f1920,plain,
spl0_203,
inference(avatar_split_clause,[],[f328,f1918]) ).
fof(f1918,plain,
( spl0_203
<=> ! [X31,X13,X21,X2] :
( c_List_Olistsp(X31,X21,X2)
| ~ c_List_Olistsp(X31,c_List_Oappend(X13,X21,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f328,axiom,
! [X31,X21,X2,X13] :
( c_List_Olistsp(X31,X21,X2)
| ~ c_List_Olistsp(X31,c_List_Oappend(X13,X21,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
fof(f1916,plain,
spl0_202,
inference(avatar_split_clause,[],[f327,f1914]) ).
fof(f1914,plain,
( spl0_202
<=> ! [X31,X13,X21,X2] :
( c_List_Olistsp(X31,X13,X2)
| ~ c_List_Olistsp(X31,c_List_Oappend(X13,X21,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f327,axiom,
! [X31,X2,X21,X13] :
( c_List_Olistsp(X31,X13,X2)
| ~ c_List_Olistsp(X31,c_List_Oappend(X13,X21,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
fof(f1912,plain,
spl0_201,
inference(avatar_split_clause,[],[f325,f1910]) ).
fof(f1910,plain,
( spl0_201
<=> ! [X13,X2,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X13,X2)
| c_List_Olinorder__class_Osorted(c_List_Odrop(X0,X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f325,axiom,
! [X2,X0,X13] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X13,X2)
| c_List_Olinorder__class_Osorted(c_List_Odrop(X0,X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
fof(f1908,plain,
spl0_200,
inference(avatar_split_clause,[],[f296,f1906]) ).
fof(f1906,plain,
( spl0_200
<=> ! [X13,X2,X28] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X13,X2)
| c_List_Olinorder__class_Osorted(c_List_OtakeWhile(X28,X13,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f296,axiom,
! [X2,X28,X13] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_List_Olinorder__class_Osorted(X13,X2)
| c_List_Olinorder__class_Osorted(c_List_OtakeWhile(X28,X13,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).
fof(f1904,plain,
spl0_199,
inference(avatar_split_clause,[],[f217,f1902]) ).
fof(f1902,plain,
( spl0_199
<=> ! [X2,X7] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f217,axiom,
! [X2,X7] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f1900,plain,
spl0_198,
inference(avatar_split_clause,[],[f97,f1898]) ).
fof(f1898,plain,
( spl0_198
<=> ! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f97,axiom,
! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
fof(f1896,plain,
spl0_197,
inference(avatar_split_clause,[],[f63,f1894]) ).
fof(f1894,plain,
( spl0_197
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f63,axiom,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f1892,plain,
spl0_196,
inference(avatar_split_clause,[],[f62,f1890]) ).
fof(f1890,plain,
( spl0_196
<=> ! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f62,axiom,
! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f1880,plain,
spl0_195,
inference(avatar_split_clause,[],[f51,f1878]) ).
fof(f1878,plain,
( spl0_195
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f51,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f1876,plain,
spl0_194,
inference(avatar_split_clause,[],[f46,f1874]) ).
fof(f1874,plain,
( spl0_194
<=> ! [X12,X0,X11] :
( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X0,tc_nat),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f46,axiom,
! [X0,X11,X12] :
( ~ c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X12,X0,tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f1872,plain,
spl0_193,
inference(avatar_split_clause,[],[f42,f1870]) ).
fof(f1870,plain,
( spl0_193
<=> ! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f42,axiom,
! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1835,plain,
( spl0_192
| ~ spl0_83
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1716,f1585,f1132,f1833]) ).
fof(f1833,plain,
( spl0_192
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1132,plain,
( spl0_83
<=> ! [X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1585,plain,
( spl0_168
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X9,X7,X2)
| c_HOL_Oord__class_Oless(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1716,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_83
| ~ spl0_168 ),
inference(duplicate_literal_removal,[],[f1708]) ).
fof(f1708,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_83
| ~ spl0_168 ),
inference(resolution,[],[f1586,f1133]) ).
fof(f1133,plain,
( ! [X2,X7] :
( ~ c_HOL_Oord__class_Oless(X7,X7,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f1586,plain,
( ! [X2,X9,X7] :
( c_HOL_Oord__class_Oless(X7,X9,X2)
| c_lessequals(X9,X7,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1585]) ).
fof(f1683,plain,
spl0_191,
inference(avatar_split_clause,[],[f596,f1681]) ).
fof(f1681,plain,
( spl0_191
<=> ! [X2,X7] : c_List_Olist_ONil(X2) = c_List_Obutlast(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f596,axiom,
! [X2,X7] : c_List_Olist_ONil(X2) = c_List_Obutlast(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
fof(f1679,plain,
( spl0_190
| ~ spl0_68
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1476,f1355,f1072,f1677]) ).
fof(f1072,plain,
( spl0_68
<=> ! [X0] : ~ c_lessequals(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1476,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_68
| ~ spl0_133 ),
inference(resolution,[],[f1356,f1073]) ).
fof(f1073,plain,
( ! [X0] : ~ c_lessequals(c_Suc(X0),X0,tc_nat)
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1675,plain,
spl0_189,
inference(avatar_split_clause,[],[f576,f1673]) ).
fof(f1673,plain,
( spl0_189
<=> ! [X13,X2,X7] : c_List_Onth(c_List_Olist_OCons(X7,X13,X2),c_HOL_Ozero__class_Ozero(tc_nat),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f576,axiom,
! [X2,X7,X13] : c_List_Onth(c_List_Olist_OCons(X7,X13,X2),c_HOL_Ozero__class_Ozero(tc_nat),X2) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).
fof(f1671,plain,
spl0_188,
inference(avatar_split_clause,[],[f558,f1669]) ).
fof(f1669,plain,
( spl0_188
<=> ! [X60,X62,X10] :
( ~ c_Type_Otyping(X60,c_Lambda_OdB_OVar(X10),X62)
| hAPP(X60,X10) = X62 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f558,axiom,
! [X10,X62,X60] :
( ~ c_Type_Otyping(X60,c_Lambda_OdB_OVar(X10),X62)
| hAPP(X60,X10) = X62 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f1667,plain,
spl0_187,
inference(avatar_split_clause,[],[f556,f1665]) ).
fof(f1665,plain,
( spl0_187
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f556,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1663,plain,
spl0_186,
inference(avatar_split_clause,[],[f555,f1661]) ).
fof(f1661,plain,
( spl0_186
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f555,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1659,plain,
spl0_185,
inference(avatar_split_clause,[],[f554,f1657]) ).
fof(f1657,plain,
( spl0_185
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f554,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1655,plain,
spl0_184,
inference(avatar_split_clause,[],[f525,f1653]) ).
fof(f1653,plain,
( spl0_184
<=> ! [X13,X2,X10] : c_List_Olist__update(X13,X10,c_List_Onth(X13,X10,X2),X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f525,axiom,
! [X2,X10,X13] : c_List_Olist__update(X13,X10,c_List_Onth(X13,X10,X2),X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__id_0) ).
fof(f1651,plain,
spl0_183,
inference(avatar_split_clause,[],[f518,f1649]) ).
fof(f1649,plain,
( spl0_183
<=> ! [X13,X2,X21] :
( X13 = X21
| c_List_Orev(X13,X2) != c_List_Orev(X21,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f518,axiom,
! [X2,X21,X13] :
( X13 = X21
| c_List_Orev(X13,X2) != c_List_Orev(X21,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
fof(f1647,plain,
spl0_182,
inference(avatar_split_clause,[],[f455,f1645]) ).
fof(f1645,plain,
( spl0_182
<=> ! [X11,X47] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X11)),X47),X11) = X47 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f455,axiom,
! [X11,X47] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X11)),X47),X11) = X47,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f1643,plain,
spl0_181,
inference(avatar_split_clause,[],[f416,f1641]) ).
fof(f1641,plain,
( spl0_181
<=> ! [X13,X2] :
( c_List_Olist_ONil(X2) = X13
| c_List_Orev(X13,X2) != c_List_Olist_ONil(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f416,axiom,
! [X2,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Orev(X13,X2) != c_List_Olist_ONil(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
fof(f1639,plain,
spl0_180,
inference(avatar_split_clause,[],[f412,f1637]) ).
fof(f1637,plain,
( spl0_180
<=> ! [X13,X2,X21] :
( c_List_Olist_ONil(X2) = X21
| c_List_Oappend(X13,X21,X2) != X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f412,axiom,
! [X2,X21,X13] :
( c_List_Olist_ONil(X2) = X21
| c_List_Oappend(X13,X21,X2) != X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
fof(f1632,plain,
spl0_179,
inference(avatar_split_clause,[],[f410,f1630]) ).
fof(f1630,plain,
( spl0_179
<=> ! [X13,X2,X21] :
( c_List_Olist_ONil(X2) = X13
| c_List_Oappend(X13,X21,X2) != X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f410,axiom,
! [X2,X21,X13] :
( c_List_Olist_ONil(X2) = X13
| c_List_Oappend(X13,X21,X2) != X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
fof(f1628,plain,
spl0_178,
inference(avatar_split_clause,[],[f215,f1626]) ).
fof(f1626,plain,
( spl0_178
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f215,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
fof(f1624,plain,
spl0_177,
inference(avatar_split_clause,[],[f214,f1622]) ).
fof(f1622,plain,
( spl0_177
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f214,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f1620,plain,
spl0_176,
inference(avatar_split_clause,[],[f154,f1618]) ).
fof(f1618,plain,
( spl0_176
<=> ! [X2,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X7,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f154,axiom,
! [X2,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X7,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f1616,plain,
spl0_175,
inference(avatar_split_clause,[],[f153,f1614]) ).
fof(f1614,plain,
( spl0_175
<=> ! [X2,X3] :
( ~ class_Power_Opower(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f153,axiom,
! [X2,X3] :
( ~ class_Power_Opower(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f1612,plain,
spl0_174,
inference(avatar_split_clause,[],[f139,f1610]) ).
fof(f1610,plain,
( spl0_174
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f139,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1608,plain,
spl0_173,
inference(avatar_split_clause,[],[f109,f1606]) ).
fof(f1606,plain,
( spl0_173
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X7,X9,X2)
| c_lessequals(X9,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f109,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X7,X9,X2)
| c_lessequals(X9,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1604,plain,
spl0_172,
inference(avatar_split_clause,[],[f107,f1602]) ).
fof(f1602,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f107,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f1600,plain,
spl0_171,
inference(avatar_split_clause,[],[f106,f1598]) ).
fof(f1598,plain,
( spl0_171
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f106,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f1596,plain,
spl0_170,
inference(avatar_split_clause,[],[f83,f1594]) ).
fof(f1594,plain,
( spl0_170
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f83,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1591,plain,
spl0_169,
inference(avatar_split_clause,[],[f79,f1589]) ).
fof(f1589,plain,
( spl0_169
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f79,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X9,X7,X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f1587,plain,
spl0_168,
inference(avatar_split_clause,[],[f76,f1585]) ).
fof(f76,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X9,X7,X2)
| c_HOL_Oord__class_Oless(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1583,plain,
spl0_167,
inference(avatar_split_clause,[],[f75,f1581]) ).
fof(f1581,plain,
( spl0_167
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f75,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X2),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1579,plain,
spl0_166,
inference(avatar_split_clause,[],[f34,f1577]) ).
fof(f1577,plain,
( spl0_166
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| c_lessequals(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f34,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| c_lessequals(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1575,plain,
spl0_165,
inference(avatar_split_clause,[],[f33,f1573]) ).
fof(f1573,plain,
( spl0_165
<=> ! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| c_lessequals(X7,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f33,axiom,
! [X2,X9,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X9,X2)
| c_lessequals(X7,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1567,plain,
( spl0_164
| ~ spl0_63
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1507,f1391,f1049,f1565]) ).
fof(f1049,plain,
( spl0_63
<=> ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1507,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_63
| ~ spl0_142 ),
inference(resolution,[],[f1392,f1050]) ).
fof(f1050,plain,
( ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f1541,plain,
( spl0_163
| ~ spl0_75
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1347,f1276,f1100,f1539]) ).
fof(f1539,plain,
( spl0_163
<=> ! [X0,X1] : c_in(c_Lambda_OdB_OVar(X0),c_InductTermi_OIT,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1100,plain,
( spl0_75
<=> ! [X0] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1276,plain,
( spl0_118
<=> ! [X2,X7,X46] :
( ~ hBOOL(hAPP(X46,X7))
| c_in(X7,X46,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1347,plain,
( ! [X0,X1] : c_in(c_Lambda_OdB_OVar(X0),c_InductTermi_OIT,X1)
| ~ spl0_75
| ~ spl0_118 ),
inference(resolution,[],[f1277,f1101]) ).
fof(f1101,plain,
( ! [X0] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X0)))
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1100]) ).
fof(f1277,plain,
( ! [X2,X46,X7] :
( ~ hBOOL(hAPP(X46,X7))
| c_in(X7,X46,X2) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1475,plain,
spl0_162,
inference(avatar_split_clause,[],[f644,f1473]) ).
fof(f1473,plain,
( spl0_162
<=> ! [X29,X2,X22,X3] : c_List_Ofoldl(X22,X3,c_List_Olist_ONil(X29),X2,X29) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f644,axiom,
! [X2,X3,X29,X22] : c_List_Ofoldl(X22,X3,c_List_Olist_ONil(X29),X2,X29) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
fof(f1471,plain,
spl0_161,
inference(avatar_split_clause,[],[f605,f1469]) ).
fof(f1469,plain,
( spl0_161
<=> ! [X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f605,axiom,
! [X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
fof(f1467,plain,
spl0_160,
inference(avatar_split_clause,[],[f595,f1465]) ).
fof(f1465,plain,
( spl0_160
<=> ! [X2,X7] : c_List_Olast(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f595,axiom,
! [X2,X7] : c_List_Olast(c_List_Olist_OCons(X7,c_List_Olist_ONil(X2),X2),X2) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
fof(f1463,plain,
spl0_159,
inference(avatar_split_clause,[],[f575,f1461]) ).
fof(f575,axiom,
! [X2] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_List_Olistsum(c_List_Olist_ONil(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
fof(f1459,plain,
spl0_158,
inference(avatar_split_clause,[],[f574,f1457]) ).
fof(f574,axiom,
! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1455,plain,
spl0_157,
inference(avatar_split_clause,[],[f563,f1453]) ).
fof(f1453,plain,
( spl0_157
<=> ! [X18] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X18))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f563,axiom,
! [X18] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X18))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X18))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f1450,plain,
spl0_156,
inference(avatar_split_clause,[],[f524,f1448]) ).
fof(f1448,plain,
( spl0_156
<=> ! [X2,X0,X7] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X0,X7,X2),tc_List_Olist(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f524,axiom,
! [X2,X0,X7] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X0,X7,X2),tc_List_Olist(X2)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
fof(f1446,plain,
spl0_155,
inference(avatar_split_clause,[],[f435,f1444]) ).
fof(f1444,plain,
( spl0_155
<=> ! [X2,X27,X10] : c_List_Olist_ONil(X2) = c_List_Olist__update(c_List_Olist_ONil(X2),X10,X27,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f435,axiom,
! [X2,X10,X27] : c_List_Olist_ONil(X2) = c_List_Olist__update(c_List_Olist_ONil(X2),X10,X27,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
fof(f1442,plain,
spl0_154,
inference(avatar_split_clause,[],[f430,f1440]) ).
fof(f1440,plain,
( spl0_154
<=> ! [X29,X2,X22] : c_List_Olist_ONil(X2) = c_List_Omap(X22,c_List_Olist_ONil(X29),X29,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f430,axiom,
! [X2,X29,X22] : c_List_Olist_ONil(X2) = c_List_Omap(X22,c_List_Olist_ONil(X29),X29,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
fof(f1438,plain,
spl0_153,
inference(avatar_split_clause,[],[f378,f1436]) ).
fof(f1436,plain,
( spl0_153
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f378,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1434,plain,
spl0_152,
inference(avatar_split_clause,[],[f291,f1432]) ).
fof(f1432,plain,
( spl0_152
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f291,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1430,plain,
spl0_151,
inference(avatar_split_clause,[],[f230,f1428]) ).
fof(f1428,plain,
( spl0_151
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f230,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1426,plain,
spl0_150,
inference(avatar_split_clause,[],[f221,f1424]) ).
fof(f1424,plain,
( spl0_150
<=> ! [X2,X7] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f221,axiom,
! [X2,X7] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1422,plain,
spl0_149,
inference(avatar_split_clause,[],[f220,f1420]) ).
fof(f220,axiom,
! [X2,X7] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f1418,plain,
spl0_148,
inference(avatar_split_clause,[],[f219,f1416]) ).
fof(f219,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1414,plain,
spl0_147,
inference(avatar_split_clause,[],[f206,f1412]) ).
fof(f1412,plain,
( spl0_147
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f206,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1409,plain,
spl0_146,
inference(avatar_split_clause,[],[f205,f1407]) ).
fof(f205,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1405,plain,
spl0_145,
inference(avatar_split_clause,[],[f199,f1403]) ).
fof(f1403,plain,
( spl0_145
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f199,axiom,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1401,plain,
spl0_144,
inference(avatar_split_clause,[],[f198,f1399]) ).
fof(f1399,plain,
( spl0_144
<=> ! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f198,axiom,
! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1397,plain,
spl0_143,
inference(avatar_split_clause,[],[f136,f1395]) ).
fof(f1395,plain,
( spl0_143
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f136,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
fof(f1393,plain,
spl0_142,
inference(avatar_split_clause,[],[f88,f1391]) ).
fof(f88,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1389,plain,
spl0_141,
inference(avatar_split_clause,[],[f87,f1387]) ).
fof(f1387,plain,
( spl0_141
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f87,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1385,plain,
spl0_140,
inference(avatar_split_clause,[],[f72,f1383]) ).
fof(f1383,plain,
( spl0_140
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f72,axiom,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1381,plain,
spl0_139,
inference(avatar_split_clause,[],[f71,f1379]) ).
fof(f1379,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f71,axiom,
! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1377,plain,
spl0_138,
inference(avatar_split_clause,[],[f58,f1375]) ).
fof(f1375,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f58,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
fof(f1373,plain,
spl0_137,
inference(avatar_split_clause,[],[f57,f1371]) ).
fof(f57,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
fof(f1369,plain,
( spl0_136
| ~ spl0_65
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1346,f1276,f1058,f1367]) ).
fof(f1367,plain,
( spl0_136
<=> ! [X0] : c_in(v_ta____,c_InductTermi_OIT,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1058,plain,
( spl0_65
<=> hBOOL(hAPP(c_InductTermi_OIT,v_ta____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1346,plain,
( ! [X0] : c_in(v_ta____,c_InductTermi_OIT,X0)
| ~ spl0_65
| ~ spl0_118 ),
inference(resolution,[],[f1277,f1060]) ).
fof(f1060,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_ta____))
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f1365,plain,
spl0_135,
inference(avatar_split_clause,[],[f43,f1363]) ).
fof(f1363,plain,
( spl0_135
<=> ! [X13,X2] : c_List_Oset(c_List_Orev(X13,X2),X2) = c_List_Oset(X13,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f43,axiom,
! [X2,X13] : c_List_Oset(c_List_Orev(X13,X2),X2) = c_List_Oset(X13,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev_0) ).
fof(f1361,plain,
spl0_134,
inference(avatar_split_clause,[],[f21,f1359]) ).
fof(f21,axiom,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1357,plain,
spl0_133,
inference(avatar_split_clause,[],[f20,f1355]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1351,plain,
( spl0_132
| ~ spl0_64
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1345,f1276,f1053,f1349]) ).
fof(f1349,plain,
( spl0_132
<=> ! [X0] : c_in(v_s____,c_InductTermi_OIT,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1053,plain,
( spl0_64
<=> hBOOL(hAPP(c_InductTermi_OIT,v_s____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1345,plain,
( ! [X0] : c_in(v_s____,c_InductTermi_OIT,X0)
| ~ spl0_64
| ~ spl0_118 ),
inference(resolution,[],[f1277,f1055]) ).
fof(f1055,plain,
( hBOOL(hAPP(c_InductTermi_OIT,v_s____))
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1341,plain,
( spl0_131
| ~ spl0_69
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1327,f1232,f1076,f1339]) ).
fof(f1076,plain,
( spl0_69
<=> ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1232,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1327,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_69
| ~ spl0_107 ),
inference(resolution,[],[f1233,f1077]) ).
fof(f1077,plain,
( ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1076]) ).
fof(f1233,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f1326,plain,
spl0_130,
inference(avatar_split_clause,[],[f642,f1324]) ).
fof(f1324,plain,
( spl0_130
<=> ! [X70,X71,X14] : c_Lambda_OdB_OVar(X14) != hAPP(hAPP(c_Lambda_OdB_OApp,X70),X71) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f642,axiom,
! [X70,X71,X14] : c_Lambda_OdB_OVar(X14) != hAPP(hAPP(c_Lambda_OdB_OApp,X70),X71),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f1322,plain,
spl0_129,
inference(avatar_split_clause,[],[f632,f1320]) ).
fof(f1320,plain,
( spl0_129
<=> ! [X14,X15] :
( X14 = X15
| c_Lambda_OdB_OVar(X14) != c_Lambda_OdB_OVar(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f632,axiom,
! [X14,X15] :
( X14 = X15
| c_Lambda_OdB_OVar(X14) != c_Lambda_OdB_OVar(X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f1318,plain,
spl0_128,
inference(avatar_split_clause,[],[f586,f1316]) ).
fof(f1316,plain,
( spl0_128
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f586,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
fof(f1314,plain,
spl0_127,
inference(avatar_split_clause,[],[f585,f1312]) ).
fof(f1312,plain,
( spl0_127
<=> ! [X2,X7] : c_List_Olist_ONil(X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X7,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f585,axiom,
! [X2,X7] : c_List_Olist_ONil(X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X7,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
fof(f1310,plain,
spl0_126,
inference(avatar_split_clause,[],[f584,f1308]) ).
fof(f1308,plain,
( spl0_126
<=> ! [X13,X2] : c_List_Olist_ONil(X2) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X13,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f584,axiom,
! [X2,X13] : c_List_Olist_ONil(X2) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X13,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__0_0) ).
fof(f1306,plain,
spl0_125,
inference(avatar_split_clause,[],[f580,f1304]) ).
fof(f1304,plain,
( spl0_125
<=> ! [X22,X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olist_Olist__size(X22,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f580,axiom,
! [X2,X22] : c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olist_Olist__size(X22,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I1_J_0) ).
fof(f1302,plain,
spl0_124,
inference(avatar_split_clause,[],[f487,f1300]) ).
fof(f1300,plain,
( spl0_124
<=> ! [X57,X51] :
( X51 = X57
| c_Lambda_OdB_OAbs(X51) != c_Lambda_OdB_OAbs(X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f487,axiom,
! [X51,X57] :
( X51 = X57
| c_Lambda_OdB_OAbs(X51) != c_Lambda_OdB_OAbs(X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f1298,plain,
spl0_123,
inference(avatar_split_clause,[],[f443,f1296]) ).
fof(f1296,plain,
( spl0_123
<=> ! [X57,X55,X56] : hAPP(hAPP(c_Lambda_OdB_OApp,X55),X56) != c_Lambda_OdB_OAbs(X57) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f443,axiom,
! [X56,X57,X55] : hAPP(hAPP(c_Lambda_OdB_OApp,X55),X56) != c_Lambda_OdB_OAbs(X57),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f1294,plain,
spl0_122,
inference(avatar_split_clause,[],[f431,f1292]) ).
fof(f1292,plain,
( spl0_122
<=> ! [X2,X31] : c_List_Olist_ONil(X2) = c_List_Osublist(c_List_Olist_ONil(X2),X31,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f431,axiom,
! [X2,X31] : c_List_Olist_ONil(X2) = c_List_Osublist(c_List_Olist_ONil(X2),X31,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
fof(f1290,plain,
spl0_121,
inference(avatar_split_clause,[],[f428,f1288]) ).
fof(f1288,plain,
( spl0_121
<=> ! [X2,X0] : c_List_Olist_ONil(X2) = c_List_Otake(X0,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f428,axiom,
! [X2,X0] : c_List_Olist_ONil(X2) = c_List_Otake(X0,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
fof(f1286,plain,
spl0_120,
inference(avatar_split_clause,[],[f421,f1284]) ).
fof(f1284,plain,
( spl0_120
<=> ! [X2,X0] : c_List_Olist_ONil(X2) = c_List_Odrop(X0,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f421,axiom,
! [X2,X0] : c_List_Olist_ONil(X2) = c_List_Odrop(X0,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
fof(f1282,plain,
spl0_119,
inference(avatar_split_clause,[],[f409,f1280]) ).
fof(f1280,plain,
( spl0_119
<=> ! [X2,X28] : c_List_Olist_ONil(X2) = c_List_OtakeWhile(X28,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f409,axiom,
! [X2,X28] : c_List_Olist_ONil(X2) = c_List_OtakeWhile(X28,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
fof(f1278,plain,
spl0_118,
inference(avatar_split_clause,[],[f309,f1276]) ).
fof(f309,axiom,
! [X2,X46,X7] :
( ~ hBOOL(hAPP(X46,X7))
| c_in(X7,X46,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1274,plain,
spl0_117,
inference(avatar_split_clause,[],[f308,f1272]) ).
fof(f1272,plain,
( spl0_117
<=> ! [X2,X7,X46] :
( ~ c_in(X7,X46,X2)
| hBOOL(hAPP(X46,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f308,axiom,
! [X2,X46,X7] :
( ~ c_in(X7,X46,X2)
| hBOOL(hAPP(X46,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1270,plain,
spl0_116,
inference(avatar_split_clause,[],[f237,f1268]) ).
fof(f1268,plain,
( spl0_116
<=> ! [X13,X2,X7] : c_List_Ohd(c_List_Olist_OCons(X7,X13,X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f237,axiom,
! [X2,X7,X13] : c_List_Ohd(c_List_Olist_OCons(X7,X13,X2),X2) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
fof(f1266,plain,
spl0_115,
inference(avatar_split_clause,[],[f235,f1264]) ).
fof(f235,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1262,plain,
spl0_114,
inference(avatar_split_clause,[],[f117,f1260]) ).
fof(f1260,plain,
( spl0_114
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f117,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1258,plain,
spl0_113,
inference(avatar_split_clause,[],[f114,f1256]) ).
fof(f1256,plain,
( spl0_113
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f114,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1254,plain,
spl0_112,
inference(avatar_split_clause,[],[f108,f1252]) ).
fof(f1252,plain,
( spl0_112
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f108,axiom,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_lessequals(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1250,plain,
spl0_111,
inference(avatar_split_clause,[],[f74,f1248]) ).
fof(f74,axiom,
! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1246,plain,
spl0_110,
inference(avatar_split_clause,[],[f53,f1244]) ).
fof(f1244,plain,
( spl0_110
<=> ! [X9,X7] :
( X7 = X9
| c_Suc(X7) != c_Suc(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f53,axiom,
! [X9,X7] :
( X7 = X9
| c_Suc(X7) != c_Suc(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
fof(f1242,plain,
spl0_109,
inference(avatar_split_clause,[],[f47,f1240]) ).
fof(f1240,plain,
( spl0_109
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f47,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1238,plain,
spl0_108,
inference(avatar_split_clause,[],[f44,f1236]) ).
fof(f1236,plain,
( spl0_108
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f44,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1234,plain,
spl0_107,
inference(avatar_split_clause,[],[f35,f1232]) ).
fof(f35,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_lessequals(X1,X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
fof(f1226,plain,
spl0_106,
inference(avatar_split_clause,[],[f723,f1224]) ).
fof(f1224,plain,
( spl0_106
<=> ! [X2,X75,X74] :
( X74 = X75
| ~ c_fequal(X74,X75,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f723,axiom,
! [X2,X74,X75] :
( X74 = X75
| ~ c_fequal(X74,X75,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1222,plain,
spl0_105,
inference(avatar_split_clause,[],[f651,f1220]) ).
fof(f1220,plain,
( spl0_105
<=> ! [X2,X69,X68] : c_List_Olist_ONil(X2) != c_List_Olist_OCons(X68,X69,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f651,axiom,
! [X2,X68,X69] : c_List_Olist_ONil(X2) != c_List_Olist_OCons(X68,X69,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
fof(f1218,plain,
spl0_104,
inference(avatar_split_clause,[],[f607,f1216]) ).
fof(f1216,plain,
( spl0_104
<=> ! [X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X14),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f607,axiom,
! [X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X14),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
fof(f1214,plain,
spl0_103,
inference(avatar_split_clause,[],[f588,f1212]) ).
fof(f1212,plain,
( spl0_103
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olength__unique(c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f588,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olength__unique(c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__unique_Osimps_I1_J_0) ).
fof(f1210,plain,
spl0_102,
inference(avatar_split_clause,[],[f560,f1208]) ).
fof(f1208,plain,
( spl0_102
<=> ! [X64,X7] : c_Type_Otyping(X64,c_Lambda_OdB_OVar(X7),hAPP(X64,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f560,axiom,
! [X7,X64] : c_Type_Otyping(X64,c_Lambda_OdB_OVar(X7),hAPP(X64,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f1206,plain,
spl0_101,
inference(avatar_split_clause,[],[f466,f1204]) ).
fof(f1204,plain,
( spl0_101
<=> ! [X13,X2] : c_List_Orev(c_List_Orev(X13,X2),X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f466,axiom,
! [X2,X13] : c_List_Orev(c_List_Orev(X13,X2),X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
fof(f1202,plain,
spl0_100,
inference(avatar_split_clause,[],[f456,f1200]) ).
fof(f1200,plain,
( spl0_100
<=> ! [X52,X10] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X10)),X52)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f456,axiom,
! [X10,X52] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X10)),X52)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f1198,plain,
spl0_99,
inference(avatar_split_clause,[],[f439,f1196]) ).
fof(f1196,plain,
( spl0_99
<=> ! [X2] : c_List_Olist_ONil(X2) = c_List_Orev(c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f439,axiom,
! [X2] : c_List_Olist_ONil(X2) = c_List_Orev(c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
fof(f1194,plain,
spl0_98,
inference(avatar_split_clause,[],[f427,f1192]) ).
fof(f1192,plain,
( spl0_98
<=> ! [X13,X2] : c_List_Oappend(X13,c_List_Olist_ONil(X2),X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f427,axiom,
! [X2,X13] : c_List_Oappend(X13,c_List_Olist_ONil(X2),X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
fof(f1190,plain,
spl0_97,
inference(avatar_split_clause,[],[f424,f1188]) ).
fof(f1188,plain,
( spl0_97
<=> ! [X2,X21] : c_List_Oappend(c_List_Olist_ONil(X2),X21,X2) = X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f424,axiom,
! [X2,X21] : c_List_Oappend(c_List_Olist_ONil(X2),X21,X2) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
fof(f1186,plain,
spl0_96,
inference(avatar_split_clause,[],[f415,f1184]) ).
fof(f1184,plain,
( spl0_96
<=> ! [X2,X21] : c_List_Osplice(c_List_Olist_ONil(X2),X21,X2) = X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f415,axiom,
! [X2,X21] : c_List_Osplice(c_List_Olist_ONil(X2),X21,X2) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
fof(f1182,plain,
spl0_95,
inference(avatar_split_clause,[],[f414,f1180]) ).
fof(f1180,plain,
( spl0_95
<=> ! [X13,X2] : c_List_Osplice(X13,c_List_Olist_ONil(X2),X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f414,axiom,
! [X2,X13] : c_List_Osplice(X13,c_List_Olist_ONil(X2),X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
fof(f1178,plain,
spl0_94,
inference(avatar_split_clause,[],[f408,f1176]) ).
fof(f1176,plain,
( spl0_94
<=> ! [X2] : c_List_Olist_ONil(X2) = c_List_Obutlast(c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f408,axiom,
! [X2] : c_List_Olist_ONil(X2) = c_List_Obutlast(c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
fof(f1174,plain,
spl0_93,
inference(avatar_split_clause,[],[f381,f1172]) ).
fof(f1172,plain,
( spl0_93
<=> ! [X13,X2] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X13,X2) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f381,axiom,
! [X2,X13] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X13,X2) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
fof(f1170,plain,
spl0_92,
inference(avatar_split_clause,[],[f232,f1168]) ).
fof(f1168,plain,
( spl0_92
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f232,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1166,plain,
spl0_91,
inference(avatar_split_clause,[],[f231,f1164]) ).
fof(f1164,plain,
( spl0_91
<=> ! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f231,axiom,
! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1162,plain,
spl0_90,
inference(avatar_split_clause,[],[f216,f1160]) ).
fof(f1160,plain,
( spl0_90
<=> ! [X2] :
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f216,axiom,
! [X2] :
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1158,plain,
spl0_89,
inference(avatar_split_clause,[],[f193,f1156]) ).
fof(f1156,plain,
( spl0_89
<=> ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f193,axiom,
! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1154,plain,
spl0_88,
inference(avatar_split_clause,[],[f661,f1152]) ).
fof(f1152,plain,
( spl0_88
<=> ! [X73,X72] :
( ~ class_Orderings_Oorder(X73)
| class_Orderings_Oorder(tc_fun(X72,X73)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f661,axiom,
! [X72,X73] :
( ~ class_Orderings_Oorder(X73)
| class_Orderings_Oorder(tc_fun(X72,X73)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1150,plain,
spl0_87,
inference(avatar_split_clause,[],[f660,f1148]) ).
fof(f1148,plain,
( spl0_87
<=> ! [X73,X72] :
( ~ class_Orderings_Opreorder(X73)
| class_Orderings_Opreorder(tc_fun(X72,X73)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f660,axiom,
! [X72,X73] :
( ~ class_Orderings_Opreorder(X73)
| class_Orderings_Opreorder(tc_fun(X72,X73)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1146,plain,
spl0_86,
inference(avatar_split_clause,[],[f654,f1144]) ).
fof(f1144,plain,
( spl0_86
<=> ! [X13,X2,X7] : c_List_Olist_OCons(X7,X13,X2) != X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f654,axiom,
! [X2,X7,X13] : c_List_Olist_OCons(X7,X13,X2) != X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
fof(f1142,plain,
spl0_85,
inference(avatar_split_clause,[],[f608,f1140]) ).
fof(f1140,plain,
( spl0_85
<=> ! [X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f608,axiom,
! [X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
fof(f1138,plain,
spl0_84,
inference(avatar_split_clause,[],[f499,f1136]) ).
fof(f1136,plain,
( spl0_84
<=> ! [X2,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f499,axiom,
! [X2,X7] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1134,plain,
spl0_83,
inference(avatar_split_clause,[],[f498,f1132]) ).
fof(f498,axiom,
! [X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1130,plain,
spl0_82,
inference(avatar_split_clause,[],[f497,f1128]) ).
fof(f1128,plain,
( spl0_82
<=> ! [X2,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f497,axiom,
! [X2,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1126,plain,
spl0_81,
inference(avatar_split_clause,[],[f432,f1124]) ).
fof(f1124,plain,
( spl0_81
<=> ! [X2] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f432,axiom,
! [X2] :
( ~ class_Orderings_Olinorder(X2)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
fof(f1122,plain,
spl0_80,
inference(avatar_split_clause,[],[f245,f1120]) ).
fof(f1120,plain,
( spl0_80
<=> ! [X13,X2,X18] : ~ c_ListOrder_Ostep1(X18,c_List_Olist_ONil(X2),X13,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f245,axiom,
! [X2,X18,X13] : ~ c_ListOrder_Ostep1(X18,c_List_Olist_ONil(X2),X13,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
fof(f1118,plain,
spl0_79,
inference(avatar_split_clause,[],[f244,f1116]) ).
fof(f1116,plain,
( spl0_79
<=> ! [X13,X2,X18] : ~ c_ListOrder_Ostep1(X18,X13,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f244,axiom,
! [X2,X18,X13] : ~ c_ListOrder_Ostep1(X18,X13,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
fof(f1114,plain,
spl0_78,
inference(avatar_split_clause,[],[f138,f1112]) ).
fof(f1112,plain,
( spl0_78
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f138,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
fof(f1110,plain,
spl0_77,
inference(avatar_split_clause,[],[f6,f1108]) ).
fof(f1108,plain,
( spl0_77
<=> ! [X2,X7] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f6,axiom,
! [X2,X7] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1106,plain,
spl0_76,
inference(avatar_split_clause,[],[f5,f1104]) ).
fof(f1104,plain,
( spl0_76
<=> ! [X2,X7] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X7,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f5,axiom,
! [X2,X7] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1102,plain,
spl0_75,
inference(avatar_split_clause,[],[f645,f1100]) ).
fof(f645,axiom,
! [X0] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
fof(f1098,plain,
spl0_74,
inference(avatar_split_clause,[],[f457,f1096]) ).
fof(f1096,plain,
( spl0_74
<=> ! [X57,X14] : c_Lambda_OdB_OAbs(X57) != c_Lambda_OdB_OVar(X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f457,axiom,
! [X57,X14] : c_Lambda_OdB_OAbs(X57) != c_Lambda_OdB_OVar(X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f1094,plain,
spl0_73,
inference(avatar_split_clause,[],[f429,f1092]) ).
fof(f1092,plain,
( spl0_73
<=> ! [X2,X31] : c_List_Olistsp(X31,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f429,axiom,
! [X31,X2] : c_List_Olistsp(X31,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
fof(f1090,plain,
spl0_72,
inference(avatar_split_clause,[],[f379,f1088]) ).
fof(f379,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f1086,plain,
spl0_71,
inference(avatar_split_clause,[],[f236,f1084]) ).
fof(f1084,plain,
( spl0_71
<=> ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f236,axiom,
! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1082,plain,
spl0_70,
inference(avatar_split_clause,[],[f228,f1080]) ).
fof(f1080,plain,
( spl0_70
<=> ! [X15] : c_Suc(X15) != c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f228,axiom,
! [X15] : c_Suc(X15) != c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
fof(f1078,plain,
spl0_69,
inference(avatar_split_clause,[],[f30,f1076]) ).
fof(f30,axiom,
! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(X7),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f1074,plain,
spl0_68,
inference(avatar_split_clause,[],[f19,f1072]) ).
fof(f19,axiom,
! [X0] : ~ c_lessequals(c_Suc(X0),X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1070,plain,
~ spl0_67,
inference(avatar_split_clause,[],[f659,f1067]) ).
fof(f659,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1065,plain,
spl0_66,
inference(avatar_split_clause,[],[f722,f1063]) ).
fof(f1063,plain,
( spl0_66
<=> ! [X2,X7] : c_fequal(X7,X7,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f722,axiom,
! [X2,X7] : c_fequal(X7,X7,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1061,plain,
spl0_65,
inference(avatar_split_clause,[],[f647,f1058]) ).
fof(f647,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ta____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
fof(f1056,plain,
spl0_64,
inference(avatar_split_clause,[],[f562,f1053]) ).
fof(f562,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_s____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
fof(f1051,plain,
spl0_63,
inference(avatar_split_clause,[],[f495,f1049]) ).
fof(f495,axiom,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1047,plain,
spl0_62,
inference(avatar_split_clause,[],[f15,f1045]) ).
fof(f1045,plain,
( spl0_62
<=> ! [X0] : c_Suc(X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f15,axiom,
! [X0] : c_Suc(X0) != X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f1043,plain,
spl0_61,
inference(avatar_split_clause,[],[f9,f1041]) ).
fof(f1041,plain,
( spl0_61
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f9,axiom,
! [X0] : c_lessequals(X0,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f1039,plain,
spl0_60,
inference(avatar_split_clause,[],[f721,f1036]) ).
fof(f1036,plain,
( spl0_60
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f721,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
fof(f1034,plain,
spl0_59,
inference(avatar_split_clause,[],[f720,f1031]) ).
fof(f1031,plain,
( spl0_59
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f720,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
fof(f1029,plain,
spl0_58,
inference(avatar_split_clause,[],[f719,f1026]) ).
fof(f1026,plain,
( spl0_58
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f719,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f1024,plain,
spl0_57,
inference(avatar_split_clause,[],[f718,f1021]) ).
fof(f1021,plain,
( spl0_57
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f718,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f1019,plain,
spl0_56,
inference(avatar_split_clause,[],[f717,f1016]) ).
fof(f1016,plain,
( spl0_56
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f717,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f1014,plain,
spl0_55,
inference(avatar_split_clause,[],[f716,f1011]) ).
fof(f1011,plain,
( spl0_55
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f716,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f1009,plain,
spl0_54,
inference(avatar_split_clause,[],[f715,f1006]) ).
fof(f1006,plain,
( spl0_54
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f715,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f1004,plain,
spl0_53,
inference(avatar_split_clause,[],[f714,f1001]) ).
fof(f1001,plain,
( spl0_53
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f714,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f999,plain,
spl0_52,
inference(avatar_split_clause,[],[f713,f996]) ).
fof(f996,plain,
( spl0_52
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f713,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f994,plain,
spl0_51,
inference(avatar_split_clause,[],[f712,f991]) ).
fof(f991,plain,
( spl0_51
<=> class_Ring__and__Field_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f712,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
fof(f989,plain,
spl0_50,
inference(avatar_split_clause,[],[f711,f986]) ).
fof(f711,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f984,plain,
spl0_49,
inference(avatar_split_clause,[],[f710,f981]) ).
fof(f710,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f979,plain,
spl0_48,
inference(avatar_split_clause,[],[f709,f976]) ).
fof(f976,plain,
( spl0_48
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f709,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f974,plain,
spl0_47,
inference(avatar_split_clause,[],[f708,f971]) ).
fof(f971,plain,
( spl0_47
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f708,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f969,plain,
spl0_46,
inference(avatar_split_clause,[],[f707,f966]) ).
fof(f966,plain,
( spl0_46
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f707,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f964,plain,
spl0_45,
inference(avatar_split_clause,[],[f706,f961]) ).
fof(f961,plain,
( spl0_45
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f706,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(f959,plain,
spl0_44,
inference(avatar_split_clause,[],[f705,f956]) ).
fof(f705,axiom,
class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
fof(f954,plain,
spl0_43,
inference(avatar_split_clause,[],[f704,f951]) ).
fof(f951,plain,
( spl0_43
<=> class_OrderedGroup_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f704,axiom,
class_OrderedGroup_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Osemigroup__add) ).
fof(f949,plain,
spl0_42,
inference(avatar_split_clause,[],[f703,f946]) ).
fof(f946,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f703,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f944,plain,
spl0_41,
inference(avatar_split_clause,[],[f702,f941]) ).
fof(f941,plain,
( spl0_41
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f702,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f939,plain,
spl0_40,
inference(avatar_split_clause,[],[f701,f936]) ).
fof(f936,plain,
( spl0_40
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f701,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f934,plain,
spl0_39,
inference(avatar_split_clause,[],[f700,f931]) ).
fof(f931,plain,
( spl0_39
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f700,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f929,plain,
spl0_38,
inference(avatar_split_clause,[],[f699,f926]) ).
fof(f926,plain,
( spl0_38
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f699,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f924,plain,
spl0_37,
inference(avatar_split_clause,[],[f698,f921]) ).
fof(f921,plain,
( spl0_37
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f698,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f919,plain,
spl0_36,
inference(avatar_split_clause,[],[f697,f916]) ).
fof(f916,plain,
( spl0_36
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f697,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f914,plain,
spl0_35,
inference(avatar_split_clause,[],[f696,f911]) ).
fof(f911,plain,
( spl0_35
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f696,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f909,plain,
spl0_34,
inference(avatar_split_clause,[],[f695,f906]) ).
fof(f906,plain,
( spl0_34
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f695,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f904,plain,
spl0_33,
inference(avatar_split_clause,[],[f694,f901]) ).
fof(f901,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f694,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f899,plain,
spl0_32,
inference(avatar_split_clause,[],[f693,f896]) ).
fof(f896,plain,
( spl0_32
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f693,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f894,plain,
spl0_31,
inference(avatar_split_clause,[],[f692,f891]) ).
fof(f891,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f692,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f889,plain,
spl0_30,
inference(avatar_split_clause,[],[f691,f886]) ).
fof(f886,plain,
( spl0_30
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f691,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f884,plain,
spl0_29,
inference(avatar_split_clause,[],[f690,f881]) ).
fof(f881,plain,
( spl0_29
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f690,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f879,plain,
spl0_28,
inference(avatar_split_clause,[],[f689,f876]) ).
fof(f876,plain,
( spl0_28
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f689,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f874,plain,
spl0_27,
inference(avatar_split_clause,[],[f688,f871]) ).
fof(f871,plain,
( spl0_27
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f688,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f869,plain,
spl0_26,
inference(avatar_split_clause,[],[f687,f866]) ).
fof(f866,plain,
( spl0_26
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f687,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f864,plain,
spl0_25,
inference(avatar_split_clause,[],[f686,f861]) ).
fof(f861,plain,
( spl0_25
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f686,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f859,plain,
spl0_24,
inference(avatar_split_clause,[],[f685,f856]) ).
fof(f856,plain,
( spl0_24
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f685,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
fof(f854,plain,
spl0_23,
inference(avatar_split_clause,[],[f684,f851]) ).
fof(f851,plain,
( spl0_23
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f684,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f849,plain,
spl0_22,
inference(avatar_split_clause,[],[f683,f846]) ).
fof(f846,plain,
( spl0_22
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f683,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f844,plain,
spl0_21,
inference(avatar_split_clause,[],[f682,f841]) ).
fof(f841,plain,
( spl0_21
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f682,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f839,plain,
spl0_20,
inference(avatar_split_clause,[],[f681,f836]) ).
fof(f836,plain,
( spl0_20
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f681,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f834,plain,
spl0_19,
inference(avatar_split_clause,[],[f680,f831]) ).
fof(f831,plain,
( spl0_19
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f680,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f829,plain,
spl0_18,
inference(avatar_split_clause,[],[f679,f826]) ).
fof(f679,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f824,plain,
spl0_17,
inference(avatar_split_clause,[],[f678,f821]) ).
fof(f821,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f678,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f819,plain,
spl0_16,
inference(avatar_split_clause,[],[f677,f816]) ).
fof(f816,plain,
( spl0_16
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f677,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f814,plain,
spl0_15,
inference(avatar_split_clause,[],[f676,f811]) ).
fof(f811,plain,
( spl0_15
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f676,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f809,plain,
spl0_14,
inference(avatar_split_clause,[],[f675,f806]) ).
fof(f675,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f804,plain,
spl0_13,
inference(avatar_split_clause,[],[f674,f801]) ).
fof(f801,plain,
( spl0_13
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f674,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(f799,plain,
spl0_12,
inference(avatar_split_clause,[],[f673,f796]) ).
fof(f796,plain,
( spl0_12
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f673,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(f794,plain,
spl0_11,
inference(avatar_split_clause,[],[f672,f791]) ).
fof(f791,plain,
( spl0_11
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f672,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f789,plain,
spl0_10,
inference(avatar_split_clause,[],[f671,f786]) ).
fof(f786,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f671,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f784,plain,
spl0_9,
inference(avatar_split_clause,[],[f670,f781]) ).
fof(f781,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f670,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(f779,plain,
spl0_8,
inference(avatar_split_clause,[],[f669,f776]) ).
fof(f776,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f669,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f774,plain,
spl0_7,
inference(avatar_split_clause,[],[f668,f771]) ).
fof(f771,plain,
( spl0_7
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f668,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(f769,plain,
spl0_6,
inference(avatar_split_clause,[],[f667,f766]) ).
fof(f766,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f667,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f764,plain,
spl0_5,
inference(avatar_split_clause,[],[f666,f761]) ).
fof(f761,plain,
( spl0_5
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f666,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f759,plain,
spl0_4,
inference(avatar_split_clause,[],[f665,f756]) ).
fof(f756,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f665,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f754,plain,
spl0_3,
inference(avatar_split_clause,[],[f664,f751]) ).
fof(f751,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f664,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f749,plain,
spl0_2,
inference(avatar_split_clause,[],[f663,f746]) ).
fof(f746,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f663,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(f744,plain,
spl0_1,
inference(avatar_split_clause,[],[f662,f741]) ).
fof(f741,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f662,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
% 0.09/0.10 % Problem : LCL848-1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:00:25 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.31 % (2672)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.35 % (2675)WARNING: value z3 for option sas not known
% 0.15/0.36 % (2674)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.36 % (2677)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)
% 0.15/0.36 % (2676)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.36 % (2678)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)
% 0.15/0.36 % (2673)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.36 % (2675)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)
% 0.15/0.36 % (2679)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)
% 0.15/0.45 TRYING [1]
% 0.15/0.45 % (2677)First to succeed.
% 0.15/0.46 % (2677)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2677)------------------------------
% 0.15/0.47 % (2677)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.47 % (2677)Termination reason: Refutation
% 0.15/0.47
% 0.15/0.47 % (2677)Memory used [KB]: 2879
% 0.15/0.47 % (2677)Time elapsed: 0.106 s
% 0.15/0.47 % (2677)Instructions burned: 190 (million)
% 0.15/0.47 % (2677)------------------------------
% 0.15/0.47 % (2677)------------------------------
% 0.15/0.47 % (2672)Success in time 0.151 s
%------------------------------------------------------------------------------