TSTP Solution File: LCL812-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL812-1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:53:36 EDT 2024
% Result : Unsatisfiable 2.16s 0.69s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1020
% Syntax : Number of formulae : 1747 ( 679 unt; 0 def)
% Number of atoms : 3866 ( 838 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 3658 (1539 ~;1585 |; 0 &)
% ( 534 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 578 ( 576 usr; 535 prp; 0-4 aty)
% Number of functors : 69 ( 69 usr; 14 con; 0-5 aty)
% Number of variables : 3057 (3057 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9343,plain,
$false,
inference(avatar_sat_refutation,[],[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,f1044,f1049,f1054,f1059,f1064,f1069,f1074,f1079,f1084,f1088,f1093,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,f1224,f1228,f1232,f1236,f1240,f1244,f1248,f1252,f1256,f1260,f1264,f1268,f1274,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1363,f1395,f1400,f1404,f1408,f1412,f1416,f1420,f1424,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1492,f1496,f1500,f1511,f1578,f1582,f1586,f1590,f1594,f1598,f1602,f1606,f1610,f1614,f1618,f1630,f1634,f1638,f1642,f1646,f1650,f1654,f1658,f1662,f1682,f1709,f1764,f1768,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1818,f1822,f1826,f1830,f1834,f1838,f1892,f1945,f1949,f1953,f1957,f1961,f1965,f1969,f1973,f1978,f1982,f1986,f1990,f1994,f1998,f2002,f2006,f2010,f2014,f2018,f2022,f2026,f2030,f2034,f2038,f2042,f2046,f2076,f2178,f2326,f2330,f2334,f2338,f2342,f2346,f2350,f2354,f2358,f2362,f2366,f2370,f2374,f2378,f2382,f2386,f2390,f2394,f2399,f2403,f2407,f2411,f2415,f2419,f2423,f2427,f2431,f2435,f2439,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2472,f2662,f2812,f2870,f2874,f2878,f2882,f2886,f2890,f2894,f2898,f2908,f2912,f2916,f2920,f2924,f2928,f2932,f2936,f2940,f2944,f2948,f2952,f2956,f2960,f3293,f3297,f3301,f3305,f3309,f3313,f3327,f3331,f3335,f3339,f3343,f3347,f3351,f3355,f3359,f3363,f3377,f3381,f3512,f3581,f3585,f3589,f3593,f3597,f3601,f3605,f3609,f3613,f3617,f3621,f3625,f3629,f3633,f3637,f3641,f3645,f3649,f3653,f3657,f3661,f3666,f3670,f3674,f3678,f3682,f3686,f3690,f3694,f3698,f3725,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4262,f4266,f4270,f4274,f4740,f4744,f4748,f4752,f4756,f4772,f4777,f4829,f4833,f4837,f4841,f4845,f4849,f4853,f4871,f4875,f4879,f4883,f5276,f5280,f5284,f5288,f5292,f5296,f5300,f5304,f5308,f5312,f5316,f5321,f5325,f5329,f5333,f5337,f5341,f5345,f5349,f5353,f5357,f5364,f5368,f5372,f5376,f5380,f5384,f5388,f5394,f5398,f5425,f6012,f6103,f6153,f6157,f6161,f6165,f6169,f6173,f6177,f6181,f6185,f6189,f6193,f6197,f6201,f6205,f6209,f6213,f6217,f6221,f6225,f6279,f6463,f6641,f6645,f6649,f6653,f6657,f6661,f6665,f6669,f6673,f6677,f6681,f6685,f6689,f6693,f6697,f6701,f6705,f6709,f6713,f6717,f6721,f6725,f6836,f7178,f7234,f7238,f7242,f7246,f7250,f7254,f7258,f7265,f7269,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7865,f7869,f7873,f7877,f7881,f7885,f7889,f8071,f8096,f8345,f8353,f8357,f8361,f8365,f8369,f8373,f8377,f8381,f8385,f8389,f8393,f8397,f8403,f8407,f8444,f8453,f8471,f8475,f8479,f8483,f8487,f8491,f8623,f8629,f8633,f8637,f8641,f8645,f8942,f8946,f8952,f8956,f8960,f8964,f8968,f8972,f8976,f8980,f8984,f8988,f8992,f9024,f9187,f9242,f9246,f9250,f9254,f9329,f9335,f9339,f9342]) ).
fof(f9342,plain,
spl0_409,
inference(avatar_split_clause,[],[f587,f5422]) ).
fof(f5422,plain,
( spl0_409
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f587,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f9339,plain,
spl0_534,
inference(avatar_split_clause,[],[f572,f9337]) ).
fof(f9337,plain,
( spl0_534
<=> ! [X18,X53,X25] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB)),X18) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X25),X18),c_List_Omap(c_COMBC(c_Lambda_Olift,X18,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f572,axiom,
! [X18,X53,X25] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB)),X18) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X25),X18),c_List_Omap(c_COMBC(c_Lambda_Olift,X18,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).
fof(f9335,plain,
spl0_533,
inference(avatar_split_clause,[],[f380,f9333]) ).
fof(f9333,plain,
( spl0_533
<=> ! [X42,X43,X41,X51,X0,X52] : c_Lambda_OdB_OdB__rec(X41,X42,X43,hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),X0) = hAPP(hAPP(hAPP(hAPP(X42,X51),X52),c_Lambda_OdB_OdB__rec(X41,X42,X43,X51,X0)),c_Lambda_OdB_OdB__rec(X41,X42,X43,X52,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f380,axiom,
! [X51,X41,X0,X52,X42,X43] : c_Lambda_OdB_OdB__rec(X41,X42,X43,hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),X0) = hAPP(hAPP(hAPP(hAPP(X42,X51),X52),c_Lambda_OdB_OdB__rec(X41,X42,X43,X51,X0)),c_Lambda_OdB_OdB__rec(X41,X42,X43,X52,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
fof(f9329,plain,
spl0_532,
inference(avatar_split_clause,[],[f289,f9327]) ).
fof(f9327,plain,
( spl0_532
<=> ! [X35,X10,X9,X0,X36,X22] :
( c_ListOrder_Ostep1(X35,X36,X22,X0)
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f289,axiom,
! [X10,X0,X36,X9,X35,X22] :
( c_ListOrder_Ostep1(X35,X36,X22,X0)
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
fof(f9254,plain,
spl0_531,
inference(avatar_split_clause,[],[f787,f9252]) ).
fof(f9252,plain,
( spl0_531
<=> ! [X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X11)),c_List_Olist_OCons(v_sko__InductTermi__XIT__Xcases__5(X11),v_sko__InductTermi__XIT__Xcases__6(X11),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = X11
| ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X11)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f787,plain,
! [X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X11)),c_List_Olist_OCons(v_sko__InductTermi__XIT__Xcases__5(X11),v_sko__InductTermi__XIT__Xcases__6(X11),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = X11
| ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X11)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ),
inference(forward_demodulation,[],[f460,f511]) ).
fof(f511,axiom,
! [X0,X11,X49,X47,X9,X22] : c_List_Ofoldl(X47,X11,c_List_Olist_OCons(X9,X22,X49),X0,X49) = c_List_Ofoldl(X47,hAPP(hAPP(X47,X11),X9),X22,X0,X49),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
fof(f460,axiom,
! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X11)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X11))),v_sko__InductTermi__XIT__Xcases__5(X11)),v_sko__InductTermi__XIT__Xcases__6(X11),tc_Lambda_OdB,tc_Lambda_OdB) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_9) ).
fof(f9250,plain,
spl0_530,
inference(avatar_split_clause,[],[f785,f9248]) ).
fof(f9248,plain,
( spl0_530
<=> ! [X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X11)),c_List_Olist_OCons(v_sko__InductTermi__XIT__Xcases__5(X11),v_sko__InductTermi__XIT__Xcases__6(X11),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = X11
| ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X11)) = X11
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f785,plain,
! [X11] :
( c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X11)),c_List_Olist_OCons(v_sko__InductTermi__XIT__Xcases__5(X11),v_sko__InductTermi__XIT__Xcases__6(X11),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = X11
| ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X11)) = X11
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ),
inference(forward_demodulation,[],[f300,f511]) ).
fof(f300,axiom,
! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X11)) = X11
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB)
| c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(X11))),v_sko__InductTermi__XIT__Xcases__5(X11)),v_sko__InductTermi__XIT__Xcases__6(X11),tc_Lambda_OdB,tc_Lambda_OdB) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_6) ).
fof(f9246,plain,
spl0_529,
inference(avatar_split_clause,[],[f566,f9244]) ).
fof(f9244,plain,
( spl0_529
<=> ! [X24,X34,X20,X25] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X34)),X24),X20) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X20)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X34),X24),X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f566,axiom,
! [X34,X24,X25,X20] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X34)),X24),X20) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X20)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X34),X24),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
fof(f9242,plain,
spl0_528,
inference(avatar_split_clause,[],[f286,f9240]) ).
fof(f9240,plain,
( spl0_528
<=> ! [X11,X0,X12,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X12
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_Power_Opower__class_Opower(X11,X7,X0) != c_Power_Opower__class_Opower(X12,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f286,axiom,
! [X0,X11,X7,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X12
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_Power_Opower__class_Opower(X11,X7,X0) != c_Power_Opower__class_Opower(X12,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
fof(f9187,plain,
( spl0_527
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_525 ),
inference(avatar_split_clause,[],[f8993,f8990,f4877,f1980,f1320,f1168,f9185]) ).
fof(f9185,plain,
( spl0_527
<=> ! [X20,X24,X25] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X25)),X24),X20) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f1168,plain,
( spl0_80
<=> ! [X20,X25] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X20) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1320,plain,
( spl0_117
<=> ! [X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ozero__class_Ozero(tc_nat)) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1980,plain,
( spl0_208
<=> ! [X7,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f4877,plain,
( spl0_377
<=> ! [X20,X7,X25] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X7,X25,X20)),X20) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X25,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f8990,plain,
( spl0_525
<=> ! [X20,X24,X25] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X25)),X24),X20) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),hAPP(hAPP(c_Lambda_Olift,X24),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f8993,plain,
( ! [X24,X25,X20] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X25)),X24),X20) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_525 ),
inference(forward_demodulation,[],[f8991,f5260]) ).
fof(f5260,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lambda_Olift,X0),X1) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377 ),
inference(forward_demodulation,[],[f5259,f1321]) ).
fof(f1321,plain,
( ! [X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ozero__class_Ozero(tc_nat)) = X15
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f5259,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lambda_Olift,X0),X1) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| ~ spl0_80
| ~ spl0_208
| ~ spl0_377 ),
inference(forward_demodulation,[],[f5244,f1981]) ).
fof(f1981,plain,
( ! [X7,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X15)
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f1980]) ).
fof(f5244,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lambda_Olift,X0),X1) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X0,X1)
| ~ spl0_80
| ~ spl0_377 ),
inference(superposition,[],[f4878,f1169]) ).
fof(f1169,plain,
( ! [X25,X20] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X20) = X25
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f4878,plain,
( ! [X7,X25,X20] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X7,X25,X20)),X20) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X25,X20)
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f4877]) ).
fof(f8991,plain,
( ! [X24,X25,X20] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X25)),X24),X20) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),hAPP(hAPP(c_Lambda_Olift,X24),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_525 ),
inference(avatar_component_clause,[],[f8990]) ).
fof(f9024,plain,
( spl0_526
| ~ spl0_85
| ~ spl0_327
| ~ spl0_514 ),
inference(avatar_split_clause,[],[f8948,f8944,f3655,f1188,f9022]) ).
fof(f9022,plain,
( spl0_526
<=> ! [X35,X36,X0,X9,X22,X10] :
( ~ c_ListOrder_Ostep1(X35,c_List_Orev(c_List_Olist_OCons(X10,c_List_Orev(X36,X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f1188,plain,
( spl0_85
<=> ! [X22,X0] : c_List_Orev(c_List_Orev(X22,X0),X0) = X22 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f3655,plain,
( spl0_327
<=> ! [X22,X9,X0] : c_List_Orev(c_List_Olist_OCons(X9,X22,X0),X0) = c_List_Oappend(c_List_Orev(X22,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f8944,plain,
( spl0_514
<=> ! [X35,X10,X0,X9,X22,X36] :
( X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f8948,plain,
( ! [X10,X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,c_List_Orev(c_List_Olist_OCons(X10,c_List_Orev(X36,X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9)) )
| ~ spl0_85
| ~ spl0_327
| ~ spl0_514 ),
inference(forward_demodulation,[],[f8947,f4009]) ).
fof(f4009,plain,
( ! [X2,X0,X1] : c_List_Orev(c_List_Olist_OCons(X2,c_List_Orev(X0,X1),X1),X1) = c_List_Oappend(X0,c_List_Olist_OCons(X2,c_List_Olist_ONil(X1),X1),X1)
| ~ spl0_85
| ~ spl0_327 ),
inference(superposition,[],[f3656,f1189]) ).
fof(f1189,plain,
( ! [X0,X22] : c_List_Orev(c_List_Orev(X22,X0),X0) = X22
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1188]) ).
fof(f3656,plain,
( ! [X0,X9,X22] : c_List_Orev(c_List_Olist_OCons(X9,X22,X0),X0) = c_List_Oappend(c_List_Orev(X22,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0)
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f3655]) ).
fof(f8947,plain,
( ! [X10,X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9)) )
| ~ spl0_85
| ~ spl0_327
| ~ spl0_514 ),
inference(forward_demodulation,[],[f8945,f4009]) ).
fof(f8945,plain,
( ! [X10,X0,X36,X9,X35,X22] :
( X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) )
| ~ spl0_514 ),
inference(avatar_component_clause,[],[f8944]) ).
fof(f8992,plain,
spl0_525,
inference(avatar_split_clause,[],[f521,f8990]) ).
fof(f521,axiom,
! [X24,X25,X20] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X25)),X24),X20) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),hAPP(hAPP(c_Lambda_Olift,X24),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
fof(f8988,plain,
spl0_524,
inference(avatar_split_clause,[],[f503,f8986]) ).
fof(f8986,plain,
( spl0_524
<=> ! [X24,X53,X35,X25] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X53
| c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,X35),X24)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X25,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X35,X24,X25,X53),tc_Lambda_OdB,tc_Lambda_OdB) = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f503,axiom,
! [X53,X35,X25,X24] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X53
| c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,X35),X24)
| c_List_Ofoldl(c_Lambda_OdB_OApp,X25,c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1(X35,X24,X25,X53),tc_Lambda_OdB,tc_Lambda_OdB) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
fof(f8984,plain,
spl0_523,
inference(avatar_split_clause,[],[f496,f8982]) ).
fof(f8982,plain,
( spl0_523
<=> ! [X48,X47,X0,X49,X22] :
( c_List_Omap(X47,X22,X49,X0) = c_List_Omap(X48,X22,X49,X0)
| hAPP(X47,c_List_Osko__List__Xmap__eq__conv__1__1(X47,X48,X22,X49,X0)) != hAPP(X48,c_List_Osko__List__Xmap__eq__conv__1__1(X47,X48,X22,X49,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f496,axiom,
! [X48,X0,X49,X47,X22] :
( c_List_Omap(X47,X22,X49,X0) = c_List_Omap(X48,X22,X49,X0)
| hAPP(X47,c_List_Osko__List__Xmap__eq__conv__1__1(X47,X48,X22,X49,X0)) != hAPP(X48,c_List_Osko__List__Xmap__eq__conv__1__1(X47,X48,X22,X49,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__conv_2) ).
fof(f8980,plain,
spl0_522,
inference(avatar_split_clause,[],[f495,f8978]) ).
fof(f8978,plain,
( spl0_522
<=> ! [X48,X47,X0,X9,X49] :
( c_List_Omap(X47,X9,X0,X49) = c_List_Omap(X48,X9,X0,X49)
| hAPP(X47,c_List_Osko__List__Xmap__cong__1__1(X47,X48,X9,X0,X49)) != hAPP(X48,c_List_Osko__List__Xmap__cong__1__1(X47,X48,X9,X0,X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f495,axiom,
! [X48,X0,X49,X47,X9] :
( c_List_Omap(X47,X9,X0,X49) = c_List_Omap(X48,X9,X0,X49)
| hAPP(X47,c_List_Osko__List__Xmap__cong__1__1(X47,X48,X9,X0,X49)) != hAPP(X48,c_List_Osko__List__Xmap__cong__1__1(X47,X48,X9,X0,X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__cong_1) ).
fof(f8976,plain,
spl0_521,
inference(avatar_split_clause,[],[f488,f8974]) ).
fof(f8974,plain,
( spl0_521
<=> ! [X48,X47,X0,X49,X22] :
( c_List_Omap(X47,X22,X0,X49) = c_List_Omap(X48,X22,X0,X49)
| hAPP(X47,c_List_Osko__List__Xmap__ext__1__1(X47,X48,X22,X0,X49)) != hAPP(X48,c_List_Osko__List__Xmap__ext__1__1(X47,X48,X22,X0,X49)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f488,axiom,
! [X48,X0,X49,X47,X22] :
( c_List_Omap(X47,X22,X0,X49) = c_List_Omap(X48,X22,X0,X49)
| hAPP(X47,c_List_Osko__List__Xmap__ext__1__1(X47,X48,X22,X0,X49)) != hAPP(X48,c_List_Osko__List__Xmap__ext__1__1(X47,X48,X22,X0,X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__ext_1) ).
fof(f8972,plain,
spl0_520,
inference(avatar_split_clause,[],[f468,f8970]) ).
fof(f8970,plain,
( spl0_520
<=> ! [X50,X65,X48,X0,X49,X47,X70,X9,X16,X68,X69] :
( hAPP(X47,hAPP(X48,X9)) != hAPP(X68,hAPP(X69,X16))
| hAPP(c_Fun_Ocomp(X47,X48,X49,X0,X50),X9) = hAPP(c_Fun_Ocomp(X68,X69,X65,X0,X70),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f468,axiom,
! [X50,X65,X48,X0,X49,X70,X47,X68,X9,X69,X16] :
( hAPP(X47,hAPP(X48,X9)) != hAPP(X68,hAPP(X69,X16))
| hAPP(c_Fun_Ocomp(X47,X48,X49,X0,X50),X9) = hAPP(c_Fun_Ocomp(X68,X69,X65,X0,X70),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
fof(f8968,plain,
spl0_519,
inference(avatar_split_clause,[],[f268,f8966]) ).
fof(f8966,plain,
( spl0_519
<=> ! [X25,X19] :
( hBOOL(hAPP(X19,X25))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X19)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X19),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X19)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f268,axiom,
! [X19,X25] :
( hBOOL(hAPP(X19,X25))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(X19)),c_ListApplication_Osko__ListApplication__Xlem__1__4(X19),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X19)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem_5) ).
fof(f8964,plain,
spl0_518,
inference(avatar_split_clause,[],[f267,f8962]) ).
fof(f8962,plain,
( spl0_518
<=> ! [X25,X19] :
( hBOOL(hAPP(X19,X25))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X19)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X19),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X19)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f267,axiom,
! [X19,X25] :
( hBOOL(hAPP(X19,X25))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X19)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(X19),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X19)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Apps__dB__induct_5) ).
fof(f8960,plain,
spl0_517,
inference(avatar_split_clause,[],[f254,f8958]) ).
fof(f8958,plain,
( spl0_517
<=> ! [X18,X35,X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X35),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f254,axiom,
! [X18,X24,X35,X25] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X35),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
fof(f8956,plain,
( spl0_516
| ~ spl0_66
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f3891,f3615,f1112,f8954]) ).
fof(f8954,plain,
( spl0_516
<=> ! [X2,X0,X1,X3] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OVar(X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f1112,plain,
( spl0_66
<=> ! [X29,X61] : c_Lambda_OdB_OAbs(X61) != c_Lambda_OdB_OVar(X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f3615,plain,
( spl0_317
<=> ! [X20,X24,X7] : c_Lambda_Oliftn(X7,c_Lambda_OdB_OAbs(X24),X20) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X7,X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f3891,plain,
( ! [X2,X3,X0,X1] : c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) != c_Lambda_OdB_OVar(X3)
| ~ spl0_66
| ~ spl0_317 ),
inference(superposition,[],[f1113,f3616]) ).
fof(f3616,plain,
( ! [X7,X24,X20] : c_Lambda_Oliftn(X7,c_Lambda_OdB_OAbs(X24),X20) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X7,X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3615]) ).
fof(f1113,plain,
( ! [X29,X61] : c_Lambda_OdB_OAbs(X61) != c_Lambda_OdB_OVar(X29)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1112]) ).
fof(f8952,plain,
spl0_515,
inference(avatar_split_clause,[],[f253,f8950]) ).
fof(f8950,plain,
( spl0_515
<=> ! [X18,X35,X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),X25),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X24),X25),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f253,axiom,
! [X18,X24,X35,X25] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),X25),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X24),X25),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
fof(f8946,plain,
spl0_514,
inference(avatar_split_clause,[],[f250,f8944]) ).
fof(f250,axiom,
! [X10,X0,X36,X9,X35,X22] :
( X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
fof(f8942,plain,
spl0_513,
inference(avatar_split_clause,[],[f196,f8940]) ).
fof(f8940,plain,
( spl0_513
<=> ! [X10,X34,X0,X9,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X8) = X34
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),X8)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f196,axiom,
! [X10,X0,X8,X9,X34] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X8) = X34
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),X8)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f8645,plain,
( spl0_512
| ~ spl0_85
| ~ spl0_327
| ~ spl0_507 ),
inference(avatar_split_clause,[],[f8625,f8621,f3655,f1188,f8643]) ).
fof(f8643,plain,
( spl0_512
<=> ! [X35,X36,X0,X9,X22,X10] :
( ~ c_ListOrder_Ostep1(X35,c_List_Orev(c_List_Olist_OCons(X10,c_List_Orev(X36,X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f8621,plain,
( spl0_507
<=> ! [X35,X10,X9,X0,X36,X22] :
( X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0)
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f8625,plain,
( ! [X10,X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,c_List_Orev(c_List_Olist_OCons(X10,c_List_Orev(X36,X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0) )
| ~ spl0_85
| ~ spl0_327
| ~ spl0_507 ),
inference(forward_demodulation,[],[f8624,f4009]) ).
fof(f8624,plain,
( ! [X10,X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0) )
| ~ spl0_85
| ~ spl0_327
| ~ spl0_507 ),
inference(forward_demodulation,[],[f8622,f4009]) ).
fof(f8622,plain,
( ! [X10,X0,X36,X9,X22,X35] :
( X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0)
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) )
| ~ spl0_507 ),
inference(avatar_component_clause,[],[f8621]) ).
fof(f8641,plain,
spl0_511,
inference(avatar_split_clause,[],[f703,f8639]) ).
fof(f8639,plain,
( spl0_511
<=> ! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X7)),c_HOL_Oone__class_Oone(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f703,plain,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X7)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f34,f87]) ).
fof(f87,axiom,
! [X7] : c_Suc(X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f34,axiom,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
fof(f8637,plain,
spl0_510,
inference(avatar_split_clause,[],[f691,f8635]) ).
fof(f8635,plain,
( spl0_510
<=> ! [X28,X18,X0,X27,X26] : c_Type_Oshift(c_Type_Oshift(X28,X18,X26,X0),c_HOL_Ozero__class_Ozero(tc_nat),X27,X0) = c_Type_Oshift(c_Type_Oshift(X28,c_HOL_Ozero__class_Ozero(tc_nat),X27,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)),X26,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f691,plain,
! [X28,X0,X18,X26,X27] : c_Type_Oshift(c_Type_Oshift(X28,X18,X26,X0),c_HOL_Ozero__class_Ozero(tc_nat),X27,X0) = c_Type_Oshift(c_Type_Oshift(X28,c_HOL_Ozero__class_Ozero(tc_nat),X27,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)),X26,X0),
inference(definition_unfolding,[],[f93,f87]) ).
fof(f93,axiom,
! [X28,X0,X18,X26,X27] : c_Type_Oshift(c_Type_Oshift(X28,X18,X26,X0),c_HOL_Ozero__class_Ozero(tc_nat),X27,X0) = c_Type_Oshift(c_Type_Oshift(X28,c_HOL_Ozero__class_Ozero(tc_nat),X27,X0),c_Suc(X18),X26,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).
fof(f8633,plain,
( spl0_509
| ~ spl0_196
| ~ spl0_208
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3288,f2958,f1980,f1836,f8631]) ).
fof(f8631,plain,
( spl0_509
<=> ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f1836,plain,
( spl0_196
<=> ! [X44] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X44)),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2958,plain,
( spl0_288
<=> ! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f3288,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat)
| ~ spl0_196
| ~ spl0_208
| ~ spl0_288 ),
inference(forward_demodulation,[],[f3285,f2129]) ).
fof(f2129,plain,
( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(X0))
| ~ spl0_196
| ~ spl0_208 ),
inference(superposition,[],[f1981,f1837]) ).
fof(f1837,plain,
( ! [X44] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X44)),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f1836]) ).
fof(f3285,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))),tc_nat)
| ~ spl0_196
| ~ spl0_288 ),
inference(superposition,[],[f2959,f1837]) ).
fof(f2959,plain,
( ! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15)),tc_nat)
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f2958]) ).
fof(f8629,plain,
spl0_508,
inference(avatar_split_clause,[],[f687,f8627]) ).
fof(f8627,plain,
( spl0_508
<=> ! [X20,X7,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),X20,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),X7,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f687,plain,
! [X7,X15,X20] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),X20,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),X7,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f149,f87,f87]) ).
fof(f149,axiom,
! [X7,X15,X20] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X15),X7,tc_nat),c_Suc(X20),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),X20,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
fof(f8623,plain,
spl0_507,
inference(avatar_split_clause,[],[f330,f8621]) ).
fof(f330,axiom,
! [X10,X0,X36,X9,X22,X35] :
( X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0)
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
fof(f8491,plain,
spl0_506,
inference(avatar_split_clause,[],[f733,f8489]) ).
fof(f8489,plain,
( spl0_506
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f733,plain,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X0),c_HOL_Oone__class_Oone(X0),X0) ),
inference(definition_unfolding,[],[f193,f87]) ).
fof(f193,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,c_Suc(X7),X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
fof(f8487,plain,
spl0_505,
inference(avatar_split_clause,[],[f499,f8485]) ).
fof(f8485,plain,
( spl0_505
<=> ! [X24,X35,X71] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X71,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f499,axiom,
! [X71,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X71,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
fof(f8483,plain,
spl0_504,
inference(avatar_split_clause,[],[f270,f8481]) ).
fof(f8481,plain,
( spl0_504
<=> ! [X11,X0,X12,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,X7,X0),c_Power_Opower__class_Opower(X12,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f270,axiom,
! [X0,X11,X7,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,X7,X0),c_Power_Opower__class_Opower(X12,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
fof(f8479,plain,
( spl0_503
| ~ spl0_196
| ~ spl0_208
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f3261,f2954,f1980,f1836,f8477]) ).
fof(f8477,plain,
( spl0_503
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2954,plain,
( spl0_287
<=> ! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f3261,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(X0))),tc_nat)
| ~ spl0_196
| ~ spl0_208
| ~ spl0_287 ),
inference(forward_demodulation,[],[f3259,f2129]) ).
fof(f3259,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))),tc_nat)
| ~ spl0_196
| ~ spl0_287 ),
inference(superposition,[],[f2955,f1837]) ).
fof(f2955,plain,
( ! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18)),tc_nat)
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f2954]) ).
fof(f8475,plain,
spl0_502,
inference(avatar_split_clause,[],[f238,f8473]) ).
fof(f8473,plain,
( spl0_502
<=> ! [X11,X0,X46,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X7,X46,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,X46,X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f238,axiom,
! [X0,X46,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X7,X46,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,X46,X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
fof(f8471,plain,
spl0_501,
inference(avatar_split_clause,[],[f234,f8469]) ).
fof(f8469,plain,
( spl0_501
<=> ! [X18,X35,X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X35),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f234,axiom,
! [X18,X24,X35,X25] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X35),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X24),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
fof(f8453,plain,
( spl0_500
| ~ spl0_85
| ~ spl0_327
| ~ spl0_496 ),
inference(avatar_split_clause,[],[f8399,f8395,f3655,f1188,f8451]) ).
fof(f8451,plain,
( spl0_500
<=> ! [X35,X36,X0,X9,X22,X10] :
( ~ c_ListOrder_Ostep1(X35,c_List_Orev(c_List_Olist_OCons(X10,c_List_Orev(X36,X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X22 = X36
| X9 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f8395,plain,
( spl0_496
<=> ! [X35,X9,X10,X0,X36,X22] :
( X22 = X36
| X9 = X10
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f8399,plain,
( ! [X10,X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,c_List_Orev(c_List_Olist_OCons(X10,c_List_Orev(X36,X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X22 = X36
| X9 = X10 )
| ~ spl0_85
| ~ spl0_327
| ~ spl0_496 ),
inference(forward_demodulation,[],[f8398,f4009]) ).
fof(f8398,plain,
( ! [X10,X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Orev(c_List_Olist_OCons(X9,c_List_Orev(X22,X0),X0),X0),X0)
| X22 = X36
| X9 = X10 )
| ~ spl0_85
| ~ spl0_327
| ~ spl0_496 ),
inference(forward_demodulation,[],[f8396,f4009]) ).
fof(f8396,plain,
( ! [X10,X0,X36,X9,X22,X35] :
( X22 = X36
| X9 = X10
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) )
| ~ spl0_496 ),
inference(avatar_component_clause,[],[f8395]) ).
fof(f8444,plain,
( spl0_499
| ~ spl0_91
| ~ spl0_116
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2866,f2470,f1316,f1212,f8442]) ).
fof(f8442,plain,
( spl0_499
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f1212,plain,
( spl0_91
<=> ! [X29] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X29),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1316,plain,
( spl0_116
<=> ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X7) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f2470,plain,
( spl0_263
<=> ! [X44] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2866,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB)
| ~ spl0_91
| ~ spl0_116
| ~ spl0_263 ),
inference(forward_demodulation,[],[f2841,f1317]) ).
fof(f1317,plain,
( ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X7) = X7
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f2841,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),tc_Lambda_OdB)
| ~ spl0_91
| ~ spl0_263 ),
inference(superposition,[],[f2471,f1213]) ).
fof(f1213,plain,
( ! [X29] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X29),tc_Lambda_OdB)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f2471,plain,
( ! [X44] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2470]) ).
fof(f8407,plain,
spl0_498,
inference(avatar_split_clause,[],[f749,f8405]) ).
fof(f8405,plain,
( spl0_498
<=> ! [X10,X0,X9,X45] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),X10,X45,X0,X0)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),X9,c_List_Olist_OCons(X10,X45,X0),X0,X0)
| ~ class_OrderedGroup_Osemigroup__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f749,plain,
! [X10,X0,X9,X45] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),X10,X45,X0,X0)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),X9,c_List_Olist_OCons(X10,X45,X0),X0,X0)
| ~ class_OrderedGroup_Osemigroup__add(X0) ),
inference(forward_demodulation,[],[f509,f511]) ).
fof(f509,axiom,
! [X10,X0,X9,X45] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X10),X45,X0,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),X10,X45,X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
fof(f8403,plain,
spl0_497,
inference(avatar_split_clause,[],[f520,f8401]) ).
fof(f8401,plain,
( spl0_497
<=> ! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X11)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X11)),v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB,tc_Lambda_OdB) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f520,axiom,
! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X11)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X11)),v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB,tc_Lambda_OdB) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_5) ).
fof(f8397,plain,
spl0_496,
inference(avatar_split_clause,[],[f426,f8395]) ).
fof(f426,axiom,
! [X10,X0,X36,X9,X22,X35] :
( X22 = X36
| X9 = X10
| ~ c_ListOrder_Ostep1(X35,c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
fof(f8393,plain,
spl0_495,
inference(avatar_split_clause,[],[f344,f8391]) ).
fof(f8391,plain,
( spl0_495
<=> ! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X11)) = X11
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X11)),v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB,tc_Lambda_OdB) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f344,axiom,
! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X11)) = X11
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(X11)),v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB,tc_Lambda_OdB) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_2) ).
fof(f8389,plain,
( spl0_494
| ~ spl0_120
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2853,f2470,f1332,f8387]) ).
fof(f8387,plain,
( spl0_494
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1332,plain,
( spl0_120
<=> ! [X18,X21] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X18),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f2853,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_120
| ~ spl0_263 ),
inference(superposition,[],[f1333,f2471]) ).
fof(f1333,plain,
( ! [X21,X18] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X18),X18,tc_nat)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1332]) ).
fof(f8385,plain,
spl0_493,
inference(avatar_split_clause,[],[f207,f8383]) ).
fof(f8383,plain,
( spl0_493
<=> ! [X10,X0,X9,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f207,axiom,
! [X10,X0,X8,X9] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f8381,plain,
spl0_492,
inference(avatar_split_clause,[],[f204,f8379]) ).
fof(f8379,plain,
( spl0_492
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f204,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f8377,plain,
spl0_491,
inference(avatar_split_clause,[],[f203,f8375]) ).
fof(f8375,plain,
( spl0_491
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f203,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f8373,plain,
spl0_490,
inference(avatar_split_clause,[],[f202,f8371]) ).
fof(f8371,plain,
( spl0_490
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f202,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f8369,plain,
spl0_489,
inference(avatar_split_clause,[],[f201,f8367]) ).
fof(f8367,plain,
( spl0_489
<=> ! [X11,X13,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f201,axiom,
! [X0,X11,X14,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14)),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(f8365,plain,
spl0_488,
inference(avatar_split_clause,[],[f200,f8363]) ).
fof(f8363,plain,
( spl0_488
<=> ! [X11,X0,X14,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f200,axiom,
! [X0,X11,X14,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12)),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f8361,plain,
spl0_487,
inference(avatar_split_clause,[],[f199,f8359]) ).
fof(f8359,plain,
( spl0_487
<=> ! [X11,X13,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f199,axiom,
! [X0,X11,X14,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f8357,plain,
spl0_486,
inference(avatar_split_clause,[],[f44,f8355]) ).
fof(f8355,plain,
( spl0_486
<=> ! [X9,X0,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f44,axiom,
! [X10,X0,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f8353,plain,
spl0_485,
inference(avatar_split_clause,[],[f43,f8351]) ).
fof(f8351,plain,
( spl0_485
<=> ! [X9,X0,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f43,axiom,
! [X10,X0,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f8345,plain,
( spl0_484
| ~ spl0_175
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2847,f2470,f1660,f8343]) ).
fof(f8343,plain,
( spl0_484
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f1660,plain,
( spl0_175
<=> ! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2847,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB),tc_nat)
| ~ spl0_175
| ~ spl0_263 ),
inference(superposition,[],[f1661,f2471]) ).
fof(f1661,plain,
( ! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1660]) ).
fof(f8096,plain,
( spl0_483
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f7861,f7857,f4877,f1980,f1320,f1168,f8094]) ).
fof(f8094,plain,
( spl0_483
<=> ! [X18,X24,X35] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X35,X18)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,X18)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f7857,plain,
( spl0_474
<=> ! [X18,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X35),X18)),hAPP(hAPP(c_Lambda_Olift,X24),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f7861,plain,
( ! [X18,X24,X35] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X35,X18)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,X18)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24)) )
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_474 ),
inference(forward_demodulation,[],[f7860,f5260]) ).
fof(f7860,plain,
( ! [X18,X24,X35] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X35),X18)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,X18)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24)) )
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_474 ),
inference(forward_demodulation,[],[f7858,f5260]) ).
fof(f7858,plain,
( ! [X18,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X35),X18)),hAPP(hAPP(c_Lambda_Olift,X24),X18))) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f7857]) ).
fof(f8071,plain,
( spl0_482
| ~ spl0_125
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2844,f2470,f1352,f8069]) ).
fof(f8069,plain,
( spl0_482
<=> ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) != c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f1352,plain,
( spl0_125
<=> ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)) != X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f2844,plain,
( ! [X0] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) != c_Nat_Osize__class_Osize(X0,tc_Lambda_OdB)
| ~ spl0_125
| ~ spl0_263 ),
inference(superposition,[],[f1353,f2471]) ).
fof(f1353,plain,
( ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)) != X7
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1352]) ).
fof(f7889,plain,
spl0_481,
inference(avatar_split_clause,[],[f748,f7887]) ).
fof(f7887,plain,
( spl0_481
<=> ! [X52,X51] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X51,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X52,tc_Lambda_OdB))),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f748,plain,
! [X51,X52] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X51,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X52,tc_Lambda_OdB))),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f747,f374]) ).
fof(f374,axiom,
! [X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ozero__class_Ozero(tc_nat)) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f747,plain,
! [X51,X52] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X51,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X52,tc_Lambda_OdB))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f692,f247]) ).
fof(f247,axiom,
! [X7,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f692,plain,
! [X51,X52] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X51,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X52,tc_Lambda_OdB))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f278,f87]) ).
fof(f278,axiom,
! [X51,X52] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X51,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(X52,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).
fof(f7885,plain,
spl0_480,
inference(avatar_split_clause,[],[f536,f7883]) ).
fof(f7883,plain,
( spl0_480
<=> ! [X1,X72,X7] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X72,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X7,X72,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f536,axiom,
! [X72,X1,X7] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X72,tc_Lambda_OdB,tc_Lambda_OdB)),X1))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X7,X72,X1),tc_Lambda_OdB,tc_Lambda_OdB) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
fof(f7881,plain,
spl0_479,
inference(avatar_split_clause,[],[f519,f7879]) ).
fof(f7879,plain,
( spl0_479
<=> ! [X18,X35,X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),X25),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X24),X25),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f519,axiom,
! [X18,X24,X35,X25] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),X25),X18)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X24),X25),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
fof(f7877,plain,
spl0_478,
inference(avatar_split_clause,[],[f507,f7875]) ).
fof(f7875,plain,
( spl0_478
<=> ! [X59,X9,X0,X10,X45] :
( ~ c_OrderedGroup_Osemigroup__add(X59,X0)
| c_List_Ofoldl(X59,hAPP(hAPP(X59,X9),X10),X45,X0,X0) = hAPP(hAPP(X59,X9),c_List_Ofoldl(X59,X10,X45,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f507,axiom,
! [X10,X59,X0,X9,X45] :
( ~ c_OrderedGroup_Osemigroup__add(X59,X0)
| c_List_Ofoldl(X59,hAPP(hAPP(X59,X9),X10),X45,X0,X0) = hAPP(hAPP(X59,X9),c_List_Ofoldl(X59,X10,X45,X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add_Ofoldl__assoc_0) ).
fof(f7873,plain,
spl0_477,
inference(avatar_split_clause,[],[f467,f7871]) ).
fof(f7871,plain,
( spl0_477
<=> ! [X50,X65,X0,X49,X1,X14,X11,X12,X13] :
( hAPP(X11,hAPP(X12,X1)) = hAPP(X14,hAPP(X13,X1))
| c_Fun_Ocomp(X11,X12,X50,X49,X0) != c_Fun_Ocomp(X14,X13,X65,X49,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f467,axiom,
! [X50,X65,X0,X11,X49,X1,X14,X12,X13] :
( hAPP(X11,hAPP(X12,X1)) = hAPP(X14,hAPP(X13,X1))
| c_Fun_Ocomp(X11,X12,X50,X49,X0) != c_Fun_Ocomp(X14,X13,X65,X49,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
fof(f7869,plain,
spl0_476,
inference(avatar_split_clause,[],[f414,f7867]) ).
fof(f7867,plain,
( spl0_476
<=> ! [X11,X0,X13,X12,X14] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f414,axiom,
! [X0,X11,X14,X12,X13] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f7865,plain,
( spl0_475
| ~ spl0_204
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2792,f2462,f1963,f7863]) ).
fof(f7863,plain,
( spl0_475
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f1963,plain,
( spl0_204
<=> ! [X9,X8,X10] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2462,plain,
( spl0_261
<=> ! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2792,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_204
| ~ spl0_261 ),
inference(resolution,[],[f2463,f1964]) ).
fof(f1964,plain,
( ! [X10,X8,X9] :
( c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f1963]) ).
fof(f2463,plain,
( ! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f2462]) ).
fof(f7859,plain,
spl0_474,
inference(avatar_split_clause,[],[f401,f7857]) ).
fof(f401,axiom,
! [X18,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X35),X24))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X35),X18)),hAPP(hAPP(c_Lambda_Olift,X24),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
fof(f7855,plain,
spl0_473,
inference(avatar_split_clause,[],[f298,f7853]) ).
fof(f7853,plain,
( spl0_473
<=> ! [X24,X25,X39] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X24),X39))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X39),X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f298,axiom,
! [X39,X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X24),X39))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X39),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
fof(f7851,plain,
spl0_472,
inference(avatar_split_clause,[],[f297,f7849]) ).
fof(f7849,plain,
( spl0_472
<=> ! [X54,X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X54))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X24),X54))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f297,axiom,
! [X54,X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X54))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X24),X54))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
fof(f7847,plain,
spl0_471,
inference(avatar_split_clause,[],[f226,f7845]) ).
fof(f7845,plain,
( spl0_471
<=> ! [X35,X10,X0,X9,X8] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X10))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X10),X8))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f226,axiom,
! [X10,X0,X8,X9,X35] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X10))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X10),X8))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
fof(f7843,plain,
spl0_470,
inference(avatar_split_clause,[],[f128,f7841]) ).
fof(f7841,plain,
( spl0_470
<=> ! [X11,X0,X13,X12,X14] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| ~ c_lessequals(X14,X13,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f128,axiom,
! [X0,X11,X14,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| ~ c_lessequals(X14,X13,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f7839,plain,
spl0_469,
inference(avatar_split_clause,[],[f49,f7837]) ).
fof(f7837,plain,
( spl0_469
<=> ! [X11,X0,X13,X12,X14] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f49,axiom,
! [X0,X11,X14,X12,X13] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f7835,plain,
spl0_468,
inference(avatar_split_clause,[],[f48,f7833]) ).
fof(f7833,plain,
( spl0_468
<=> ! [X11,X13,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f48,axiom,
! [X0,X11,X14,X12,X13] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f7831,plain,
spl0_467,
inference(avatar_split_clause,[],[f14,f7829]) ).
fof(f7829,plain,
( spl0_467
<=> ! [X11,X13,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0)
| c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f14,axiom,
! [X0,X11,X14,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0)
| c_lessequals(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X13),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f7269,plain,
spl0_466,
inference(avatar_split_clause,[],[f723,f7267]) ).
fof(f7267,plain,
( spl0_466
<=> ! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)) = X7
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f723,plain,
! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)) = X7
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),X7,tc_nat) ),
inference(definition_unfolding,[],[f148,f87,f87]) ).
fof(f148,axiom,
! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_Suc(X15) = X7
| c_HOL_Oord__class_Oless(c_Suc(X15),X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f7265,plain,
spl0_465,
inference(avatar_split_clause,[],[f688,f7263]) ).
fof(f7263,plain,
( spl0_465
<=> ! [X18,X9,X0,X10,X22] : c_List_Olist_OCons(X9,c_List_Olist__update(X22,X18,X10,X0),X0) = c_List_Olist__update(c_List_Olist_OCons(X9,X22,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)),X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f688,plain,
! [X10,X0,X18,X9,X22] : c_List_Olist_OCons(X9,c_List_Olist__update(X22,X18,X10,X0),X0) = c_List_Olist__update(c_List_Olist_OCons(X9,X22,X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)),X10,X0),
inference(definition_unfolding,[],[f91,f87]) ).
fof(f91,axiom,
! [X10,X0,X18,X9,X22] : c_List_Olist__update(c_List_Olist_OCons(X9,X22,X0),c_Suc(X18),X10,X0) = c_List_Olist_OCons(X9,c_List_Olist__update(X22,X18,X10,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
fof(f7258,plain,
spl0_464,
inference(avatar_split_clause,[],[f579,f7256]) ).
fof(f7256,plain,
( spl0_464
<=> ! [X20,X24,X25] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25)),X20) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X24),X20)),hAPP(hAPP(c_Lambda_Olift,X25),X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f579,axiom,
! [X24,X25,X20] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25)),X20) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X24),X20)),hAPP(hAPP(c_Lambda_Olift,X25),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
fof(f7254,plain,
spl0_463,
inference(avatar_split_clause,[],[f558,f7252]) ).
fof(f7252,plain,
( spl0_463
<=> ! [X28,X18,X53,X27,X26] :
( X26 = X27
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X53,tc_Lambda_OdB,tc_Lambda_OdB),X27)
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X53,tc_Lambda_OdB,tc_Lambda_OdB),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f558,axiom,
! [X28,X18,X26,X27,X53] :
( X26 = X27
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X53,tc_Lambda_OdB,tc_Lambda_OdB),X27)
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X53,tc_Lambda_OdB,tc_Lambda_OdB),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
fof(f7250,plain,
spl0_462,
inference(avatar_split_clause,[],[f541,f7248]) ).
fof(f7248,plain,
( spl0_462
<=> ! [X45,X9,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0),X45,X0,X0)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),X9,X45,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f541,axiom,
! [X0,X9,X45] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0),X45,X0,X0)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),X9,X45,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
fof(f7246,plain,
spl0_461,
inference(avatar_split_clause,[],[f432,f7244]) ).
fof(f7244,plain,
( spl0_461
<=> ! [X48,X47,X0,X64,X50,X49,X65] : c_Fun_Ocomp(X47,c_Fun_Ocomp(X48,X64,X65,X50,X0),X50,X49,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X47,X48,X50,X49,X65),X64,X65,X49,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f432,axiom,
! [X50,X65,X48,X0,X49,X47,X64] : c_Fun_Ocomp(X47,c_Fun_Ocomp(X48,X64,X65,X50,X0),X50,X49,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X47,X48,X50,X49,X65),X64,X65,X49,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f7242,plain,
spl0_460,
inference(avatar_split_clause,[],[f284,f7240]) ).
fof(f7240,plain,
( spl0_460
<=> ! [X0,X9,X22,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_List_Otake(X7,c_List_Olist_OCons(X9,X22,X0),X0) = c_List_Olist_OCons(X9,c_List_Otake(c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f284,axiom,
! [X0,X9,X7,X22] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_List_Otake(X7,c_List_Olist_OCons(X9,X22,X0),X0) = c_List_Olist_OCons(X9,c_List_Otake(c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X22,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).
fof(f7238,plain,
spl0_459,
inference(avatar_split_clause,[],[f206,f7236]) ).
fof(f7236,plain,
( spl0_459
<=> ! [X9,X8,X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f206,axiom,
! [X10,X8,X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f7234,plain,
spl0_458,
inference(avatar_split_clause,[],[f205,f7232]) ).
fof(f7232,plain,
( spl0_458
<=> ! [X20,X7,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)),X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f205,axiom,
! [X7,X15,X20] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)),X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f7178,plain,
( ~ spl0_456
| spl0_198
| ~ spl0_457
| ~ spl0_95
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2671,f2376,f1230,f7175,f1890,f7171]) ).
fof(f7171,plain,
( spl0_456
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f1890,plain,
( spl0_198
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f7175,plain,
( spl0_457
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f1230,plain,
( spl0_95
<=> ! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f2376,plain,
( spl0_240
<=> ! [X9,X0,X10] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X9 = X10
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2671,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_95
| ~ spl0_240 ),
inference(trivial_inequality_removal,[],[f2666]) ).
fof(f2666,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_95
| ~ spl0_240 ),
inference(superposition,[],[f2377,f1231]) ).
fof(f1231,plain,
( ! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f2377,plain,
( ! [X10,X0,X9] :
( c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Int_Onumber__ring(X0)
| X9 = X10
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2376]) ).
fof(f6836,plain,
( spl0_455
| ~ spl0_58
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1546,f1450,f1076,f6834]) ).
fof(f6834,plain,
( spl0_455
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1076,plain,
( spl0_58
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1450,plain,
( spl0_142
<=> ! [X0,X11] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X11,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1546,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_58
| ~ spl0_142 ),
inference(resolution,[],[f1451,f1078]) ).
fof(f1078,plain,
( class_Power_Opower(tc_Int_Oint)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1076]) ).
fof(f1451,plain,
( ! [X0,X11] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X11,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1450]) ).
fof(f6725,plain,
spl0_454,
inference(avatar_split_clause,[],[f550,f6723]) ).
fof(f6723,plain,
( spl0_454
<=> ! [X24,X35,X71] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X71,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f550,axiom,
! [X71,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X71,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
fof(f6721,plain,
spl0_453,
inference(avatar_split_clause,[],[f483,f6719]) ).
fof(f6719,plain,
( spl0_453
<=> ! [X35,X11,X14,X0,X12] :
( ~ hBOOL(hAPP(hAPP(X35,X12),X14))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X11),X12))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X11),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f483,axiom,
! [X0,X11,X14,X35,X12] :
( ~ hBOOL(hAPP(hAPP(X35,X12),X14))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X11),X12))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X11),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(f6717,plain,
spl0_452,
inference(avatar_split_clause,[],[f482,f6715]) ).
fof(f6715,plain,
( spl0_452
<=> ! [X35,X11,X14,X0,X12] :
( ~ hBOOL(hAPP(hAPP(X35,X11),X12))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X12),X14))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X11),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f482,axiom,
! [X0,X11,X14,X35,X12] :
( ~ hBOOL(hAPP(hAPP(X35,X11),X12))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X12),X14))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X11),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
fof(f6713,plain,
spl0_451,
inference(avatar_split_clause,[],[f466,f6711]) ).
fof(f6711,plain,
( spl0_451
<=> ! [X18,X0,X22,X9,X67,X16] :
( X18 = X67
| c_List_Olist__update(c_List_Olist__update(X22,X18,X9,X0),X67,X16,X0) = c_List_Olist__update(c_List_Olist__update(X22,X67,X16,X0),X18,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f466,axiom,
! [X0,X18,X9,X16,X22,X67] :
( X18 = X67
| c_List_Olist__update(c_List_Olist__update(X22,X18,X9,X0),X67,X16,X0) = c_List_Olist__update(c_List_Olist__update(X22,X67,X16,X0),X18,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
fof(f6709,plain,
spl0_450,
inference(avatar_split_clause,[],[f464,f6707]) ).
fof(f6707,plain,
( spl0_450
<=> ! [X35,X10,X9,X0,X36,X22] :
( c_ListOrder_Ostep1(X35,X36,X22,X0)
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f464,axiom,
! [X10,X0,X36,X9,X35,X22] :
( c_ListOrder_Ostep1(X35,X36,X22,X0)
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
fof(f6705,plain,
( spl0_449
| ~ spl0_23
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1545,f1450,f901,f6703]) ).
fof(f6703,plain,
( spl0_449
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f901,plain,
( spl0_23
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1545,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_23
| ~ spl0_142 ),
inference(resolution,[],[f1451,f903]) ).
fof(f903,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f901]) ).
fof(f6701,plain,
spl0_448,
inference(avatar_split_clause,[],[f415,f6699]) ).
fof(f6699,plain,
( spl0_448
<=> ! [X18,X20,X31,X21] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X31,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X31),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f415,axiom,
! [X31,X21,X18,X20] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X20,X31,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X31),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f6697,plain,
spl0_447,
inference(avatar_split_clause,[],[f404,f6695]) ).
fof(f6695,plain,
( spl0_447
<=> ! [X59,X11,X0,X14,X12] :
( ~ c_OrderedGroup_Osemigroup__add(X59,X0)
| hAPP(hAPP(X59,hAPP(hAPP(X59,X11),X12)),X14) = hAPP(hAPP(X59,X11),hAPP(hAPP(X59,X12),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f404,axiom,
! [X59,X0,X11,X14,X12] :
( ~ c_OrderedGroup_Osemigroup__add(X59,X0)
| hAPP(hAPP(X59,hAPP(hAPP(X59,X11),X12)),X14) = hAPP(hAPP(X59,X11),hAPP(hAPP(X59,X12),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add_Oadd__assoc_0) ).
fof(f6693,plain,
spl0_446,
inference(avatar_split_clause,[],[f402,f6691]) ).
fof(f6691,plain,
( spl0_446
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f402,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f6689,plain,
spl0_445,
inference(avatar_split_clause,[],[f329,f6687]) ).
fof(f6687,plain,
( spl0_445
<=> ! [X18,X34,X27,X25,X58,X26] :
( ~ c_Type_Otyping(X58,X34,X26)
| ~ c_Type_Otyping(c_Type_Oshift(X58,X18,X26,tc_Type_Otype),X25,X27)
| c_Type_Otyping(X58,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X34),X18),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f329,axiom,
! [X58,X18,X26,X27,X34,X25] :
( ~ c_Type_Otyping(X58,X34,X26)
| ~ c_Type_Otyping(c_Type_Oshift(X58,X18,X26,tc_Type_Otype),X25,X27)
| c_Type_Otyping(X58,hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X34),X18),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
fof(f6685,plain,
spl0_444,
inference(avatar_split_clause,[],[f294,f6683]) ).
fof(f6683,plain,
( spl0_444
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f294,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f6681,plain,
spl0_443,
inference(avatar_split_clause,[],[f185,f6679]) ).
fof(f6679,plain,
( spl0_443
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f185,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f6677,plain,
spl0_442,
inference(avatar_split_clause,[],[f184,f6675]) ).
fof(f6675,plain,
( spl0_442
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f184,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f6673,plain,
spl0_441,
inference(avatar_split_clause,[],[f183,f6671]) ).
fof(f6671,plain,
( spl0_441
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X12,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f183,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X12,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f6669,plain,
spl0_440,
inference(avatar_split_clause,[],[f182,f6667]) ).
fof(f6667,plain,
( spl0_440
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X12,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f182,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X12,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f6665,plain,
spl0_439,
inference(avatar_split_clause,[],[f181,f6663]) ).
fof(f6663,plain,
( spl0_439
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f181,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f6661,plain,
( spl0_438
| ~ spl0_48
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1537,f1438,f1026,f6659]) ).
fof(f6659,plain,
( spl0_438
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f1026,plain,
( spl0_48
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1438,plain,
( spl0_139
<=> ! [X0,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1537,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint)
| ~ spl0_48
| ~ spl0_139 ),
inference(resolution,[],[f1439,f1028]) ).
fof(f1028,plain,
( class_OrderedGroup_Omonoid__mult(tc_Int_Oint)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f1439,plain,
( ! [X0,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X7,X0) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f6657,plain,
spl0_437,
inference(avatar_split_clause,[],[f180,f6655]) ).
fof(f6655,plain,
( spl0_437
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f180,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f6653,plain,
spl0_436,
inference(avatar_split_clause,[],[f47,f6651]) ).
fof(f6651,plain,
( spl0_436
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f47,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X12,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f6649,plain,
spl0_435,
inference(avatar_split_clause,[],[f42,f6647]) ).
fof(f6647,plain,
( spl0_435
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X12,X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X14,X0)
| c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f42,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X12,X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X14,X0)
| c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f6645,plain,
spl0_434,
inference(avatar_split_clause,[],[f41,f6643]) ).
fof(f6643,plain,
( spl0_434
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X12,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f41,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X12,X14,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f6641,plain,
spl0_433,
inference(avatar_split_clause,[],[f37,f6639]) ).
fof(f6639,plain,
( spl0_433
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f37,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f6463,plain,
( spl0_432
| ~ spl0_17
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1536,f1438,f871,f6461]) ).
fof(f6461,plain,
( spl0_432
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f871,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1536,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_17
| ~ spl0_139 ),
inference(resolution,[],[f1439,f873]) ).
fof(f873,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f871]) ).
fof(f6279,plain,
( spl0_431
| ~ spl0_44
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1535,f1434,f1006,f6277]) ).
fof(f6277,plain,
( spl0_431
<=> ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat__aux(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f1006,plain,
( spl0_44
<=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1434,plain,
( spl0_138
<=> ! [X18,X0,X32] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X32,c_HOL_Ozero__class_Ozero(tc_nat),X18,X0) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1535,plain,
( ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat__aux(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_Int_Oint) = X1
| ~ spl0_44
| ~ spl0_138 ),
inference(resolution,[],[f1435,f1008]) ).
fof(f1008,plain,
( class_Ring__and__Field_Osemiring__1(tc_Int_Oint)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1435,plain,
( ! [X0,X18,X32] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X32,c_HOL_Ozero__class_Ozero(tc_nat),X18,X0) = X18 )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f6225,plain,
spl0_430,
inference(avatar_split_clause,[],[f746,f6223]) ).
fof(f6223,plain,
( spl0_430
<=> ! [X52,X51] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X51)),c_Lambda_OdB_OdB__size(X52))),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f746,plain,
! [X51,X52] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X51)),c_Lambda_OdB_OdB__size(X52))),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f745,f374]) ).
fof(f745,plain,
! [X51,X52] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X51)),c_Lambda_OdB_OdB__size(X52))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f690,f247]) ).
fof(f690,plain,
! [X51,X52] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X51)),c_Lambda_OdB_OdB__size(X52))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f273,f87]) ).
fof(f273,axiom,
! [X51,X52] : c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X51)),c_Lambda_OdB_OdB__size(X52))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).
fof(f6221,plain,
spl0_429,
inference(avatar_split_clause,[],[f717,f6219]) ).
fof(f6219,plain,
( spl0_429
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f717,plain,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X0),X0) ),
inference(definition_unfolding,[],[f187,f87]) ).
fof(f187,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X11,c_Suc(X7),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
fof(f6217,plain,
spl0_428,
inference(avatar_split_clause,[],[f694,f6215]) ).
fof(f6215,plain,
( spl0_428
<=> ! [X18,X0,X32,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X32,X7,hAPP(X32,X18),X0) = c_Nat_Osemiring__1__class_Oof__nat__aux(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f694,plain,
! [X0,X18,X7,X32] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X32,X7,hAPP(X32,X18),X0) = c_Nat_Osemiring__1__class_Oof__nat__aux(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X18,X0) ),
inference(definition_unfolding,[],[f138,f87]) ).
fof(f138,axiom,
! [X0,X18,X7,X32] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X32,c_Suc(X7),X18,X0) = c_Nat_Osemiring__1__class_Oof__nat__aux(X32,X7,hAPP(X32,X18),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I2_J_0) ).
fof(f6213,plain,
spl0_427,
inference(avatar_split_clause,[],[f693,f6211]) ).
fof(f6211,plain,
( spl0_427
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_Oof__nat(X15,X0)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f693,plain,
! [X0,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_Oof__nat(X15,X0)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
inference(definition_unfolding,[],[f188,f87]) ).
fof(f188,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X15),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_Oof__nat(X15,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
fof(f6209,plain,
spl0_426,
inference(avatar_split_clause,[],[f685,f6207]) ).
fof(f6207,plain,
( spl0_426
<=> ! [X0,X9,X22,X7] : c_List_Olist_OCons(X9,c_List_Otake(X7,X22,X0),X0) = c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(X9,X22,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f685,plain,
! [X0,X9,X7,X22] : c_List_Olist_OCons(X9,c_List_Otake(X7,X22,X0),X0) = c_List_Otake(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),c_List_Olist_OCons(X9,X22,X0),X0),
inference(definition_unfolding,[],[f89,f87]) ).
fof(f89,axiom,
! [X0,X9,X7,X22] : c_List_Otake(c_Suc(X7),c_List_Olist_OCons(X9,X22,X0),X0) = c_List_Olist_OCons(X9,c_List_Otake(X7,X22,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
fof(f6205,plain,
spl0_425,
inference(avatar_split_clause,[],[f556,f6203]) ).
fof(f6203,plain,
( spl0_425
<=> ! [X18,X53,X73,X28,X26] :
( ~ c_Type_Otypings(X28,X53,X73)
| c_Type_Otypings(c_Type_Oshift(X28,X18,X26,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X18,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),X73) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f556,axiom,
! [X28,X73,X18,X26,X53] :
( ~ c_Type_Otypings(X28,X53,X73)
| c_Type_Otypings(c_Type_Oshift(X28,X18,X26,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,X18,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),X73) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).
fof(f6201,plain,
spl0_424,
inference(avatar_split_clause,[],[f515,f6199]) ).
fof(f6199,plain,
( spl0_424
<=> ! [X25,X19] :
( hBOOL(hAPP(X19,X25))
| hBOOL(hAPP(X19,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X19)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X19)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f515,axiom,
! [X19,X25] :
( hBOOL(hAPP(X19,X25))
| hBOOL(hAPP(X19,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(X19)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(X19)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Apps__dB__induct_3) ).
fof(f6197,plain,
( spl0_423
| ~ spl0_14
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1534,f1434,f856,f6195]) ).
fof(f6195,plain,
( spl0_423
<=> ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat__aux(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f856,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1534,plain,
( ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat__aux(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1
| ~ spl0_14
| ~ spl0_138 ),
inference(resolution,[],[f1435,f858]) ).
fof(f858,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f6193,plain,
spl0_422,
inference(avatar_split_clause,[],[f513,f6191]) ).
fof(f6191,plain,
( spl0_422
<=> ! [X25,X19] :
( hBOOL(hAPP(X19,X25))
| hBOOL(hAPP(X19,c_ListApplication_Osko__ListApplication__Xlem__1__3(X19)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X19)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f513,axiom,
! [X19,X25] :
( hBOOL(hAPP(X19,X25))
| hBOOL(hAPP(X19,c_ListApplication_Osko__ListApplication__Xlem__1__3(X19)))
| ~ hBOOL(hAPP(X19,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(X19)),c_ListApplication_Osko__ListApplication__Xlem__1__2(X19),tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem_3) ).
fof(f6189,plain,
spl0_421,
inference(avatar_split_clause,[],[f512,f6187]) ).
fof(f6187,plain,
( spl0_421
<=> ! [X49,X11,X47,X0,X36,X22] : c_List_Ofoldl(X47,X11,c_List_Oappend(X22,X36,X49),X0,X49) = c_List_Ofoldl(X47,c_List_Ofoldl(X47,X11,X22,X0,X49),X36,X0,X49) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f512,axiom,
! [X0,X11,X36,X49,X47,X22] : c_List_Ofoldl(X47,X11,c_List_Oappend(X22,X36,X49),X0,X49) = c_List_Ofoldl(X47,c_List_Ofoldl(X47,X11,X22,X0,X49),X36,X0,X49),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
fof(f6185,plain,
spl0_420,
inference(avatar_split_clause,[],[f500,f6183]) ).
fof(f6183,plain,
( spl0_420
<=> ! [X71,X35,X72] :
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X72,X71,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X72,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X71,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f500,axiom,
! [X72,X71,X35] :
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X72,X71,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X72,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X71,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
fof(f6181,plain,
spl0_419,
inference(avatar_split_clause,[],[f497,f6179]) ).
fof(f6179,plain,
( spl0_419
<=> ! [X47,X20,X0,X22,X10,X49] : c_List_Omap(X47,c_List_Olist__update(X22,X20,X10,X49),X49,X0) = c_List_Olist__update(c_List_Omap(X47,X22,X49,X0),X20,hAPP(X47,X10),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f497,axiom,
! [X10,X0,X49,X47,X22,X20] : c_List_Omap(X47,c_List_Olist__update(X22,X20,X10,X49),X49,X0) = c_List_Olist__update(c_List_Omap(X47,X22,X49,X0),X20,hAPP(X47,X10),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__update_0) ).
fof(f6177,plain,
spl0_418,
inference(avatar_split_clause,[],[f470,f6175]) ).
fof(f6175,plain,
( spl0_418
<=> ! [X0,X7,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Nat_Osemiring__1__class_Oof__nat(X15,X0)),c_Nat_Osemiring__1__class_Oof__nat(X7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f470,axiom,
! [X0,X7,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Nat_Osemiring__1__class_Oof__nat(X15,X0)),c_Nat_Osemiring__1__class_Oof__nat(X7,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
fof(f6173,plain,
spl0_417,
inference(avatar_split_clause,[],[f441,f6171]) ).
fof(f6171,plain,
( spl0_417
<=> ! [X10,X0,X12,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X12,X9,X0),c_Power_Opower__class_Opower(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f441,axiom,
! [X10,X0,X9,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X12,X9,X0),c_Power_Opower__class_Opower(X12,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
fof(f6169,plain,
spl0_416,
inference(avatar_split_clause,[],[f440,f6167]) ).
fof(f6167,plain,
( spl0_416
<=> ! [X10,X0,X12,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X12,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X12,X9,X0),c_Power_Opower__class_Opower(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f440,axiom,
! [X10,X0,X9,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X12,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X12,X9,X0),c_Power_Opower__class_Opower(X12,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
fof(f6165,plain,
spl0_415,
inference(avatar_split_clause,[],[f385,f6163]) ).
fof(f6163,plain,
( spl0_415
<=> ! [X47,X0,X22,X36,X49] : c_List_Omap(X47,c_List_Oappend(X22,X36,X49),X49,X0) = c_List_Oappend(c_List_Omap(X47,X22,X49,X0),c_List_Omap(X47,X36,X49,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f385,axiom,
! [X0,X36,X49,X47,X22] : c_List_Omap(X47,c_List_Oappend(X22,X36,X49),X49,X0) = c_List_Oappend(c_List_Omap(X47,X22,X49,X0),c_List_Omap(X47,X36,X49,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).
fof(f6161,plain,
spl0_414,
inference(avatar_split_clause,[],[f248,f6159]) ).
fof(f6159,plain,
( spl0_414
<=> ! [X31,X20,X15,X7] :
( ~ c_HOL_Oord__class_Oless(X20,X31,tc_nat)
| c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f248,axiom,
! [X31,X7,X15,X20] :
( ~ c_HOL_Oord__class_Oless(X20,X31,tc_nat)
| c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f6157,plain,
spl0_413,
inference(avatar_split_clause,[],[f186,f6155]) ).
fof(f6155,plain,
( spl0_413
<=> ! [X11,X0,X12,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,X7,X0),c_Power_Opower__class_Opower(X12,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f186,axiom,
! [X0,X11,X7,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X11,X7,X0),c_Power_Opower__class_Opower(X12,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f6153,plain,
spl0_412,
inference(avatar_split_clause,[],[f62,f6151]) ).
fof(f6151,plain,
( spl0_412
<=> ! [X11,X0,X12,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X11,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(c_Power_Opower__class_Opower(X11,X7,X0),c_Power_Opower__class_Opower(X12,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f62,axiom,
! [X0,X11,X7,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X11,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(c_Power_Opower__class_Opower(X11,X7,X0),c_Power_Opower__class_Opower(X12,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f6103,plain,
( spl0_411
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f5390,f5386,f4877,f1980,f1320,f1168,f6101]) ).
fof(f6101,plain,
( spl0_411
<=> ! [X18,X24,X35] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X35,X18)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,X18)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f5386,plain,
( spl0_406
<=> ! [X18,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X35),X18)),hAPP(hAPP(c_Lambda_Olift,X24),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f5390,plain,
( ! [X18,X24,X35] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X35,X18)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,X18)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24)) )
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_406 ),
inference(forward_demodulation,[],[f5389,f5260]) ).
fof(f5389,plain,
( ! [X18,X24,X35] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X35),X18)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X24,X18)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24)) )
| ~ spl0_80
| ~ spl0_117
| ~ spl0_208
| ~ spl0_377
| ~ spl0_406 ),
inference(forward_demodulation,[],[f5387,f5260]) ).
fof(f5387,plain,
( ! [X18,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X35),X18)),hAPP(hAPP(c_Lambda_Olift,X24),X18))) )
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f5386]) ).
fof(f6012,plain,
( ~ spl0_410
| ~ spl0_355
| spl0_409 ),
inference(avatar_split_clause,[],[f5646,f5422,f4228,f6009]) ).
fof(f6009,plain,
( spl0_410
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f4228,plain,
( spl0_355
<=> ! [X53] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X53,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f5646,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ spl0_355
| spl0_409 ),
inference(resolution,[],[f5424,f4229]) ).
fof(f4229,plain,
( ! [X53] :
( c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ c_List_Olistsp(c_InductTermi_OIT,X53,tc_Lambda_OdB) )
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f4228]) ).
fof(f5424,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| spl0_409 ),
inference(avatar_component_clause,[],[f5422]) ).
fof(f5425,plain,
( ~ spl0_409
| spl0_129
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2784,f2446,f1397,f5422]) ).
fof(f1397,plain,
( spl0_129
<=> 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_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2446,plain,
( spl0_257
<=> ! [X72,X7] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X72,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X72,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2784,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| spl0_129
| ~ spl0_257 ),
inference(resolution,[],[f2447,f1399]) ).
fof(f1399,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_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| spl0_129 ),
inference(avatar_component_clause,[],[f1397]) ).
fof(f2447,plain,
( ! [X72,X7] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X72,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ c_List_Olistsp(c_InductTermi_OIT,X72,tc_Lambda_OdB) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2446]) ).
fof(f5398,plain,
spl0_408,
inference(avatar_split_clause,[],[f707,f5396]) ).
fof(f5396,plain,
( spl0_408
<=> ! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f707,plain,
! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f159,f87,f87]) ).
fof(f159,axiom,
! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X15),c_Suc(X7),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f5394,plain,
spl0_407,
inference(avatar_split_clause,[],[f537,f5392]) ).
fof(f5392,plain,
( spl0_407
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f537,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f5388,plain,
spl0_406,
inference(avatar_split_clause,[],[f533,f5386]) ).
fof(f533,axiom,
! [X18,X24,X35] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X35),X24))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X35),X18)),hAPP(hAPP(c_Lambda_Olift,X24),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
fof(f5384,plain,
spl0_405,
inference(avatar_split_clause,[],[f517,f5382]) ).
fof(f5382,plain,
( spl0_405
<=> ! [X1,X72,X7] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X72,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X7,X72,X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X72,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f517,axiom,
! [X72,X1,X7] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X72,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X7,X72,X1),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X72,tc_Lambda_OdB,tc_Lambda_OdB)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
fof(f5380,plain,
spl0_404,
inference(avatar_split_clause,[],[f511,f5378]) ).
fof(f5378,plain,
( spl0_404
<=> ! [X49,X11,X47,X0,X9,X22] : c_List_Ofoldl(X47,X11,c_List_Olist_OCons(X9,X22,X49),X0,X49) = c_List_Ofoldl(X47,hAPP(hAPP(X47,X11),X9),X22,X0,X49) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f5376,plain,
spl0_403,
inference(avatar_split_clause,[],[f491,f5374]) ).
fof(f5374,plain,
( spl0_403
<=> ! [X48,X47,X0,X50,X49,X22] : c_List_Omap(X47,c_List_Omap(X48,X22,X50,X49),X49,X0) = c_List_Omap(c_Fun_Ocomp(X47,X48,X49,X0,X50),X22,X50,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f491,axiom,
! [X50,X48,X0,X49,X47,X22] : c_List_Omap(X47,c_List_Omap(X48,X22,X50,X49),X49,X0) = c_List_Omap(c_Fun_Ocomp(X47,X48,X49,X0,X50),X22,X50,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__map_0) ).
fof(f5372,plain,
spl0_402,
inference(avatar_split_clause,[],[f472,f5370]) ).
fof(f5370,plain,
( spl0_402
<=> ! [X10,X0,X9,X22,X36] :
( X9 = X10
| c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f472,axiom,
! [X10,X0,X36,X9,X22] :
( X9 = X10
| c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
fof(f5368,plain,
spl0_401,
inference(avatar_split_clause,[],[f471,f5366]) ).
fof(f5366,plain,
( spl0_401
<=> ! [X10,X9,X0,X36,X22] :
( X22 = X36
| c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f471,axiom,
! [X10,X0,X36,X9,X22] :
( X22 = X36
| c_List_Oappend(X36,c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X22,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
fof(f5364,plain,
spl0_400,
inference(avatar_split_clause,[],[f456,f5362]) ).
fof(f5362,plain,
( spl0_400
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f456,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f5357,plain,
spl0_399,
inference(avatar_split_clause,[],[f455,f5355]) ).
fof(f5355,plain,
( spl0_399
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f455,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f5353,plain,
spl0_398,
inference(avatar_split_clause,[],[f454,f5351]) ).
fof(f5351,plain,
( spl0_398
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f454,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f5349,plain,
spl0_397,
inference(avatar_split_clause,[],[f453,f5347]) ).
fof(f5347,plain,
( spl0_397
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f453,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f5345,plain,
spl0_396,
inference(avatar_split_clause,[],[f452,f5343]) ).
fof(f5343,plain,
( spl0_396
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f452,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f5341,plain,
spl0_395,
inference(avatar_split_clause,[],[f451,f5339]) ).
fof(f5339,plain,
( spl0_395
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f451,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f5337,plain,
spl0_394,
inference(avatar_split_clause,[],[f437,f5335]) ).
fof(f5335,plain,
( spl0_394
<=> ! [X11,X0,X14,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X12,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f437,axiom,
! [X0,X11,X14,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X12,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f5333,plain,
spl0_393,
inference(avatar_split_clause,[],[f382,f5331]) ).
fof(f5331,plain,
( spl0_393
<=> ! [X34,X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X24),X25))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X34)),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X34))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f382,axiom,
! [X34,X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X24),X25))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X34)),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
fof(f5329,plain,
spl0_392,
inference(avatar_split_clause,[],[f381,f5327]) ).
fof(f5327,plain,
( spl0_392
<=> ! [X34,X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X24),X25))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X34),X24)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f381,axiom,
! [X34,X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X24),X25))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X34),X24)),hAPP(hAPP(c_Lambda_OdB_OApp,X34),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
fof(f5325,plain,
spl0_391,
inference(avatar_split_clause,[],[f315,f5323]) ).
fof(f5323,plain,
( spl0_391
<=> ! [X35,X10,X0,X9,X22,X36] :
( X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f315,axiom,
! [X10,X0,X36,X9,X35,X22] :
( X9 = X10
| hBOOL(hAPP(hAPP(X35,X10),X9))
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
fof(f5321,plain,
spl0_390,
inference(avatar_split_clause,[],[f307,f5319]) ).
fof(f5319,plain,
( spl0_390
<=> ! [X10,X0,X9,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X8 = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X10) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f307,axiom,
! [X10,X0,X8,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X8 = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X10) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f5316,plain,
spl0_389,
inference(avatar_split_clause,[],[f292,f5314]) ).
fof(f5314,plain,
( spl0_389
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f292,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
fof(f5312,plain,
spl0_388,
inference(avatar_split_clause,[],[f291,f5310]) ).
fof(f5310,plain,
( spl0_388
<=> ! [X10,X0,X36,X22] :
( c_List_Orev(X22,X0) != c_List_Olist_OCons(X10,X36,X0)
| c_List_Oappend(c_List_Orev(X36,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) = X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f291,axiom,
! [X10,X0,X36,X22] :
( c_List_Orev(X22,X0) != c_List_Olist_OCons(X10,X36,X0)
| c_List_Oappend(c_List_Orev(X36,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0) = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
fof(f5308,plain,
spl0_387,
inference(avatar_split_clause,[],[f197,f5306]) ).
fof(f5306,plain,
( spl0_387
<=> ! [X7,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f197,axiom,
! [X7,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f5304,plain,
spl0_386,
inference(avatar_split_clause,[],[f179,f5302]) ).
fof(f5302,plain,
( spl0_386
<=> ! [X24,X20,X25,X7] : c_Lambda_Oliftn(X7,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25),X20) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X7,X24,X20)),c_Lambda_Oliftn(X7,X25,X20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f179,axiom,
! [X7,X24,X25,X20] : c_Lambda_Oliftn(X7,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25),X20) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X7,X24,X20)),c_Lambda_Oliftn(X7,X25,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
fof(f5300,plain,
spl0_385,
inference(avatar_split_clause,[],[f101,f5298]) ).
fof(f5298,plain,
( spl0_385
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f101,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f5296,plain,
spl0_384,
inference(avatar_split_clause,[],[f100,f5294]) ).
fof(f5294,plain,
( spl0_384
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X11,X12,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f100,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X11,X12,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f5292,plain,
spl0_383,
inference(avatar_split_clause,[],[f99,f5290]) ).
fof(f5290,plain,
( spl0_383
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f99,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f5288,plain,
spl0_382,
inference(avatar_split_clause,[],[f98,f5286]) ).
fof(f5286,plain,
( spl0_382
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X11,X12,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f98,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X11,X12,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f5284,plain,
spl0_381,
inference(avatar_split_clause,[],[f97,f5282]) ).
fof(f5282,plain,
( spl0_381
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f97,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f5280,plain,
spl0_380,
inference(avatar_split_clause,[],[f96,f5278]) ).
fof(f5278,plain,
( spl0_380
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f96,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f5276,plain,
( spl0_379
| ~ spl0_226
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f5089,f3723,f2176,f5274]) ).
fof(f5274,plain,
( spl0_379
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2176,plain,
( spl0_226
<=> ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f3723,plain,
( spl0_338
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f5089,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X0))
| ~ spl0_226
| ~ spl0_338 ),
inference(superposition,[],[f2177,f3724]) ).
fof(f3724,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f3723]) ).
fof(f2177,plain,
( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0)
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2176]) ).
fof(f4883,plain,
spl0_378,
inference(avatar_split_clause,[],[f735,f4881]) ).
fof(f4881,plain,
( spl0_378
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f735,plain,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
inference(duplicate_literal_removal,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f4879,plain,
spl0_377,
inference(avatar_split_clause,[],[f680,f4877]) ).
fof(f680,plain,
! [X7,X25,X20] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X7,X25,X20)),X20) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X25,X20),
inference(definition_unfolding,[],[f120,f87]) ).
fof(f120,axiom,
! [X7,X25,X20] : c_Lambda_Oliftn(c_Suc(X7),X25,X20) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X7,X25,X20)),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
fof(f4875,plain,
spl0_376,
inference(avatar_split_clause,[],[f494,f4873]) ).
fof(f4873,plain,
( spl0_376
<=> ! [X9,X47,X0,X49,X22] : c_List_Omap(X47,c_List_Olist_OCons(X9,X22,X49),X49,X0) = c_List_Olist_OCons(hAPP(X47,X9),c_List_Omap(X47,X22,X49,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f494,axiom,
! [X0,X49,X47,X9,X22] : c_List_Omap(X47,c_List_Olist_OCons(X9,X22,X49),X49,X0) = c_List_Olist_OCons(hAPP(X47,X9),c_List_Omap(X47,X22,X49,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
fof(f4871,plain,
spl0_375,
inference(avatar_split_clause,[],[f474,f4869]) ).
fof(f4869,plain,
( spl0_375
<=> ! [X20,X24] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X24)),X20) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f474,axiom,
! [X24,X20] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X24)),X20) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X24),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
fof(f4853,plain,
spl0_374,
inference(avatar_split_clause,[],[f427,f4851]) ).
fof(f4851,plain,
( spl0_374
<=> ! [X11,X0,X15,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X7 = X15
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_Power_Opower__class_Opower(X11,X7,X0) != c_Power_Opower__class_Opower(X11,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f427,axiom,
! [X0,X11,X7,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X7 = X15
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_Power_Opower__class_Opower(X11,X7,X0) != c_Power_Opower__class_Opower(X11,X15,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f4849,plain,
spl0_373,
inference(avatar_split_clause,[],[f403,f4847]) ).
fof(f4847,plain,
( spl0_373
<=> ! [X35,X10,X9,X0,X36,X22] :
( X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0)
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f403,axiom,
! [X10,X0,X36,X9,X22,X35] :
( X22 = X36
| c_ListOrder_Ostep1(X35,X36,X22,X0)
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
fof(f4845,plain,
spl0_372,
inference(avatar_split_clause,[],[f395,f4843]) ).
fof(f4843,plain,
( spl0_372
<=> ! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X11)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f395,axiom,
! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(X11)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_11) ).
fof(f4841,plain,
spl0_371,
inference(avatar_split_clause,[],[f347,f4839]) ).
fof(f4839,plain,
( spl0_371
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X11,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f347,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X11,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f4837,plain,
spl0_370,
inference(avatar_split_clause,[],[f283,f4835]) ).
fof(f4835,plain,
( spl0_370
<=> ! [X20,X18,X24] :
( ~ c_HOL_Oord__class_Oless(X20,X18,tc_nat)
| c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X18)),X24),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f283,axiom,
! [X18,X24,X20] :
( ~ c_HOL_Oord__class_Oless(X20,X18,tc_nat)
| c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X18,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X18)),X24),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).
fof(f4833,plain,
spl0_369,
inference(avatar_split_clause,[],[f271,f4831]) ).
fof(f4831,plain,
( spl0_369
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(X7,X0) = c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0),X0,X0,X0),X7,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f271,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(X7,X0) = c_Nat_Osemiring__1__class_Oof__nat__aux(c_COMBC(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0),X0,X0,X0),X7,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__1__class_Oof__nat__code_0) ).
fof(f4829,plain,
spl0_368,
inference(avatar_split_clause,[],[f228,f4827]) ).
fof(f4827,plain,
( spl0_368
<=> ! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X11)) = X11
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f228,axiom,
! [X11] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X11))
| c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(X11)) = X11
| hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(X11)))
| c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(X11),tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_8) ).
fof(f4777,plain,
( spl0_367
| ~ spl0_65
| ~ spl0_316
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f4773,f4770,f3611,f1108,f4775]) ).
fof(f4775,plain,
( spl0_367
<=> ! [X20,X18] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X20) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OVar(X18),c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X18,X20,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f1108,plain,
( spl0_65
<=> ! [X7] : ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f3611,plain,
( spl0_316
<=> ! [X20,X7,X18] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| c_Lambda_Oliftn(X7,c_Lambda_OdB_OVar(X18),X20) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f4770,plain,
( spl0_366
<=> ! [X20,X18] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X20) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f4773,plain,
( ! [X18,X20] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X20) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OVar(X18),c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X18,X20,tc_nat) )
| ~ spl0_65
| ~ spl0_316
| ~ spl0_366 ),
inference(forward_demodulation,[],[f4771,f3831]) ).
fof(f3831,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_65
| ~ spl0_316 ),
inference(resolution,[],[f3612,f1109]) ).
fof(f1109,plain,
( ! [X7] : ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f3612,plain,
( ! [X18,X7,X20] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| c_Lambda_Oliftn(X7,c_Lambda_OdB_OVar(X18),X20) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X7)) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f3611]) ).
fof(f4771,plain,
( ! [X18,X20] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X20) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat))) )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f4770]) ).
fof(f4772,plain,
spl0_366,
inference(avatar_split_clause,[],[f195,f4770]) ).
fof(f195,axiom,
! [X18,X20] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X20) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
fof(f4756,plain,
spl0_365,
inference(avatar_split_clause,[],[f191,f4754]) ).
fof(f4754,plain,
( spl0_365
<=> ! [X28,X18,X0,X27,X21] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| hAPP(c_Type_Oshift(X28,X18,X27,X0),X21) = hAPP(X28,c_HOL_Ominus__class_Ominus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f191,axiom,
! [X21,X28,X0,X18,X27] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| hAPP(c_Type_Oshift(X28,X18,X27,X0),X21) = hAPP(X28,c_HOL_Ominus__class_Ominus(X21,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__lt_0) ).
fof(f4752,plain,
spl0_364,
inference(avatar_split_clause,[],[f145,f4750]) ).
fof(f4750,plain,
( spl0_364
<=> ! [X20,X7,X15] : c_HOL_Ominus__class_Ominus(X15,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f145,axiom,
! [X7,X15,X20] : c_HOL_Ominus__class_Ominus(X15,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f4748,plain,
spl0_363,
inference(avatar_split_clause,[],[f144,f4746]) ).
fof(f4746,plain,
( spl0_363
<=> ! [X20,X7,X15] : c_HOL_Ominus__class_Ominus(X15,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f144,axiom,
! [X7,X15,X20] : c_HOL_Ominus__class_Ominus(X15,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f4744,plain,
spl0_362,
inference(avatar_split_clause,[],[f20,f4742]) ).
fof(f4742,plain,
( spl0_362
<=> ! [X17,X10,X0,X9,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X16,X17,X0)
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ominus__class_Ominus(X16,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f20,axiom,
! [X10,X0,X9,X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X16,X17,X0)
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ominus__class_Ominus(X16,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f4740,plain,
spl0_361,
inference(avatar_split_clause,[],[f18,f4738]) ).
fof(f4738,plain,
( spl0_361
<=> ! [X17,X10,X0,X9,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X9,X0)
| c_lessequals(X17,X16,X0)
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ominus__class_Ominus(X16,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f18,axiom,
! [X10,X0,X9,X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X9,X0)
| c_lessequals(X17,X16,X0)
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ominus__class_Ominus(X16,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f4274,plain,
spl0_360,
inference(avatar_split_clause,[],[f754,f4272]) ).
fof(f4272,plain,
( spl0_360
<=> ! [X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X7
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f754,plain,
! [X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X7
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(forward_demodulation,[],[f709,f247]) ).
fof(f709,plain,
! [X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X7 ),
inference(definition_unfolding,[],[f33,f87]) ).
fof(f33,axiom,
! [X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
fof(f4270,plain,
spl0_359,
inference(avatar_split_clause,[],[f722,f4268]) ).
fof(f4268,plain,
( spl0_359
<=> ! [X20,X18,X21] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)),X20,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f722,plain,
! [X21,X18,X20] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)),X20,tc_nat) ),
inference(definition_unfolding,[],[f102,f87]) ).
fof(f102,axiom,
! [X21,X18,X20] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X18),X20,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f4266,plain,
spl0_358,
inference(avatar_split_clause,[],[f716,f4264]) ).
fof(f4264,plain,
( spl0_358
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f716,plain,
! [X0,X7] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
inference(definition_unfolding,[],[f64,f87]) ).
fof(f64,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X7),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f4262,plain,
spl0_357,
inference(avatar_split_clause,[],[f569,f4260]) ).
fof(f4260,plain,
( spl0_357
<=> ! [X7,X72,X71,X15] :
( X71 = X72
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X72,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f569,axiom,
! [X72,X71,X7,X15] :
( X71 = X72
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X72,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(f4234,plain,
spl0_356,
inference(avatar_split_clause,[],[f568,f4232]) ).
fof(f4232,plain,
( spl0_356
<=> ! [X7,X71,X15,X72] :
( X7 = X15
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X72,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f568,axiom,
! [X72,X71,X7,X15] :
( X7 = X15
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X15),X72,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(f4230,plain,
spl0_355,
inference(avatar_split_clause,[],[f565,f4228]) ).
fof(f565,axiom,
! [X53] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X53,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X53,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
fof(f4226,plain,
spl0_354,
inference(avatar_split_clause,[],[f554,f4224]) ).
fof(f4224,plain,
( spl0_354
<=> ! [X20,X24,X18] :
( X18 = X20
| c_HOL_Oord__class_Oless(X20,X18,tc_nat)
| c_Lambda_OdB_OVar(X18) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X18)),X24),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f554,axiom,
! [X18,X24,X20] :
( X18 = X20
| c_HOL_Oord__class_Oless(X20,X18,tc_nat)
| c_Lambda_OdB_OVar(X18) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X18)),X24),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
fof(f4222,plain,
spl0_353,
inference(avatar_split_clause,[],[f549,f4220]) ).
fof(f4220,plain,
( spl0_353
<=> ! [X24,X72,X71,X35] :
( X71 = X72
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X35),X72,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24),X71,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f549,axiom,
! [X72,X71,X24,X35] :
( X71 = X72
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X35),X72,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24),X71,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(f4218,plain,
spl0_352,
inference(avatar_split_clause,[],[f548,f4216]) ).
fof(f4216,plain,
( spl0_352
<=> ! [X24,X71,X35,X72] :
( X24 = X35
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X35),X72,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24),X71,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f548,axiom,
! [X72,X71,X24,X35] :
( X24 = X35
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X35),X72,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24),X71,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(f4214,plain,
spl0_351,
inference(avatar_split_clause,[],[f534,f4212]) ).
fof(f4212,plain,
( spl0_351
<=> ! [X25,X24] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24)),X25)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X24),X25),c_HOL_Ozero__class_Ozero(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f534,axiom,
! [X24,X25] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24)),X25)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X24),X25),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f4210,plain,
spl0_350,
inference(avatar_split_clause,[],[f514,f4208]) ).
fof(f4208,plain,
( spl0_350
<=> ! [X18,X53,X27,X28] :
( c_Type_Otypings(X28,X53,c_Type_Osko__Type__Xvar__app__typesE__1__1(X27,X28,X18,X53))
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X53,tc_Lambda_OdB,tc_Lambda_OdB),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f514,axiom,
! [X28,X18,X27,X53] :
( c_Type_Otypings(X28,X53,c_Type_Osko__Type__Xvar__app__typesE__1__1(X27,X28,X18,X53))
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X18),X53,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
fof(f4206,plain,
spl0_349,
inference(avatar_split_clause,[],[f459,f4204]) ).
fof(f4204,plain,
( spl0_349
<=> ! [X20,X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f459,axiom,
! [X7,X15,X20] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f4202,plain,
spl0_348,
inference(avatar_split_clause,[],[f458,f4200]) ).
fof(f4200,plain,
( spl0_348
<=> ! [X20,X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f458,axiom,
! [X7,X15,X20] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f4198,plain,
spl0_347,
inference(avatar_split_clause,[],[f457,f4196]) ).
fof(f4196,plain,
( spl0_347
<=> ! [X20,X18,X21] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X20),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f457,axiom,
! [X21,X18,X20] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X20),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f4194,plain,
( spl0_346
| ~ spl0_153
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2845,f2470,f1494,f4192]) ).
fof(f4192,plain,
( spl0_346
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f1494,plain,
( spl0_153
<=> ! [X30] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f2845,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X0),tc_Lambda_OdB)
| ~ spl0_153
| ~ spl0_263 ),
inference(superposition,[],[f1495,f2471]) ).
fof(f1495,plain,
( ! [X30] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1494]) ).
fof(f4190,plain,
spl0_345,
inference(avatar_split_clause,[],[f433,f4188]) ).
fof(f4188,plain,
( spl0_345
<=> ! [X44,X41,X42,X0,X43] : c_Lambda_OdB_OdB__rec(X41,X42,X43,c_Lambda_OdB_OAbs(X44),X0) = hAPP(hAPP(X43,X44),c_Lambda_OdB_OdB__rec(X41,X42,X43,X44,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f433,axiom,
! [X41,X0,X44,X42,X43] : c_Lambda_OdB_OdB__rec(X41,X42,X43,c_Lambda_OdB_OAbs(X44),X0) = hAPP(hAPP(X43,X44),c_Lambda_OdB_OdB__rec(X41,X42,X43,X44,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
fof(f4186,plain,
spl0_344,
inference(avatar_split_clause,[],[f310,f4184]) ).
fof(f4184,plain,
( spl0_344
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X12 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f310,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X12 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f4182,plain,
spl0_343,
inference(avatar_split_clause,[],[f309,f4180]) ).
fof(f4180,plain,
( spl0_343
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X12 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f309,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X12 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f4178,plain,
spl0_342,
inference(avatar_split_clause,[],[f308,f4176]) ).
fof(f4176,plain,
( spl0_342
<=> ! [X11,X0,X14,X12] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X12 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f308,axiom,
! [X0,X11,X14,X12] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X12 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f4174,plain,
spl0_341,
inference(avatar_split_clause,[],[f215,f4172]) ).
fof(f4172,plain,
( spl0_341
<=> ! [X24,X39] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X24),X39))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X24)),c_Lambda_OdB_OAbs(X39))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f215,axiom,
! [X39,X24] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X24),X39))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X24)),c_Lambda_OdB_OAbs(X39))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
fof(f4170,plain,
spl0_340,
inference(avatar_split_clause,[],[f121,f4168]) ).
fof(f4168,plain,
( spl0_340
<=> ! [X31,X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X31,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X31,X7,tc_nat),c_HOL_Ominus__class_Ominus(X31,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f121,axiom,
! [X31,X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X31,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X31,X7,tc_nat),c_HOL_Ominus__class_Ominus(X31,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f4166,plain,
spl0_339,
inference(avatar_split_clause,[],[f92,f4164]) ).
fof(f4164,plain,
( spl0_339
<=> ! [X24,X23,X27,X25,X26] :
( ~ c_Type_Otyping(X23,X25,X27)
| ~ c_Type_Otyping(X23,X24,c_Type_Otype_OFun(X27,X26))
| c_Type_Otyping(X23,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f92,axiom,
! [X26,X27,X24,X25,X23] :
( ~ c_Type_Otyping(X23,X25,X27)
| ~ c_Type_Otyping(X23,X24,c_Type_Otype_OFun(X27,X26))
| c_Type_Otyping(X23,hAPP(hAPP(c_Lambda_OdB_OApp,X24),X25),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
fof(f3725,plain,
( spl0_338
| ~ spl0_77
| ~ spl0_116
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1941,f1836,f1316,f1156,f3723]) ).
fof(f1156,plain,
( spl0_77
<=> ! [X29] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1941,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
| ~ spl0_77
| ~ spl0_116
| ~ spl0_196 ),
inference(forward_demodulation,[],[f1928,f1317]) ).
fof(f1928,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
| ~ spl0_77
| ~ spl0_196 ),
inference(superposition,[],[f1837,f1157]) ).
fof(f1157,plain,
( ! [X29] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X29))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f3698,plain,
spl0_337,
inference(avatar_split_clause,[],[f781,f3696]) ).
fof(f3696,plain,
( spl0_337
<=> ! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Oone__class_Oone(tc_nat) = X7
| c_HOL_Oone__class_Oone(tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f781,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Oone__class_Oone(tc_nat) = X7
| c_HOL_Oone__class_Oone(tc_nat) = X15 ),
inference(forward_demodulation,[],[f780,f373]) ).
fof(f373,axiom,
! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X7) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f780,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) = X7
| c_HOL_Oone__class_Oone(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f779,f373]) ).
fof(f779,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f730,f373]) ).
fof(f730,plain,
! [X7,X15] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f76,f87,f87,f87]) ).
fof(f76,axiom,
! [X7,X15] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X15
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
fof(f3694,plain,
spl0_336,
inference(avatar_split_clause,[],[f774,f3692]) ).
fof(f3692,plain,
( spl0_336
<=> ! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Oone__class_Oone(tc_nat) = X15
| c_HOL_Ozero__class_Ozero(tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f774,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Oone__class_Oone(tc_nat) = X15
| c_HOL_Ozero__class_Ozero(tc_nat) = X15 ),
inference(forward_demodulation,[],[f773,f373]) ).
fof(f773,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) = X15
| c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f727,f373]) ).
fof(f727,plain,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f65,f87,f87]) ).
fof(f65,axiom,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X15
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
fof(f3690,plain,
spl0_335,
inference(avatar_split_clause,[],[f772,f3688]) ).
fof(f3688,plain,
( spl0_335
<=> ! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Oone__class_Oone(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f772,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Oone__class_Oone(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X7 ),
inference(forward_demodulation,[],[f771,f373]) ).
fof(f771,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f726,f373]) ).
fof(f726,plain,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f68,f87,f87]) ).
fof(f68,axiom,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
fof(f3686,plain,
spl0_334,
inference(avatar_split_clause,[],[f769,f3684]) ).
fof(f3684,plain,
( spl0_334
<=> ! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f769,plain,
! [X7,X15] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X15 ),
inference(forward_demodulation,[],[f724,f373]) ).
fof(f724,plain,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f77,f87]) ).
fof(f77,axiom,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X15
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
fof(f3682,plain,
spl0_333,
inference(avatar_split_clause,[],[f718,f3680]) ).
fof(f3680,plain,
( spl0_333
<=> ! [X7,X15] :
( X7 = X15
| c_HOL_Oord__class_Oless(X7,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f718,plain,
! [X7,X15] :
( X7 = X15
| c_HOL_Oord__class_Oless(X7,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f114,f87]) ).
fof(f114,axiom,
! [X7,X15] :
( X7 = X15
| c_HOL_Oord__class_Oless(X7,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
fof(f3678,plain,
spl0_332,
inference(avatar_split_clause,[],[f489,f3676]) ).
fof(f3676,plain,
( spl0_332
<=> ! [X47,X0,X49,X22,X7] : c_List_Otake(X7,c_List_Omap(X47,X22,X49,X0),X0) = c_List_Omap(X47,c_List_Otake(X7,X22,X49),X49,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f489,axiom,
! [X0,X49,X47,X7,X22] : c_List_Otake(X7,c_List_Omap(X47,X22,X49,X0),X0) = c_List_Omap(X47,c_List_Otake(X7,X22,X49),X49,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__map_0) ).
fof(f3674,plain,
spl0_331,
inference(avatar_split_clause,[],[f342,f3672]) ).
fof(f3672,plain,
( spl0_331
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f342,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f3670,plain,
( spl0_330
| ~ spl0_119
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1939,f1836,f1328,f3668]) ).
fof(f3668,plain,
( spl0_330
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f1328,plain,
( spl0_119
<=> ! [X18,X21] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X21),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1939,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat)
| ~ spl0_119
| ~ spl0_196 ),
inference(superposition,[],[f1329,f1837]) ).
fof(f1329,plain,
( ! [X21,X18] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X21),X18,tc_nat)
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f3666,plain,
spl0_329,
inference(avatar_split_clause,[],[f341,f3664]) ).
fof(f3664,plain,
( spl0_329
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f341,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f3661,plain,
spl0_328,
inference(avatar_split_clause,[],[f318,f3659]) ).
fof(f3659,plain,
( spl0_328
<=> ! [X36,X0,X10] : c_List_Olist_OCons(X10,X36,X0) = c_List_Orev(c_List_Oappend(c_List_Orev(X36,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f318,axiom,
! [X10,X0,X36] : c_List_Olist_OCons(X10,X36,X0) = c_List_Orev(c_List_Oappend(c_List_Orev(X36,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil(X0),X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
fof(f3657,plain,
spl0_327,
inference(avatar_split_clause,[],[f288,f3655]) ).
fof(f288,axiom,
! [X0,X9,X22] : c_List_Orev(c_List_Olist_OCons(X9,X22,X0),X0) = c_List_Oappend(c_List_Orev(X22,X0),c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
fof(f3653,plain,
spl0_326,
inference(avatar_split_clause,[],[f280,f3651]) ).
fof(f3651,plain,
( spl0_326
<=> ! [X28,X53,X27,X25] :
( c_Type_Otypings(X28,X53,c_Type_Osko__Type__Xlist__app__typeD__1__1(X27,X28,X25,X53))
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f280,axiom,
! [X28,X27,X53,X25] :
( c_Type_Otypings(X28,X53,c_Type_Osko__Type__Xlist__app__typeD__1__1(X27,X28,X25,X53))
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
fof(f3649,plain,
spl0_325,
inference(avatar_split_clause,[],[f279,f3647]) ).
fof(f3647,plain,
( spl0_325
<=> ! [X28,X53,X27,X25] :
( c_Type_Otypings(X28,X53,c_Type_Osko__Type__Xlist__app__typeE__1__1(X27,X28,X25,X53))
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f279,axiom,
! [X28,X27,X53,X25] :
( c_Type_Otypings(X28,X53,c_Type_Osko__Type__Xlist__app__typeE__1__1(X27,X28,X25,X53))
| ~ c_Type_Otyping(X28,c_List_Ofoldl(c_Lambda_OdB_OApp,X25,X53,tc_Lambda_OdB,tc_Lambda_OdB),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
fof(f3645,plain,
spl0_324,
inference(avatar_split_clause,[],[f265,f3643]) ).
fof(f3643,plain,
( spl0_324
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f265,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f3641,plain,
spl0_323,
inference(avatar_split_clause,[],[f264,f3639]) ).
fof(f3639,plain,
( spl0_323
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f264,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f3637,plain,
spl0_322,
inference(avatar_split_clause,[],[f263,f3635]) ).
fof(f3635,plain,
( spl0_322
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f263,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f3633,plain,
spl0_321,
inference(avatar_split_clause,[],[f262,f3631]) ).
fof(f3631,plain,
( spl0_321
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f262,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f3629,plain,
spl0_320,
inference(avatar_split_clause,[],[f220,f3627]) ).
fof(f3627,plain,
( spl0_320
<=> ! [X35,X33,X9,X0,X10] :
( ~ hBOOL(hAPP(hAPP(X35,X10),X33))
| c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X9,X0),c_List_Olist_OCons(X33,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f220,axiom,
! [X10,X0,X9,X35,X33] :
( ~ hBOOL(hAPP(hAPP(X35,X10),X33))
| c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X9,X0),c_List_Olist_OCons(X33,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
fof(f3625,plain,
( spl0_319
| ~ spl0_120
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1938,f1836,f1332,f3623]) ).
fof(f3623,plain,
( spl0_319
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f1938,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_120
| ~ spl0_196 ),
inference(superposition,[],[f1333,f1837]) ).
fof(f3621,plain,
spl0_318,
inference(avatar_split_clause,[],[f219,f3619]) ).
fof(f3619,plain,
( spl0_318
<=> ! [X35,X10,X36,X0,X9,X22] :
( X9 = X10
| X22 = X36
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f219,axiom,
! [X10,X0,X36,X9,X22,X35] :
( X9 = X10
| X22 = X36
| ~ c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X10,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
fof(f3617,plain,
spl0_317,
inference(avatar_split_clause,[],[f190,f3615]) ).
fof(f190,axiom,
! [X7,X24,X20] : c_Lambda_Oliftn(X7,c_Lambda_OdB_OAbs(X24),X20) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X7,X24,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
fof(f3613,plain,
spl0_316,
inference(avatar_split_clause,[],[f189,f3611]) ).
fof(f189,axiom,
! [X18,X7,X20] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| c_Lambda_Oliftn(X7,c_Lambda_OdB_OVar(X18),X20) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
fof(f3609,plain,
spl0_315,
inference(avatar_split_clause,[],[f173,f3607]) ).
fof(f3607,plain,
( spl0_315
<=> ! [X7,X15] :
( X7 = X15
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X15,X7,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X7,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f173,axiom,
! [X7,X15] :
( X7 = X15
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X15,X7,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X7,X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f3605,plain,
spl0_314,
inference(avatar_split_clause,[],[f139,f3603]) ).
fof(f3603,plain,
( spl0_314
<=> ! [X20,X21,X18] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X21,tc_nat),X20,tc_nat) = c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X20),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f139,axiom,
! [X21,X18,X20] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X21,tc_nat),X20,tc_nat) = c_HOL_Ominus__class_Ominus(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X20),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f3601,plain,
spl0_313,
inference(avatar_split_clause,[],[f61,f3599]) ).
fof(f3599,plain,
( spl0_313
<=> ! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f61,axiom,
! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f3597,plain,
spl0_312,
inference(avatar_split_clause,[],[f46,f3595]) ).
fof(f3595,plain,
( spl0_312
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f46,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f3593,plain,
spl0_311,
inference(avatar_split_clause,[],[f45,f3591]) ).
fof(f3591,plain,
( spl0_311
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f45,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X11,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f3589,plain,
spl0_310,
inference(avatar_split_clause,[],[f40,f3587]) ).
fof(f3587,plain,
( spl0_310
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f40,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f3585,plain,
spl0_309,
inference(avatar_split_clause,[],[f39,f3583]) ).
fof(f3583,plain,
( spl0_309
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f39,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f3581,plain,
( spl0_308
| ~ spl0_154
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1930,f1836,f1498,f3579]) ).
fof(f3579,plain,
( spl0_308
<=> ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f1498,plain,
( spl0_154
<=> ! [X9] : c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1930,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
| ~ spl0_154
| ~ spl0_196 ),
inference(superposition,[],[f1499,f1837]) ).
fof(f1499,plain,
( ! [X9] : c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1498]) ).
fof(f3512,plain,
( spl0_307
| ~ spl0_175
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1929,f1836,f1660,f3510]) ).
fof(f3510,plain,
( spl0_307
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f1929,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
| ~ spl0_175
| ~ spl0_196 ),
inference(superposition,[],[f1661,f1837]) ).
fof(f3381,plain,
spl0_306,
inference(avatar_split_clause,[],[f756,f3379]) ).
fof(f3379,plain,
( spl0_306
<=> ! [X18,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X18,tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f756,plain,
! [X18,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X18,tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
inference(forward_demodulation,[],[f711,f679]) ).
fof(f679,plain,
! [X7,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f150,f87]) ).
fof(f150,axiom,
! [X7,X15] : c_HOL_Ominus__class_Ominus(X15,c_Suc(X7),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X7,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
fof(f711,plain,
! [X18,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),X7,tc_nat) ),
inference(definition_unfolding,[],[f22,f87]) ).
fof(f22,axiom,
! [X18,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,c_Suc(X18),tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f3377,plain,
spl0_305,
inference(avatar_split_clause,[],[f582,f3375]) ).
fof(f3375,plain,
( spl0_305
<=> ! [X53,X24,X35] :
( X24 = X35
| c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X53,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X53,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f582,axiom,
! [X24,X35,X53] :
( X24 = X35
| c_List_Ofoldl(c_Lambda_OdB_OApp,X35,X53,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X53,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
fof(f3363,plain,
spl0_304,
inference(avatar_split_clause,[],[f539,f3361]) ).
fof(f3361,plain,
( spl0_304
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X11,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f539,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X11,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f3359,plain,
spl0_303,
inference(avatar_split_clause,[],[f538,f3357]) ).
fof(f3357,plain,
( spl0_303
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f538,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f3355,plain,
spl0_302,
inference(avatar_split_clause,[],[f480,f3353]) ).
fof(f3353,plain,
( spl0_302
<=> ! [X28,X18,X27,X25,X26] :
( ~ c_Type_Otyping(X28,X25,X27)
| c_Type_Otyping(c_Type_Oshift(X28,X18,X26,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X25),X18),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f480,axiom,
! [X28,X18,X26,X27,X25] :
( ~ c_Type_Otyping(X28,X25,X27)
| c_Type_Otyping(c_Type_Oshift(X28,X18,X26,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,X25),X18),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
fof(f3351,plain,
spl0_301,
inference(avatar_split_clause,[],[f465,f3349]) ).
fof(f3349,plain,
( spl0_301
<=> ! [X35,X9,X0,X36,X22] :
( ~ c_ListOrder_Ostep1(X35,X36,X22,X0)
| c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X9,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f465,axiom,
! [X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,X36,X22,X0)
| c_ListOrder_Ostep1(X35,c_List_Olist_OCons(X9,X36,X0),c_List_Olist_OCons(X9,X22,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
fof(f3347,plain,
spl0_300,
inference(avatar_split_clause,[],[f379,f3345]) ).
fof(f3345,plain,
( spl0_300
<=> ! [X42,X43,X41,X51,X0,X52] : hAPP(hAPP(X42,X51),X52) = c_Lambda_OdB_OdB__case(X41,X42,X43,hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f379,axiom,
! [X51,X41,X0,X52,X42,X43] : hAPP(hAPP(X42,X51),X52) = c_Lambda_OdB_OdB__case(X41,X42,X43,hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
fof(f3343,plain,
spl0_299,
inference(avatar_split_clause,[],[f351,f3341]) ).
fof(f3341,plain,
( spl0_299
<=> ! [X9,X0,X11] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X11) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f351,axiom,
! [X0,X11,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),X11) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f3339,plain,
spl0_298,
inference(avatar_split_clause,[],[f320,f3337]) ).
fof(f3337,plain,
( spl0_298
<=> ! [X28,X54,X27,X25] :
( ~ c_Type_Otyping(X28,X25,X27)
| c_Type_Otyping(X28,X54,X27)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X54)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f320,axiom,
! [X28,X54,X27,X25] :
( ~ c_Type_Otyping(X28,X25,X27)
| c_Type_Otyping(X28,X54,X27)
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X25),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
fof(f3335,plain,
spl0_297,
inference(avatar_split_clause,[],[f306,f3333]) ).
fof(f3333,plain,
( spl0_297
<=> ! [X20,X7,X15] :
( X7 = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f306,axiom,
! [X7,X15,X20] :
( X7 = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
fof(f3331,plain,
spl0_296,
inference(avatar_split_clause,[],[f305,f3329]) ).
fof(f3329,plain,
( spl0_296
<=> ! [X20,X7,X15] :
( X7 = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f305,axiom,
! [X7,X15,X20] :
( X7 = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f3327,plain,
spl0_295,
inference(avatar_split_clause,[],[f277,f3325]) ).
fof(f3325,plain,
( spl0_295
<=> ! [X23,X27,X25,X26] :
( c_Type_Otyping(X23,c_Lambda_OdB_OAbs(X25),c_Type_Otype_OFun(X27,X26))
| ~ c_Type_Otyping(c_Type_Oshift(X23,c_HOL_Ozero__class_Ozero(tc_nat),X27,tc_Type_Otype),X25,X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f277,axiom,
! [X26,X27,X25,X23] :
( c_Type_Otyping(X23,c_Lambda_OdB_OAbs(X25),c_Type_Otype_OFun(X27,X26))
| ~ c_Type_Otyping(c_Type_Oshift(X23,c_HOL_Ozero__class_Ozero(tc_nat),X27,tc_Type_Otype),X25,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
fof(f3313,plain,
spl0_294,
inference(avatar_split_clause,[],[f213,f3311]) ).
fof(f3311,plain,
( spl0_294
<=> ! [X38,X0,X9,X35,X37] :
( ~ c_ListOrder_Ostep1(X35,X37,X38,X0)
| c_ListOrder_Ostep1(X35,c_List_Oappend(X9,X37,X0),c_List_Oappend(X9,X38,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f213,axiom,
! [X38,X0,X37,X9,X35] :
( ~ c_ListOrder_Ostep1(X35,X37,X38,X0)
| c_ListOrder_Ostep1(X35,c_List_Oappend(X9,X37,X0),c_List_Oappend(X9,X38,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).
fof(f3309,plain,
spl0_293,
inference(avatar_split_clause,[],[f212,f3307]) ).
fof(f3307,plain,
( spl0_293
<=> ! [X35,X9,X0,X36,X22] :
( ~ c_ListOrder_Ostep1(X35,X36,X22,X0)
| c_ListOrder_Ostep1(X35,c_List_Oappend(X36,X9,X0),c_List_Oappend(X22,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f212,axiom,
! [X0,X36,X9,X35,X22] :
( ~ c_ListOrder_Ostep1(X35,X36,X22,X0)
| c_ListOrder_Ostep1(X35,c_List_Oappend(X36,X9,X0),c_List_Oappend(X22,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).
fof(f3305,plain,
spl0_292,
inference(avatar_split_clause,[],[f211,f3303]) ).
fof(f3303,plain,
( spl0_292
<=> ! [X22,X9,X0] :
( c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = X22
| c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) != c_List_Orev(X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f211,axiom,
! [X0,X9,X22] :
( c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = X22
| c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) != c_List_Orev(X22,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
fof(f3301,plain,
spl0_291,
inference(avatar_split_clause,[],[f82,f3299]) ).
fof(f3299,plain,
( spl0_291
<=> ! [X20,X21,X18] :
( c_HOL_Oord__class_Oless(X18,c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f82,axiom,
! [X21,X18,X20] :
( c_HOL_Oord__class_Oless(X18,c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f3297,plain,
spl0_290,
inference(avatar_split_clause,[],[f81,f3295]) ).
fof(f3295,plain,
( spl0_290
<=> ! [X20,X21,X18] :
( ~ c_HOL_Oord__class_Oless(X18,c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f81,axiom,
! [X21,X18,X20] :
( ~ c_HOL_Oord__class_Oless(X18,c_HOL_Ominus__class_Ominus(X21,X20,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X20),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f3293,plain,
spl0_289,
inference(avatar_split_clause,[],[f58,f3291]) ).
fof(f3291,plain,
( spl0_289
<=> ! [X11,X12,X19] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| hBOOL(hAPP(X19,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X19,c_HOL_Ominus__class_Ominus(X11,X12,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f58,axiom,
! [X11,X19,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| hBOOL(hAPP(X19,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X19,c_HOL_Ominus__class_Ominus(X11,X12,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
fof(f2960,plain,
spl0_288,
inference(avatar_split_clause,[],[f737,f2958]) ).
fof(f737,plain,
! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15)),tc_nat),
inference(forward_demodulation,[],[f670,f668]) ).
fof(f668,plain,
! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X7),
inference(definition_unfolding,[],[f88,f87]) ).
fof(f88,axiom,
! [X7] : c_Suc(X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
fof(f670,plain,
! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f78,f87]) ).
fof(f78,axiom,
! [X18,X15] : c_HOL_Oord__class_Oless(X18,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X15)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
fof(f2956,plain,
spl0_287,
inference(avatar_split_clause,[],[f736,f2954]) ).
fof(f736,plain,
! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18)),tc_nat),
inference(forward_demodulation,[],[f669,f668]) ).
fof(f669,plain,
! [X18,X15] : c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f79,f87]) ).
fof(f79,axiom,
! [X18,X15] : c_HOL_Oord__class_Oless(X18,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X18)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f2952,plain,
spl0_286,
inference(avatar_split_clause,[],[f571,f2950]) ).
fof(f2950,plain,
( spl0_286
<=> ! [X18,X21,X35] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X35))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),c_Lambda_OdB_OVar(X18)),X21))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f571,axiom,
! [X21,X18,X35] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X35))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X35),c_Lambda_OdB_OVar(X18)),X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
fof(f2948,plain,
( spl0_285
| ~ spl0_60
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1663,f1580,f1086,f2946]) ).
fof(f2946,plain,
( spl0_285
<=> ! [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_285])]) ).
fof(f1086,plain,
( spl0_60
<=> ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1580,plain,
( spl0_157
<=> ! [X20,X21,X7] :
( ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X7,tc_nat),X20,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1663,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_60
| ~ spl0_157 ),
inference(resolution,[],[f1581,f1087]) ).
fof(f1087,plain,
( ! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1581,plain,
( ! [X21,X7,X20] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X7,tc_nat),X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f2944,plain,
spl0_284,
inference(avatar_split_clause,[],[f559,f2942]) ).
fof(f2942,plain,
( spl0_284
<=> ! [X53,X71,X35,X7] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X53,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X35),X71,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f559,axiom,
! [X71,X7,X53,X35] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X53,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X35),X71,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
fof(f2940,plain,
spl0_283,
inference(avatar_split_clause,[],[f553,f2938]) ).
fof(f2938,plain,
( spl0_283
<=> ! [X34,X18,X21] :
( ~ c_HOL_Oord__class_Oless(X21,X18,tc_nat)
| c_Lambda_OdB_OVar(X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X21)),X34),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f553,axiom,
! [X21,X18,X34] :
( ~ c_HOL_Oord__class_Oless(X21,X18,tc_nat)
| c_Lambda_OdB_OVar(X21) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X21)),X34),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
fof(f2936,plain,
spl0_282,
inference(avatar_split_clause,[],[f487,f2934]) ).
fof(f2934,plain,
( spl0_282
<=> ! [X47,X0,X49,X22] : c_List_Orev(c_List_Omap(X47,X22,X49,X0),X0) = c_List_Omap(X47,c_List_Orev(X22,X49),X49,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f487,axiom,
! [X0,X49,X47,X22] : c_List_Orev(c_List_Omap(X47,X22,X49,X0),X0) = c_List_Omap(X47,c_List_Orev(X22,X49),X49,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__map_0) ).
fof(f2932,plain,
spl0_281,
inference(avatar_split_clause,[],[f479,f2930]) ).
fof(f2930,plain,
( spl0_281
<=> ! [X53,X0,X9,X22] : c_List_Oappend(X22,c_List_Oappend(X9,X53,X0),X0) = c_List_Oappend(c_List_Oappend(X22,X9,X0),X53,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f479,axiom,
! [X0,X9,X53,X22] : c_List_Oappend(X22,c_List_Oappend(X9,X53,X0),X0) = c_List_Oappend(c_List_Oappend(X22,X9,X0),X53,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
fof(f2928,plain,
spl0_280,
inference(avatar_split_clause,[],[f475,f2926]) ).
fof(f2926,plain,
( spl0_280
<=> ! [X18,X10,X0,X9,X22] : c_List_Olist__update(X22,X18,X10,X0) = c_List_Olist__update(c_List_Olist__update(X22,X18,X9,X0),X18,X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f475,axiom,
! [X10,X0,X18,X9,X22] : c_List_Olist__update(X22,X18,X10,X0) = c_List_Olist__update(c_List_Olist__update(X22,X18,X9,X0),X18,X10,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
fof(f2924,plain,
spl0_279,
inference(avatar_split_clause,[],[f435,f2922]) ).
fof(f2922,plain,
( spl0_279
<=> ! [X28,X18,X0,X27,X21] :
( ~ c_HOL_Oord__class_Oless(X21,X18,tc_nat)
| hAPP(c_Type_Oshift(X28,X18,X27,X0),X21) = hAPP(X28,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f435,axiom,
! [X21,X28,X0,X18,X27] :
( ~ c_HOL_Oord__class_Oless(X21,X18,tc_nat)
| hAPP(c_Type_Oshift(X28,X18,X27,X0),X21) = hAPP(X28,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
fof(f2920,plain,
spl0_278,
inference(avatar_split_clause,[],[f431,f2918]) ).
fof(f2918,plain,
( spl0_278
<=> ! [X40,X0,X36,X22] :
( ~ c_List_Olistsp(X40,X22,X0)
| ~ c_List_Olistsp(X40,X36,X0)
| c_List_Olistsp(X40,c_List_Oappend(X22,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f431,axiom,
! [X40,X0,X36,X22] :
( ~ c_List_Olistsp(X40,X22,X0)
| ~ c_List_Olistsp(X40,X36,X0)
| c_List_Olistsp(X40,c_List_Oappend(X22,X36,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
fof(f2916,plain,
spl0_277,
inference(avatar_split_clause,[],[f350,f2914]) ).
fof(f2914,plain,
( spl0_277
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f350,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f2912,plain,
spl0_276,
inference(avatar_split_clause,[],[f336,f2910]) ).
fof(f2910,plain,
( spl0_276
<=> ! [X22,X36,X0] : c_List_Orev(c_List_Oappend(X22,X36,X0),X0) = c_List_Oappend(c_List_Orev(X36,X0),c_List_Orev(X22,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f336,axiom,
! [X0,X36,X22] : c_List_Orev(c_List_Oappend(X22,X36,X0),X0) = c_List_Oappend(c_List_Orev(X36,X0),c_List_Orev(X22,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
fof(f2908,plain,
spl0_275,
inference(avatar_split_clause,[],[f299,f2906]) ).
fof(f2906,plain,
( spl0_275
<=> ! [X22,X0,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_List_Olist_ONil(X0) = X22
| c_List_Otake(X7,X22,X0) != c_List_Olist_ONil(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f299,axiom,
! [X0,X7,X22] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_List_Olist_ONil(X0) = X22
| c_List_Otake(X7,X22,X0) != c_List_Olist_ONil(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
fof(f2898,plain,
spl0_274,
inference(avatar_split_clause,[],[f295,f2896]) ).
fof(f2896,plain,
( spl0_274
<=> ! [X33,X0,X9,X45] : c_List_Oappend(c_List_Olist_OCons(X9,X33,X0),X45,X0) = c_List_Olist_OCons(X9,c_List_Oappend(X33,X45,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f295,axiom,
! [X0,X9,X45,X33] : c_List_Oappend(c_List_Olist_OCons(X9,X33,X0),X45,X0) = c_List_Olist_OCons(X9,c_List_Oappend(X33,X45,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
fof(f2894,plain,
spl0_273,
inference(avatar_split_clause,[],[f266,f2892]) ).
fof(f2892,plain,
( spl0_273
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f266,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f2890,plain,
spl0_272,
inference(avatar_split_clause,[],[f246,f2888]) ).
fof(f2888,plain,
( spl0_272
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f246,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X12),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2886,plain,
spl0_271,
inference(avatar_split_clause,[],[f245,f2884]) ).
fof(f2884,plain,
( spl0_271
<=> ! [X0,X11,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f245,axiom,
! [X0,X11,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X14),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2882,plain,
spl0_270,
inference(avatar_split_clause,[],[f147,f2880]) ).
fof(f2880,plain,
( spl0_270
<=> ! [X20,X21,X18] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X21,tc_nat),X20,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X20,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f147,axiom,
! [X21,X18,X20] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X21,tc_nat),X20,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X18,X20,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f2878,plain,
spl0_269,
inference(avatar_split_clause,[],[f84,f2876]) ).
fof(f2876,plain,
( spl0_269
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f84,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X11,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f2874,plain,
spl0_268,
inference(avatar_split_clause,[],[f83,f2872]) ).
fof(f2872,plain,
( spl0_268
<=> ! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X15,X7,tc_nat)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f83,axiom,
! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X15,X7,tc_nat)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f2870,plain,
spl0_267,
inference(avatar_split_clause,[],[f63,f2868]) ).
fof(f2868,plain,
( spl0_267
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f63,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X11,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X11,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f2812,plain,
( ~ spl0_21
| spl0_266
| ~ spl0_65
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1515,f1422,f1108,f2810,f891]) ).
fof(f891,plain,
( spl0_21
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f2810,plain,
( spl0_266
<=> ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1422,plain,
( spl0_135
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1515,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_65
| ~ spl0_135 ),
inference(resolution,[],[f1423,f1109]) ).
fof(f1423,plain,
( ! [X10,X0,X9] :
( c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X10,X9,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1422]) ).
fof(f2662,plain,
( ~ spl0_264
| spl0_265
| ~ spl0_65
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2580,f2352,f1108,f2660,f2656]) ).
fof(f2656,plain,
( spl0_264
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2660,plain,
( spl0_265
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2352,plain,
( spl0_234
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2580,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_65
| ~ spl0_234 ),
inference(resolution,[],[f2353,f1109]) ).
fof(f2353,plain,
( ! [X0,X11,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2352]) ).
fof(f2472,plain,
spl0_263,
inference(avatar_split_clause,[],[f742,f2470]) ).
fof(f742,plain,
! [X44] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f741,f374]) ).
fof(f741,plain,
! [X44] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f681,f247]) ).
fof(f681,plain,
! [X44] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f276,f87]) ).
fof(f276,axiom,
! [X44] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X44),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X44,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).
fof(f2468,plain,
spl0_262,
inference(avatar_split_clause,[],[f705,f2466]) ).
fof(f2466,plain,
( spl0_262
<=> ! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f705,plain,
! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f153,f87]) ).
fof(f153,axiom,
! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f2464,plain,
spl0_261,
inference(avatar_split_clause,[],[f697,f2462]) ).
fof(f697,plain,
! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f152,f87]) ).
fof(f152,axiom,
! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f2460,plain,
spl0_260,
inference(avatar_split_clause,[],[f650,f2458]) ).
fof(f2458,plain,
( spl0_260
<=> ! [X50,X0,X77,X78,X49,X19] : hAPP(c_COMBC(X19,X77,X49,X50,X0),X78) = hAPP(hAPP(X19,X78),X77) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f650,axiom,
! [X50,X0,X49,X78,X19,X77] : hAPP(c_COMBC(X19,X77,X49,X50,X0),X78) = hAPP(hAPP(X19,X78),X77),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
fof(f2456,plain,
spl0_259,
inference(avatar_split_clause,[],[f574,f2454]) ).
fof(f2454,plain,
( spl0_259
<=> ! [X52,X76,X51,X75] :
( X52 = X76
| hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52) != hAPP(hAPP(c_Lambda_OdB_OApp,X75),X76) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f574,axiom,
! [X51,X76,X52,X75] :
( X52 = X76
| hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52) != hAPP(hAPP(c_Lambda_OdB_OApp,X75),X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f2452,plain,
spl0_258,
inference(avatar_split_clause,[],[f573,f2450]) ).
fof(f2450,plain,
( spl0_258
<=> ! [X51,X75,X76,X52] :
( X51 = X75
| hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52) != hAPP(hAPP(c_Lambda_OdB_OApp,X75),X76) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f573,axiom,
! [X51,X76,X52,X75] :
( X51 = X75
| hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52) != hAPP(hAPP(c_Lambda_OdB_OApp,X75),X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f2448,plain,
spl0_257,
inference(avatar_split_clause,[],[f563,f2446]) ).
fof(f563,axiom,
! [X72,X7] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X72,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X72,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
fof(f2444,plain,
( spl0_256
| ~ spl0_44
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1387,f1348,f1006,f2441]) ).
fof(f2441,plain,
( spl0_256
<=> 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_256])]) ).
fof(f1348,plain,
( spl0_124
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1387,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_124 ),
inference(resolution,[],[f1349,f1008]) ).
fof(f1349,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1348]) ).
fof(f2439,plain,
spl0_255,
inference(avatar_split_clause,[],[f562,f2437]) ).
fof(f2437,plain,
( spl0_255
<=> ! [X24,X25,X71,X7] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24)),X25) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X71,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f562,axiom,
! [X71,X7,X24,X25] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X24)),X25) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X7),X71,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f2435,plain,
spl0_254,
inference(avatar_split_clause,[],[f463,f2433]) ).
fof(f2433,plain,
( spl0_254
<=> ! [X28,X54,X27,X25] :
( ~ c_Type_Otyping(X28,X25,X27)
| c_Type_Otyping(X28,X54,X27)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X54)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f463,axiom,
! [X28,X54,X27,X25] :
( ~ c_Type_Otyping(X28,X25,X27)
| c_Type_Otyping(X28,X54,X27)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X25),X54)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f2431,plain,
spl0_253,
inference(avatar_split_clause,[],[f425,f2429]) ).
fof(f2429,plain,
( spl0_253
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f425,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f2427,plain,
spl0_252,
inference(avatar_split_clause,[],[f424,f2425]) ).
fof(f2425,plain,
( spl0_252
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f424,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f2423,plain,
spl0_251,
inference(avatar_split_clause,[],[f418,f2421]) ).
fof(f2421,plain,
( spl0_251
<=> ! [X0,X7,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X15,X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f418,axiom,
! [X0,X7,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X15,X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f2419,plain,
spl0_250,
inference(avatar_split_clause,[],[f417,f2417]) ).
fof(f2417,plain,
( spl0_250
<=> ! [X0,X7,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X15,X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f417,axiom,
! [X0,X7,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X15,X0),c_Nat_Osemiring__1__class_Oof__nat(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f2415,plain,
spl0_249,
inference(avatar_split_clause,[],[f334,f2413]) ).
fof(f2413,plain,
( spl0_249
<=> ! [X25,X24] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X24),X25))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X24)),c_Lambda_OdB_OAbs(X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f334,axiom,
! [X24,X25] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X24),X25))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X24)),c_Lambda_OdB_OAbs(X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f2411,plain,
spl0_248,
inference(avatar_split_clause,[],[f331,f2409]) ).
fof(f2409,plain,
( spl0_248
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f331,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f2407,plain,
spl0_247,
inference(avatar_split_clause,[],[f324,f2405]) ).
fof(f2405,plain,
( spl0_247
<=> ! [X22,X9,X0,X10] : c_List_Olist__update(c_List_Olist_OCons(X9,X22,X0),c_HOL_Ozero__class_Ozero(tc_nat),X10,X0) = c_List_Olist_OCons(X10,X22,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f324,axiom,
! [X10,X0,X9,X22] : c_List_Olist__update(c_List_Olist_OCons(X9,X22,X0),c_HOL_Ozero__class_Ozero(tc_nat),X10,X0) = c_List_Olist_OCons(X10,X22,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
fof(f2403,plain,
spl0_246,
inference(avatar_split_clause,[],[f259,f2401]) ).
fof(f2401,plain,
( spl0_246
<=> ! [X35,X10,X0,X9] :
( ~ hBOOL(hAPP(hAPP(X35,X9),X10))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f259,axiom,
! [X10,X0,X9,X35] :
( ~ hBOOL(hAPP(hAPP(X35,X9),X10))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
fof(f2399,plain,
( spl0_245
| ~ spl0_14
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1386,f1348,f856,f2396]) ).
fof(f2396,plain,
( spl0_245
<=> 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_245])]) ).
fof(f1386,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_124 ),
inference(resolution,[],[f1349,f858]) ).
fof(f2394,plain,
spl0_244,
inference(avatar_split_clause,[],[f256,f2392]) ).
fof(f2392,plain,
( spl0_244
<=> ! [X11,X0,X12,X50,X49,X1] : hAPP(X11,hAPP(X12,X1)) = hAPP(c_Fun_Ocomp(X11,X12,X50,X49,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f256,axiom,
! [X50,X0,X11,X49,X1,X12] : hAPP(X11,hAPP(X12,X1)) = hAPP(c_Fun_Ocomp(X11,X12,X50,X49,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f2390,plain,
spl0_243,
inference(avatar_split_clause,[],[f214,f2388]) ).
fof(f2388,plain,
( spl0_243
<=> ! [X22,X9,X0] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X9,X22,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f214,axiom,
! [X0,X9,X22] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X9,X22,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
fof(f2386,plain,
spl0_242,
inference(avatar_split_clause,[],[f210,f2384]) ).
fof(f2384,plain,
( spl0_242
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X8,X0)
| c_HOL_Oord__class_Oless(X9,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f210,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X8,X0)
| c_HOL_Oord__class_Oless(X9,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f2382,plain,
spl0_241,
inference(avatar_split_clause,[],[f209,f2380]) ).
fof(f2380,plain,
( spl0_241
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,X10,X0)
| c_HOL_Oord__class_Oless(X8,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f209,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,X10,X0)
| c_HOL_Oord__class_Oless(X8,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f2378,plain,
spl0_240,
inference(avatar_split_clause,[],[f166,f2376]) ).
fof(f166,axiom,
! [X10,X0,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X9 = X10
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f2374,plain,
spl0_239,
inference(avatar_split_clause,[],[f143,f2372]) ).
fof(f2372,plain,
( spl0_239
<=> ! [X9,X0,X10] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X9 = X10
| c_Int_Onumber__class_Onumber__of(X9,X0) != c_Int_Onumber__class_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f143,axiom,
! [X10,X0,X9] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X9 = X10
| c_Int_Onumber__class_Onumber__of(X9,X0) != c_Int_Onumber__class_Onumber__of(X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f2370,plain,
spl0_238,
inference(avatar_split_clause,[],[f141,f2368]) ).
fof(f2368,plain,
( spl0_238
<=> ! [X17,X0,X9,X16] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X16 = X17
| c_HOL_Ominus__class_Ominus(X16,X17,X0) != c_HOL_Ominus__class_Ominus(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f141,axiom,
! [X0,X9,X16,X17] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X16 = X17
| c_HOL_Ominus__class_Ominus(X16,X17,X0) != c_HOL_Ominus__class_Ominus(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f2366,plain,
spl0_237,
inference(avatar_split_clause,[],[f112,f2364]) ).
fof(f2364,plain,
( spl0_237
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f112,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f2362,plain,
spl0_236,
inference(avatar_split_clause,[],[f108,f2360]) ).
fof(f2360,plain,
( spl0_236
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X11,X12,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f108,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X11,X12,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f2358,plain,
spl0_235,
inference(avatar_split_clause,[],[f107,f2356]) ).
fof(f2356,plain,
( spl0_235
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f107,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X11,X12,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f2354,plain,
spl0_234,
inference(avatar_split_clause,[],[f36,f2352]) ).
fof(f36,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f2350,plain,
spl0_233,
inference(avatar_split_clause,[],[f35,f2348]) ).
fof(f2348,plain,
( spl0_233
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f35,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X11,X12,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f2346,plain,
spl0_232,
inference(avatar_split_clause,[],[f13,f2344]) ).
fof(f2344,plain,
( spl0_232
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X8,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f13,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X8,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f2342,plain,
spl0_231,
inference(avatar_split_clause,[],[f12,f2340]) ).
fof(f2340,plain,
( spl0_231
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X8,X0)
| c_HOL_Oord__class_Oless(X9,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f12,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X8,X0)
| c_HOL_Oord__class_Oless(X9,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f2338,plain,
spl0_230,
inference(avatar_split_clause,[],[f9,f2336]) ).
fof(f2336,plain,
( spl0_230
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(X10,X8,X0)
| c_lessequals(X9,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f9,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(X10,X8,X0)
| c_lessequals(X9,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2334,plain,
spl0_229,
inference(avatar_split_clause,[],[f8,f2332]) ).
fof(f2332,plain,
( spl0_229
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,X10,X0)
| c_HOL_Oord__class_Oless(X8,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f8,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X8,X10,X0)
| c_HOL_Oord__class_Oless(X8,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f2330,plain,
spl0_228,
inference(avatar_split_clause,[],[f7,f2328]) ).
fof(f2328,plain,
( spl0_228
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X8,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f7,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X8,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f2326,plain,
spl0_227,
inference(avatar_split_clause,[],[f6,f2324]) ).
fof(f2324,plain,
( spl0_227
<=> ! [X10,X0,X9,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X8,X10,X0)
| c_lessequals(X8,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f6,axiom,
! [X10,X0,X8,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_lessequals(X8,X10,X0)
| c_lessequals(X8,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2178,plain,
( spl0_226
| ~ spl0_125
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1932,f1836,f1352,f2176]) ).
fof(f1932,plain,
( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0)
| ~ spl0_125
| ~ spl0_196 ),
inference(superposition,[],[f1353,f1837]) ).
fof(f2076,plain,
( spl0_225
| ~ spl0_153
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1931,f1836,f1494,f2074]) ).
fof(f2074,plain,
( spl0_225
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1931,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))
| ~ spl0_153
| ~ spl0_196 ),
inference(superposition,[],[f1495,f1837]) ).
fof(f2046,plain,
spl0_224,
inference(avatar_split_clause,[],[f667,f2044]) ).
fof(f2044,plain,
( spl0_224
<=> ! [X7,X15] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f667,plain,
! [X7,X15] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f129,f87]) ).
fof(f129,axiom,
! [X7,X15] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X7,tc_nat),c_Suc(X15),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f2042,plain,
spl0_223,
inference(avatar_split_clause,[],[f585,f2040]) ).
fof(f2040,plain,
( spl0_223
<=> ! [X25,X18] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X25),c_Lambda_OdB_OVar(X18)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f585,axiom,
! [X18,X25] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X25),c_Lambda_OdB_OVar(X18)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
fof(f2038,plain,
spl0_222,
inference(avatar_split_clause,[],[f584,f2036]) ).
fof(f2036,plain,
( spl0_222
<=> ! [X20,X25,X24] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X25),X20)),X24),X20) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f584,axiom,
! [X24,X25,X20] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X25),X20)),X24),X20) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f2034,plain,
spl0_221,
inference(avatar_split_clause,[],[f575,f2032]) ).
fof(f2032,plain,
( spl0_221
<=> ! [X24,X71,X15] :
( c_Lambda_OdB_OVar(X15) = X24
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f575,axiom,
! [X71,X15,X24] :
( c_Lambda_OdB_OVar(X15) = X24
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
fof(f2030,plain,
spl0_220,
inference(avatar_split_clause,[],[f561,f2028]) ).
fof(f2028,plain,
( spl0_220
<=> ! [X24,X71,X15] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X71
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f561,axiom,
! [X71,X24,X15] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X71
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
fof(f2026,plain,
spl0_219,
inference(avatar_split_clause,[],[f557,f2024]) ).
fof(f2024,plain,
( spl0_219
<=> ! [X20,X18] :
( ~ c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| c_Lambda_OdB_OVar(X18) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f557,axiom,
! [X18,X20] :
( ~ c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| c_Lambda_OdB_OVar(X18) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X18)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f2022,plain,
spl0_218,
inference(avatar_split_clause,[],[f551,f2020]) ).
fof(f2020,plain,
( spl0_218
<=> ! [X24,X35,X71] :
( c_Lambda_OdB_OAbs(X35) = X24
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f551,axiom,
! [X71,X24,X35] :
( c_Lambda_OdB_OAbs(X35) = X24
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
fof(f2018,plain,
spl0_217,
inference(avatar_split_clause,[],[f501,f2016]) ).
fof(f2016,plain,
( spl0_217
<=> ! [X24,X71,X35] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X71
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f501,axiom,
! [X71,X24,X35] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X71
| c_List_Ofoldl(c_Lambda_OdB_OApp,X24,X71,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
fof(f2014,plain,
spl0_216,
inference(avatar_split_clause,[],[f412,f2012]) ).
fof(f2012,plain,
( spl0_216
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f412,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
fof(f2010,plain,
spl0_215,
inference(avatar_split_clause,[],[f406,f2008]) ).
fof(f2008,plain,
( spl0_215
<=> ! [X9,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f406,axiom,
! [X10,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X10,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f2006,plain,
spl0_214,
inference(avatar_split_clause,[],[f366,f2004]) ).
fof(f2004,plain,
( spl0_214
<=> ! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f366,axiom,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f2002,plain,
spl0_213,
inference(avatar_split_clause,[],[f365,f2000]) ).
fof(f2000,plain,
( spl0_213
<=> ! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f365,axiom,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1998,plain,
spl0_212,
inference(avatar_split_clause,[],[f356,f1996]) ).
fof(f1996,plain,
( spl0_212
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_HOL_Ozero__class_Ozero(X0)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f356,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_HOL_Ozero__class_Ozero(X0)) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f1994,plain,
spl0_211,
inference(avatar_split_clause,[],[f352,f1992]) ).
fof(f1992,plain,
( spl0_211
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f352,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f1990,plain,
spl0_210,
inference(avatar_split_clause,[],[f348,f1988]) ).
fof(f1988,plain,
( spl0_210
<=> ! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X11,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f348,axiom,
! [X0,X11,X7] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X11,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f1986,plain,
spl0_209,
inference(avatar_split_clause,[],[f328,f1984]) ).
fof(f1984,plain,
( spl0_209
<=> ! [X9,X0] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f328,axiom,
! [X0,X9] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
fof(f1982,plain,
spl0_208,
inference(avatar_split_clause,[],[f247,f1980]) ).
fof(f1978,plain,
( ~ spl0_207
| spl0_198
| ~ spl0_95
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1900,f1787,f1230,f1890,f1975]) ).
fof(f1975,plain,
( spl0_207
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1787,plain,
( spl0_184
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X11 = X12
| c_HOL_Ominus__class_Ominus(X11,X12,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1900,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_95
| ~ spl0_184 ),
inference(trivial_inequality_removal,[],[f1896]) ).
fof(f1896,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_95
| ~ spl0_184 ),
inference(superposition,[],[f1788,f1231]) ).
fof(f1788,plain,
( ! [X0,X11,X12] :
( c_HOL_Ominus__class_Ominus(X11,X12,X0) != c_HOL_Ozero__class_Ozero(X0)
| X11 = X12
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1787]) ).
fof(f1973,plain,
spl0_206,
inference(avatar_split_clause,[],[f243,f1971]) ).
fof(f1971,plain,
( spl0_206
<=> ! [X18,X21,X15] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X21),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f243,axiom,
! [X21,X18,X15] :
( ~ c_HOL_Oord__class_Oless(X18,X21,tc_nat)
| c_HOL_Oord__class_Oless(X18,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X21),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f1969,plain,
spl0_205,
inference(avatar_split_clause,[],[f241,f1967]) ).
fof(f1967,plain,
( spl0_205
<=> ! [X20,X21,X18] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X21),X20,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f241,axiom,
! [X21,X18,X20] :
( c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X21),X20,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f1965,plain,
spl0_204,
inference(avatar_split_clause,[],[f239,f1963]) ).
fof(f239,axiom,
! [X10,X8,X9] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f1961,plain,
spl0_203,
inference(avatar_split_clause,[],[f157,f1959]) ).
fof(f1959,plain,
( spl0_203
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X12,X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f157,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),X12),X12,X0) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f1957,plain,
spl0_202,
inference(avatar_split_clause,[],[f125,f1955]) ).
fof(f1955,plain,
( spl0_202
<=> ! [X12,X0,X11] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X11,X12,X0)),X12) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f125,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ominus__class_Ominus(X11,X12,X0)),X12) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f1953,plain,
spl0_201,
inference(avatar_split_clause,[],[f110,f1951]) ).
fof(f1951,plain,
( spl0_201
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Oorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f110,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(X10,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
fof(f1949,plain,
spl0_200,
inference(avatar_split_clause,[],[f29,f1947]) ).
fof(f1947,plain,
( spl0_200
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f29,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| ~ c_lessequals(X9,X10,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f1945,plain,
spl0_199,
inference(avatar_split_clause,[],[f24,f1943]) ).
fof(f1943,plain,
( spl0_199
<=> ! [X11,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| X11 = X12
| ~ c_lessequals(X12,X11,X0)
| c_HOL_Oord__class_Oless(X12,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f24,axiom,
! [X0,X11,X12] :
( ~ class_Orderings_Oorder(X0)
| X11 = X12
| ~ c_lessequals(X12,X11,X0)
| c_HOL_Oord__class_Oless(X12,X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
fof(f1892,plain,
( ~ spl0_197
| spl0_198
| ~ spl0_95
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1883,f1783,f1230,f1890,f1886]) ).
fof(f1886,plain,
( spl0_197
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1783,plain,
( spl0_183
<=> ! [X11,X0,X12] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X11 = X12
| c_HOL_Ominus__class_Ominus(X11,X12,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1883,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_95
| ~ spl0_183 ),
inference(trivial_inequality_removal,[],[f1879]) ).
fof(f1879,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_95
| ~ spl0_183 ),
inference(superposition,[],[f1784,f1231]) ).
fof(f1784,plain,
( ! [X0,X11,X12] :
( c_HOL_Ominus__class_Ominus(X11,X12,X0) != c_HOL_Ozero__class_Ozero(X0)
| X11 = X12
| ~ class_OrderedGroup_Ogroup__add(X0) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1783]) ).
fof(f1838,plain,
spl0_196,
inference(avatar_split_clause,[],[f740,f1836]) ).
fof(f740,plain,
! [X44] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X44)),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f739,f374]) ).
fof(f739,plain,
! [X44] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X44)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f677,f668]) ).
fof(f677,plain,
! [X44] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X44)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f272,f87]) ).
fof(f272,axiom,
! [X44] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X44)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X44)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).
fof(f1834,plain,
spl0_195,
inference(avatar_split_clause,[],[f577,f1832]) ).
fof(f1832,plain,
( spl0_195
<=> ! [X25,X18] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X25),X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f577,axiom,
! [X18,X25] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X25),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f1830,plain,
spl0_194,
inference(avatar_split_clause,[],[f462,f1828]) ).
fof(f1828,plain,
( spl0_194
<=> ! [X57,X11,X0,X56,X66] :
( X57 = X66
| c_List_Olist_OCons(X56,X57,X0) != c_List_Olist_OCons(X11,X66,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f462,axiom,
! [X0,X11,X56,X57,X66] :
( X57 = X66
| c_List_Olist_OCons(X56,X57,X0) != c_List_Olist_OCons(X11,X66,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
fof(f1826,plain,
spl0_193,
inference(avatar_split_clause,[],[f461,f1824]) ).
fof(f1824,plain,
( spl0_193
<=> ! [X11,X57,X0,X56,X66] :
( X11 = X56
| c_List_Olist_OCons(X56,X57,X0) != c_List_Olist_OCons(X11,X66,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f461,axiom,
! [X0,X11,X56,X57,X66] :
( X11 = X56
| c_List_Olist_OCons(X56,X57,X0) != c_List_Olist_OCons(X11,X66,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
fof(f1822,plain,
spl0_192,
inference(avatar_split_clause,[],[f421,f1820]) ).
fof(f1820,plain,
( spl0_192
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Oone__class_Oone(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f421,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Oone__class_Oone(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f1818,plain,
( spl0_191
| ~ spl0_44
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1371,f1296,f1006,f1815]) ).
fof(f1815,plain,
( spl0_191
<=> c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1296,plain,
( spl0_111
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1371,plain,
( c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint)
| ~ spl0_44
| ~ spl0_111 ),
inference(resolution,[],[f1297,f1008]) ).
fof(f1297,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f1813,plain,
spl0_190,
inference(avatar_split_clause,[],[f384,f1811]) ).
fof(f1811,plain,
( spl0_190
<=> ! [X47,X0,X49,X22] :
( c_List_Olist_ONil(X49) = X22
| c_List_Olist_ONil(X0) != c_List_Omap(X47,X22,X49,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f384,axiom,
! [X0,X49,X47,X22] :
( c_List_Olist_ONil(X49) = X22
| c_List_Olist_ONil(X0) != c_List_Omap(X47,X22,X49,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
fof(f1809,plain,
spl0_189,
inference(avatar_split_clause,[],[f368,f1807]) ).
fof(f1807,plain,
( spl0_189
<=> ! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f368,axiom,
! [X7,X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7) != X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f1805,plain,
spl0_188,
inference(avatar_split_clause,[],[f343,f1803]) ).
fof(f1803,plain,
( spl0_188
<=> ! [X0,X9,X22,X20] :
( c_List_Olist_ONil(X0) = X22
| c_List_Olist_ONil(X0) != c_List_Olist__update(X22,X20,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f343,axiom,
! [X0,X9,X22,X20] :
( c_List_Olist_ONil(X0) = X22
| c_List_Olist_ONil(X0) != c_List_Olist__update(X22,X20,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
fof(f1801,plain,
spl0_187,
inference(avatar_split_clause,[],[f251,f1799]) ).
fof(f1799,plain,
( spl0_187
<=> ! [X0,X7,X15] :
( ~ class_Nat_Osemiring__char__0(X0)
| X7 = X15
| c_Nat_Osemiring__1__class_Oof__nat(X15,X0) != c_Nat_Osemiring__1__class_Oof__nat(X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f251,axiom,
! [X0,X7,X15] :
( ~ class_Nat_Osemiring__char__0(X0)
| X7 = X15
| c_Nat_Osemiring__1__class_Oof__nat(X15,X0) != c_Nat_Osemiring__1__class_Oof__nat(X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f1797,plain,
spl0_186,
inference(avatar_split_clause,[],[f223,f1795]) ).
fof(f1795,plain,
( spl0_186
<=> ! [X0,X22,X36,X45] :
( X36 = X45
| c_List_Oappend(X22,X36,X0) != c_List_Oappend(X22,X45,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f223,axiom,
! [X0,X36,X45,X22] :
( X36 = X45
| c_List_Oappend(X22,X36,X0) != c_List_Oappend(X22,X45,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
fof(f1793,plain,
spl0_185,
inference(avatar_split_clause,[],[f222,f1791]) ).
fof(f1791,plain,
( spl0_185
<=> ! [X0,X22,X36,X45] :
( X36 = X45
| c_List_Oappend(X36,X22,X0) != c_List_Oappend(X45,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f222,axiom,
! [X0,X36,X45,X22] :
( X36 = X45
| c_List_Oappend(X36,X22,X0) != c_List_Oappend(X45,X22,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
fof(f1789,plain,
spl0_184,
inference(avatar_split_clause,[],[f168,f1787]) ).
fof(f168,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X11 = X12
| c_HOL_Ominus__class_Ominus(X11,X12,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f1785,plain,
spl0_183,
inference(avatar_split_clause,[],[f167,f1783]) ).
fof(f167,axiom,
! [X0,X11,X12] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X11 = X12
| c_HOL_Ominus__class_Ominus(X11,X12,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f1781,plain,
spl0_182,
inference(avatar_split_clause,[],[f90,f1779]) ).
fof(f1779,plain,
( spl0_182
<=> ! [X20,X7,X18] :
( ~ c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| c_Lambda_OdB_OVar(X18) = c_Lambda_Oliftn(X7,c_Lambda_OdB_OVar(X18),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f90,axiom,
! [X18,X7,X20] :
( ~ c_HOL_Oord__class_Oless(X18,X20,tc_nat)
| c_Lambda_OdB_OVar(X18) = c_Lambda_Oliftn(X7,c_Lambda_OdB_OVar(X18),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
fof(f1777,plain,
spl0_181,
inference(avatar_split_clause,[],[f69,f1775]) ).
fof(f1775,plain,
( spl0_181
<=> ! [X7,X15] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X15),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f69,axiom,
! [X7,X15] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X15),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f1773,plain,
( spl0_180
| ~ spl0_14
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1370,f1296,f856,f1770]) ).
fof(f1770,plain,
( spl0_180
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1370,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_111 ),
inference(resolution,[],[f1297,f858]) ).
fof(f1768,plain,
spl0_179,
inference(avatar_split_clause,[],[f60,f1766]) ).
fof(f1766,plain,
( spl0_179
<=> ! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f60,axiom,
! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f1764,plain,
spl0_178,
inference(avatar_split_clause,[],[f59,f1762]) ).
fof(f1762,plain,
( spl0_178
<=> ! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f59,axiom,
! [X7,X15] :
( c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f1709,plain,
( spl0_177
| ~ spl0_38
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1367,f1288,f976,f1707]) ).
fof(f1707,plain,
( spl0_177
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f976,plain,
( spl0_38
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1288,plain,
( spl0_109
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X9,c_HOL_Oone__class_Oone(tc_nat),X0) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1367,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0
| ~ spl0_38
| ~ spl0_109 ),
inference(resolution,[],[f1289,f978]) ).
fof(f978,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f976]) ).
fof(f1289,plain,
( ! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X9,c_HOL_Oone__class_Oone(tc_nat),X0) = X9 )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1288]) ).
fof(f1682,plain,
( spl0_176
| ~ spl0_9
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1366,f1288,f831,f1680]) ).
fof(f1680,plain,
( spl0_176
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f831,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1366,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_9
| ~ spl0_109 ),
inference(resolution,[],[f1289,f833]) ).
fof(f833,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f1662,plain,
spl0_175,
inference(avatar_split_clause,[],[f663,f1660]) ).
fof(f663,plain,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f54,f87]) ).
fof(f54,axiom,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X9),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f1658,plain,
spl0_174,
inference(avatar_split_clause,[],[f529,f1656]) ).
fof(f1656,plain,
( spl0_174
<=> ! [X42,X41,X0,X29,X43] : hAPP(X41,X29) = c_Lambda_OdB_OdB__case(X41,X42,X43,c_Lambda_OdB_OVar(X29),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f529,axiom,
! [X41,X29,X0,X42,X43] : hAPP(X41,X29) = c_Lambda_OdB_OdB__case(X41,X42,X43,c_Lambda_OdB_OVar(X29),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
fof(f1654,plain,
spl0_173,
inference(avatar_split_clause,[],[f526,f1652]) ).
fof(f1652,plain,
( spl0_173
<=> ! [X42,X41,X0,X29,X43] : hAPP(X41,X29) = c_Lambda_OdB_OdB__rec(X41,X42,X43,c_Lambda_OdB_OVar(X29),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f526,axiom,
! [X41,X29,X0,X42,X43] : hAPP(X41,X29) = c_Lambda_OdB_OdB__rec(X41,X42,X43,c_Lambda_OdB_OVar(X29),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
fof(f1650,plain,
spl0_172,
inference(avatar_split_clause,[],[f408,f1648]) ).
fof(f1648,plain,
( spl0_172
<=> ! [X7,X15] :
( X7 = X15
| c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f408,axiom,
! [X7,X15] :
( X7 = X15
| c_HOL_Oord__class_Oless(X15,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f1646,plain,
spl0_171,
inference(avatar_split_clause,[],[f394,f1644]) ).
fof(f1644,plain,
( spl0_171
<=> ! [X22,X36,X0] :
( c_List_Olist_ONil(X0) = X36
| c_List_Olist_ONil(X0) != c_List_Oappend(X22,X36,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f394,axiom,
! [X0,X36,X22] :
( c_List_Olist_ONil(X0) = X36
| c_List_Olist_ONil(X0) != c_List_Oappend(X22,X36,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
fof(f1642,plain,
spl0_170,
inference(avatar_split_clause,[],[f393,f1640]) ).
fof(f1640,plain,
( spl0_170
<=> ! [X22,X36,X0] :
( c_List_Olist_ONil(X0) = X22
| c_List_Olist_ONil(X0) != c_List_Oappend(X22,X36,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f393,axiom,
! [X0,X36,X22] :
( c_List_Olist_ONil(X0) = X22
| c_List_Olist_ONil(X0) != c_List_Oappend(X22,X36,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
fof(f1638,plain,
spl0_169,
inference(avatar_split_clause,[],[f360,f1636]) ).
fof(f1636,plain,
( spl0_169
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Ozero__class_Ozero(X0)) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f360,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Ozero__class_Ozero(X0)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1634,plain,
spl0_168,
inference(avatar_split_clause,[],[f359,f1632]) ).
fof(f1632,plain,
( spl0_168
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Ozero__class_Ozero(X0)) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f359,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Ozero__class_Ozero(X0)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1630,plain,
spl0_167,
inference(avatar_split_clause,[],[f358,f1628]) ).
fof(f1628,plain,
( spl0_167
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X11) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f358,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1618,plain,
spl0_166,
inference(avatar_split_clause,[],[f357,f1616]) ).
fof(f1616,plain,
( spl0_166
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Ozero__class_Ozero(X0)) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f357,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X11),c_HOL_Ozero__class_Ozero(X0)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1614,plain,
spl0_165,
inference(avatar_split_clause,[],[f355,f1612]) ).
fof(f1612,plain,
( spl0_165
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X11) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f355,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1610,plain,
spl0_164,
inference(avatar_split_clause,[],[f354,f1608]) ).
fof(f1608,plain,
( spl0_164
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X9) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f354,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f1606,plain,
spl0_163,
inference(avatar_split_clause,[],[f218,f1604]) ).
fof(f1604,plain,
( spl0_163
<=> ! [X44,X41,X42,X0,X43] : c_Lambda_OdB_OdB__case(X41,X42,X43,c_Lambda_OdB_OAbs(X44),X0) = hAPP(X43,X44) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f218,axiom,
! [X41,X0,X44,X42,X43] : c_Lambda_OdB_OdB__case(X41,X42,X43,c_Lambda_OdB_OAbs(X44),X0) = hAPP(X43,X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
fof(f1602,plain,
spl0_162,
inference(avatar_split_clause,[],[f217,f1600]) ).
fof(f1600,plain,
( spl0_162
<=> ! [X40,X0,X36,X22] :
( c_List_Olistsp(X40,X36,X0)
| ~ c_List_Olistsp(X40,c_List_Oappend(X22,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f217,axiom,
! [X40,X0,X36,X22] :
( c_List_Olistsp(X40,X36,X0)
| ~ c_List_Olistsp(X40,c_List_Oappend(X22,X36,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
fof(f1598,plain,
spl0_161,
inference(avatar_split_clause,[],[f216,f1596]) ).
fof(f1596,plain,
( spl0_161
<=> ! [X40,X0,X36,X22] :
( c_List_Olistsp(X40,X22,X0)
| ~ c_List_Olistsp(X40,c_List_Oappend(X22,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f216,axiom,
! [X40,X0,X36,X22] :
( c_List_Olistsp(X40,X22,X0)
| ~ c_List_Olistsp(X40,c_List_Oappend(X22,X36,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
fof(f1594,plain,
spl0_160,
inference(avatar_split_clause,[],[f161,f1592]) ).
fof(f1592,plain,
( spl0_160
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f161,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f1590,plain,
spl0_159,
inference(avatar_split_clause,[],[f156,f1588]) ).
fof(f1588,plain,
( spl0_159
<=> ! [X7,X15] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X15),X7,tc_nat) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f156,axiom,
! [X7,X15] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X15),X7,tc_nat) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1586,plain,
spl0_158,
inference(avatar_split_clause,[],[f155,f1584]) ).
fof(f1584,plain,
( spl0_158
<=> ! [X7,X15] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7),X7,tc_nat) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f155,axiom,
! [X7,X15] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X7),X7,tc_nat) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f1582,plain,
spl0_157,
inference(avatar_split_clause,[],[f113,f1580]) ).
fof(f113,axiom,
! [X21,X7,X20] :
( ~ c_HOL_Oord__class_Oless(X21,X20,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X21,X7,tc_nat),X20,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f1578,plain,
( spl0_156
| ~ spl0_116
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1573,f1498,f1316,f1575]) ).
fof(f1575,plain,
( spl0_156
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1573,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_116
| ~ spl0_154 ),
inference(superposition,[],[f1499,f1317]) ).
fof(f1511,plain,
( spl0_155
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1505,f1410,f1509]) ).
fof(f1509,plain,
( spl0_155
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1410,plain,
( spl0_132
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1505,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_132 ),
inference(factoring,[],[f1411]) ).
fof(f1411,plain,
( ! [X10,X0,X9] :
( c_lessequals(X10,X9,X0)
| c_lessequals(X9,X10,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1410]) ).
fof(f1500,plain,
spl0_154,
inference(avatar_split_clause,[],[f660,f1498]) ).
fof(f660,plain,
! [X9] : c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f103,f87]) ).
fof(f103,axiom,
! [X9] : c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f1496,plain,
spl0_153,
inference(avatar_split_clause,[],[f656,f1494]) ).
fof(f656,plain,
! [X30] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X30),c_HOL_Oone__class_Oone(tc_nat)),
inference(definition_unfolding,[],[f177,f87]) ).
fof(f177,axiom,
! [X30] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f1492,plain,
spl0_152,
inference(avatar_split_clause,[],[f570,f1490]) ).
fof(f1490,plain,
( spl0_152
<=> ! [X20,X34] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X20)),X34),X20) = X34 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f570,axiom,
! [X34,X20] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X20)),X34),X20) = X34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f1488,plain,
spl0_151,
inference(avatar_split_clause,[],[f528,f1486]) ).
fof(f1486,plain,
( spl0_151
<=> ! [X18,X27,X28] :
( ~ c_Type_Otyping(X28,c_Lambda_OdB_OVar(X18),X27)
| hAPP(X28,X18) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f528,axiom,
! [X28,X18,X27] :
( ~ c_Type_Otyping(X28,c_Lambda_OdB_OVar(X18),X27)
| hAPP(X28,X18) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f1484,plain,
spl0_150,
inference(avatar_split_clause,[],[f504,f1482]) ).
fof(f1482,plain,
( spl0_150
<=> ! [X25] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X25),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X25),tc_Lambda_OdB,tc_Lambda_OdB) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f504,axiom,
! [X25] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X25),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X25),tc_Lambda_OdB,tc_Lambda_OdB) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__head__tail_0) ).
fof(f1480,plain,
spl0_149,
inference(avatar_split_clause,[],[f486,f1478]) ).
fof(f1478,plain,
( spl0_149
<=> ! [X11,X0,X12] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(X12,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f486,axiom,
! [X0,X11,X12] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0)
| ~ c_HOL_Oord__class_Oless(X12,X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f1476,plain,
( spl0_148
| ~ spl0_50
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1364,f1280,f1036,f1474]) ).
fof(f1474,plain,
( spl0_148
<=> ! [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_148])]) ).
fof(f1036,plain,
( spl0_50
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1280,plain,
( spl0_107
<=> ! [X9,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1364,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
| ~ spl0_50
| ~ spl0_107 ),
inference(resolution,[],[f1281,f1038]) ).
fof(f1038,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1281,plain,
( ! [X0,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X9,X9,X0) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f1472,plain,
spl0_147,
inference(avatar_split_clause,[],[f484,f1470]) ).
fof(f1470,plain,
( spl0_147
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f484,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1468,plain,
spl0_146,
inference(avatar_split_clause,[],[f481,f1466]) ).
fof(f1466,plain,
( spl0_146
<=> ! [X12,X0,X11] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X12,X11,X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f481,axiom,
! [X0,X11,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X12,X11,X0)
| ~ c_HOL_Oord__class_Oless(X11,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1464,plain,
spl0_145,
inference(avatar_split_clause,[],[f449,f1462]) ).
fof(f1462,plain,
( spl0_145
<=> ! [X22,X36,X0] :
( c_List_Olist_ONil(X0) = X22
| c_List_Oappend(X22,X36,X0) != X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f449,axiom,
! [X0,X36,X22] :
( c_List_Olist_ONil(X0) = X22
| c_List_Oappend(X22,X36,X0) != X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
fof(f1460,plain,
spl0_144,
inference(avatar_split_clause,[],[f447,f1458]) ).
fof(f1458,plain,
( spl0_144
<=> ! [X22,X36,X0] :
( c_List_Olist_ONil(X0) = X36
| c_List_Oappend(X22,X36,X0) != X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f447,axiom,
! [X0,X36,X22] :
( c_List_Olist_ONil(X0) = X36
| c_List_Oappend(X22,X36,X0) != X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
fof(f1456,plain,
spl0_143,
inference(avatar_split_clause,[],[f430,f1454]) ).
fof(f1454,plain,
( spl0_143
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X9,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f430,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X9,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f1452,plain,
spl0_142,
inference(avatar_split_clause,[],[f429,f1450]) ).
fof(f429,axiom,
! [X0,X11] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X11,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f1448,plain,
spl0_141,
inference(avatar_split_clause,[],[f423,f1446]) ).
fof(f1446,plain,
( spl0_141
<=> ! [X22,X36,X0] :
( X22 = X36
| c_List_Orev(X22,X0) != c_List_Orev(X36,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f423,axiom,
! [X0,X36,X22] :
( X22 = X36
| c_List_Orev(X22,X0) != c_List_Orev(X36,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
fof(f1444,plain,
spl0_140,
inference(avatar_split_clause,[],[f321,f1442]) ).
fof(f1442,plain,
( spl0_140
<=> ! [X22,X0] :
( c_List_Olist_ONil(X0) = X22
| c_List_Olist_ONil(X0) != c_List_Orev(X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f321,axiom,
! [X0,X22] :
( c_List_Olist_ONil(X0) = X22
| c_List_Olist_ONil(X0) != c_List_Orev(X22,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
fof(f1440,plain,
spl0_139,
inference(avatar_split_clause,[],[f194,f1438]) ).
fof(f194,axiom,
! [X0,X7] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1436,plain,
spl0_138,
inference(avatar_split_clause,[],[f169,f1434]) ).
fof(f169,axiom,
! [X0,X18,X32] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X32,c_HOL_Ozero__class_Ozero(tc_nat),X18,X0) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I1_J_0) ).
fof(f1432,plain,
spl0_137,
inference(avatar_split_clause,[],[f137,f1430]) ).
fof(f1430,plain,
( spl0_137
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f137,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1428,plain,
spl0_136,
inference(avatar_split_clause,[],[f135,f1426]) ).
fof(f1426,plain,
( spl0_136
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f135,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1424,plain,
spl0_135,
inference(avatar_split_clause,[],[f134,f1422]) ).
fof(f134,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f1420,plain,
spl0_134,
inference(avatar_split_clause,[],[f106,f1418]) ).
fof(f1418,plain,
( spl0_134
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f106,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1416,plain,
spl0_133,
inference(avatar_split_clause,[],[f105,f1414]) ).
fof(f1414,plain,
( spl0_133
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f105,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_lessequals(X9,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1412,plain,
spl0_132,
inference(avatar_split_clause,[],[f31,f1410]) ).
fof(f31,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X10,X0)
| c_lessequals(X10,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1408,plain,
spl0_131,
inference(avatar_split_clause,[],[f3,f1406]) ).
fof(f1406,plain,
( spl0_131
<=> ! [X5,X4,X6,X3] :
( X3 = X5
| c_Type_Otype_OFun(X3,X4) != c_Type_Otype_OFun(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f3,axiom,
! [X3,X6,X4,X5] :
( X3 = X5
| c_Type_Otype_OFun(X3,X4) != c_Type_Otype_OFun(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
fof(f1404,plain,
spl0_130,
inference(avatar_split_clause,[],[f2,f1402]) ).
fof(f1402,plain,
( spl0_130
<=> ! [X6,X4,X5,X3] :
( X4 = X6
| c_Type_Otype_OFun(X3,X4) != c_Type_Otype_OFun(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f2,axiom,
! [X3,X6,X4,X5] :
( X4 = X6
| c_Type_Otype_OFun(X3,X4) != c_Type_Otype_OFun(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
fof(f1400,plain,
~ spl0_129,
inference(avatar_split_clause,[],[f588,f1397]) ).
fof(f588,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_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1395,plain,
( ~ spl0_128
| ~ spl0_116
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1388,f1352,f1316,f1392]) ).
fof(f1392,plain,
( spl0_128
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1388,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| ~ spl0_116
| ~ spl0_125 ),
inference(superposition,[],[f1353,f1317]) ).
fof(f1363,plain,
( spl0_127
| ~ spl0_50
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1359,f1276,f1036,f1361]) ).
fof(f1361,plain,
( spl0_127
<=> ! [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_127])]) ).
fof(f1276,plain,
( spl0_106
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X11,c_HOL_Ozero__class_Ozero(X0),X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1359,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_50
| ~ spl0_106 ),
inference(resolution,[],[f1277,f1038]) ).
fof(f1277,plain,
( ! [X0,X11] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X11,c_HOL_Ozero__class_Ozero(X0),X0) = X11 )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1358,plain,
spl0_126,
inference(avatar_split_clause,[],[f751,f1356]) ).
fof(f1356,plain,
( spl0_126
<=> ! [X7] :
( ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f751,plain,
! [X7] :
( ~ c_HOL_Oord__class_Oless(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7 ),
inference(forward_demodulation,[],[f750,f374]) ).
fof(f750,plain,
! [X7] :
( ~ c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7 ),
inference(forward_demodulation,[],[f702,f247]) ).
fof(f702,plain,
! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| ~ c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f56,f87]) ).
fof(f56,axiom,
! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| ~ c_HOL_Oord__class_Oless(X7,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1354,plain,
spl0_125,
inference(avatar_split_clause,[],[f654,f1352]) ).
fof(f654,plain,
! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Oone__class_Oone(tc_nat)) != X7,
inference(definition_unfolding,[],[f5,f87]) ).
fof(f5,axiom,
! [X7] : c_Suc(X7) != X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f1350,plain,
spl0_124,
inference(avatar_split_clause,[],[f540,f1348]) ).
fof(f540,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1346,plain,
spl0_123,
inference(avatar_split_clause,[],[f532,f1344]) ).
fof(f1344,plain,
( spl0_123
<=> ! [X35] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X35))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X35))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f532,axiom,
! [X35] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X35))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X35))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f1342,plain,
spl0_122,
inference(avatar_split_clause,[],[f508,f1340]) ).
fof(f1340,plain,
( spl0_122
<=> ! [X0,X11,X47,X49] : c_List_Ofoldl(X47,X11,c_List_Olist_ONil(X49),X0,X49) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f508,axiom,
! [X0,X11,X49,X47] : c_List_Ofoldl(X47,X11,c_List_Olist_ONil(X49),X0,X49) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
fof(f1338,plain,
spl0_121,
inference(avatar_split_clause,[],[f498,f1336]) ).
fof(f1336,plain,
( spl0_121
<=> ! [X0,X47,X49] : c_List_Olist_ONil(X0) = c_List_Omap(X47,c_List_Olist_ONil(X49),X49,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f498,axiom,
! [X0,X49,X47] : c_List_Olist_ONil(X0) = c_List_Omap(X47,c_List_Olist_ONil(X49),X49,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
fof(f1334,plain,
spl0_120,
inference(avatar_split_clause,[],[f445,f1332]) ).
fof(f445,axiom,
! [X21,X18] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X21),X18),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1330,plain,
spl0_119,
inference(avatar_split_clause,[],[f444,f1328]) ).
fof(f444,axiom,
! [X21,X18] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X18),X21),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1326,plain,
spl0_118,
inference(avatar_split_clause,[],[f387,f1324]) ).
fof(f1324,plain,
( spl0_118
<=> ! [X9,X0,X27,X28] : hAPP(c_Type_Oshift(X28,X9,X27,X0),X9) = X27 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f387,axiom,
! [X28,X0,X9,X27] : hAPP(c_Type_Oshift(X28,X9,X27,X0),X9) = X27,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f1322,plain,
spl0_117,
inference(avatar_split_clause,[],[f374,f1320]) ).
fof(f1318,plain,
spl0_116,
inference(avatar_split_clause,[],[f373,f1316]) ).
fof(f1314,plain,
spl0_115,
inference(avatar_split_clause,[],[f364,f1312]) ).
fof(f1312,plain,
( spl0_115
<=> ! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f364,axiom,
! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1310,plain,
spl0_114,
inference(avatar_split_clause,[],[f333,f1308]) ).
fof(f1308,plain,
( spl0_114
<=> ! [X0,X35] : c_Transitive__Closure_Ortranclp(X35,X0) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X35,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f333,axiom,
! [X0,X35] : c_Transitive__Closure_Ortranclp(X35,X0) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X35,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
fof(f1306,plain,
spl0_113,
inference(avatar_split_clause,[],[f319,f1304]) ).
fof(f1304,plain,
( spl0_113
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X15,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f319,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X15,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1302,plain,
spl0_112,
inference(avatar_split_clause,[],[f301,f1300]) ).
fof(f1300,plain,
( spl0_112
<=> ! [X20,X9,X0] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X20,X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f301,axiom,
! [X0,X9,X20] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X20,X9,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
fof(f1298,plain,
spl0_111,
inference(avatar_split_clause,[],[f287,f1296]) ).
fof(f287,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
fof(f1294,plain,
spl0_110,
inference(avatar_split_clause,[],[f258,f1292]) ).
fof(f1292,plain,
( spl0_110
<=> ! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X11,c_HOL_Oone__class_Oone(tc_nat),X0) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f258,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X11,c_HOL_Oone__class_Oone(tc_nat),X0) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
fof(f1290,plain,
spl0_109,
inference(avatar_split_clause,[],[f257,f1288]) ).
fof(f257,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X9,c_HOL_Oone__class_Oone(tc_nat),X0) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1286,plain,
spl0_108,
inference(avatar_split_clause,[],[f165,f1284]) ).
fof(f1284,plain,
( spl0_108
<=> ! [X9,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f165,axiom,
! [X0,X9] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1282,plain,
spl0_107,
inference(avatar_split_clause,[],[f164,f1280]) ).
fof(f164,axiom,
! [X0,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f1278,plain,
spl0_106,
inference(avatar_split_clause,[],[f163,f1276]) ).
fof(f163,axiom,
! [X0,X11] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X11,c_HOL_Ozero__class_Ozero(X0),X0) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1274,plain,
spl0_105,
inference(avatar_split_clause,[],[f52,f1272]) ).
fof(f1272,plain,
( spl0_105
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f52,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X15,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
fof(f1268,plain,
spl0_104,
inference(avatar_split_clause,[],[f576,f1266]) ).
fof(f1266,plain,
( spl0_104
<=> ! [X29,X75,X76] : c_Lambda_OdB_OVar(X29) != hAPP(hAPP(c_Lambda_OdB_OApp,X75),X76) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f576,axiom,
! [X29,X76,X75] : c_Lambda_OdB_OVar(X29) != hAPP(hAPP(c_Lambda_OdB_OApp,X75),X76),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f1264,plain,
spl0_103,
inference(avatar_split_clause,[],[f567,f1262]) ).
fof(f1262,plain,
( spl0_103
<=> ! [X29,X30] :
( X29 = X30
| c_Lambda_OdB_OVar(X29) != c_Lambda_OdB_OVar(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f567,axiom,
! [X29,X30] :
( X29 = X30
| c_Lambda_OdB_OVar(X29) != c_Lambda_OdB_OVar(X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f1260,plain,
spl0_102,
inference(avatar_split_clause,[],[f422,f1258]) ).
fof(f1258,plain,
( spl0_102
<=> ! [X22,X0] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X22,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f422,axiom,
! [X0,X22] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X22,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).
fof(f1256,plain,
spl0_101,
inference(avatar_split_clause,[],[f419,f1254]) ).
fof(f1254,plain,
( spl0_101
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f419,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1252,plain,
spl0_100,
inference(avatar_split_clause,[],[f392,f1250]) ).
fof(f1250,plain,
( spl0_100
<=> ! [X61,X44] :
( X44 = X61
| c_Lambda_OdB_OAbs(X44) != c_Lambda_OdB_OAbs(X61) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f392,axiom,
! [X44,X61] :
( X44 = X61
| c_Lambda_OdB_OAbs(X44) != c_Lambda_OdB_OAbs(X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f1248,plain,
spl0_99,
inference(avatar_split_clause,[],[f389,f1246]) ).
fof(f1246,plain,
( spl0_99
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f389,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1244,plain,
spl0_98,
inference(avatar_split_clause,[],[f376,f1242]) ).
fof(f1242,plain,
( spl0_98
<=> ! [X61,X52,X51] : hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52) != c_Lambda_OdB_OAbs(X61) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f376,axiom,
! [X51,X52,X61] : hAPP(hAPP(c_Lambda_OdB_OApp,X51),X52) != c_Lambda_OdB_OAbs(X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f1240,plain,
spl0_97,
inference(avatar_split_clause,[],[f227,f1238]) ).
fof(f1238,plain,
( spl0_97
<=> ! [X0,X7] : c_List_Olist_ONil(X0) = c_List_Otake(X7,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f227,axiom,
! [X0,X7] : c_List_Olist_ONil(X0) = c_List_Otake(X7,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
fof(f1236,plain,
spl0_96,
inference(avatar_split_clause,[],[f225,f1234]) ).
fof(f1234,plain,
( spl0_96
<=> ! [X9,X0,X35] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f225,axiom,
! [X0,X9,X35] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X35,X0),X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
fof(f1232,plain,
spl0_95,
inference(avatar_split_clause,[],[f178,f1230]) ).
fof(f178,axiom,
! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1228,plain,
spl0_94,
inference(avatar_split_clause,[],[f51,f1226]) ).
fof(f1226,plain,
( spl0_94
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f51,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1224,plain,
spl0_93,
inference(avatar_split_clause,[],[f50,f1222]) ).
fof(f1222,plain,
( spl0_93
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f50,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1218,plain,
spl0_92,
inference(avatar_split_clause,[],[f653,f1216]) ).
fof(f1216,plain,
( spl0_92
<=> ! [X82,X0,X81] :
( X81 = X82
| ~ c_fequal(X81,X82,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f653,axiom,
! [X82,X0,X81] :
( X81 = X82
| ~ c_fequal(X81,X82,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1214,plain,
spl0_91,
inference(avatar_split_clause,[],[f543,f1212]) ).
fof(f543,axiom,
! [X29] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X29),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
fof(f1210,plain,
spl0_90,
inference(avatar_split_clause,[],[f530,f1208]) ).
fof(f1208,plain,
( spl0_90
<=> ! [X9,X23] : c_Type_Otyping(X23,c_Lambda_OdB_OVar(X9),hAPP(X23,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f530,axiom,
! [X9,X23] : c_Type_Otyping(X23,c_Lambda_OdB_OVar(X9),hAPP(X23,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f1206,plain,
spl0_89,
inference(avatar_split_clause,[],[f525,f1204]) ).
fof(f1204,plain,
( spl0_89
<=> ! [X25,X18] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X18)),X25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f525,axiom,
! [X18,X25] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X18)),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f1202,plain,
spl0_88,
inference(avatar_split_clause,[],[f469,f1200]) ).
fof(f1200,plain,
( spl0_88
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f469,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
fof(f1198,plain,
spl0_87,
inference(avatar_split_clause,[],[f416,f1196]) ).
fof(f1196,plain,
( spl0_87
<=> ! [X57,X0,X56] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X56,X57,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f416,axiom,
! [X0,X56,X57] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X56,X57,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
fof(f1194,plain,
spl0_86,
inference(avatar_split_clause,[],[f349,f1192]) ).
fof(f1192,plain,
( spl0_86
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f349,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1190,plain,
spl0_85,
inference(avatar_split_clause,[],[f237,f1188]) ).
fof(f237,axiom,
! [X0,X22] : c_List_Orev(c_List_Orev(X22,X0),X0) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
fof(f1186,plain,
spl0_84,
inference(avatar_split_clause,[],[f232,f1184]) ).
fof(f1184,plain,
( spl0_84
<=> ! [X36,X0] : c_List_Oappend(c_List_Olist_ONil(X0),X36,X0) = X36 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f232,axiom,
! [X0,X36] : c_List_Oappend(c_List_Olist_ONil(X0),X36,X0) = X36,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
fof(f1182,plain,
spl0_83,
inference(avatar_split_clause,[],[f231,f1180]) ).
fof(f1180,plain,
( spl0_83
<=> ! [X22,X0] : c_List_Oappend(X22,c_List_Olist_ONil(X0),X0) = X22 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f231,axiom,
! [X0,X22] : c_List_Oappend(X22,c_List_Olist_ONil(X0),X0) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
fof(f1178,plain,
spl0_82,
inference(avatar_split_clause,[],[f175,f1176]) ).
fof(f1176,plain,
( spl0_82
<=> ! [X15] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f175,axiom,
! [X15] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X15,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1174,plain,
spl0_81,
inference(avatar_split_clause,[],[f174,f1172]) ).
fof(f1172,plain,
( spl0_81
<=> ! [X15] : c_HOL_Ominus__class_Ominus(X15,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f174,axiom,
! [X15] : c_HOL_Ominus__class_Ominus(X15,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1170,plain,
spl0_80,
inference(avatar_split_clause,[],[f170,f1168]) ).
fof(f170,axiom,
! [X25,X20] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X20) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
fof(f1166,plain,
spl0_79,
inference(avatar_split_clause,[],[f590,f1164]) ).
fof(f1164,plain,
( spl0_79
<=> ! [X80,X79] :
( ~ class_Orderings_Oorder(X80)
| class_Orderings_Oorder(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f590,axiom,
! [X80,X79] :
( ~ class_Orderings_Oorder(X80)
| class_Orderings_Oorder(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1162,plain,
spl0_78,
inference(avatar_split_clause,[],[f589,f1160]) ).
fof(f1160,plain,
( spl0_78
<=> ! [X80,X79] :
( ~ class_Orderings_Opreorder(X80)
| class_Orderings_Opreorder(tc_fun(X79,X80)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f589,axiom,
! [X80,X79] :
( ~ class_Orderings_Opreorder(X80)
| class_Orderings_Opreorder(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1158,plain,
spl0_77,
inference(avatar_split_clause,[],[f544,f1156]) ).
fof(f544,axiom,
! [X29] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
fof(f1154,plain,
spl0_76,
inference(avatar_split_clause,[],[f434,f1152]) ).
fof(f1152,plain,
( spl0_76
<=> ! [X0] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f434,axiom,
! [X0] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add__class_Oaxioms_0) ).
fof(f1150,plain,
spl0_75,
inference(avatar_split_clause,[],[f400,f1148]) ).
fof(f1148,plain,
( spl0_75
<=> ! [X9,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f400,axiom,
! [X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1146,plain,
spl0_74,
inference(avatar_split_clause,[],[f399,f1144]) ).
fof(f1144,plain,
( spl0_74
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f399,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1142,plain,
spl0_73,
inference(avatar_split_clause,[],[f398,f1140]) ).
fof(f1140,plain,
( spl0_73
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f398,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1138,plain,
spl0_72,
inference(avatar_split_clause,[],[f322,f1136]) ).
fof(f1136,plain,
( spl0_72
<=> ! [X25,X0,X9] : c_List_Olist_OCons(X9,X25,X0) != X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f322,axiom,
! [X0,X9,X25] : c_List_Olist_OCons(X9,X25,X0) != X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f1134,plain,
spl0_71,
inference(avatar_split_clause,[],[f261,f1132]) ).
fof(f1132,plain,
( spl0_71
<=> ! [X22,X0,X35] : ~ c_ListOrder_Ostep1(X35,X22,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f261,axiom,
! [X0,X35,X22] : ~ c_ListOrder_Ostep1(X35,X22,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
fof(f1130,plain,
spl0_70,
inference(avatar_split_clause,[],[f260,f1128]) ).
fof(f1128,plain,
( spl0_70
<=> ! [X22,X0,X35] : ~ c_ListOrder_Ostep1(X35,c_List_Olist_ONil(X0),X22,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f260,axiom,
! [X0,X35,X22] : ~ c_ListOrder_Ostep1(X35,c_List_Olist_ONil(X0),X22,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
fof(f1126,plain,
spl0_69,
inference(avatar_split_clause,[],[f11,f1124]) ).
fof(f1124,plain,
( spl0_69
<=> ! [X9,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f11,axiom,
! [X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1122,plain,
spl0_68,
inference(avatar_split_clause,[],[f10,f1120]) ).
fof(f1120,plain,
( spl0_68
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f10,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X9,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1118,plain,
spl0_67,
inference(avatar_split_clause,[],[f578,f1116]) ).
fof(f1116,plain,
( spl0_67
<=> ! [X7] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f578,axiom,
! [X7] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
fof(f1114,plain,
spl0_66,
inference(avatar_split_clause,[],[f522,f1112]) ).
fof(f522,axiom,
! [X29,X61] : c_Lambda_OdB_OAbs(X61) != c_Lambda_OdB_OVar(X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f1110,plain,
spl0_65,
inference(avatar_split_clause,[],[f371,f1108]) ).
fof(f371,axiom,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f1106,plain,
spl0_64,
inference(avatar_split_clause,[],[f221,f1104]) ).
fof(f1104,plain,
( spl0_64
<=> ! [X0,X40] : c_List_Olistsp(X40,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f221,axiom,
! [X40,X0] : c_List_Olistsp(X40,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
fof(f1102,plain,
spl0_63,
inference(avatar_split_clause,[],[f652,f1100]) ).
fof(f1100,plain,
( spl0_63
<=> ! [X9,X0] : c_fequal(X9,X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f652,axiom,
! [X0,X9] : c_fequal(X9,X9,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1098,plain,
spl0_62,
inference(avatar_split_clause,[],[f583,f1095]) ).
fof(f1095,plain,
( spl0_62
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f583,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
fof(f1093,plain,
spl0_61,
inference(avatar_split_clause,[],[f531,f1090]) ).
fof(f1090,plain,
( spl0_61
<=> hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f531,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
fof(f1088,plain,
spl0_60,
inference(avatar_split_clause,[],[f397,f1086]) ).
fof(f397,axiom,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,X7,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f1084,plain,
spl0_59,
inference(avatar_split_clause,[],[f649,f1081]) ).
fof(f1081,plain,
( spl0_59
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f649,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
fof(f1079,plain,
spl0_58,
inference(avatar_split_clause,[],[f648,f1076]) ).
fof(f648,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
fof(f1074,plain,
spl0_57,
inference(avatar_split_clause,[],[f647,f1071]) ).
fof(f1071,plain,
( spl0_57
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f647,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f1069,plain,
spl0_56,
inference(avatar_split_clause,[],[f646,f1066]) ).
fof(f1066,plain,
( spl0_56
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f646,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f1064,plain,
spl0_55,
inference(avatar_split_clause,[],[f645,f1061]) ).
fof(f1061,plain,
( spl0_55
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f645,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f1059,plain,
spl0_54,
inference(avatar_split_clause,[],[f644,f1056]) ).
fof(f1056,plain,
( spl0_54
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f644,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f1054,plain,
spl0_53,
inference(avatar_split_clause,[],[f643,f1051]) ).
fof(f1051,plain,
( spl0_53
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f643,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f1049,plain,
spl0_52,
inference(avatar_split_clause,[],[f642,f1046]) ).
fof(f1046,plain,
( spl0_52
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f642,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f1044,plain,
spl0_51,
inference(avatar_split_clause,[],[f641,f1041]) ).
fof(f1041,plain,
( spl0_51
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f641,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f1039,plain,
spl0_50,
inference(avatar_split_clause,[],[f640,f1036]) ).
fof(f640,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f1034,plain,
spl0_49,
inference(avatar_split_clause,[],[f639,f1031]) ).
fof(f1031,plain,
( spl0_49
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f639,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f1029,plain,
spl0_48,
inference(avatar_split_clause,[],[f638,f1026]) ).
fof(f638,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f1024,plain,
spl0_47,
inference(avatar_split_clause,[],[f637,f1021]) ).
fof(f1021,plain,
( spl0_47
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f637,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f1019,plain,
spl0_46,
inference(avatar_split_clause,[],[f636,f1016]) ).
fof(f1016,plain,
( spl0_46
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f636,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f1014,plain,
spl0_45,
inference(avatar_split_clause,[],[f635,f1011]) ).
fof(f1011,plain,
( spl0_45
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f635,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(f1009,plain,
spl0_44,
inference(avatar_split_clause,[],[f634,f1006]) ).
fof(f634,axiom,
class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
fof(f1004,plain,
spl0_43,
inference(avatar_split_clause,[],[f633,f1001]) ).
fof(f1001,plain,
( spl0_43
<=> class_OrderedGroup_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f633,axiom,
class_OrderedGroup_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Osemigroup__add) ).
fof(f999,plain,
spl0_42,
inference(avatar_split_clause,[],[f632,f996]) ).
fof(f996,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f632,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f994,plain,
spl0_41,
inference(avatar_split_clause,[],[f631,f991]) ).
fof(f991,plain,
( spl0_41
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f631,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f989,plain,
spl0_40,
inference(avatar_split_clause,[],[f630,f986]) ).
fof(f986,plain,
( spl0_40
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f630,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f984,plain,
spl0_39,
inference(avatar_split_clause,[],[f629,f981]) ).
fof(f981,plain,
( spl0_39
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f629,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f979,plain,
spl0_38,
inference(avatar_split_clause,[],[f628,f976]) ).
fof(f628,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f974,plain,
spl0_37,
inference(avatar_split_clause,[],[f627,f971]) ).
fof(f971,plain,
( spl0_37
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f627,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f969,plain,
spl0_36,
inference(avatar_split_clause,[],[f626,f966]) ).
fof(f966,plain,
( spl0_36
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f626,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f964,plain,
spl0_35,
inference(avatar_split_clause,[],[f625,f961]) ).
fof(f961,plain,
( spl0_35
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f625,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f959,plain,
spl0_34,
inference(avatar_split_clause,[],[f624,f956]) ).
fof(f956,plain,
( spl0_34
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f624,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f954,plain,
spl0_33,
inference(avatar_split_clause,[],[f623,f951]) ).
fof(f951,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f623,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f949,plain,
spl0_32,
inference(avatar_split_clause,[],[f622,f946]) ).
fof(f946,plain,
( spl0_32
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f622,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f944,plain,
spl0_31,
inference(avatar_split_clause,[],[f621,f941]) ).
fof(f941,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f621,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f939,plain,
spl0_30,
inference(avatar_split_clause,[],[f620,f936]) ).
fof(f936,plain,
( spl0_30
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f620,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f934,plain,
spl0_29,
inference(avatar_split_clause,[],[f619,f931]) ).
fof(f931,plain,
( spl0_29
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f619,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f929,plain,
spl0_28,
inference(avatar_split_clause,[],[f618,f926]) ).
fof(f926,plain,
( spl0_28
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f618,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f924,plain,
spl0_27,
inference(avatar_split_clause,[],[f617,f921]) ).
fof(f921,plain,
( spl0_27
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f617,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f919,plain,
spl0_26,
inference(avatar_split_clause,[],[f616,f916]) ).
fof(f916,plain,
( spl0_26
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f616,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f914,plain,
spl0_25,
inference(avatar_split_clause,[],[f615,f911]) ).
fof(f911,plain,
( spl0_25
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f615,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f909,plain,
spl0_24,
inference(avatar_split_clause,[],[f614,f906]) ).
fof(f906,plain,
( spl0_24
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f614,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
fof(f904,plain,
spl0_23,
inference(avatar_split_clause,[],[f613,f901]) ).
fof(f613,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f899,plain,
spl0_22,
inference(avatar_split_clause,[],[f612,f896]) ).
fof(f896,plain,
( spl0_22
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f612,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f894,plain,
spl0_21,
inference(avatar_split_clause,[],[f611,f891]) ).
fof(f611,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f889,plain,
spl0_20,
inference(avatar_split_clause,[],[f610,f886]) ).
fof(f886,plain,
( spl0_20
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f610,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f884,plain,
spl0_19,
inference(avatar_split_clause,[],[f609,f881]) ).
fof(f881,plain,
( spl0_19
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f609,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f879,plain,
spl0_18,
inference(avatar_split_clause,[],[f608,f876]) ).
fof(f876,plain,
( spl0_18
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f608,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f874,plain,
spl0_17,
inference(avatar_split_clause,[],[f607,f871]) ).
fof(f607,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f869,plain,
spl0_16,
inference(avatar_split_clause,[],[f606,f866]) ).
fof(f866,plain,
( spl0_16
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f606,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f864,plain,
spl0_15,
inference(avatar_split_clause,[],[f605,f861]) ).
fof(f861,plain,
( spl0_15
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f605,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f859,plain,
spl0_14,
inference(avatar_split_clause,[],[f604,f856]) ).
fof(f604,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f854,plain,
spl0_13,
inference(avatar_split_clause,[],[f603,f851]) ).
fof(f851,plain,
( spl0_13
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f603,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(f849,plain,
spl0_12,
inference(avatar_split_clause,[],[f602,f846]) ).
fof(f846,plain,
( spl0_12
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f602,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f844,plain,
spl0_11,
inference(avatar_split_clause,[],[f601,f841]) ).
fof(f841,plain,
( spl0_11
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f601,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f839,plain,
spl0_10,
inference(avatar_split_clause,[],[f600,f836]) ).
fof(f836,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f600,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f834,plain,
spl0_9,
inference(avatar_split_clause,[],[f599,f831]) ).
fof(f599,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f829,plain,
spl0_8,
inference(avatar_split_clause,[],[f598,f826]) ).
fof(f826,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f598,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f824,plain,
spl0_7,
inference(avatar_split_clause,[],[f597,f821]) ).
fof(f821,plain,
( spl0_7
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f597,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f819,plain,
spl0_6,
inference(avatar_split_clause,[],[f596,f816]) ).
fof(f816,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f596,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f814,plain,
spl0_5,
inference(avatar_split_clause,[],[f595,f811]) ).
fof(f811,plain,
( spl0_5
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f595,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f809,plain,
spl0_4,
inference(avatar_split_clause,[],[f594,f806]) ).
fof(f806,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f594,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f804,plain,
spl0_3,
inference(avatar_split_clause,[],[f593,f801]) ).
fof(f801,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f593,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f799,plain,
spl0_2,
inference(avatar_split_clause,[],[f592,f796]) ).
fof(f796,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f592,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f794,plain,
spl0_1,
inference(avatar_split_clause,[],[f591,f791]) ).
fof(f791,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f591,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL812-1 : TPTP v8.1.2. Released v4.1.0.
% 0.15/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 13:33:42 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (18936)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.39 % (18942)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)
% 0.20/0.40 % (18940)WARNING: value z3 for option sas not known
% 0.20/0.40 % (18937)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.40 % (18939)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.40 % (18941)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.40 % (18940)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)
% 0.20/0.40 % (18944)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)
% 0.20/0.40 % (18943)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)
% 0.20/0.53 TRYING [1]
% 1.27/0.54 TRYING [2]
% 2.16/0.68 % (18942)First to succeed.
% 2.16/0.69 % (18942)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18936"
% 2.16/0.69 % (18942)Refutation found. Thanks to Tanya!
% 2.16/0.69 % SZS status Unsatisfiable for theBenchmark
% 2.16/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.16/0.70 % (18942)------------------------------
% 2.16/0.70 % (18942)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.16/0.70 % (18942)Termination reason: Refutation
% 2.16/0.70
% 2.16/0.70 % (18942)Memory used [KB]: 6410
% 2.16/0.70 % (18942)Time elapsed: 0.302 s
% 2.16/0.70 % (18942)Instructions burned: 859 (million)
% 2.16/0.70 % (18936)Success in time 0.339 s
%------------------------------------------------------------------------------