TSTP Solution File: SWV854-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV854-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 06:36:56 EDT 2024
% Result : Unsatisfiable 2.50s 0.73s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1011
% Syntax : Number of formulae : 1700 ( 629 unt; 0 def)
% Number of atoms : 3758 ( 710 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 3572 (1514 ~;1523 |; 0 &)
% ( 535 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 566 ( 564 usr; 536 prp; 0-4 aty)
% Number of functors : 57 ( 57 usr; 13 con; 0-10 aty)
% Number of variables : 3384 (3384 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10731,plain,
$false,
inference(avatar_sat_refutation,[],[f783,f788,f793,f798,f803,f808,f813,f818,f823,f828,f833,f838,f843,f848,f853,f858,f863,f868,f873,f878,f883,f888,f892,f897,f901,f905,f909,f913,f918,f922,f926,f930,f934,f938,f942,f946,f950,f954,f958,f962,f966,f970,f974,f978,f982,f986,f990,f994,f998,f1002,f1006,f1010,f1014,f1018,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1050,f1054,f1058,f1062,f1066,f1070,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1107,f1111,f1115,f1119,f1123,f1127,f1131,f1135,f1139,f1143,f1147,f1151,f1155,f1159,f1163,f1172,f1176,f1180,f1184,f1188,f1192,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1224,f1228,f1232,f1236,f1240,f1244,f1248,f1252,f1256,f1260,f1264,f1268,f1272,f1276,f1280,f1284,f1295,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1341,f1345,f1349,f1353,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1401,f1405,f1409,f1413,f1417,f1421,f1471,f1480,f1484,f1488,f1492,f1496,f1500,f1504,f1508,f1513,f1517,f1521,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1589,f1593,f1597,f1601,f1605,f1609,f1613,f1617,f1621,f1625,f1629,f1711,f1751,f1860,f1864,f1868,f1872,f1876,f1880,f1884,f1888,f1892,f1896,f1900,f1904,f1908,f1912,f1916,f1920,f1924,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1976,f1980,f2185,f2236,f2240,f2245,f2249,f2253,f2257,f2261,f2265,f2269,f2273,f2277,f2282,f2286,f2295,f2300,f2304,f2308,f2312,f2317,f2321,f2325,f2329,f2333,f2338,f2342,f2346,f2351,f2356,f2360,f2365,f2370,f2374,f2378,f2382,f2386,f2390,f2511,f2549,f2559,f2563,f2570,f2639,f2643,f2758,f2762,f2766,f2770,f2774,f2778,f2782,f2786,f2790,f2794,f2802,f2806,f2810,f2814,f2818,f2822,f2828,f2834,f2838,f2842,f2846,f2850,f2854,f2858,f2862,f2866,f2870,f2874,f2878,f2882,f2886,f2890,f2894,f2898,f2902,f2906,f2910,f2914,f2918,f2922,f2926,f2930,f3244,f3248,f3334,f3524,f3807,f3819,f3823,f3827,f3831,f3835,f3839,f3843,f3847,f3851,f3855,f3859,f3863,f3867,f3871,f3875,f3879,f3883,f3887,f3891,f3895,f3899,f3903,f3907,f3911,f3915,f3919,f3924,f3929,f3935,f3944,f3948,f3952,f3956,f4252,f4404,f4433,f4473,f4477,f4481,f4485,f4489,f4493,f4497,f4501,f4538,f4543,f4583,f4588,f4629,f4633,f4637,f4641,f4660,f4664,f4768,f4857,f4861,f4865,f4869,f4888,f4892,f4896,f4900,f4904,f4908,f4912,f4916,f4920,f4924,f4928,f4932,f4936,f4941,f4947,f4951,f4955,f4959,f5371,f5444,f5448,f5516,f5520,f5524,f5528,f5532,f5536,f5540,f5544,f5548,f5552,f5556,f5560,f5564,f5568,f5572,f5576,f5580,f5584,f5588,f5594,f5599,f5623,f5627,f5633,f5637,f5641,f5645,f5649,f5653,f5748,f6138,f6142,f6148,f6152,f6365,f6377,f6381,f6385,f6389,f6393,f6397,f6401,f6405,f6409,f6413,f6417,f6421,f6425,f6429,f6433,f6437,f6441,f6933,f6944,f6948,f6952,f6956,f6960,f6964,f6968,f6985,f6989,f6993,f7127,f7131,f7286,f7290,f7294,f7298,f7305,f7309,f7325,f7329,f7333,f7337,f7341,f7345,f7349,f7353,f7357,f7361,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7509,f8240,f8244,f8251,f8255,f8262,f8266,f8270,f8285,f8311,f8406,f8707,f8720,f8724,f8728,f8732,f8736,f8740,f8744,f8748,f8752,f8784,f8788,f8792,f8796,f8800,f8804,f8808,f8812,f8816,f8820,f8824,f8828,f8832,f8836,f8840,f8844,f8848,f8852,f9361,f9630,f9634,f9638,f9645,f9649,f9653,f9657,f9661,f9665,f9669,f9673,f9677,f9681,f9685,f10170,f10730]) ).
fof(f10730,plain,
( ~ spl0_1
| spl0_24
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f10174,f9659,f894,f780]) ).
fof(f780,plain,
( spl0_1
<=> hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f894,plain,
( spl0_24
<=> c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f9659,plain,
( spl0_528
<=> ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X0),c_Com_Ocom_OBODY(X0),hAPP(v_Q,X0),t_a),t_a)
| ~ hBOOL(c_in(X0,v_Procs,tc_Com_Opname)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f10174,plain,
( ~ hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
| spl0_24
| ~ spl0_528 ),
inference(resolution,[],[f9660,f896]) ).
fof(f896,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a)
| spl0_24 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f9660,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X0),c_Com_Ocom_OBODY(X0),hAPP(v_Q,X0),t_a),t_a)
| ~ hBOOL(c_in(X0,v_Procs,tc_Com_Opname)) )
| ~ spl0_528 ),
inference(avatar_component_clause,[],[f9659]) ).
fof(f10170,plain,
( spl0_535
| ~ spl0_219
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f9641,f9636,f1973,f10168]) ).
fof(f10168,plain,
( spl0_535
<=> ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X7
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f1973,plain,
( spl0_219
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f9636,plain,
( spl0_523
<=> ! [X6,X7] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f9641,plain,
( ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X7
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X6 )
| ~ spl0_219
| ~ spl0_523 ),
inference(forward_demodulation,[],[f9640,f1975]) ).
fof(f1975,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f1973]) ).
fof(f9640,plain,
( ! [X6,X7] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X7
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_523 ),
inference(forward_demodulation,[],[f9639,f1975]) ).
fof(f9639,plain,
( ! [X6,X7] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_523 ),
inference(forward_demodulation,[],[f9637,f1975]) ).
fof(f9637,plain,
( ! [X6,X7] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f9636]) ).
fof(f9685,plain,
spl0_534,
inference(avatar_split_clause,[],[f771,f9683]) ).
fof(f9683,plain,
( spl0_534
<=> ! [X6,X16,X17] :
( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)),X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),X16,tc_nat),X6,tc_nat)
| ~ c_lessequals(X16,X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f771,plain,
! [X6,X16,X17] :
( c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)),X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),X16,tc_nat),X6,tc_nat)
| ~ c_lessequals(X16,X17,tc_nat) ),
inference(forward_demodulation,[],[f34,f242]) ).
fof(f242,axiom,
! [X16,X17,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X17,tc_nat),X16,tc_nat) = c_HOL_Ominus__class_Ominus(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f34,axiom,
! [X6,X16,X17] :
( ~ c_lessequals(X16,X17,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)),X6,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
fof(f9681,plain,
spl0_533,
inference(avatar_split_clause,[],[f626,f9679]) ).
fof(f9679,plain,
( spl0_533
<=> ! [X37,X40,X49,X75,X23,X76,X2] : c_Fun_Ofcomp(c_Fun_Ofcomp(X37,X40,X2,X76,X49),X75,X2,X49,X23) = c_Fun_Ofcomp(X37,c_Fun_Ofcomp(X40,X75,X76,X49,X23),X2,X76,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f626,axiom,
! [X40,X2,X49,X37,X76,X23,X75] : c_Fun_Ofcomp(c_Fun_Ofcomp(X37,X40,X2,X76,X49),X75,X2,X49,X23) = c_Fun_Ofcomp(X37,c_Fun_Ofcomp(X40,X75,X76,X49,X23),X2,X76,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
fof(f9677,plain,
spl0_532,
inference(avatar_split_clause,[],[f496,f9675]) ).
fof(f9675,plain,
( spl0_532
<=> ! [X37,X7,X6,X23,X2] :
( ~ class_Orderings_Olinorder(X23)
| ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oorder__class_Omono(X37,X2,X23)
| c_Orderings_Oord__class_Omax(hAPP(X37,X6),hAPP(X37,X7),X23) = hAPP(X37,c_Orderings_Oord__class_Omax(X6,X7,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f496,axiom,
! [X2,X37,X6,X7,X23] :
( ~ class_Orderings_Olinorder(X23)
| ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oorder__class_Omono(X37,X2,X23)
| c_Orderings_Oord__class_Omax(hAPP(X37,X6),hAPP(X37,X7),X23) = hAPP(X37,c_Orderings_Oord__class_Omax(X6,X7,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__of__mono_0) ).
fof(f9673,plain,
spl0_531,
inference(avatar_split_clause,[],[f453,f9671]) ).
fof(f9671,plain,
( spl0_531
<=> ! [X37,X7,X6,X23,X2] :
( ~ class_Orderings_Olinorder(X23)
| ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oorder__class_Omono(X37,X2,X23)
| c_Orderings_Oord__class_Omin(hAPP(X37,X6),hAPP(X37,X7),X23) = hAPP(X37,c_Orderings_Oord__class_Omin(X6,X7,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f453,axiom,
! [X2,X37,X6,X7,X23] :
( ~ class_Orderings_Olinorder(X23)
| ~ class_Orderings_Olinorder(X2)
| ~ c_Orderings_Oorder__class_Omono(X37,X2,X23)
| c_Orderings_Oord__class_Omin(hAPP(X37,X6),hAPP(X37,X7),X23) = hAPP(X37,c_Orderings_Oord__class_Omin(X6,X7,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__of__mono_0) ).
fof(f9669,plain,
spl0_530,
inference(avatar_split_clause,[],[f447,f9667]) ).
fof(f9667,plain,
( spl0_530
<=> ! [X2,X23,X60,X13,X9,X8,X49] :
( hAPP(X8,hAPP(X9,X60)) = hAPP(X13,X60)
| c_Fun_Ocomp(X8,X9,X49,X23,X2) != c_Fun_Ocomp(c_Fun_Oid(X23),X13,X23,X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f447,axiom,
! [X2,X49,X8,X9,X60,X23,X13] :
( hAPP(X8,hAPP(X9,X60)) = hAPP(X13,X60)
| c_Fun_Ocomp(X8,X9,X49,X23,X2) != c_Fun_Ocomp(c_Fun_Oid(X23),X13,X23,X23,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
fof(f9665,plain,
spl0_529,
inference(avatar_split_clause,[],[f422,f9663]) ).
fof(f9663,plain,
( spl0_529
<=> ! [X37,X40,X49,X75,X23,X76,X2] : c_Fun_Ocomp(X37,c_Fun_Ocomp(X40,X75,X76,X49,X2),X49,X23,X2) = c_Fun_Ocomp(c_Fun_Ocomp(X37,X40,X49,X23,X76),X75,X76,X23,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f422,axiom,
! [X40,X2,X49,X37,X76,X23,X75] : c_Fun_Ocomp(X37,c_Fun_Ocomp(X40,X75,X76,X49,X2),X49,X23,X2) = c_Fun_Ocomp(c_Fun_Ocomp(X37,X40,X49,X23,X76),X75,X76,X23,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f9661,plain,
( spl0_528
| ~ spl0_33
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f9625,f8846,f932,f9659]) ).
fof(f932,plain,
( spl0_33
<=> ! [X3] :
( ~ hBOOL(c_in(X3,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X3),c_Option_Othe(c_Com_Obody(X3),tc_Com_Ocom),hAPP(v_Q,X3),t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f8846,plain,
( spl0_518
<=> ! [X47,X7,X36,X2,X68] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X47,X2),X2)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X68),X47,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f9625,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X0),c_Com_Ocom_OBODY(X0),hAPP(v_Q,X0),t_a),t_a)
| ~ hBOOL(c_in(X0,v_Procs,tc_Com_Opname)) )
| ~ spl0_33
| ~ spl0_518 ),
inference(resolution,[],[f8847,f933]) ).
fof(f933,plain,
( ! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X3),c_Option_Othe(c_Com_Obody(X3),tc_Com_Ocom),hAPP(v_Q,X3),t_a),t_a)
| ~ hBOOL(c_in(X3,v_Procs,tc_Com_Opname)) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f8847,plain,
( ! [X2,X36,X47,X68,X7] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X47,X2),X2)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X68),X47,X2),X2) )
| ~ spl0_518 ),
inference(avatar_component_clause,[],[f8846]) ).
fof(f9657,plain,
spl0_527,
inference(avatar_split_clause,[],[f415,f9655]) ).
fof(f9655,plain,
( spl0_527
<=> ! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),X16,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f415,axiom,
! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),X16,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
fof(f9653,plain,
spl0_526,
inference(avatar_split_clause,[],[f414,f9651]) ).
fof(f9651,plain,
( spl0_526
<=> ! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17),X16,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f414,axiom,
! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17),X16,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Ominus__class_Ominus(X17,X16,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
fof(f9649,plain,
spl0_525,
inference(avatar_split_clause,[],[f289,f9647]) ).
fof(f9647,plain,
( spl0_525
<=> ! [X6,X16,X7] :
( ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X16,tc_nat),c_HOL_Ominus__class_Ominus(X7,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f289,axiom,
! [X6,X16,X7] :
( ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X16,tc_nat),c_HOL_Ominus__class_Ominus(X7,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
fof(f9645,plain,
spl0_524,
inference(avatar_split_clause,[],[f243,f9643]) ).
fof(f9643,plain,
( spl0_524
<=> ! [X44,X64,X7,X13,X63,X9] :
( ~ hBOOL(hAPP(X9,X63))
| ~ c_Natural_Oevaln(X13,X63,X7,X44)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X44,X7,X64)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X63,X7,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f243,axiom,
! [X44,X9,X7,X63,X13,X64] :
( ~ hBOOL(hAPP(X9,X63))
| ~ c_Natural_Oevaln(X13,X63,X7,X44)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X44,X7,X64)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X63,X7,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).
fof(f9638,plain,
spl0_523,
inference(avatar_split_clause,[],[f209,f9636]) ).
fof(f209,axiom,
! [X6,X7] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
fof(f9634,plain,
spl0_522,
inference(avatar_split_clause,[],[f87,f9632]) ).
fof(f9632,plain,
( spl0_522
<=> ! [X6,X16,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f87,axiom,
! [X6,X7,X16] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7)),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f9630,plain,
spl0_521,
inference(avatar_split_clause,[],[f86,f9628]) ).
fof(f9628,plain,
( spl0_521
<=> ! [X4,X5,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f86,axiom,
! [X3,X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f9361,plain,
( spl0_520
| ~ spl0_115
| ~ spl0_492 ),
inference(avatar_split_clause,[],[f8769,f8705,f1266,f9359]) ).
fof(f9359,plain,
( spl0_520
<=> ! [X2,X0,X1,X3] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f1266,plain,
( spl0_115
<=> ! [X2,X3,X78] : hBOOL(c_in(X3,c_Set_Oinsert(X3,X78,X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f8705,plain,
( spl0_492
<=> ! [X0,X3,X2,X1] : c_Set_Oinsert(X3,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X3,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f8769,plain,
( ! [X2,X3,X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname))
| ~ spl0_115
| ~ spl0_492 ),
inference(superposition,[],[f1267,f8706]) ).
fof(f8706,plain,
( ! [X2,X3,X0,X1] : c_Set_Oinsert(X3,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X3,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)
| ~ spl0_492 ),
inference(avatar_component_clause,[],[f8705]) ).
fof(f1267,plain,
( ! [X2,X3,X78] : hBOOL(c_in(X3,c_Set_Oinsert(X3,X78,X2),X2))
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f8852,plain,
spl0_519,
inference(avatar_split_clause,[],[f732,f8850]) ).
fof(f8850,plain,
( spl0_519
<=> ! [X47,X7,X36,X2,X68] :
( ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X68),X47,X2),X2)
| c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X47,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f732,axiom,
! [X2,X36,X47,X68,X7] :
( ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X68),X47,X2),X2)
| c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X47,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_1) ).
fof(f8848,plain,
spl0_518,
inference(avatar_split_clause,[],[f731,f8846]) ).
fof(f731,axiom,
! [X2,X36,X47,X68,X7] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X47,X2),X2)
| c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X68),X47,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).
fof(f8844,plain,
spl0_517,
inference(avatar_split_clause,[],[f705,f8842]) ).
fof(f8842,plain,
( spl0_517
<=> ! [X69,X62,X7,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__valids(X62,X69,t_a)
| c_Hoare__Mirabelle_Otriple__valid(X7,X93,t_a)
| ~ hBOOL(c_in(X93,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| hBOOL(c_in(v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(X62,X7),X62,tc_Hoare__Mirabelle_Otriple(t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f705,axiom,
! [X69,X62,X7,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__valids(X62,X69,t_a)
| c_Hoare__Mirabelle_Otriple__valid(X7,X93,t_a)
| ~ hBOOL(c_in(X93,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| hBOOL(c_in(v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(X62,X7),X62,tc_Hoare__Mirabelle_Otriple(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__valids__def_0) ).
fof(f8840,plain,
spl0_516,
inference(avatar_split_clause,[],[f700,f8838]) ).
fof(f8838,plain,
( spl0_516
<=> ! [X47,X13,X36,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,X13,X47,t_a),t_a)
| hBOOL(hAPP(hAPP(X36,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(X36,X47,X13,X7)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(X36,X47,X13,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f700,axiom,
! [X36,X47,X7,X13] :
( c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,X13,X47,t_a),t_a)
| hBOOL(hAPP(hAPP(X36,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(X36,X47,X13,X7)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(X36,X47,X13,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_1) ).
fof(f8836,plain,
spl0_515,
inference(avatar_split_clause,[],[f699,f8834]) ).
fof(f8834,plain,
( spl0_515
<=> ! [X47,X13,X36,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,X13,X47,t_a),t_a)
| ~ hBOOL(hAPP(hAPP(X47,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(X36,X47,X13,X7)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(X36,X47,X13,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f699,axiom,
! [X36,X47,X7,X13] :
( c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,X13,X47,t_a),t_a)
| ~ hBOOL(hAPP(hAPP(X47,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(X36,X47,X13,X7)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(X36,X47,X13,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_3) ).
fof(f8832,plain,
spl0_514,
inference(avatar_split_clause,[],[f585,f8830]) ).
fof(f8830,plain,
( spl0_514
<=> ! [X31,X28,X29,X11,X2,X18,X19,X26,X27,X24,X25,X30] : hAPP(hAPP(hAPP(X28,X11),X18),X19) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OCond(X11,X18,X19),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f585,axiom,
! [X31,X2,X28,X29,X11,X18,X19,X26,X27,X24,X25,X30] : hAPP(hAPP(hAPP(X28,X11),X18),X19) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OCond(X11,X18,X19),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).
fof(f8828,plain,
spl0_513,
inference(avatar_split_clause,[],[f569,f8826]) ).
fof(f8826,plain,
( spl0_513
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f569,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f8824,plain,
( spl0_512
| ~ spl0_77
| ~ spl0_492 ),
inference(avatar_split_clause,[],[f8768,f8705,f1109,f8822]) ).
fof(f8822,plain,
( spl0_512
<=> ! [X2,X0,X1,X3] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f1109,plain,
( spl0_77
<=> ! [X22,X2,X3] : hBOOL(hAPP(c_Set_Oinsert(X3,X22,X2),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f8768,plain,
( ! [X2,X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Set_Oinsert(X3,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),v_x))
| ~ spl0_77
| ~ spl0_492 ),
inference(superposition,[],[f1110,f8706]) ).
fof(f1110,plain,
( ! [X2,X3,X22] : hBOOL(hAPP(c_Set_Oinsert(X3,X22,X2),X3))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f8820,plain,
spl0_511,
inference(avatar_split_clause,[],[f522,f8818]) ).
fof(f8818,plain,
( spl0_511
<=> ! [X2,X78,X3,X22] :
( X22 = X78
| hBOOL(c_in(X3,X22,X2))
| hBOOL(c_in(X3,X78,X2))
| c_Set_Oinsert(X3,X22,X2) != c_Set_Oinsert(X3,X78,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f522,axiom,
! [X2,X3,X78,X22] :
( X22 = X78
| hBOOL(c_in(X3,X22,X2))
| hBOOL(c_in(X3,X78,X2))
| c_Set_Oinsert(X3,X22,X2) != c_Set_Oinsert(X3,X78,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f8816,plain,
spl0_510,
inference(avatar_split_clause,[],[f459,f8814]) ).
fof(f8814,plain,
( spl0_510
<=> ! [X31,X28,X29,X11,X2,X26,X27,X24,X25,X32,X30,X33] : hAPP(hAPP(hAPP(X31,X32),X33),X11) = c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OCall(X32,X33,X11),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f459,axiom,
! [X31,X2,X28,X29,X11,X26,X27,X24,X25,X32,X30,X33] : hAPP(hAPP(hAPP(X31,X32),X33),X11) = c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OCall(X32,X33,X11),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I8_J_0) ).
fof(f8812,plain,
spl0_509,
inference(avatar_split_clause,[],[f433,f8810]) ).
fof(f8810,plain,
( spl0_509
<=> ! [X6,X16,X7] :
( ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X16,tc_nat),c_HOL_Ominus__class_Ominus(X7,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f433,axiom,
! [X6,X16,X7] :
( ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X16,tc_nat),c_HOL_Ominus__class_Ominus(X7,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
fof(f8808,plain,
spl0_508,
inference(avatar_split_clause,[],[f417,f8806]) ).
fof(f8806,plain,
( spl0_508
<=> ! [X31,X28,X10,X29,X11,X2,X26,X27,X25,X24,X12,X30] : hAPP(hAPP(hAPP(X26,X10),X11),X12) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OLocal(X10,X11,X12),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f417,axiom,
! [X31,X2,X28,X10,X29,X11,X26,X27,X24,X12,X25,X30] : hAPP(hAPP(hAPP(X26,X10),X11),X12) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OLocal(X10,X11,X12),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).
fof(f8804,plain,
spl0_507,
inference(avatar_split_clause,[],[f382,f8802]) ).
fof(f8802,plain,
( spl0_507
<=> ! [X15,X17,X16,X39] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X39,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X39),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f382,axiom,
! [X39,X16,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(X16,X39,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X39),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f8800,plain,
spl0_506,
inference(avatar_split_clause,[],[f352,f8798]) ).
fof(f8798,plain,
( spl0_506
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f352,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f8796,plain,
spl0_505,
inference(avatar_split_clause,[],[f295,f8794]) ).
fof(f8794,plain,
( spl0_505
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f295,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f8792,plain,
spl0_504,
inference(avatar_split_clause,[],[f294,f8790]) ).
fof(f8790,plain,
( spl0_504
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f294,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f8788,plain,
spl0_503,
inference(avatar_split_clause,[],[f279,f8786]) ).
fof(f8786,plain,
( spl0_503
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f279,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f8784,plain,
spl0_502,
inference(avatar_split_clause,[],[f240,f8782]) ).
fof(f8782,plain,
( spl0_502
<=> ! [X6,X16,X7] :
( ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X16,tc_nat),c_HOL_Ominus__class_Ominus(X7,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f240,axiom,
! [X6,X16,X7] :
( ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X6,X16,tc_nat),c_HOL_Ominus__class_Ominus(X7,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
fof(f8752,plain,
spl0_501,
inference(avatar_split_clause,[],[f236,f8750]) ).
fof(f8750,plain,
( spl0_501
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X9,X13,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f236,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X9,X13,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f8748,plain,
spl0_500,
inference(avatar_split_clause,[],[f227,f8746]) ).
fof(f8746,plain,
( spl0_500
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f227,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f8744,plain,
spl0_499,
inference(avatar_split_clause,[],[f226,f8742]) ).
fof(f8742,plain,
( spl0_499
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f226,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f8740,plain,
spl0_498,
inference(avatar_split_clause,[],[f134,f8738]) ).
fof(f8738,plain,
( spl0_498
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X9,X8,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X13,X2)
| c_lessequals(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f134,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X9,X8,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X13,X2)
| c_lessequals(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f8736,plain,
spl0_497,
inference(avatar_split_clause,[],[f106,f8734]) ).
fof(f8734,plain,
( spl0_497
<=> ! [X2,X31,X28,X29,X11,X26,X27,X24,X25,X32,X30,X33] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OCall(X32,X33,X11),X2) = hAPP(hAPP(hAPP(X31,X32),X33),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f106,axiom,
! [X31,X2,X28,X29,X11,X26,X27,X24,X25,X32,X30,X33] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OCall(X32,X33,X11),X2) = hAPP(hAPP(hAPP(X31,X32),X33),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).
fof(f8732,plain,
spl0_496,
inference(avatar_split_clause,[],[f77,f8730]) ).
fof(f8730,plain,
( spl0_496
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f77,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X9,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f8728,plain,
spl0_495,
inference(avatar_split_clause,[],[f61,f8726]) ).
fof(f8726,plain,
( spl0_495
<=> ! [X15,X17,X16,X39] :
( ~ c_lessequals(X15,X17,tc_nat)
| ~ c_lessequals(X16,X39,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X39),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f61,axiom,
! [X39,X16,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| ~ c_lessequals(X16,X39,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X39),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
fof(f8724,plain,
spl0_494,
inference(avatar_split_clause,[],[f40,f8722]) ).
fof(f8722,plain,
( spl0_494
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X9,X13,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f40,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X9,X13,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f8720,plain,
spl0_493,
inference(avatar_split_clause,[],[f33,f8718]) ).
fof(f8718,plain,
( spl0_493
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X9,X13,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_lessequals(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f33,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X9,X13,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_lessequals(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f8707,plain,
( spl0_492
| ~ spl0_348
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f6570,f6415,f4471,f8705]) ).
fof(f4471,plain,
( spl0_348
<=> ! [X2,X4,X3,X22] : c_Set_Oinsert(X3,c_Set_Oinsert(X4,X22,X2),X2) = c_Set_Oinsert(X4,c_Set_Oinsert(X3,X22,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f6415,plain,
( spl0_437
<=> ! [X2,X0,X1] : c_Set_Oinsert(X2,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X2,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f6570,plain,
( ! [X2,X3,X0,X1] : c_Set_Oinsert(X3,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X3,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)
| ~ spl0_348
| ~ spl0_437 ),
inference(superposition,[],[f4472,f6416]) ).
fof(f6416,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X2,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X2,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)
| ~ spl0_437 ),
inference(avatar_component_clause,[],[f6415]) ).
fof(f4472,plain,
( ! [X2,X3,X4,X22] : c_Set_Oinsert(X3,c_Set_Oinsert(X4,X22,X2),X2) = c_Set_Oinsert(X4,c_Set_Oinsert(X3,X22,X2),X2)
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f4471]) ).
fof(f8406,plain,
( spl0_491
| ~ spl0_219
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f8258,f8253,f1973,f8404]) ).
fof(f8404,plain,
( spl0_491
<=> ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X6
| c_Orderings_Obot__class_Obot(tc_nat) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f8253,plain,
( spl0_485
<=> ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f8258,plain,
( ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X6
| c_Orderings_Obot__class_Obot(tc_nat) = X6 )
| ~ spl0_219
| ~ spl0_485 ),
inference(forward_demodulation,[],[f8257,f1975]) ).
fof(f8257,plain,
( ! [X6,X7] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X6
| c_Orderings_Obot__class_Obot(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_485 ),
inference(forward_demodulation,[],[f8256,f1975]) ).
fof(f8256,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_485 ),
inference(forward_demodulation,[],[f8254,f1975]) ).
fof(f8254,plain,
( ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_485 ),
inference(avatar_component_clause,[],[f8253]) ).
fof(f8311,plain,
( spl0_490
| ~ spl0_219
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f8247,f8242,f1973,f8309]) ).
fof(f8309,plain,
( spl0_490
<=> ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X7
| c_Orderings_Obot__class_Obot(tc_nat) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f8242,plain,
( spl0_483
<=> ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f8247,plain,
( ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X7
| c_Orderings_Obot__class_Obot(tc_nat) = X7 )
| ~ spl0_219
| ~ spl0_483 ),
inference(forward_demodulation,[],[f8246,f1975]) ).
fof(f8246,plain,
( ! [X6,X7] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X7
| c_Orderings_Obot__class_Obot(tc_nat) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_483 ),
inference(forward_demodulation,[],[f8245,f1975]) ).
fof(f8245,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_483 ),
inference(forward_demodulation,[],[f8243,f1975]) ).
fof(f8243,plain,
( ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_483 ),
inference(avatar_component_clause,[],[f8242]) ).
fof(f8285,plain,
spl0_489,
inference(avatar_split_clause,[],[f656,f8283]) ).
fof(f8283,plain,
( spl0_489
<=> ! [X6,X7] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) = X7
| hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f656,axiom,
! [X6,X7] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) = X7
| hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
fof(f8270,plain,
spl0_488,
inference(avatar_split_clause,[],[f596,f8268]) ).
fof(f8268,plain,
( spl0_488
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X2),c_Orderings_Oord__class_Omax(X3,X5,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f596,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X2),c_Orderings_Oord__class_Omax(X3,X5,X2),X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
fof(f8266,plain,
spl0_487,
inference(avatar_split_clause,[],[f506,f8264]) ).
fof(f8264,plain,
( spl0_487
<=> ! [X47,X13,X36,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,X13,X47,t_a),t_a)
| c_Natural_Oevaln(X13,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(X36,X47,X13,X7),X7,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(X36,X47,X13,X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f506,axiom,
! [X36,X47,X7,X13] :
( c_Hoare__Mirabelle_Otriple__valid(X7,c_Hoare__Mirabelle_Otriple_Otriple(X36,X13,X47,t_a),t_a)
| c_Natural_Oevaln(X13,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(X36,X47,X13,X7),X7,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(X36,X47,X13,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_2) ).
fof(f8262,plain,
spl0_486,
inference(avatar_split_clause,[],[f461,f8260]) ).
fof(f8260,plain,
( spl0_486
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X2),c_Orderings_Oord__class_Omin(X3,X5,X2),X2),c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f461,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X2),c_Orderings_Oord__class_Omin(X3,X5,X2),X2),c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
fof(f8255,plain,
spl0_485,
inference(avatar_split_clause,[],[f449,f8253]) ).
fof(f449,axiom,
! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
fof(f8251,plain,
spl0_484,
inference(avatar_split_clause,[],[f335,f8249]) ).
fof(f8249,plain,
( spl0_484
<=> ! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| c_HOL_Ominus__class_Ominus(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f335,axiom,
! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| c_HOL_Ominus__class_Ominus(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
fof(f8244,plain,
spl0_483,
inference(avatar_split_clause,[],[f253,f8242]) ).
fof(f253,axiom,
! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
fof(f8240,plain,
spl0_482,
inference(avatar_split_clause,[],[f155,f8238]) ).
fof(f8238,plain,
( spl0_482
<=> ! [X7,X6,X16,X39] :
( ~ c_HOL_Oord__class_Oless(X16,X39,tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X39) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f155,axiom,
! [X39,X6,X16,X7] :
( ~ c_HOL_Oord__class_Oless(X16,X39,tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X39) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f7509,plain,
( spl0_481
| ~ spl0_219
| ~ spl0_460 ),
inference(avatar_split_clause,[],[f7301,f7296,f1973,f7507]) ).
fof(f7507,plain,
( spl0_481
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f7296,plain,
( spl0_460
<=> ! [X6,X7] :
( 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),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f7301,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat) )
| ~ spl0_219
| ~ spl0_460 ),
inference(forward_demodulation,[],[f7300,f1975]) ).
fof(f7300,plain,
( ! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat) )
| ~ spl0_219
| ~ spl0_460 ),
inference(forward_demodulation,[],[f7299,f1975]) ).
fof(f7299,plain,
( ! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat) )
| ~ spl0_219
| ~ spl0_460 ),
inference(forward_demodulation,[],[f7297,f1975]) ).
fof(f7297,plain,
( ! [X6,X7] :
( 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),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat) )
| ~ spl0_460 ),
inference(avatar_component_clause,[],[f7296]) ).
fof(f7435,plain,
spl0_480,
inference(avatar_split_clause,[],[f707,f7433]) ).
fof(f7433,plain,
( spl0_480
<=> ! [X69,X62,X7,X94] :
( ~ c_Hoare__Mirabelle_Ohoare__valids(X62,X69,t_a)
| c_Hoare__Mirabelle_Otriple__valid(X7,X94,t_a)
| ~ hBOOL(c_in(X94,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| ~ c_Hoare__Mirabelle_Otriple__valid(X7,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(X62,X7),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f707,axiom,
! [X69,X62,X7,X94] :
( ~ c_Hoare__Mirabelle_Ohoare__valids(X62,X69,t_a)
| c_Hoare__Mirabelle_Otriple__valid(X7,X94,t_a)
| ~ hBOOL(c_in(X94,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| ~ c_Hoare__Mirabelle_Otriple__valid(X7,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(X62,X7),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__valids__def_1) ).
fof(f7431,plain,
spl0_479,
inference(avatar_split_clause,[],[f610,f7429]) ).
fof(f7429,plain,
( spl0_479
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X2),c_Orderings_Oord__class_Omax(X3,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f610,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X3,X4,X2),c_Orderings_Oord__class_Omax(X3,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
fof(f7427,plain,
spl0_478,
inference(avatar_split_clause,[],[f609,f7425]) ).
fof(f7425,plain,
( spl0_478
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X5,X2),X3,X2) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X3,X2),c_Orderings_Oord__class_Omax(X5,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f609,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X5,X2),X3,X2) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X3,X2),c_Orderings_Oord__class_Omax(X5,X3,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
fof(f7423,plain,
spl0_477,
inference(avatar_split_clause,[],[f560,f7421]) ).
fof(f7421,plain,
( spl0_477
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_HOL_Oord__class_Oless(X8,X9,X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f560,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_HOL_Oord__class_Oless(X8,X9,X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f7419,plain,
spl0_476,
inference(avatar_split_clause,[],[f559,f7417]) ).
fof(f7417,plain,
( spl0_476
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f559,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f7415,plain,
spl0_475,
inference(avatar_split_clause,[],[f558,f7413]) ).
fof(f7413,plain,
( spl0_475
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f558,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f7411,plain,
spl0_474,
inference(avatar_split_clause,[],[f557,f7409]) ).
fof(f7409,plain,
( spl0_474
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_HOL_Oord__class_Oless(X8,X9,X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f557,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_HOL_Oord__class_Oless(X8,X9,X2)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f7407,plain,
spl0_473,
inference(avatar_split_clause,[],[f556,f7405]) ).
fof(f7405,plain,
( spl0_473
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f556,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f7361,plain,
spl0_472,
inference(avatar_split_clause,[],[f555,f7359]) ).
fof(f7359,plain,
( spl0_472
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f555,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f7357,plain,
spl0_471,
inference(avatar_split_clause,[],[f535,f7355]) ).
fof(f7355,plain,
( spl0_471
<=> ! [X13,X8,X9,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X9,X13,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f535,axiom,
! [X2,X8,X9,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X9,X13,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X8,X2)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f7353,plain,
spl0_470,
inference(avatar_split_clause,[],[f460,f7351]) ).
fof(f7351,plain,
( spl0_470
<=> ! [X37,X4,X3,X23,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ class_Orderings_Oorder(X23)
| ~ c_Orderings_Oorder__class_Omono(X37,X2,X23)
| ~ c_lessequals(X3,X4,X2)
| c_lessequals(hAPP(X37,X3),hAPP(X37,X4),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f460,axiom,
! [X2,X3,X37,X4,X23] :
( ~ class_Orderings_Oorder(X2)
| ~ class_Orderings_Oorder(X23)
| ~ c_Orderings_Oorder__class_Omono(X37,X2,X23)
| ~ c_lessequals(X3,X4,X2)
| c_lessequals(hAPP(X37,X3),hAPP(X37,X4),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoD_0) ).
fof(f7349,plain,
spl0_469,
inference(avatar_split_clause,[],[f400,f7347]) ).
fof(f7347,plain,
( spl0_469
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f400,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f7345,plain,
spl0_468,
inference(avatar_split_clause,[],[f399,f7343]) ).
fof(f7343,plain,
( spl0_468
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f399,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f7341,plain,
spl0_467,
inference(avatar_split_clause,[],[f398,f7339]) ).
fof(f7339,plain,
( spl0_467
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X8,X9,X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f398,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X8,X9,X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f7337,plain,
spl0_466,
inference(avatar_split_clause,[],[f397,f7335]) ).
fof(f7335,plain,
( spl0_466
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f397,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X9),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f7333,plain,
spl0_465,
inference(avatar_split_clause,[],[f396,f7331]) ).
fof(f7331,plain,
( spl0_465
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X8,X9,X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f396,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X8,X9,X2)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f7329,plain,
spl0_464,
inference(avatar_split_clause,[],[f395,f7327]) ).
fof(f7327,plain,
( spl0_464
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f395,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X8,X9,X2)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X13),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f7325,plain,
spl0_463,
inference(avatar_split_clause,[],[f293,f7323]) ).
fof(f7323,plain,
( spl0_463
<=> ! [X2,X62,X69,X45] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(X45,X69,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(X45,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f293,axiom,
! [X2,X69,X62,X45] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(X45,X69,tc_Hoare__Mirabelle_Otriple(X2)),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(X45,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
fof(f7309,plain,
spl0_462,
inference(avatar_split_clause,[],[f250,f7307]) ).
fof(f7307,plain,
( spl0_462
<=> ! [X6,X16,X7] :
( X6 = X7
| ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X16,tc_nat) != c_HOL_Ominus__class_Ominus(X7,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f250,axiom,
! [X6,X7,X16] :
( X6 = X7
| ~ c_lessequals(X16,X6,tc_nat)
| ~ c_lessequals(X16,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X16,tc_nat) != c_HOL_Ominus__class_Ominus(X7,X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
fof(f7305,plain,
spl0_461,
inference(avatar_split_clause,[],[f246,f7303]) ).
fof(f7303,plain,
( spl0_461
<=> ! [X44,X13,X64,X63,X9] :
( ~ hBOOL(hAPP(X9,X63))
| ~ c_Natural_Oevalc(X13,X63,X44)
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X44,X64)
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X63,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f246,axiom,
! [X44,X9,X63,X13,X64] :
( ~ hBOOL(hAPP(X9,X63))
| ~ c_Natural_Oevalc(X13,X63,X44)
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X44,X64)
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X63,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
fof(f7298,plain,
spl0_460,
inference(avatar_split_clause,[],[f95,f7296]) ).
fof(f95,axiom,
! [X6,X7] :
( 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),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f7294,plain,
spl0_459,
inference(avatar_split_clause,[],[f28,f7292]) ).
fof(f7292,plain,
( spl0_459
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X2),c_Orderings_Oord__class_Omin(X3,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f28,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X3,X4,X2),c_Orderings_Oord__class_Omin(X3,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
fof(f7290,plain,
spl0_458,
inference(avatar_split_clause,[],[f27,f7288]) ).
fof(f7288,plain,
( spl0_458
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X5,X2),X3,X2) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X3,X2),c_Orderings_Oord__class_Omin(X5,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f27,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X4,X5,X2),X3,X2) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X4,X3,X2),c_Orderings_Oord__class_Omin(X5,X3,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
fof(f7286,plain,
spl0_457,
inference(avatar_split_clause,[],[f16,f7284]) ).
fof(f7284,plain,
( spl0_457
<=> ! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| ~ c_lessequals(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f16,axiom,
! [X16,X17,X15] :
( ~ c_lessequals(X16,X17,tc_nat)
| ~ c_lessequals(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
fof(f7131,plain,
( spl0_456
| ~ spl0_115
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f6563,f6415,f1266,f7129]) ).
fof(f7129,plain,
( spl0_456
<=> ! [X2,X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f6563,plain,
( ! [X2,X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname))
| ~ spl0_115
| ~ spl0_437 ),
inference(superposition,[],[f1267,f6416]) ).
fof(f7127,plain,
( spl0_455
| ~ spl0_219
| ~ spl0_451 ),
inference(avatar_split_clause,[],[f6971,f6966,f1973,f7125]) ).
fof(f7125,plain,
( spl0_455
<=> ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| c_Orderings_Obot__class_Obot(tc_nat) = X6
| c_Orderings_Obot__class_Obot(tc_nat) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f6966,plain,
( spl0_451
<=> ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f6971,plain,
( ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| c_Orderings_Obot__class_Obot(tc_nat) = X6
| c_Orderings_Obot__class_Obot(tc_nat) = X7 )
| ~ spl0_219
| ~ spl0_451 ),
inference(forward_demodulation,[],[f6970,f1975]) ).
fof(f6970,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X6
| c_Orderings_Obot__class_Obot(tc_nat) = X7
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_451 ),
inference(forward_demodulation,[],[f6969,f1975]) ).
fof(f6969,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_451 ),
inference(forward_demodulation,[],[f6967,f1975]) ).
fof(f6967,plain,
( ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_451 ),
inference(avatar_component_clause,[],[f6966]) ).
fof(f6993,plain,
spl0_454,
inference(avatar_split_clause,[],[f767,f6991]) ).
fof(f6991,plain,
( spl0_454
<=> ! [X2] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Ozero__class_Ozero(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),c_HOL_Ozero__class_Ozero(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f767,plain,
! [X2] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Ozero__class_Ozero(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),c_HOL_Ozero__class_Ozero(X2)) ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f70,axiom,
! [X2] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Ozero__class_Ozero(X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),c_HOL_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f6989,plain,
spl0_453,
inference(avatar_split_clause,[],[f664,f6987]) ).
fof(f6987,plain,
( spl0_453
<=> ! [X6,X16,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X6),X7,tc_nat),hAPP(c_Suc,X16),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f664,axiom,
! [X6,X7,X16] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X6),X7,tc_nat),hAPP(c_Suc,X16),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X16,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
fof(f6985,plain,
spl0_452,
inference(avatar_split_clause,[],[f648,f6983]) ).
fof(f6983,plain,
( spl0_452
<=> ! [X81,X7,X8,X80,X2] : c_Power_Opower_Opower(X80,X81,X8,hAPP(c_Suc,X7),X2) = hAPP(hAPP(X81,X8),c_Power_Opower_Opower(X80,X81,X8,X7,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f648,axiom,
! [X2,X80,X81,X8,X7] : c_Power_Opower_Opower(X80,X81,X8,hAPP(c_Suc,X7),X2) = hAPP(hAPP(X81,X8),c_Power_Opower_Opower(X80,X81,X8,X7,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power_Opower_Opower__Suc_0) ).
fof(f6968,plain,
spl0_451,
inference(avatar_split_clause,[],[f608,f6966]) ).
fof(f608,axiom,
! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
fof(f6964,plain,
spl0_450,
inference(avatar_split_clause,[],[f471,f6962]) ).
fof(f6962,plain,
( spl0_450
<=> ! [X31,X28,X29,X11,X2,X26,X27,X24,X25,X32,X30] : hAPP(hAPP(X25,X32),X11) = c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OAss(X32,X11),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f471,axiom,
! [X31,X2,X28,X29,X11,X26,X27,X24,X25,X32,X30] : hAPP(hAPP(X25,X32),X11) = c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OAss(X32,X11),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I2_J_0) ).
fof(f6960,plain,
spl0_449,
inference(avatar_split_clause,[],[f450,f6958]) ).
fof(f6958,plain,
( spl0_449
<=> ! [X31,X28,X29,X2,X18,X19,X26,X27,X24,X25,X30] : hAPP(hAPP(X27,X18),X19) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OSemi(X18,X19),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f450,axiom,
! [X31,X2,X28,X29,X18,X19,X26,X27,X24,X25,X30] : hAPP(hAPP(X27,X18),X19) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OSemi(X18,X19),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).
fof(f6956,plain,
spl0_448,
inference(avatar_split_clause,[],[f418,f6954]) ).
fof(f6954,plain,
( spl0_448
<=> ! [X31,X28,X29,X11,X2,X26,X27,X25,X24,X12,X30] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OWhile(X11,X12),X2) = hAPP(hAPP(X29,X11),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f418,axiom,
! [X31,X2,X28,X29,X11,X26,X27,X24,X25,X12,X30] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OWhile(X11,X12),X2) = hAPP(hAPP(X29,X11),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).
fof(f6952,plain,
spl0_447,
inference(avatar_split_clause,[],[f263,f6950]) ).
fof(f6950,plain,
( spl0_447
<=> ! [X6,X16,X7] : c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f263,axiom,
! [X6,X7,X16] : c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f6948,plain,
spl0_446,
inference(avatar_split_clause,[],[f262,f6946]) ).
fof(f6946,plain,
( spl0_446
<=> ! [X6,X16,X7] : c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X16),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f262,axiom,
! [X6,X7,X16] : c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X16),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f6944,plain,
spl0_445,
inference(avatar_split_clause,[],[f122,f6942]) ).
fof(f6942,plain,
( spl0_445
<=> ! [X2,X31,X28,X29,X11,X26,X27,X24,X25,X32,X30] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OAss(X32,X11),X2) = hAPP(hAPP(X25,X32),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f122,axiom,
! [X31,X2,X28,X29,X11,X26,X27,X24,X25,X32,X30] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OAss(X32,X11),X2) = hAPP(hAPP(X25,X32),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I65_J_0) ).
fof(f6933,plain,
( spl0_444
| ~ spl0_77
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f6562,f6415,f1109,f6931]) ).
fof(f6931,plain,
( spl0_444
<=> ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f6562,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X2,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),v_x))
| ~ spl0_77
| ~ spl0_437 ),
inference(superposition,[],[f1110,f6416]) ).
fof(f6441,plain,
spl0_443,
inference(avatar_split_clause,[],[f717,f6439]) ).
fof(f6439,plain,
( spl0_443
<=> ! [X69,X59,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,X59,t_a)
| ~ hBOOL(c_in(X59,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(X7,X69),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f717,axiom,
! [X59,X69,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,X59,t_a)
| ~ hBOOL(c_in(X59,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(X7,X69),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triples__valid__Suc_1) ).
fof(f6437,plain,
spl0_442,
inference(avatar_split_clause,[],[f715,f6435]) ).
fof(f6435,plain,
( spl0_442
<=> ! [X69,X7,X3] :
( c_Hoare__Mirabelle_Otriple__valid(X7,X3,t_a)
| ~ hBOOL(c_in(X3,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| hBOOL(c_in(v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(X7,X69),X69,tc_Hoare__Mirabelle_Otriple(t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f715,axiom,
! [X3,X69,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,X3,t_a)
| ~ hBOOL(c_in(X3,X69,tc_Hoare__Mirabelle_Otriple(t_a)))
| hBOOL(c_in(v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(X7,X69),X69,tc_Hoare__Mirabelle_Otriple(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triples__valid__Suc_0) ).
fof(f6433,plain,
spl0_441,
inference(avatar_split_clause,[],[f711,f6431]) ).
fof(f6431,plain,
( spl0_441
<=> ! [X44,X7,X14,X36] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X36),X14,X7,X44)
| c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X36),tc_Com_Ocom),X14,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X36,X7,X14,X44),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f711,axiom,
! [X36,X44,X7,X14] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X36),X14,X7,X44)
| c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X36),tc_Com_Ocom),X14,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X36,X7,X14,X44),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
fof(f6429,plain,
spl0_440,
inference(avatar_split_clause,[],[f606,f6427]) ).
fof(f6427,plain,
( spl0_440
<=> ! [X43,X46,X14,X9,X45,X7] :
( c_Natural_Oevaln(X46,X14,X7,X45)
| c_Natural_Oevaln(X43,X14,X7,X45)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X43,X46),X14,X7,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f606,axiom,
! [X46,X9,X7,X14,X45,X43] :
( c_Natural_Oevaln(X46,X14,X7,X45)
| c_Natural_Oevaln(X43,X14,X7,X45)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X43,X46),X14,X7,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).
fof(f6425,plain,
spl0_439,
inference(avatar_split_clause,[],[f581,f6423]) ).
fof(f6423,plain,
( spl0_439
<=> ! [X6,X7,X15] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X6,X7,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f581,axiom,
! [X6,X7,X15] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X6,X7,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff_0) ).
fof(f6421,plain,
spl0_438,
inference(avatar_split_clause,[],[f563,f6419]) ).
fof(f6419,plain,
( spl0_438
<=> ! [X6,X16,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f563,axiom,
! [X6,X7,X16] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f6417,plain,
( spl0_437
| ~ spl0_348
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5615,f5554,f4471,f6415]) ).
fof(f5554,plain,
( spl0_402
<=> ! [X0,X1] : c_Set_Oinsert(X1,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X1,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f5615,plain,
( ! [X2,X0,X1] : c_Set_Oinsert(X2,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X2,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)
| ~ spl0_348
| ~ spl0_402 ),
inference(superposition,[],[f4472,f5555]) ).
fof(f5555,plain,
( ! [X0,X1] : c_Set_Oinsert(X1,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X1,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f5554]) ).
fof(f6413,plain,
spl0_436,
inference(avatar_split_clause,[],[f562,f6411]) ).
fof(f6411,plain,
( spl0_436
<=> ! [X6,X16,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f562,axiom,
! [X6,X7,X16] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f6409,plain,
spl0_435,
inference(avatar_split_clause,[],[f561,f6407]) ).
fof(f6407,plain,
( spl0_435
<=> ! [X16,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f561,axiom,
! [X16,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f6405,plain,
spl0_434,
inference(avatar_split_clause,[],[f403,f6403]) ).
fof(f6403,plain,
( spl0_434
<=> ! [X6,X16,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f403,axiom,
! [X6,X7,X16] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
fof(f6401,plain,
spl0_433,
inference(avatar_split_clause,[],[f402,f6399]) ).
fof(f6399,plain,
( spl0_433
<=> ! [X6,X16,X7] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f402,axiom,
! [X6,X7,X16] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
fof(f6397,plain,
spl0_432,
inference(avatar_split_clause,[],[f401,f6395]) ).
fof(f6395,plain,
( spl0_432
<=> ! [X16,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f401,axiom,
! [X16,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
fof(f6393,plain,
spl0_431,
inference(avatar_split_clause,[],[f307,f6391]) ).
fof(f6391,plain,
( spl0_431
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X9 = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f307,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X9 = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X13),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f6389,plain,
spl0_430,
inference(avatar_split_clause,[],[f306,f6387]) ).
fof(f6387,plain,
( spl0_430
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X9 = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f306,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X9 = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f6385,plain,
spl0_429,
inference(avatar_split_clause,[],[f305,f6383]) ).
fof(f6383,plain,
( spl0_429
<=> ! [X13,X8,X9,X2] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2)
| X9 = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f305,axiom,
! [X2,X8,X9,X13] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2)
| X9 = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f6381,plain,
spl0_428,
inference(avatar_split_clause,[],[f297,f6379]) ).
fof(f6379,plain,
( spl0_428
<=> ! [X13,X9,X8] :
( ~ c_lessequals(X13,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,X13,tc_nat),c_HOL_Ominus__class_Ominus(X9,X13,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f297,axiom,
! [X8,X9,X13] :
( ~ c_lessequals(X13,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,X13,tc_nat),c_HOL_Ominus__class_Ominus(X9,X13,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
fof(f6377,plain,
spl0_427,
inference(avatar_split_clause,[],[f278,f6375]) ).
fof(f6375,plain,
( spl0_427
<=> ! [X9,X2,X8] :
( X8 = X9
| c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f278,axiom,
! [X2,X8,X9] :
( X8 = X9
| c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f6365,plain,
spl0_426,
inference(avatar_split_clause,[],[f159,f6363]) ).
fof(f6363,plain,
( spl0_426
<=> ! [X6,X39,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X39,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X39,X7,tc_nat),c_HOL_Ominus__class_Ominus(X39,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f159,axiom,
! [X39,X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X39,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X39,X7,tc_nat),c_HOL_Ominus__class_Ominus(X39,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f6152,plain,
( spl0_425
| ~ spl0_115
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5608,f5554,f1266,f6150]) ).
fof(f6150,plain,
( spl0_425
<=> ! [X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f5608,plain,
( ! [X0,X1] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname))
| ~ spl0_115
| ~ spl0_402 ),
inference(superposition,[],[f1267,f5555]) ).
fof(f6148,plain,
( spl0_424
| ~ spl0_219
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f5629,f5625,f1973,f6146]) ).
fof(f6146,plain,
( spl0_424
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f5625,plain,
( spl0_414
<=> ! [X6,X7] :
( ~ 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),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f5629,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat) )
| ~ spl0_219
| ~ spl0_414 ),
inference(forward_demodulation,[],[f5628,f1975]) ).
fof(f5628,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat) )
| ~ spl0_219
| ~ spl0_414 ),
inference(forward_demodulation,[],[f5626,f1975]) ).
fof(f5626,plain,
( ! [X6,X7] :
( ~ 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),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat) )
| ~ spl0_414 ),
inference(avatar_component_clause,[],[f5625]) ).
fof(f6142,plain,
( spl0_423
| ~ spl0_219
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f5595,f5592,f1973,f6140]) ).
fof(f6140,plain,
( spl0_423
<=> ! [X6,X7] :
( c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f5592,plain,
( spl0_411
<=> ! [X6,X7] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) != X7
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f5595,plain,
( ! [X6,X7] :
( c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) != X7 )
| ~ spl0_219
| ~ spl0_411 ),
inference(forward_demodulation,[],[f5593,f1975]) ).
fof(f5593,plain,
( ! [X6,X7] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) != X7
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f5592]) ).
fof(f6138,plain,
( spl0_422
| ~ spl0_219
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f5590,f5586,f1973,f6136]) ).
fof(f6136,plain,
( spl0_422
<=> ! [X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| X6 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f5586,plain,
( spl0_410
<=> ! [X6,X7] :
( X6 = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f5590,plain,
( ! [X6,X7] :
( c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| X6 = X7 )
| ~ spl0_219
| ~ spl0_410 ),
inference(forward_demodulation,[],[f5589,f1975]) ).
fof(f5589,plain,
( ! [X6,X7] :
( c_HOL_Ominus__class_Ominus(X7,X6,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| X6 = X7
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ spl0_219
| ~ spl0_410 ),
inference(forward_demodulation,[],[f5587,f1975]) ).
fof(f5587,plain,
( ! [X6,X7] :
( X6 = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f5586]) ).
fof(f5748,plain,
( spl0_421
| ~ spl0_77
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5607,f5554,f1109,f5746]) ).
fof(f5746,plain,
( spl0_421
<=> ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f5607,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,v_Procs,tc_Com_Opname),tc_Com_Opname),v_x))
| ~ spl0_77
| ~ spl0_402 ),
inference(superposition,[],[f1110,f5555]) ).
fof(f5653,plain,
spl0_420,
inference(avatar_split_clause,[],[f697,f5651]) ).
fof(f5651,plain,
( spl0_420
<=> ! [X24,X12,X23,X91,X2,X92] : hAPP(hAPP(hAPP(X24,X91),X12),X92) = c_Hoare__Mirabelle_Otriple_Otriple__case(X24,c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X23),X23,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f697,axiom,
! [X2,X91,X24,X12,X92,X23] : hAPP(hAPP(hAPP(X24,X91),X12),X92) = c_Hoare__Mirabelle_Otriple_Otriple__case(X24,c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X23),X23,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).
fof(f5649,plain,
spl0_419,
inference(avatar_split_clause,[],[f696,f5647]) ).
fof(f5647,plain,
( spl0_419
<=> ! [X24,X12,X23,X91,X2,X92] : hAPP(hAPP(hAPP(X24,X91),X12),X92) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X24,c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X23),X23,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f696,axiom,
! [X2,X91,X24,X12,X92,X23] : hAPP(hAPP(hAPP(X24,X91),X12),X92) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X24,c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X23),X23,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).
fof(f5645,plain,
spl0_418,
inference(avatar_split_clause,[],[f657,f5643]) ).
fof(f5643,plain,
( spl0_418
<=> ! [X15,X7,X2,X79] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X79,hAPP(c_Suc,X7),X15,X2) = c_Nat_Osemiring__1__class_Oof__nat__aux(X79,X7,hAPP(X79,X15),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f657,axiom,
! [X2,X79,X7,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X79,hAPP(c_Suc,X7),X15,X2) = c_Nat_Osemiring__1__class_Oof__nat__aux(X79,X7,hAPP(X79,X15),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I2_J_0) ).
fof(f5641,plain,
spl0_417,
inference(avatar_split_clause,[],[f654,f5639]) ).
fof(f5639,plain,
( spl0_417
<=> ! [X6,X7] : hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),hAPP(c_Suc,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f654,axiom,
! [X6,X7] : hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),hAPP(c_Suc,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f5637,plain,
spl0_416,
inference(avatar_split_clause,[],[f653,f5635]) ).
fof(f5635,plain,
( spl0_416
<=> ! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X6)),X7) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f653,axiom,
! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X6)),X7) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
fof(f5633,plain,
spl0_415,
inference(avatar_split_clause,[],[f650,f5631]) ).
fof(f5631,plain,
( spl0_415
<=> ! [X24,X87,X25,X2] : c_Nat_Onat_Onat__rec(X24,X25,hAPP(c_Suc,X87),X2) = hAPP(hAPP(X25,X87),c_Nat_Onat_Onat__rec(X24,X25,X87,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f650,axiom,
! [X2,X87,X24,X25] : c_Nat_Onat_Onat__rec(X24,X25,hAPP(c_Suc,X87),X2) = hAPP(hAPP(X25,X87),c_Nat_Onat_Onat__rec(X24,X25,X87,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__rec__Suc_0) ).
fof(f5627,plain,
spl0_414,
inference(avatar_split_clause,[],[f595,f5625]) ).
fof(f595,axiom,
! [X6,X7] :
( ~ 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),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f5623,plain,
spl0_413,
inference(avatar_split_clause,[],[f475,f5621]) ).
fof(f5621,plain,
( spl0_413
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2) = c_Orderings_Oord__class_Omax(X4,c_Orderings_Oord__class_Omax(X3,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f475,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2) = c_Orderings_Oord__class_Omax(X4,c_Orderings_Oord__class_Omax(X3,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
fof(f5599,plain,
spl0_412,
inference(avatar_split_clause,[],[f474,f5597]) ).
fof(f5597,plain,
( spl0_412
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f474,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X4,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
fof(f5594,plain,
spl0_411,
inference(avatar_split_clause,[],[f446,f5592]) ).
fof(f446,axiom,
! [X6,X7] :
( hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)) != X7
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
fof(f5588,plain,
spl0_410,
inference(avatar_split_clause,[],[f368,f5586]) ).
fof(f368,axiom,
! [X6,X7] :
( X6 = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f5584,plain,
spl0_409,
inference(avatar_split_clause,[],[f358,f5582]) ).
fof(f5582,plain,
( spl0_409
<=> ! [X44,X42,X7,X14,X9,X43] :
( hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevaln(X43,X14,X7,X44)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X42,X43),X14,X7,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f358,axiom,
! [X44,X9,X7,X14,X42,X43] :
( hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevaln(X43,X14,X7,X44)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X42,X43),X14,X7,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).
fof(f5580,plain,
spl0_408,
inference(avatar_split_clause,[],[f357,f5578]) ).
fof(f5578,plain,
( spl0_408
<=> ! [X43,X7,X14,X9,X45,X46] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevaln(X46,X14,X7,X45)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X43,X46),X14,X7,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f357,axiom,
! [X46,X9,X7,X14,X45,X43] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevaln(X46,X14,X7,X45)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X43,X46),X14,X7,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).
fof(f5576,plain,
spl0_407,
inference(avatar_split_clause,[],[f251,f5574]) ).
fof(f5574,plain,
( spl0_407
<=> ! [X42,X64,X7,X44,X63,X43] :
( ~ c_Natural_Oevaln(X42,X63,X7,X44)
| ~ c_Natural_Oevaln(X43,X44,X7,X64)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X42,X43),X63,X7,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f251,axiom,
! [X44,X7,X63,X42,X43,X64] :
( ~ c_Natural_Oevaln(X42,X63,X7,X44)
| ~ c_Natural_Oevaln(X43,X44,X7,X64)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X42,X43),X63,X7,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
fof(f5572,plain,
spl0_406,
inference(avatar_split_clause,[],[f242,f5570]) ).
fof(f5570,plain,
( spl0_406
<=> ! [X16,X17,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X17,tc_nat),X16,tc_nat) = c_HOL_Ominus__class_Ominus(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X16),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f5568,plain,
spl0_405,
inference(avatar_split_clause,[],[f234,f5566]) ).
fof(f5566,plain,
( spl0_405
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) = c_Orderings_Oord__class_Omin(X4,c_Orderings_Oord__class_Omin(X3,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f234,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) = c_Orderings_Oord__class_Omin(X4,c_Orderings_Oord__class_Omin(X3,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
fof(f5564,plain,
spl0_404,
inference(avatar_split_clause,[],[f225,f5562]) ).
fof(f5562,plain,
( spl0_404
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X3,X5,X2)
| c_HOL_Oord__class_Oless(X4,X5,X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f225,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X3,X5,X2)
| c_HOL_Oord__class_Oless(X4,X5,X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
fof(f5560,plain,
spl0_403,
inference(avatar_split_clause,[],[f221,f5558]) ).
fof(f5558,plain,
( spl0_403
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X5,X3,X2)
| c_HOL_Oord__class_Oless(X5,X4,X2)
| ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f221,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X5,X3,X2)
| c_HOL_Oord__class_Oless(X5,X4,X2)
| ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
fof(f5556,plain,
( spl0_402
| ~ spl0_348
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f4881,f4766,f4471,f5554]) ).
fof(f4766,plain,
( spl0_366
<=> ! [X0] : c_Set_Oinsert(X0,v_Procs,tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f4881,plain,
( ! [X0,X1] : c_Set_Oinsert(X1,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X1,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname),tc_Com_Opname)
| ~ spl0_348
| ~ spl0_366 ),
inference(superposition,[],[f4472,f4767]) ).
fof(f4767,plain,
( ! [X0] : c_Set_Oinsert(X0,v_Procs,tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname)
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f4766]) ).
fof(f5552,plain,
spl0_401,
inference(avatar_split_clause,[],[f201,f5550]) ).
fof(f5550,plain,
( spl0_401
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X5,X2)
| c_lessequals(X4,X5,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f201,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X5,X2)
| c_lessequals(X4,X5,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
fof(f5548,plain,
spl0_400,
inference(avatar_split_clause,[],[f174,f5546]) ).
fof(f5546,plain,
( spl0_400
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X5,X3,X2)
| c_lessequals(X5,X4,X2)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f174,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X5,X3,X2)
| c_lessequals(X5,X4,X2)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
fof(f5544,plain,
spl0_399,
inference(avatar_split_clause,[],[f148,f5542]) ).
fof(f5542,plain,
( spl0_399
<=> ! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X6),X7,tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f148,axiom,
! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X6),X7,tc_nat) = hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
fof(f5540,plain,
spl0_398,
inference(avatar_split_clause,[],[f133,f5538]) ).
fof(f5538,plain,
( spl0_398
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f133,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
fof(f5536,plain,
spl0_397,
inference(avatar_split_clause,[],[f108,f5534]) ).
fof(f5534,plain,
( spl0_397
<=> ! [X43,X7,X14,X9,X45,X46] :
( ~ hBOOL(hAPP(X9,X14))
| c_Natural_Oevaln(X43,X14,X7,X45)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X43,X46),X14,X7,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f108,axiom,
! [X46,X9,X7,X14,X45,X43] :
( ~ hBOOL(hAPP(X9,X14))
| c_Natural_Oevaln(X43,X14,X7,X45)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X43,X46),X14,X7,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).
fof(f5532,plain,
spl0_396,
inference(avatar_split_clause,[],[f107,f5530]) ).
fof(f5530,plain,
( spl0_396
<=> ! [X44,X42,X7,X14,X9,X43] :
( ~ hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevaln(X42,X14,X7,X44)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X42,X43),X14,X7,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f107,axiom,
! [X44,X9,X7,X14,X42,X43] :
( ~ hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevaln(X42,X14,X7,X44)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X9,X42,X43),X14,X7,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).
fof(f5528,plain,
spl0_395,
inference(avatar_split_clause,[],[f48,f5526]) ).
fof(f5526,plain,
( spl0_395
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X5,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,X4,X2)
| c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f48,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X5,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,X4,X2)
| c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
fof(f5524,plain,
spl0_394,
inference(avatar_split_clause,[],[f19,f5522]) ).
fof(f5522,plain,
( spl0_394
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_lessequals(X5,X3,X2)
| c_lessequals(c_Orderings_Oord__class_Omax(X4,X5,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f19,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_lessequals(X5,X3,X2)
| c_lessequals(c_Orderings_Oord__class_Omax(X4,X5,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
fof(f5520,plain,
spl0_393,
inference(avatar_split_clause,[],[f7,f5518]) ).
fof(f5518,plain,
( spl0_393
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_lessequals(X3,X5,X2)
| c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f7,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_lessequals(X3,X5,X2)
| c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
fof(f5516,plain,
spl0_392,
inference(avatar_split_clause,[],[f2,f5514]) ).
fof(f5514,plain,
( spl0_392
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X5,X2)
| ~ c_HOL_Oord__class_Oless(X4,X5,X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X5,X2)
| ~ c_HOL_Oord__class_Oless(X4,X5,X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
fof(f5448,plain,
( spl0_391
| ~ spl0_219
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f4943,f4939,f1973,f5446]) ).
fof(f5446,plain,
( spl0_391
<=> ! [X7] :
( hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat)) = X7
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f4939,plain,
( spl0_384
<=> ! [X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f4943,plain,
( ! [X7] :
( hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat)) = X7
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat) )
| ~ spl0_219
| ~ spl0_384 ),
inference(forward_demodulation,[],[f4942,f1975]) ).
fof(f4942,plain,
( ! [X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X7 )
| ~ spl0_219
| ~ spl0_384 ),
inference(forward_demodulation,[],[f4940,f1975]) ).
fof(f4940,plain,
( ! [X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X7 )
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f4939]) ).
fof(f5444,plain,
( spl0_390
| ~ spl0_219
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f4937,f4934,f1973,f5442]) ).
fof(f5442,plain,
( spl0_390
<=> ! [X36,X9,X8] :
( hBOOL(hAPP(X36,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| ~ hBOOL(hAPP(X36,c_HOL_Ominus__class_Ominus(X8,X9,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f4934,plain,
( spl0_383
<=> ! [X9,X36,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| hBOOL(hAPP(X36,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X36,c_HOL_Ominus__class_Ominus(X8,X9,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f4937,plain,
( ! [X36,X8,X9] :
( hBOOL(hAPP(X36,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| ~ hBOOL(hAPP(X36,c_HOL_Ominus__class_Ominus(X8,X9,tc_nat))) )
| ~ spl0_219
| ~ spl0_383 ),
inference(forward_demodulation,[],[f4935,f1975]) ).
fof(f4935,plain,
( ! [X36,X8,X9] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| hBOOL(hAPP(X36,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X36,c_HOL_Ominus__class_Ominus(X8,X9,tc_nat))) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f4934]) ).
fof(f5371,plain,
( spl0_389
| ~ spl0_115
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f4874,f4766,f1266,f5369]) ).
fof(f5369,plain,
( spl0_389
<=> ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f4874,plain,
( ! [X0] : hBOOL(c_in(v_x,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname))
| ~ spl0_115
| ~ spl0_366 ),
inference(superposition,[],[f1267,f4767]) ).
fof(f4959,plain,
spl0_388,
inference(avatar_split_clause,[],[f720,f4957]) ).
fof(f4957,plain,
( spl0_388
<=> ! [X44,X7,X63,X68] :
( ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X63,X7,X44)
| c_Natural_Oevaln(c_Com_Ocom_OBODY(X68),X63,hAPP(c_Suc,X7),X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f720,axiom,
! [X68,X44,X7,X63] :
( ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X63,X7,X44)
| c_Natural_Oevaln(c_Com_Ocom_OBODY(X68),X63,hAPP(c_Suc,X7),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
fof(f4955,plain,
spl0_387,
inference(avatar_split_clause,[],[f706,f4953]) ).
fof(f4953,plain,
( spl0_387
<=> ! [X3,X69,X62] :
( c_Hoare__Mirabelle_Ohoare__valids(X62,X69,t_a)
| ~ hBOOL(c_in(X3,X62,tc_Hoare__Mirabelle_Otriple(t_a)))
| c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(X62,X69),X3,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f706,axiom,
! [X3,X69,X62] :
( c_Hoare__Mirabelle_Ohoare__valids(X62,X69,t_a)
| ~ hBOOL(c_in(X3,X62,tc_Hoare__Mirabelle_Otriple(t_a)))
| c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(X62,X69),X3,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__valids__def_2) ).
fof(f4951,plain,
spl0_386,
inference(avatar_split_clause,[],[f692,f4949]) ).
fof(f4949,plain,
( spl0_386
<=> ! [X31,X28,X29,X2,X26,X27,X24,X25,X30,X33] : hAPP(X30,X33) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OBODY(X33),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f692,axiom,
! [X31,X2,X28,X29,X26,X27,X24,X25,X30,X33] : hAPP(X30,X33) = c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OBODY(X33),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).
fof(f4947,plain,
spl0_385,
inference(avatar_split_clause,[],[f680,f4945]) ).
fof(f4945,plain,
( spl0_385
<=> ! [X31,X28,X29,X2,X26,X27,X24,X25,X30,X33] : c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OBODY(X33),X2) = hAPP(X30,X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f680,axiom,
! [X31,X2,X28,X29,X26,X27,X24,X25,X30,X33] : c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OBODY(X33),X2) = hAPP(X30,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I7_J_0) ).
fof(f4941,plain,
spl0_384,
inference(avatar_split_clause,[],[f594,f4939]) ).
fof(f594,axiom,
! [X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| hAPP(c_Suc,c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
fof(f4936,plain,
spl0_383,
inference(avatar_split_clause,[],[f582,f4934]) ).
fof(f582,axiom,
! [X36,X8,X9] :
( ~ c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| hBOOL(hAPP(X36,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X36,c_HOL_Ominus__class_Ominus(X8,X9,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
fof(f4932,plain,
spl0_382,
inference(avatar_split_clause,[],[f552,f4930]) ).
fof(f4930,plain,
( spl0_382
<=> ! [X16,X17,X15] :
( c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f552,axiom,
! [X16,X17,X15] :
( c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f4928,plain,
( spl0_381
| ~ spl0_77
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f4873,f4766,f1109,f4926]) ).
fof(f4926,plain,
( spl0_381
<=> ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f4873,plain,
( ! [X0] : hBOOL(hAPP(c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),v_x))
| ~ spl0_77
| ~ spl0_366 ),
inference(superposition,[],[f1110,f4767]) ).
fof(f4924,plain,
spl0_380,
inference(avatar_split_clause,[],[f551,f4922]) ).
fof(f4922,plain,
( spl0_380
<=> ! [X16,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f551,axiom,
! [X16,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),X17,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f4920,plain,
spl0_379,
inference(avatar_split_clause,[],[f548,f4918]) ).
fof(f4918,plain,
( spl0_379
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_Divides_Odiv__class_Omod(X6,X7,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f548,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_Divides_Odiv__class_Omod(X6,X7,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
fof(f4916,plain,
spl0_378,
inference(avatar_split_clause,[],[f528,f4914]) ).
fof(f4914,plain,
( spl0_378
<=> ! [X6,X7] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f528,axiom,
! [X6,X7] : c_Divides_Odiv__class_Omod(hAPP(c_Suc,X6),X7,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(c_Suc,c_Divides_Odiv__class_Omod(X6,X7,tc_nat)),X7,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
fof(f4912,plain,
spl0_377,
inference(avatar_split_clause,[],[f513,f4910]) ).
fof(f4910,plain,
( spl0_377
<=> ! [X2,X8,X9,X22] :
( X8 = X9
| hBOOL(c_in(X8,X22,X2))
| ~ hBOOL(c_in(X8,c_Set_Oinsert(X9,X22,X2),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f513,axiom,
! [X2,X8,X9,X22] :
( X8 = X9
| hBOOL(c_in(X8,X22,X2))
| ~ hBOOL(c_in(X8,c_Set_Oinsert(X9,X22,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f4908,plain,
spl0_376,
inference(avatar_split_clause,[],[f430,f4906]) ).
fof(f4906,plain,
( spl0_376
<=> ! [X2,X9,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,X9,X2) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X8),X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f430,axiom,
! [X2,X8,X9] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,X9,X2) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X8),X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f4904,plain,
spl0_375,
inference(avatar_split_clause,[],[f429,f4902]) ).
fof(f4902,plain,
( spl0_375
<=> ! [X2,X9,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,X9,X2) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f429,axiom,
! [X2,X8,X9] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,X9,X2) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9),X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f4900,plain,
spl0_374,
inference(avatar_split_clause,[],[f428,f4898]) ).
fof(f4898,plain,
( spl0_374
<=> ! [X2,X36,X62] : c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OSKIP,X36,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f428,axiom,
! [X2,X36,X62] : c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OSKIP,X36,X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
fof(f4896,plain,
spl0_373,
inference(avatar_split_clause,[],[f310,f4894]) ).
fof(f4894,plain,
( spl0_373
<=> ! [X6,X16,X7] :
( ~ c_lessequals(X16,X7,tc_nat)
| c_lessequals(X6,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f310,axiom,
! [X6,X16,X7] :
( ~ c_lessequals(X16,X7,tc_nat)
| c_lessequals(X6,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
fof(f4892,plain,
spl0_372,
inference(avatar_split_clause,[],[f302,f4890]) ).
fof(f4890,plain,
( spl0_372
<=> ! [X6,X16,X7] :
( X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f302,axiom,
! [X6,X7,X16] :
( X6 = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X16) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f4888,plain,
spl0_371,
inference(avatar_split_clause,[],[f301,f4886]) ).
fof(f4886,plain,
( spl0_371
<=> ! [X4,X5,X3] :
( X4 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f301,axiom,
! [X3,X4,X5] :
( X4 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
fof(f4869,plain,
spl0_370,
inference(avatar_split_clause,[],[f296,f4867]) ).
fof(f4867,plain,
( spl0_370
<=> ! [X2,X37,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oorder__class_Omono(X37,tc_nat,X2)
| c_lessequals(hAPP(X37,X7),hAPP(X37,hAPP(c_Suc,X7)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f296,axiom,
! [X2,X37,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_Orderings_Oorder__class_Omono(X37,tc_nat,X2)
| c_lessequals(hAPP(X37,X7),hAPP(X37,hAPP(c_Suc,X7)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mono__iff__le__Suc_0) ).
fof(f4865,plain,
spl0_369,
inference(avatar_split_clause,[],[f220,f4863]) ).
fof(f4863,plain,
( spl0_369
<=> ! [X16,X17,X15] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat)
| ~ c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f220,axiom,
! [X16,X17,X15] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat)
| ~ c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
fof(f4861,plain,
spl0_368,
inference(avatar_split_clause,[],[f219,f4859]) ).
fof(f4859,plain,
( spl0_368
<=> ! [X16,X17,X15] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat)
| c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f219,axiom,
! [X16,X17,X15] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X17,X16,tc_nat),X15,tc_nat)
| c_lessequals(X17,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X16),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
fof(f4857,plain,
spl0_367,
inference(avatar_split_clause,[],[f200,f4855]) ).
fof(f4855,plain,
( spl0_367
<=> ! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_Divides_Odiv__class_Omod(X6,X7,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f200,axiom,
! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_Divides_Odiv__class_Omod(X6,X7,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
fof(f4768,plain,
( spl0_366
| ~ spl0_224
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4665,f4471,f2242,f4766]) ).
fof(f2242,plain,
( spl0_224
<=> v_Procs = c_Set_Oinsert(v_x,v_Procs,tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f4665,plain,
( ! [X0] : c_Set_Oinsert(X0,v_Procs,tc_Com_Opname) = c_Set_Oinsert(v_x,c_Set_Oinsert(X0,v_Procs,tc_Com_Opname),tc_Com_Opname)
| ~ spl0_224
| ~ spl0_348 ),
inference(superposition,[],[f4472,f2244]) ).
fof(f2244,plain,
( v_Procs = c_Set_Oinsert(v_x,v_Procs,tc_Com_Opname)
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2242]) ).
fof(f4664,plain,
spl0_365,
inference(avatar_split_clause,[],[f674,f4662]) ).
fof(f4662,plain,
( spl0_365
<=> ! [X44,X7,X14,X36] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X36),X14,X7,X44)
| hAPP(c_Suc,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X36,X7,X14,X44)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f674,axiom,
! [X36,X44,X7,X14] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(X36),X14,X7,X44)
| hAPP(c_Suc,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X36,X7,X14,X44)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
fof(f4660,plain,
spl0_364,
inference(avatar_split_clause,[],[f667,f4658]) ).
fof(f4658,plain,
( spl0_364
<=> ! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| hAPP(c_Suc,X7) = X6
| ~ c_lessequals(X6,hAPP(c_Suc,X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f667,axiom,
! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| hAPP(c_Suc,X7) = X6
| ~ c_lessequals(X6,hAPP(c_Suc,X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
fof(f4641,plain,
spl0_363,
inference(avatar_split_clause,[],[f666,f4639]) ).
fof(f4639,plain,
( spl0_363
<=> ! [X6,X7] : c_Orderings_Oord__class_Omin(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat) = hAPP(c_Suc,c_Orderings_Oord__class_Omin(X6,X7,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f666,axiom,
! [X6,X7] : c_Orderings_Oord__class_Omin(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat) = hAPP(c_Suc,c_Orderings_Oord__class_Omin(X6,X7,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
fof(f4637,plain,
spl0_362,
inference(avatar_split_clause,[],[f661,f4635]) ).
fof(f4635,plain,
( spl0_362
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hAPP(c_Suc,X6) = X7
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X6),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f661,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hAPP(c_Suc,X6) = X7
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X6),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f4633,plain,
spl0_361,
inference(avatar_split_clause,[],[f655,f4631]) ).
fof(f4631,plain,
( spl0_361
<=> ! [X6,X7] : c_Orderings_Oord__class_Omax(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat) = hAPP(c_Suc,c_Orderings_Oord__class_Omax(X6,X7,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f655,axiom,
! [X6,X7] : c_Orderings_Oord__class_Omax(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat) = hAPP(c_Suc,c_Orderings_Oord__class_Omax(X6,X7,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
fof(f4629,plain,
spl0_360,
inference(avatar_split_clause,[],[f623,f4627]) ).
fof(f4627,plain,
( spl0_360
<=> ! [X43,X46,X14,X9,X45] :
( c_Natural_Oevalc(X46,X14,X45)
| c_Natural_Oevalc(X43,X14,X45)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X43,X46),X14,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f623,axiom,
! [X46,X9,X45,X14,X43] :
( c_Natural_Oevalc(X46,X14,X45)
| c_Natural_Oevalc(X43,X14,X45)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X43,X46),X14,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
fof(f4588,plain,
( spl0_359
| ~ spl0_274
| ~ spl0_325
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4584,f4581,f3869,f2792,f4586]) ).
fof(f4586,plain,
( spl0_359
<=> ! [X6,X7] :
( c_Orderings_Oord__class_Omax(X6,X7,tc_nat) = X6
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2792,plain,
( spl0_274
<=> ! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3869,plain,
( spl0_325
<=> ! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)),X6) = c_Orderings_Oord__class_Omax(X7,X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f4581,plain,
( spl0_358
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f4584,plain,
( ! [X6,X7] :
( c_Orderings_Oord__class_Omax(X6,X7,tc_nat) = X6
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) )
| ~ spl0_274
| ~ spl0_325
| ~ spl0_358 ),
inference(forward_demodulation,[],[f4582,f4142]) ).
fof(f4142,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat))
| ~ spl0_274
| ~ spl0_325 ),
inference(superposition,[],[f3870,f2793]) ).
fof(f2793,plain,
( ! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6)
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2792]) ).
fof(f3870,plain,
( ! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)),X6) = c_Orderings_Oord__class_Omax(X7,X6,tc_nat)
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f3869]) ).
fof(f4582,plain,
( ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) = X6 )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f4581]) ).
fof(f4583,plain,
spl0_358,
inference(avatar_split_clause,[],[f604,f4581]) ).
fof(f604,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f4543,plain,
( spl0_357
| ~ spl0_274
| ~ spl0_325
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f4539,f4536,f3869,f2792,f4541]) ).
fof(f4541,plain,
( spl0_357
<=> ! [X6,X7] :
( c_Orderings_Oord__class_Omax(X6,X7,tc_nat) = X6
| ~ c_lessequals(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f4536,plain,
( spl0_356
<=> ! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f4539,plain,
( ! [X6,X7] :
( c_Orderings_Oord__class_Omax(X6,X7,tc_nat) = X6
| ~ c_lessequals(X7,X6,tc_nat) )
| ~ spl0_274
| ~ spl0_325
| ~ spl0_356 ),
inference(forward_demodulation,[],[f4537,f4142]) ).
fof(f4537,plain,
( ! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) = X6 )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f4536]) ).
fof(f4538,plain,
spl0_356,
inference(avatar_split_clause,[],[f407,f4536]) ).
fof(f407,axiom,
! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
fof(f4501,plain,
spl0_355,
inference(avatar_split_clause,[],[f405,f4499]) ).
fof(f4499,plain,
( spl0_355
<=> ! [X44,X42,X14,X9,X43] :
( ~ c_Natural_Oevalc(X43,X14,X44)
| hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X42,X43),X14,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f405,axiom,
! [X44,X9,X14,X42,X43] :
( ~ c_Natural_Oevalc(X43,X14,X44)
| hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X42,X43),X14,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
fof(f4497,plain,
spl0_354,
inference(avatar_split_clause,[],[f404,f4495]) ).
fof(f4495,plain,
( spl0_354
<=> ! [X43,X46,X14,X9,X45] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(X46,X14,X45)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X43,X46),X14,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f404,axiom,
! [X46,X9,X45,X14,X43] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(X46,X14,X45)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X43,X46),X14,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
fof(f4493,plain,
spl0_353,
inference(avatar_split_clause,[],[f290,f4491]) ).
fof(f4491,plain,
( spl0_353
<=> ! [X16,X17,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X17,tc_nat),X16,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X16,tc_nat),X17,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f290,axiom,
! [X16,X17,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X17,tc_nat),X16,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X15,X16,tc_nat),X17,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f4489,plain,
spl0_352,
inference(avatar_split_clause,[],[f257,f4487]) ).
fof(f4487,plain,
( spl0_352
<=> ! [X43,X14,X9,X45,X46] :
( ~ hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(X43,X14,X45)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X43,X46),X14,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f257,axiom,
! [X46,X9,X45,X14,X43] :
( ~ hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(X43,X14,X45)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X43,X46),X14,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
fof(f4485,plain,
spl0_351,
inference(avatar_split_clause,[],[f256,f4483]) ).
fof(f4483,plain,
( spl0_351
<=> ! [X44,X42,X14,X9,X43] :
( ~ hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevalc(X42,X14,X44)
| c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X42,X43),X14,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f256,axiom,
! [X44,X9,X14,X42,X43] :
( ~ hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevalc(X42,X14,X44)
| c_Natural_Oevalc(c_Com_Ocom_OCond(X9,X42,X43),X14,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
fof(f4481,plain,
spl0_350,
inference(avatar_split_clause,[],[f156,f4479]) ).
fof(f4479,plain,
( spl0_350
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f156,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X4),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f4477,plain,
spl0_349,
inference(avatar_split_clause,[],[f153,f4475]) ).
fof(f4475,plain,
( spl0_349
<=> ! [X2,X9,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f153,axiom,
! [X2,X8,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X9),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f4473,plain,
spl0_348,
inference(avatar_split_clause,[],[f111,f4471]) ).
fof(f111,axiom,
! [X2,X3,X4,X22] : c_Set_Oinsert(X3,c_Set_Oinsert(X4,X22,X2),X2) = c_Set_Oinsert(X4,c_Set_Oinsert(X3,X22,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f4433,plain,
( spl0_347
| ~ spl0_144
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4148,f3869,f1395,f4431]) ).
fof(f4431,plain,
( spl0_347
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f1395,plain,
( spl0_144
<=> ! [X17,X15] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f4148,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_144
| ~ spl0_325 ),
inference(superposition,[],[f1396,f3870]) ).
fof(f1396,plain,
( ! [X17,X15] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),X15,tc_nat)
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1395]) ).
fof(f4404,plain,
( spl0_346
| ~ spl0_219
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f3920,f3917,f1973,f4402]) ).
fof(f4402,plain,
( spl0_346
<=> ! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,X15),tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f3917,plain,
( spl0_337
<=> ! [X7,X15] :
( ~ 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(c_Suc,X15),tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f3920,plain,
( ! [X7,X15] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,hAPP(c_Suc,X15),tc_nat),X7,tc_nat) )
| ~ spl0_219
| ~ spl0_337 ),
inference(forward_demodulation,[],[f3918,f1975]) ).
fof(f3918,plain,
( ! [X7,X15] :
( ~ 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(c_Suc,X15),tc_nat),X7,tc_nat) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f3917]) ).
fof(f4252,plain,
( spl0_345
| ~ spl0_135
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4145,f3869,f1359,f4250]) ).
fof(f4250,plain,
( spl0_345
<=> ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f1359,plain,
( spl0_135
<=> ! [X6,X7] : c_lessequals(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f4145,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_135
| ~ spl0_325 ),
inference(superposition,[],[f1360,f3870]) ).
fof(f1360,plain,
( ! [X6,X7] : c_lessequals(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat)
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f3956,plain,
spl0_344,
inference(avatar_split_clause,[],[f725,f3954]) ).
fof(f3954,plain,
( spl0_344
<=> ! [X1,X92,X97,X12,X91,X2,X96] :
( X91 = X96
| c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X96,X1,X97,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f725,axiom,
! [X2,X91,X1,X96,X97,X12,X92] :
( X91 = X96
| c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X96,X1,X97,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
fof(f3952,plain,
spl0_343,
inference(avatar_split_clause,[],[f724,f3950]) ).
fof(f3950,plain,
( spl0_343
<=> ! [X92,X96,X97,X12,X91,X2,X1] :
( X1 = X12
| c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X96,X1,X97,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f724,axiom,
! [X2,X91,X1,X96,X97,X12,X92] :
( X1 = X12
| c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X96,X1,X97,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
fof(f3948,plain,
spl0_342,
inference(avatar_split_clause,[],[f723,f3946]) ).
fof(f3946,plain,
( spl0_342
<=> ! [X1,X96,X97,X12,X91,X2,X92] :
( X92 = X97
| c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X96,X1,X97,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f723,axiom,
! [X2,X91,X1,X96,X97,X12,X92] :
( X92 = X97
| c_Hoare__Mirabelle_Otriple_Otriple(X91,X12,X92,X2) != c_Hoare__Mirabelle_Otriple_Otriple(X96,X1,X97,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
fof(f3944,plain,
( ~ spl0_341
| ~ spl0_114
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f3936,f3932,f1262,f3941]) ).
fof(f3941,plain,
( spl0_341
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f1262,plain,
( spl0_114
<=> ! [X2,X3] : ~ hBOOL(c_in(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f3932,plain,
( spl0_340
<=> c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f3936,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_114
| ~ spl0_340 ),
inference(superposition,[],[f1263,f3934]) ).
fof(f3934,plain,
( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f3932]) ).
fof(f1263,plain,
( ! [X2,X3] : ~ hBOOL(c_in(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f3935,plain,
( spl0_340
| ~ spl0_22
| ~ spl0_196
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f3930,f3926,f1874,f885,f3932]) ).
fof(f885,plain,
( spl0_22
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1874,plain,
( spl0_196
<=> ! [X23] :
( ~ class_Orderings_Obot(X23)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X23)),v_x) = c_Orderings_Obot__class_Obot(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f3926,plain,
( spl0_339
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f3930,plain,
( c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_22
| ~ spl0_196
| ~ spl0_339 ),
inference(forward_demodulation,[],[f3928,f2055]) ).
fof(f2055,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_22
| ~ spl0_196 ),
inference(resolution,[],[f1875,f887]) ).
fof(f887,plain,
( class_Orderings_Obot(tc_bool)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f1875,plain,
( ! [X23] :
( ~ class_Orderings_Obot(X23)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X23)),v_x) = c_Orderings_Obot__class_Obot(X23) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f1874]) ).
fof(f3928,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a)
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f3926]) ).
fof(f3929,plain,
spl0_339,
inference(avatar_split_clause,[],[f712,f3926]) ).
fof(f712,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
fof(f3924,plain,
spl0_338,
inference(avatar_split_clause,[],[f636,f3922]) ).
fof(f3922,plain,
( spl0_338
<=> ! [X16,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X15),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f636,axiom,
! [X16,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X15),X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f3919,plain,
spl0_337,
inference(avatar_split_clause,[],[f605,f3917]) ).
fof(f605,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_Ominus__class_Ominus(X7,hAPP(c_Suc,X15),tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f3915,plain,
spl0_336,
inference(avatar_split_clause,[],[f589,f3913]) ).
fof(f3913,plain,
( spl0_336
<=> ! [X7,X14,X13,X9,X45] :
( X14 = X45
| hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X14,X7,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f589,axiom,
! [X9,X45,X14,X7,X13] :
( X14 = X45
| hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X14,X7,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).
fof(f3911,plain,
spl0_335,
inference(avatar_split_clause,[],[f578,f3909]) ).
fof(f3909,plain,
( spl0_335
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X4,X5,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_HOL_Oord__class_Oless(X3,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f578,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X4,X5,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_HOL_Oord__class_Oless(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f3907,plain,
spl0_334,
inference(avatar_split_clause,[],[f577,f3905]) ).
fof(f3905,plain,
( spl0_334
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X5,X2)
| c_HOL_Oord__class_Oless(X3,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f577,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X5,X2)
| c_HOL_Oord__class_Oless(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3903,plain,
spl0_333,
inference(avatar_split_clause,[],[f575,f3901]) ).
fof(f3901,plain,
( spl0_333
<=> ! [X7,X14,X13,X6,X45] :
( ~ c_lessequals(X7,X6,tc_nat)
| ~ c_Natural_Oevaln(X13,X14,X7,X45)
| c_Natural_Oevaln(X13,X14,X6,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f575,axiom,
! [X6,X7,X14,X45,X13] :
( ~ c_lessequals(X7,X6,tc_nat)
| ~ c_Natural_Oevaln(X13,X14,X7,X45)
| c_Natural_Oevaln(X13,X14,X6,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__nonstrict_0) ).
fof(f3899,plain,
spl0_332,
inference(avatar_split_clause,[],[f570,f3897]) ).
fof(f3897,plain,
( spl0_332
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_lessequals(X4,X5,X2)
| c_lessequals(X3,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f570,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_lessequals(X4,X5,X2)
| c_lessequals(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3895,plain,
( spl0_331
| ~ spl0_151
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2751,f1973,f1469,f3893]) ).
fof(f3893,plain,
( spl0_331
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f1469,plain,
( spl0_151
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f2751,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0
| ~ spl0_151
| ~ spl0_219 ),
inference(superposition,[],[f1470,f1975]) ).
fof(f1470,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f3891,plain,
spl0_330,
inference(avatar_split_clause,[],[f568,f3889]) ).
fof(f3889,plain,
( spl0_330
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,X4,X2)
| c_HOL_Oord__class_Oless(X5,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f568,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,X4,X2)
| c_HOL_Oord__class_Oless(X5,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3887,plain,
spl0_329,
inference(avatar_split_clause,[],[f567,f3885]) ).
fof(f3885,plain,
( spl0_329
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X5,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| c_HOL_Oord__class_Oless(X5,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f567,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X5,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| c_HOL_Oord__class_Oless(X5,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3883,plain,
spl0_328,
inference(avatar_split_clause,[],[f566,f3881]) ).
fof(f3881,plain,
( spl0_328
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_lessequals(X5,X4,X2)
| c_lessequals(X5,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f566,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_lessequals(X5,X4,X2)
| c_lessequals(X5,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3879,plain,
spl0_327,
inference(avatar_split_clause,[],[f489,f3877]) ).
fof(f3877,plain,
( spl0_327
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f489,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f3875,plain,
spl0_326,
inference(avatar_split_clause,[],[f420,f3873]) ).
fof(f3873,plain,
( spl0_326
<=> ! [X37,X23,X40,X49,X3,X2] : hAPP(c_Fun_Ofcomp(X37,X40,X23,X49,X2),X3) = hAPP(X40,hAPP(X37,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f420,axiom,
! [X40,X2,X3,X49,X37,X23] : hAPP(c_Fun_Ofcomp(X37,X40,X23,X49,X2),X3) = hAPP(X40,hAPP(X37,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
fof(f3871,plain,
spl0_325,
inference(avatar_split_clause,[],[f356,f3869]) ).
fof(f356,axiom,
! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat)),X6) = c_Orderings_Oord__class_Omax(X7,X6,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
fof(f3867,plain,
spl0_324,
inference(avatar_split_clause,[],[f343,f3865]) ).
fof(f3865,plain,
( spl0_324
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f343,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3863,plain,
spl0_323,
inference(avatar_split_clause,[],[f339,f3861]) ).
fof(f3861,plain,
( spl0_323
<=> ! [X2,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f339,axiom,
! [X2,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2),X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__one_0) ).
fof(f3859,plain,
spl0_322,
inference(avatar_split_clause,[],[f258,f3857]) ).
fof(f3857,plain,
( spl0_322
<=> ! [X42,X43,X64,X63,X44] :
( ~ c_Natural_Oevalc(X42,X63,X44)
| ~ c_Natural_Oevalc(X43,X44,X64)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(X42,X43),X63,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f258,axiom,
! [X44,X63,X42,X43,X64] :
( ~ c_Natural_Oevalc(X42,X63,X44)
| ~ c_Natural_Oevalc(X43,X44,X64)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(X42,X43),X63,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
fof(f3855,plain,
spl0_321,
inference(avatar_split_clause,[],[f238,f3853]) ).
fof(f3853,plain,
( spl0_321
<=> ! [X6,X39,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X39,tc_nat),c_HOL_Ominus__class_Ominus(X7,X39,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f238,axiom,
! [X39,X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X6,X39,tc_nat),c_HOL_Ominus__class_Ominus(X7,X39,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f3851,plain,
( spl0_320
| ~ spl0_81
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2072,f1973,f1125,f3849]) ).
fof(f3849,plain,
( spl0_320
<=> ! [X0] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f1125,plain,
( spl0_81
<=> ! [X7] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2072,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) = X0
| ~ spl0_81
| ~ spl0_219 ),
inference(superposition,[],[f1126,f1975]) ).
fof(f1126,plain,
( ! [X7] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) = X7
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1125]) ).
fof(f3847,plain,
spl0_319,
inference(avatar_split_clause,[],[f237,f3845]) ).
fof(f3845,plain,
( spl0_319
<=> ! [X6,X39,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X39,X7,tc_nat),c_HOL_Ominus__class_Ominus(X39,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f237,axiom,
! [X39,X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X39,X7,tc_nat),c_HOL_Ominus__class_Ominus(X39,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f3843,plain,
spl0_318,
inference(avatar_split_clause,[],[f193,f3841]) ).
fof(f3841,plain,
( spl0_318
<=> ! [X9,X60,X49,X8,X23,X2] : hAPP(X8,hAPP(X9,X60)) = hAPP(c_Fun_Ocomp(X8,X9,X49,X23,X2),X60) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f193,axiom,
! [X2,X49,X8,X9,X60,X23] : hAPP(X8,hAPP(X9,X60)) = hAPP(c_Fun_Ocomp(X8,X9,X49,X23,X2),X60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f3839,plain,
spl0_317,
inference(avatar_split_clause,[],[f146,f3837]) ).
fof(f3837,plain,
( spl0_317
<=> ! [X2,X4,X3,X22] :
( X3 = X4
| hBOOL(hAPP(X22,X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X4,X22,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f146,axiom,
! [X2,X3,X4,X22] :
( X3 = X4
| hBOOL(hAPP(X22,X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X4,X22,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f3835,plain,
spl0_316,
inference(avatar_split_clause,[],[f79,f3833]) ).
fof(f3833,plain,
( spl0_316
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,X4,X2)
| c_HOL_Oord__class_Oless(X5,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f79,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,X4,X2)
| c_HOL_Oord__class_Oless(X5,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3831,plain,
spl0_315,
inference(avatar_split_clause,[],[f78,f3829]) ).
fof(f3829,plain,
( spl0_315
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X5,X2)
| c_HOL_Oord__class_Oless(X3,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f78,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X5,X2)
| c_HOL_Oord__class_Oless(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f3827,plain,
spl0_314,
inference(avatar_split_clause,[],[f60,f3825]) ).
fof(f3825,plain,
( spl0_314
<=> ! [X9,X2,X8] :
( X8 = X9
| ~ hBOOL(c_in(X9,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f60,axiom,
! [X2,X8,X9] :
( X8 = X9
| ~ hBOOL(c_in(X9,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f3823,plain,
spl0_313,
inference(avatar_split_clause,[],[f53,f3821]) ).
fof(f3821,plain,
( spl0_313
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f53,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f3819,plain,
spl0_312,
inference(avatar_split_clause,[],[f42,f3817]) ).
fof(f3817,plain,
( spl0_312
<=> ! [X2,X9,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,X9,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X8,X9,X2),X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f42,axiom,
! [X2,X8,X9] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,X9,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X8,X9,X2),X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f3807,plain,
( spl0_311
| ~ spl0_80
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2071,f1973,f1121,f3805]) ).
fof(f3805,plain,
( spl0_311
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f1121,plain,
( spl0_80
<=> ! [X7] : c_Orderings_Oord__class_Omax(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f2071,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0
| ~ spl0_80
| ~ spl0_219 ),
inference(superposition,[],[f1122,f1975]) ).
fof(f1122,plain,
( ! [X7] : c_Orderings_Oord__class_Omax(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X7
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f3524,plain,
( spl0_310
| ~ spl0_71
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2070,f1973,f1085,f3522]) ).
fof(f3522,plain,
( spl0_310
<=> ! [X0] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f1085,plain,
( spl0_71
<=> ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X7),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f2070,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X0),tc_nat)
| ~ spl0_71
| ~ spl0_219 ),
inference(superposition,[],[f1086,f1975]) ).
fof(f1086,plain,
( ! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X7),tc_nat)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f3334,plain,
( spl0_309
| ~ spl0_70
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2069,f1973,f1081,f3332]) ).
fof(f3332,plain,
( spl0_309
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f1081,plain,
( spl0_70
<=> ! [X6] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f2069,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0
| ~ spl0_70
| ~ spl0_219 ),
inference(superposition,[],[f1082,f1975]) ).
fof(f1082,plain,
( ! [X6] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f3248,plain,
( spl0_308
| ~ spl0_219
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f2830,f2826,f1973,f3246]) ).
fof(f3246,plain,
( spl0_308
<=> ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2826,plain,
( spl0_281
<=> ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2830,plain,
( ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X7 )
| ~ spl0_219
| ~ spl0_281 ),
inference(forward_demodulation,[],[f2829,f1975]) ).
fof(f2829,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_281 ),
inference(forward_demodulation,[],[f2827,f1975]) ).
fof(f2827,plain,
( ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f2826]) ).
fof(f3244,plain,
( spl0_307
| ~ spl0_219
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2824,f2820,f1973,f3242]) ).
fof(f3242,plain,
( spl0_307
<=> ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2820,plain,
( spl0_280
<=> ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2824,plain,
( ! [X6,X7] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X6 )
| ~ spl0_219
| ~ spl0_280 ),
inference(forward_demodulation,[],[f2823,f1975]) ).
fof(f2823,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_219
| ~ spl0_280 ),
inference(forward_demodulation,[],[f2821,f1975]) ).
fof(f2821,plain,
( ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2820]) ).
fof(f2930,plain,
spl0_306,
inference(avatar_split_clause,[],[f645,f2928]) ).
fof(f2928,plain,
( spl0_306
<=> ! [X6,X7] : c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f645,axiom,
! [X6,X7] : c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f2926,plain,
spl0_305,
inference(avatar_split_clause,[],[f642,f2924]) ).
fof(f2924,plain,
( spl0_305
<=> ! [X6,X7] :
( X6 = X7
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f642,axiom,
! [X6,X7] :
( X6 = X7
| c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
fof(f2922,plain,
spl0_304,
inference(avatar_split_clause,[],[f621,f2920]) ).
fof(f2920,plain,
( spl0_304
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| X3 = X4
| ~ c_lessequals(X3,X4,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f621,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| X3 = X4
| ~ c_lessequals(X3,X4,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f2918,plain,
spl0_303,
inference(avatar_split_clause,[],[f618,f2916]) ).
fof(f2916,plain,
( spl0_303
<=> ! [X2,X9,X8] :
( ~ class_Orderings_Oorder(X2)
| X8 = X9
| ~ c_lessequals(X8,X9,X2)
| c_HOL_Oord__class_Oless(X8,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f618,axiom,
! [X2,X8,X9] :
( ~ class_Orderings_Oorder(X2)
| X8 = X9
| ~ c_lessequals(X8,X9,X2)
| c_HOL_Oord__class_Oless(X8,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
fof(f2914,plain,
spl0_302,
inference(avatar_split_clause,[],[f586,f2912]) ).
fof(f2912,plain,
( spl0_302
<=> ! [X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f586,axiom,
! [X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f2910,plain,
spl0_301,
inference(avatar_split_clause,[],[f553,f2908]) ).
fof(f2908,plain,
( spl0_301
<=> ! [X14,X13,X9,X45] :
( X14 = X45
| hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X14,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f553,axiom,
! [X9,X45,X14,X13] :
( X14 = X45
| hBOOL(hAPP(X9,X14))
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X14,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
fof(f2906,plain,
spl0_300,
inference(avatar_split_clause,[],[f508,f2904]) ).
fof(f2904,plain,
( spl0_300
<=> ! [X8,X78,X9,X2] :
( ~ hBOOL(c_in(X8,X78,X2))
| hBOOL(c_in(X8,c_Set_Oinsert(X9,X78,X2),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f508,axiom,
! [X2,X78,X8,X9] :
( ~ hBOOL(c_in(X8,X78,X2))
| hBOOL(c_in(X8,c_Set_Oinsert(X9,X78,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
fof(f2902,plain,
spl0_299,
inference(avatar_split_clause,[],[f469,f2900]) ).
fof(f2900,plain,
( spl0_299
<=> ! [X7,X15] :
( ~ c_lessequals(X15,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f469,axiom,
! [X7,X15] :
( ~ c_lessequals(X15,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X7,c_HOL_Ominus__class_Ominus(X7,X15,tc_nat),tc_nat) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f2898,plain,
spl0_298,
inference(avatar_split_clause,[],[f373,f2896]) ).
fof(f2896,plain,
( spl0_298
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| X3 = X4
| ~ c_lessequals(X4,X3,X2)
| ~ c_lessequals(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f373,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| X3 = X4
| ~ c_lessequals(X4,X3,X2)
| ~ c_lessequals(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f2894,plain,
spl0_297,
inference(avatar_split_clause,[],[f371,f2892]) ).
fof(f2892,plain,
( spl0_297
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f371,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X2)
| c_HOL_Oord__class_Oless(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f2890,plain,
( spl0_296
| ~ spl0_141
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2720,f2568,f1383,f2888]) ).
fof(f2888,plain,
( spl0_296
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f1383,plain,
( spl0_141
<=> ! [X6] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),c_HOL_Ozero__class_Ozero(tc_nat)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f2568,plain,
( spl0_262
<=> ! [X6,X7] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2720,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_141
| ~ spl0_262 ),
inference(superposition,[],[f2569,f1384]) ).
fof(f1384,plain,
( ! [X6] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f2569,plain,
( ! [X6,X7] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2568]) ).
fof(f2886,plain,
spl0_295,
inference(avatar_split_clause,[],[f286,f2884]) ).
fof(f2884,plain,
( spl0_295
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X5,X4,X2)
| ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f286,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X5,X4,X2)
| ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f2882,plain,
spl0_294,
inference(avatar_split_clause,[],[f285,f2880]) ).
fof(f2880,plain,
( spl0_294
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X5,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f285,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X5,X3,X2)
| ~ c_HOL_Oord__class_Oless(X5,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f2878,plain,
spl0_293,
inference(avatar_split_clause,[],[f284,f2876]) ).
fof(f2876,plain,
( spl0_293
<=> ! [X2,X9,X8,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X3,X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X8,X9,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f284,axiom,
! [X2,X3,X8,X9] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X3,X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X8,X9,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
fof(f2874,plain,
spl0_292,
inference(avatar_split_clause,[],[f283,f2872]) ).
fof(f2872,plain,
( spl0_292
<=> ! [X3,X8,X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X8,X3,X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X8,X9,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f283,axiom,
! [X2,X3,X8,X9] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X8,X3,X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X8,X9,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
fof(f2870,plain,
spl0_291,
inference(avatar_split_clause,[],[f273,f2868]) ).
fof(f2868,plain,
( spl0_291
<=> ! [X2,X5,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X4,X5,X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f273,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X4,X5,X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f2866,plain,
spl0_290,
inference(avatar_split_clause,[],[f272,f2864]) ).
fof(f2864,plain,
( spl0_290
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X3,X5,X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f272,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X3,X5,X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f2862,plain,
spl0_289,
inference(avatar_split_clause,[],[f269,f2860]) ).
fof(f2860,plain,
( spl0_289
<=> ! [X3,X8,X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X9,X2)
| c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X8,X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f269,axiom,
! [X2,X3,X8,X9] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X9,X2)
| c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X8,X9,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
fof(f2858,plain,
spl0_288,
inference(avatar_split_clause,[],[f268,f2856]) ).
fof(f2856,plain,
( spl0_288
<=> ! [X3,X8,X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X8,X2)
| c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X8,X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f268,axiom,
! [X2,X3,X8,X9] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X8,X2)
| c_HOL_Oord__class_Oless(X3,c_Orderings_Oord__class_Omax(X8,X9,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
fof(f2854,plain,
spl0_287,
inference(avatar_split_clause,[],[f223,f2852]) ).
fof(f2852,plain,
( spl0_287
<=> ! [X31,X28,X29,X2,X26,X27,X24,X25,X30] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OSKIP,X2) = X24 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f223,axiom,
! [X31,X2,X28,X29,X26,X27,X24,X25,X30] : c_Com_Ocom_Ocom__case(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OSKIP,X2) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).
fof(f2850,plain,
spl0_286,
inference(avatar_split_clause,[],[f218,f2848]) ).
fof(f2848,plain,
( spl0_286
<=> ! [X3,X8,X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X8,X3,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X8,X9,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f218,axiom,
! [X2,X3,X8,X9] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X8,X3,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X8,X9,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
fof(f2846,plain,
( spl0_285
| ~ spl0_128
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1831,f1611,f1331,f2844]) ).
fof(f2844,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(f1331,plain,
( spl0_128
<=> ! [X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),hAPP(c_Suc,X6),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1611,plain,
( spl0_185
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1831,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_185 ),
inference(resolution,[],[f1612,f1332]) ).
fof(f1332,plain,
( ! [X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),hAPP(c_Suc,X6),tc_nat)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1331]) ).
fof(f1612,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1611]) ).
fof(f2842,plain,
spl0_284,
inference(avatar_split_clause,[],[f214,f2840]) ).
fof(f2840,plain,
( spl0_284
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X5,X3,X2)
| c_lessequals(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f214,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X5,X3,X2)
| c_lessequals(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
fof(f2838,plain,
spl0_283,
inference(avatar_split_clause,[],[f213,f2836]) ).
fof(f2836,plain,
( spl0_283
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X5,X4,X2)
| c_lessequals(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f213,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X5,X4,X2)
| c_lessequals(X5,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
fof(f2834,plain,
spl0_282,
inference(avatar_split_clause,[],[f211,f2832]) ).
fof(f2832,plain,
( spl0_282
<=> ! [X2,X5,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X5,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f211,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X5,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
fof(f2828,plain,
spl0_281,
inference(avatar_split_clause,[],[f197,f2826]) ).
fof(f197,axiom,
! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f2822,plain,
spl0_280,
inference(avatar_split_clause,[],[f196,f2820]) ).
fof(f196,axiom,
! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f2818,plain,
spl0_279,
inference(avatar_split_clause,[],[f182,f2816]) ).
fof(f2816,plain,
( spl0_279
<=> ! [X3,X8,X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X9,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X8,X9,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f182,axiom,
! [X2,X3,X8,X9] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X9,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X8,X9,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
fof(f2814,plain,
spl0_278,
inference(avatar_split_clause,[],[f181,f2812]) ).
fof(f2812,plain,
( spl0_278
<=> ! [X3,X8,X9,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X8,X3,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X8,X9,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f181,axiom,
! [X2,X3,X8,X9] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X8,X3,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X8,X9,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
fof(f2810,plain,
spl0_277,
inference(avatar_split_clause,[],[f178,f2808]) ).
fof(f2808,plain,
( spl0_277
<=> ! [X2,X5,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X5,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f178,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X5,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
fof(f2806,plain,
spl0_276,
inference(avatar_split_clause,[],[f177,f2804]) ).
fof(f2804,plain,
( spl0_276
<=> ! [X3,X4,X5,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f177,axiom,
! [X2,X3,X4,X5] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X5,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
fof(f2802,plain,
spl0_275,
inference(avatar_split_clause,[],[f158,f2800]) ).
fof(f2800,plain,
( spl0_275
<=> ! [X37,X13,X23,X49] : hAPP(c_Fun_Ocomp(c_COMBK(X13,X23,X49),X37,X49,X23,t_a),v_x) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f158,axiom,
! [X49,X37,X23,X13] : hAPP(c_Fun_Ocomp(c_COMBK(X13,X23,X49),X37,X49,X23,t_a),v_x) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
fof(f2794,plain,
spl0_274,
inference(avatar_split_clause,[],[f154,f2792]) ).
fof(f154,axiom,
! [X6,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f2790,plain,
spl0_273,
inference(avatar_split_clause,[],[f142,f2788]) ).
fof(f2788,plain,
( spl0_273
<=> ! [X16,X17,X15] :
( c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f142,axiom,
! [X16,X17,X15] :
( c_HOL_Oord__class_Oless(X15,X16,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17),X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f2786,plain,
spl0_272,
inference(avatar_split_clause,[],[f141,f2784]) ).
fof(f2784,plain,
( spl0_272
<=> ! [X4,X5,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X5,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f141,axiom,
! [X3,X4,X5] :
( ~ c_HOL_Oord__class_Oless(X3,X5,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
fof(f2782,plain,
spl0_271,
inference(avatar_split_clause,[],[f140,f2780]) ).
fof(f2780,plain,
( spl0_271
<=> ! [X4,X5,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f140,axiom,
! [X3,X4,X5] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f2778,plain,
spl0_270,
inference(avatar_split_clause,[],[f103,f2776]) ).
fof(f2776,plain,
( spl0_270
<=> ! [X6,X16,X7] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f103,axiom,
! [X6,X7,X16] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f2774,plain,
spl0_269,
inference(avatar_split_clause,[],[f102,f2772]) ).
fof(f2772,plain,
( spl0_269
<=> ! [X6,X16,X7] :
( c_lessequals(X16,X7,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f102,axiom,
! [X6,X16,X7] :
( c_lessequals(X16,X7,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X16),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f2770,plain,
spl0_268,
inference(avatar_split_clause,[],[f101,f2768]) ).
fof(f2768,plain,
( spl0_268
<=> ! [X6,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f101,axiom,
! [X6,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
fof(f2766,plain,
spl0_267,
inference(avatar_split_clause,[],[f100,f2764]) ).
fof(f2764,plain,
( spl0_267
<=> ! [X6,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f100,axiom,
! [X6,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| c_lessequals(X15,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X17),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
fof(f2762,plain,
spl0_266,
inference(avatar_split_clause,[],[f55,f2760]) ).
fof(f2760,plain,
( spl0_266
<=> ! [X2,X37,X8,X23,X22] :
( c_Fun_Oinj__on(X37,X22,X2,X23)
| ~ c_Fun_Oinj__on(X37,c_Set_Oinsert(X8,X22,X2),X2,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f55,axiom,
! [X2,X37,X8,X22,X23] :
( c_Fun_Oinj__on(X37,X22,X2,X23)
| ~ c_Fun_Oinj__on(X37,c_Set_Oinsert(X8,X22,X2),X2,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
fof(f2758,plain,
spl0_265,
inference(avatar_split_clause,[],[f45,f2756]) ).
fof(f2756,plain,
( spl0_265
<=> ! [X31,X28,X29,X2,X26,X27,X24,X25,X30] : c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OSKIP,X2) = X24 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f45,axiom,
! [X31,X2,X28,X29,X26,X27,X24,X25,X30] : c_Com_Ocom_Ocom__rec(X24,X25,X26,X27,X28,X29,X30,X31,c_Com_Ocom_OSKIP,X2) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Orecs_I1_J_0) ).
fof(f2643,plain,
( spl0_264
| ~ spl0_219
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2366,f2363,f1973,f2641]) ).
fof(f2641,plain,
( spl0_264
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2363,plain,
( spl0_251
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2366,plain,
( ! [X6,X7] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat) )
| ~ spl0_219
| ~ spl0_251 ),
inference(forward_demodulation,[],[f2364,f1975]) ).
fof(f2364,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2363]) ).
fof(f2639,plain,
( spl0_263
| ~ spl0_219
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2361,f2358,f1973,f2637]) ).
fof(f2637,plain,
( spl0_263
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2358,plain,
( spl0_250
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2361,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) )
| ~ spl0_219
| ~ spl0_250 ),
inference(forward_demodulation,[],[f2359,f1975]) ).
fof(f2359,plain,
( ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2358]) ).
fof(f2570,plain,
( spl0_262
| ~ spl0_219
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2313,f2310,f1973,f2568]) ).
fof(f2310,plain,
( spl0_239
<=> ! [X6,X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2313,plain,
( ! [X6,X7] : c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_219
| ~ spl0_239 ),
inference(forward_demodulation,[],[f2311,f1975]) ).
fof(f2311,plain,
( ! [X6,X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat)
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f2563,plain,
( spl0_261
| ~ spl0_219
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2296,f2293,f1973,f2561]) ).
fof(f2561,plain,
( spl0_261
<=> ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2293,plain,
( spl0_235
<=> ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2296,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != X6 )
| ~ spl0_219
| ~ spl0_235 ),
inference(forward_demodulation,[],[f2294,f1975]) ).
fof(f2294,plain,
( ! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != X6 )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2293]) ).
fof(f2559,plain,
( spl0_260
| ~ spl0_219
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2287,f2284,f1973,f2557]) ).
fof(f2557,plain,
( spl0_260
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2284,plain,
( spl0_234
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2287,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) )
| ~ spl0_219
| ~ spl0_234 ),
inference(forward_demodulation,[],[f2285,f1975]) ).
fof(f2285,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2284]) ).
fof(f2549,plain,
( spl0_259
| ~ spl0_219
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2278,f2275,f1973,f2547]) ).
fof(f2547,plain,
( spl0_259
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2275,plain,
( spl0_232
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2278,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) )
| ~ spl0_219
| ~ spl0_232 ),
inference(forward_demodulation,[],[f2276,f1975]) ).
fof(f2276,plain,
( ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2275]) ).
fof(f2511,plain,
( spl0_258
| ~ spl0_36
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2068,f1973,f944,f2509]) ).
fof(f2509,plain,
( spl0_258
<=> ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f944,plain,
( spl0_36
<=> ! [X7] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2068,plain,
( ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)
| ~ spl0_36
| ~ spl0_219 ),
inference(superposition,[],[f945,f1975]) ).
fof(f945,plain,
( ! [X7] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f2390,plain,
spl0_257,
inference(avatar_split_clause,[],[f719,f2388]) ).
fof(f2388,plain,
( spl0_257
<=> ! [X36,X44,X14] :
( ~ c_Natural_Oevalc(c_Com_Ocom_OBODY(X36),X14,X44)
| c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(X36),tc_Com_Ocom),X14,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f719,axiom,
! [X36,X44,X14] :
( ~ c_Natural_Oevalc(c_Com_Ocom_OBODY(X36),X14,X44)
| c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(X36),tc_Com_Ocom),X14,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
fof(f2386,plain,
spl0_256,
inference(avatar_split_clause,[],[f718,f2384]) ).
fof(f2384,plain,
( spl0_256
<=> ! [X44,X68,X63] :
( c_Natural_Oevalc(c_Com_Ocom_OBODY(X68),X63,X44)
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X63,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f718,axiom,
! [X68,X44,X63] :
( c_Natural_Oevalc(c_Com_Ocom_OBODY(X68),X63,X44)
| ~ c_Natural_Oevalc(c_Option_Othe(c_Com_Obody(X68),tc_Com_Ocom),X63,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
fof(f2382,plain,
spl0_255,
inference(avatar_split_clause,[],[f672,f2380]) ).
fof(f2380,plain,
( spl0_255
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f672,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X6),hAPP(c_Suc,X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f2378,plain,
spl0_254,
inference(avatar_split_clause,[],[f671,f2376]) ).
fof(f2376,plain,
( spl0_254
<=> ! [X7,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X7,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X3),hAPP(c_Suc,X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f671,axiom,
! [X3,X7] :
( ~ c_HOL_Oord__class_Oless(X3,X7,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(c_Suc,X3),hAPP(c_Suc,X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
fof(f2374,plain,
spl0_253,
inference(avatar_split_clause,[],[f641,f2372]) ).
fof(f2372,plain,
( spl0_253
<=> ! [X7,X14,X13,X86] :
( ~ c_Natural_Oevaln(X13,X14,X7,X86)
| c_Natural_Oevaln(X13,X14,hAPP(c_Suc,X7),X86) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f641,axiom,
! [X86,X7,X14,X13] :
( ~ c_Natural_Oevaln(X13,X14,X7,X86)
| c_Natural_Oevaln(X13,X14,hAPP(c_Suc,X7),X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
fof(f2370,plain,
spl0_252,
inference(avatar_split_clause,[],[f592,f2368]) ).
fof(f2368,plain,
( spl0_252
<=> ! [X2,X62,X69,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X62,X69,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(X45,X69,tc_Hoare__Mirabelle_Otriple(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f592,axiom,
! [X2,X69,X62,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X62,X69,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Set_Oinsert(X45,X69,tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
fof(f2365,plain,
spl0_251,
inference(avatar_split_clause,[],[f591,f2363]) ).
fof(f591,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2360,plain,
spl0_250,
inference(avatar_split_clause,[],[f590,f2358]) ).
fof(f590,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2356,plain,
spl0_249,
inference(avatar_split_clause,[],[f572,f2354]) ).
fof(f2354,plain,
( spl0_249
<=> ! [X16,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat)
| c_lessequals(X15,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f572,axiom,
! [X16,X17,X15] :
( ~ c_lessequals(X15,X17,tc_nat)
| ~ c_lessequals(X17,X16,tc_nat)
| c_lessequals(X15,X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2351,plain,
spl0_248,
inference(avatar_split_clause,[],[f565,f2349]) ).
fof(f2349,plain,
( spl0_248
<=> ! [X36,X7] :
( ~ hBOOL(hAPP(X36,X7))
| hBOOL(hAPP(X36,c_Divides_Odiv__class_Omod(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f565,axiom,
! [X36,X7] :
( ~ hBOOL(hAPP(X36,X7))
| hBOOL(hAPP(X36,c_Divides_Odiv__class_Omod(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_5) ).
fof(f2346,plain,
spl0_247,
inference(avatar_split_clause,[],[f564,f2344]) ).
fof(f2344,plain,
( spl0_247
<=> ! [X36,X7] :
( hBOOL(hAPP(X36,X7))
| ~ hBOOL(hAPP(X36,c_Divides_Odiv__class_Omod(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f564,axiom,
! [X36,X7] :
( hBOOL(hAPP(X36,X7))
| ~ hBOOL(hAPP(X36,c_Divides_Odiv__class_Omod(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mod_0) ).
fof(f2342,plain,
spl0_246,
inference(avatar_split_clause,[],[f539,f2340]) ).
fof(f2340,plain,
( spl0_246
<=> ! [X11,X0,X12,X50,X10,X1] :
( X10 = X50
| c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OLocal(X50,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f539,axiom,
! [X50,X10,X0,X11,X1,X12] :
( X10 = X50
| c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OLocal(X50,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
fof(f2338,plain,
( ~ spl0_245
| ~ spl0_138
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2289,f2242,f1371,f2335]) ).
fof(f2335,plain,
( spl0_245
<=> v_Procs = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f1371,plain,
( spl0_138
<=> ! [X22,X2,X8] : c_Set_Oinsert(X8,X22,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f2289,plain,
( v_Procs != c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))
| ~ spl0_138
| ~ spl0_224 ),
inference(superposition,[],[f1372,f2244]) ).
fof(f1372,plain,
( ! [X2,X8,X22] : c_Set_Oinsert(X8,X22,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f2333,plain,
spl0_244,
inference(avatar_split_clause,[],[f538,f2331]) ).
fof(f2331,plain,
( spl0_244
<=> ! [X10,X11,X0,X50,X12,X1] :
( X0 = X11
| c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OLocal(X50,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f538,axiom,
! [X50,X10,X0,X11,X1,X12] :
( X0 = X11
| c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OLocal(X50,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
fof(f2329,plain,
spl0_243,
inference(avatar_split_clause,[],[f537,f2327]) ).
fof(f2327,plain,
( spl0_243
<=> ! [X10,X11,X0,X50,X12,X1] :
( X1 = X12
| c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OLocal(X50,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f537,axiom,
! [X50,X10,X0,X11,X1,X12] :
( X1 = X12
| c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OLocal(X50,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
fof(f2325,plain,
spl0_242,
inference(avatar_split_clause,[],[f525,f2323]) ).
fof(f2323,plain,
( spl0_242
<=> ! [X6,X7] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X7),hAPP(c_Suc,X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f525,axiom,
! [X6,X7] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X7),hAPP(c_Suc,X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f2321,plain,
spl0_241,
inference(avatar_split_clause,[],[f524,f2319]) ).
fof(f2319,plain,
( spl0_241
<=> ! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_lessequals(hAPP(c_Suc,X7),hAPP(c_Suc,X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f524,axiom,
! [X6,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_lessequals(hAPP(c_Suc,X7),hAPP(c_Suc,X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f2317,plain,
spl0_240,
inference(avatar_split_clause,[],[f419,f2315]) ).
fof(f2315,plain,
( spl0_240
<=> ! [X62,X74,X69,X2] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X69,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X62,X74,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X62,X69,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f419,axiom,
! [X2,X69,X62,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X69,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X62,X74,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X62,X69,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
fof(f2312,plain,
spl0_239,
inference(avatar_split_clause,[],[f241,f2310]) ).
fof(f241,axiom,
! [X6,X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f2308,plain,
spl0_238,
inference(avatar_split_clause,[],[f166,f2306]) ).
fof(f2306,plain,
( spl0_238
<=> ! [X18,X11,X0,X21,X19,X20] :
( X0 = X11
| c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OCond(X11,X18,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f166,axiom,
! [X21,X0,X11,X18,X19,X20] :
( X0 = X11
| c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OCond(X11,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
fof(f2304,plain,
spl0_237,
inference(avatar_split_clause,[],[f165,f2302]) ).
fof(f2302,plain,
( spl0_237
<=> ! [X18,X11,X21,X0,X19,X20] :
( X18 = X20
| c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OCond(X11,X18,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f165,axiom,
! [X21,X0,X11,X18,X19,X20] :
( X18 = X20
| c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OCond(X11,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
fof(f2300,plain,
spl0_236,
inference(avatar_split_clause,[],[f164,f2298]) ).
fof(f2298,plain,
( spl0_236
<=> ! [X18,X19,X11,X0,X21,X20] :
( X19 = X21
| c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OCond(X11,X18,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f164,axiom,
! [X21,X0,X11,X18,X19,X20] :
( X19 = X21
| c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OCond(X11,X18,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
fof(f2295,plain,
spl0_235,
inference(avatar_split_clause,[],[f162,f2293]) ).
fof(f162,axiom,
! [X6,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7) != X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f2286,plain,
spl0_234,
inference(avatar_split_clause,[],[f157,f2284]) ).
fof(f157,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
fof(f2282,plain,
spl0_233,
inference(avatar_split_clause,[],[f139,f2280]) ).
fof(f2280,plain,
( spl0_233
<=> ! [X22,X2,X3] : c_Set_Oinsert(X3,X22,X2) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X22,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f139,axiom,
! [X2,X3,X22] : c_Set_Oinsert(X3,X22,X2) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X22,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f2277,plain,
spl0_232,
inference(avatar_split_clause,[],[f121,f2275]) ).
fof(f121,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f2273,plain,
spl0_231,
inference(avatar_split_clause,[],[f114,f2271]) ).
fof(f2271,plain,
( spl0_231
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f114,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2269,plain,
spl0_230,
inference(avatar_split_clause,[],[f113,f2267]) ).
fof(f2267,plain,
( spl0_230
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f113,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2265,plain,
spl0_229,
inference(avatar_split_clause,[],[f112,f2263]) ).
fof(f2263,plain,
( spl0_229
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f112,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2261,plain,
spl0_228,
inference(avatar_split_clause,[],[f83,f2259]) ).
fof(f2259,plain,
( spl0_228
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f83,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2257,plain,
spl0_227,
inference(avatar_split_clause,[],[f82,f2255]) ).
fof(f2255,plain,
( spl0_227
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f82,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2253,plain,
spl0_226,
inference(avatar_split_clause,[],[f81,f2251]) ).
fof(f2251,plain,
( spl0_226
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f81,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2249,plain,
spl0_225,
inference(avatar_split_clause,[],[f39,f2247]) ).
fof(f2247,plain,
( spl0_225
<=> ! [X35,X11,X34,X0,X33,X32] :
( X0 = X11
| c_Com_Ocom_OCall(X32,X33,X11) != c_Com_Ocom_OCall(X34,X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f39,axiom,
! [X0,X11,X34,X35,X32,X33] :
( X0 = X11
| c_Com_Ocom_OCall(X32,X33,X11) != c_Com_Ocom_OCall(X34,X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
fof(f2245,plain,
( spl0_224
| ~ spl0_1
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2207,f1965,f780,f2242]) ).
fof(f1965,plain,
( spl0_217
<=> ! [X22,X2,X8] :
( ~ hBOOL(c_in(X8,X22,X2))
| c_Set_Oinsert(X8,X22,X2) = X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f2207,plain,
( v_Procs = c_Set_Oinsert(v_x,v_Procs,tc_Com_Opname)
| ~ spl0_1
| ~ spl0_217 ),
inference(resolution,[],[f1966,f782]) ).
fof(f782,plain,
( hBOOL(c_in(v_x,v_Procs,tc_Com_Opname))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f1966,plain,
( ! [X2,X8,X22] :
( ~ hBOOL(c_in(X8,X22,X2))
| c_Set_Oinsert(X8,X22,X2) = X22 )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f1965]) ).
fof(f2240,plain,
spl0_223,
inference(avatar_split_clause,[],[f38,f2238]) ).
fof(f2238,plain,
( spl0_223
<=> ! [X35,X11,X34,X0,X33,X32] :
( X33 = X35
| c_Com_Ocom_OCall(X32,X33,X11) != c_Com_Ocom_OCall(X34,X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f38,axiom,
! [X0,X11,X34,X35,X32,X33] :
( X33 = X35
| c_Com_Ocom_OCall(X32,X33,X11) != c_Com_Ocom_OCall(X34,X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
fof(f2236,plain,
spl0_222,
inference(avatar_split_clause,[],[f37,f2234]) ).
fof(f2234,plain,
( spl0_222
<=> ! [X35,X11,X34,X0,X33,X32] :
( X32 = X34
| c_Com_Ocom_OCall(X32,X33,X11) != c_Com_Ocom_OCall(X34,X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f37,axiom,
! [X0,X11,X34,X35,X32,X33] :
( X32 = X34
| c_Com_Ocom_OCall(X32,X33,X11) != c_Com_Ocom_OCall(X34,X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
fof(f2185,plain,
( spl0_221
| ~ spl0_34
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2067,f1973,f936,f2183]) ).
fof(f2183,plain,
( spl0_221
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f936,plain,
( spl0_34
<=> ! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f2067,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_34
| ~ spl0_219 ),
inference(superposition,[],[f937,f1975]) ).
fof(f937,plain,
( ! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f936]) ).
fof(f1980,plain,
spl0_220,
inference(avatar_split_clause,[],[f646,f1978]) ).
fof(f1978,plain,
( spl0_220
<=> ! [X24,X25,X2,X87] : c_Nat_Onat_Onat__case(X24,X25,hAPP(c_Suc,X87),X2) = hAPP(X25,X87) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f646,axiom,
! [X2,X87,X24,X25] : c_Nat_Onat_Onat__case(X24,X25,hAPP(c_Suc,X87),X2) = hAPP(X25,X87),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__Suc_0) ).
fof(f1976,plain,
( ~ spl0_19
| spl0_219
| ~ spl0_68
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1449,f1355,f1073,f1973,f870]) ).
fof(f870,plain,
( spl0_19
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1073,plain,
( spl0_68
<=> ! [X2,X3] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1355,plain,
( spl0_134
<=> ! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1449,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ class_Orderings_Obot(tc_nat)
| ~ spl0_68
| ~ spl0_134 ),
inference(resolution,[],[f1356,f1074]) ).
fof(f1074,plain,
( ! [X2,X3] :
( c_lessequals(c_Orderings_Obot__class_Obot(X2),X3,X2)
| ~ class_Orderings_Obot(X2) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f1356,plain,
( ! [X7] :
( ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X7 )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1355]) ).
fof(f1971,plain,
spl0_218,
inference(avatar_split_clause,[],[f613,f1969]) ).
fof(f1969,plain,
( spl0_218
<=> ! [X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f613,axiom,
! [X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
fof(f1967,plain,
spl0_217,
inference(avatar_split_clause,[],[f523,f1965]) ).
fof(f523,axiom,
! [X2,X8,X22] :
( ~ hBOOL(c_in(X8,X22,X2))
| c_Set_Oinsert(X8,X22,X2) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f1963,plain,
spl0_216,
inference(avatar_split_clause,[],[f493,f1961]) ).
fof(f1961,plain,
( spl0_216
<=> ! [X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),X7,tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f493,axiom,
! [X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X6),X7,tc_nat) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1959,plain,
spl0_215,
inference(avatar_split_clause,[],[f492,f1957]) ).
fof(f1957,plain,
( spl0_215
<=> ! [X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),X7,tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f492,axiom,
! [X6,X7] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),X7,tc_nat) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f1955,plain,
spl0_214,
inference(avatar_split_clause,[],[f486,f1953]) ).
fof(f1953,plain,
( spl0_214
<=> ! [X2,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),c_HOL_Ozero__class_Ozero(X2)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f486,axiom,
! [X2,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),c_HOL_Ozero__class_Ozero(X2)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1951,plain,
spl0_213,
inference(avatar_split_clause,[],[f485,f1949]) ).
fof(f1949,plain,
( spl0_213
<=> ! [X2,X8] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),c_HOL_Ozero__class_Ozero(X2)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f485,axiom,
! [X2,X8] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),c_HOL_Ozero__class_Ozero(X2)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1947,plain,
spl0_212,
inference(avatar_split_clause,[],[f484,f1945]) ).
fof(f1945,plain,
( spl0_212
<=> ! [X2,X8] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X8) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f484,axiom,
! [X2,X8] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1943,plain,
spl0_211,
inference(avatar_split_clause,[],[f483,f1941]) ).
fof(f1941,plain,
( spl0_211
<=> ! [X2,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),c_HOL_Ozero__class_Ozero(X2)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f483,axiom,
! [X2,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X8),c_HOL_Ozero__class_Ozero(X2)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1939,plain,
spl0_210,
inference(avatar_split_clause,[],[f478,f1937]) ).
fof(f1937,plain,
( spl0_210
<=> ! [X2,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X8) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f478,axiom,
! [X2,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X8) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1935,plain,
spl0_209,
inference(avatar_split_clause,[],[f477,f1933]) ).
fof(f1933,plain,
( spl0_209
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f477,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f1924,plain,
spl0_208,
inference(avatar_split_clause,[],[f467,f1922]) ).
fof(f1922,plain,
( spl0_208
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f467,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f1920,plain,
spl0_207,
inference(avatar_split_clause,[],[f456,f1918]) ).
fof(f1918,plain,
( spl0_207
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = c_Orderings_Oord__class_Omax(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f456,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = c_Orderings_Oord__class_Omax(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f1916,plain,
spl0_206,
inference(avatar_split_clause,[],[f366,f1914]) ).
fof(f1914,plain,
( spl0_206
<=> ! [X41,X14,X13,X45] :
( X41 = X45
| ~ c_Natural_Oevalc(X13,X14,X45)
| ~ c_Natural_Oevalc(X13,X14,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f366,axiom,
! [X41,X45,X14,X13] :
( X41 = X45
| ~ c_Natural_Oevalc(X13,X14,X45)
| ~ c_Natural_Oevalc(X13,X14,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
fof(f1912,plain,
spl0_205,
inference(avatar_split_clause,[],[f365,f1910]) ).
fof(f1910,plain,
( spl0_205
<=> ! [X6,X7] :
( X6 = X7
| c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f365,axiom,
! [X6,X7] :
( X6 = X7
| c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f1908,plain,
spl0_204,
inference(avatar_split_clause,[],[f364,f1906]) ).
fof(f1906,plain,
( spl0_204
<=> ! [X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f364,axiom,
! [X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1904,plain,
spl0_203,
inference(avatar_split_clause,[],[f340,f1902]) ).
fof(f1902,plain,
( spl0_203
<=> ! [X16,X17,X7] :
( ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X7,tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f340,axiom,
! [X16,X7,X17] :
( ~ c_HOL_Oord__class_Oless(X17,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X7,tc_nat),X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f1900,plain,
spl0_202,
inference(avatar_split_clause,[],[f300,f1898]) ).
fof(f1898,plain,
( spl0_202
<=> ! [X22,X2,X4,X3] :
( ~ hBOOL(hAPP(X22,X3))
| hBOOL(hAPP(c_Set_Oinsert(X4,X22,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f300,axiom,
! [X2,X3,X4,X22] :
( ~ hBOOL(hAPP(X22,X3))
| hBOOL(hAPP(c_Set_Oinsert(X4,X22,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1896,plain,
spl0_201,
inference(avatar_split_clause,[],[f274,f1894]) ).
fof(f1894,plain,
( spl0_201
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = c_Orderings_Oord__class_Omin(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f274,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = c_Orderings_Oord__class_Omin(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f1892,plain,
spl0_200,
inference(avatar_split_clause,[],[f252,f1890]) ).
fof(f1890,plain,
( spl0_200
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f252,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f1888,plain,
spl0_199,
inference(avatar_split_clause,[],[f56,f1886]) ).
fof(f1886,plain,
( spl0_199
<=> ! [X13,X14,X9,X7] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X14,X7,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f56,axiom,
! [X9,X7,X14,X13] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X9,X13),X14,X7,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).
fof(f1884,plain,
( spl0_198
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1796,f1591,f1882]) ).
fof(f1882,plain,
( spl0_198
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1591,plain,
( spl0_180
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_lessequals(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1796,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_180 ),
inference(factoring,[],[f1592]) ).
fof(f1592,plain,
( ! [X2,X3,X4] :
( c_lessequals(X4,X3,X2)
| c_lessequals(X3,X4,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1591]) ).
fof(f1880,plain,
spl0_197,
inference(avatar_split_clause,[],[f49,f1878]) ).
fof(f1878,plain,
( spl0_197
<=> ! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f49,axiom,
! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1876,plain,
spl0_196,
inference(avatar_split_clause,[],[f35,f1874]) ).
fof(f35,axiom,
! [X23] :
( ~ class_Orderings_Obot(X23)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X23)),v_x) = c_Orderings_Obot__class_Obot(X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f1872,plain,
spl0_195,
inference(avatar_split_clause,[],[f15,f1870]) ).
fof(f1870,plain,
( spl0_195
<=> ! [X6,X3] : c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X3)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f15,axiom,
! [X3,X6] : c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X3)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f1868,plain,
spl0_194,
inference(avatar_split_clause,[],[f14,f1866]) ).
fof(f1866,plain,
( spl0_194
<=> ! [X6,X15] : c_HOL_Oord__class_Oless(X15,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X15)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f14,axiom,
! [X6,X15] : c_HOL_Oord__class_Oless(X15,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X15)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1864,plain,
spl0_193,
inference(avatar_split_clause,[],[f5,f1862]) ).
fof(f1862,plain,
( spl0_193
<=> ! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f5,axiom,
! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f1860,plain,
spl0_192,
inference(avatar_split_clause,[],[f4,f1858]) ).
fof(f1858,plain,
( spl0_192
<=> ! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f4,axiom,
! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f1751,plain,
( spl0_191
| ~ spl0_26
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1733,f1563,f903,f1749]) ).
fof(f1749,plain,
( spl0_191
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f903,plain,
( spl0_26
<=> ! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1563,plain,
( spl0_173
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1733,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X0),X0,tc_nat)
| ~ spl0_26
| ~ spl0_173 ),
inference(resolution,[],[f1564,f904]) ).
fof(f904,plain,
( ! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_nat)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f1564,plain,
( ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,X7),tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f1711,plain,
( spl0_190
| ~ spl0_15
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1439,f1347,f850,f1709]) ).
fof(f1709,plain,
( spl0_190
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f850,plain,
( spl0_15
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1347,plain,
( spl0_132
<=> ! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X8,X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1439,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_15
| ~ spl0_132 ),
inference(resolution,[],[f1348,f852]) ).
fof(f852,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f1348,plain,
( ! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X8,X8,X2) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f1629,plain,
spl0_189,
inference(avatar_split_clause,[],[f728,f1627]) ).
fof(f1627,plain,
( spl0_189
<=> ! [X45,X2,X7] :
( c_Hoare__Mirabelle_Otriple__valid(X7,X45,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),X45,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f728,axiom,
! [X2,X7,X45] :
( c_Hoare__Mirabelle_Otriple__valid(X7,X45,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,X7),X45,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
fof(f1625,plain,
spl0_188,
inference(avatar_split_clause,[],[f727,f1623]) ).
fof(f1623,plain,
( spl0_188
<=> ! [X4,X3] :
( X3 = X4
| hAPP(c_Suc,X3) != hAPP(c_Suc,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f727,axiom,
! [X3,X4] :
( X3 = X4
| hAPP(c_Suc,X3) != hAPP(c_Suc,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
fof(f1621,plain,
spl0_187,
inference(avatar_split_clause,[],[f716,f1619]) ).
fof(f1619,plain,
( spl0_187
<=> ! [X2,X36,X68,X47] : c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X68),X47,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f716,axiom,
! [X2,X36,X47,X68] : c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X68),X47,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__0_0) ).
fof(f1617,plain,
spl0_186,
inference(avatar_split_clause,[],[f670,f1615]) ).
fof(f1615,plain,
( spl0_186
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f670,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1613,plain,
spl0_185,
inference(avatar_split_clause,[],[f669,f1611]) ).
fof(f669,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,hAPP(c_Suc,X6),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1609,plain,
spl0_184,
inference(avatar_split_clause,[],[f663,f1607]) ).
fof(f1607,plain,
( spl0_184
<=> ! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| c_lessequals(hAPP(c_Suc,X7),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f663,axiom,
! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| c_lessequals(hAPP(c_Suc,X7),X6,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1605,plain,
spl0_183,
inference(avatar_split_clause,[],[f662,f1603]) ).
fof(f1603,plain,
( spl0_183
<=> ! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X7),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f662,axiom,
! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X7),X6,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1601,plain,
spl0_182,
inference(avatar_split_clause,[],[f632,f1599]) ).
fof(f1599,plain,
( spl0_182
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f632,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1597,plain,
( spl0_181
| ~ spl0_23
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1472,f1415,f890,f1595]) ).
fof(f1595,plain,
( spl0_181
<=> ! [X0] :
( ~ hBOOL(hAPP(v_G,X0))
| c_Hoare__Mirabelle_Otriple__valid(v_na,X0,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f890,plain,
( spl0_23
<=> ! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(v_na,X3,t_a)
| ~ hBOOL(c_in(X3,v_G,tc_Hoare__Mirabelle_Otriple(t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1415,plain,
( spl0_149
<=> ! [X98,X2,X3] :
( ~ hBOOL(hAPP(X98,X3))
| hBOOL(c_in(X3,X98,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1472,plain,
( ! [X0] :
( ~ hBOOL(hAPP(v_G,X0))
| c_Hoare__Mirabelle_Otriple__valid(v_na,X0,t_a) )
| ~ spl0_23
| ~ spl0_149 ),
inference(resolution,[],[f1416,f891]) ).
fof(f891,plain,
( ! [X3] :
( ~ hBOOL(c_in(X3,v_G,tc_Hoare__Mirabelle_Otriple(t_a)))
| c_Hoare__Mirabelle_Otriple__valid(v_na,X3,t_a) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f1416,plain,
( ! [X2,X3,X98] :
( hBOOL(c_in(X3,X98,X2))
| ~ hBOOL(hAPP(X98,X3)) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1415]) ).
fof(f1593,plain,
spl0_180,
inference(avatar_split_clause,[],[f631,f1591]) ).
fof(f631,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_lessequals(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1589,plain,
spl0_179,
inference(avatar_split_clause,[],[f629,f1587]) ).
fof(f1587,plain,
( spl0_179
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f629,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1585,plain,
spl0_178,
inference(avatar_split_clause,[],[f628,f1583]) ).
fof(f1583,plain,
( spl0_178
<=> ! [X2,X9,X8] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X8,X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f628,axiom,
! [X2,X8,X9] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X9,X8,X2)
| ~ c_HOL_Oord__class_Oless(X8,X9,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1581,plain,
spl0_177,
inference(avatar_split_clause,[],[f536,f1579]) ).
fof(f1579,plain,
( spl0_177
<=> ! [X2,X79,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X79,c_HOL_Ozero__class_Ozero(tc_nat),X15,X2) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f536,axiom,
! [X2,X79,X15] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X79,c_HOL_Ozero__class_Ozero(tc_nat),X15,X2) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I1_J_0) ).
fof(f1577,plain,
spl0_176,
inference(avatar_split_clause,[],[f531,f1575]) ).
fof(f1575,plain,
( spl0_176
<=> ! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X6),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f531,axiom,
! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X6),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1573,plain,
spl0_175,
inference(avatar_split_clause,[],[f530,f1571]) ).
fof(f1571,plain,
( spl0_175
<=> ! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(X6,hAPP(c_Suc,X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f530,axiom,
! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_lessequals(X6,hAPP(c_Suc,X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1569,plain,
spl0_174,
inference(avatar_split_clause,[],[f527,f1567]) ).
fof(f1567,plain,
( spl0_174
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X6),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f527,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(c_Suc,X6),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1565,plain,
spl0_173,
inference(avatar_split_clause,[],[f526,f1563]) ).
fof(f526,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1561,plain,
spl0_172,
inference(avatar_split_clause,[],[f455,f1559]) ).
fof(f1559,plain,
( spl0_172
<=> ! [X11,X0,X12,X1] :
( X1 = X12
| c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OWhile(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f455,axiom,
! [X0,X11,X1,X12] :
( X1 = X12
| c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OWhile(X11,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
fof(f1557,plain,
spl0_171,
inference(avatar_split_clause,[],[f454,f1555]) ).
fof(f1555,plain,
( spl0_171
<=> ! [X11,X0,X12,X1] :
( X0 = X11
| c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OWhile(X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f454,axiom,
! [X0,X11,X1,X12] :
( X0 = X11
| c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OWhile(X11,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
fof(f1553,plain,
spl0_170,
inference(avatar_split_clause,[],[f424,f1551]) ).
fof(f1551,plain,
( spl0_170
<=> ! [X34,X11,X0,X32] :
( X32 = X34
| c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OAss(X34,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f424,axiom,
! [X0,X11,X34,X32] :
( X32 = X34
| c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OAss(X34,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).
fof(f1549,plain,
spl0_169,
inference(avatar_split_clause,[],[f423,f1547]) ).
fof(f1547,plain,
( spl0_169
<=> ! [X34,X0,X11,X32] :
( X0 = X11
| c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OAss(X34,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f423,axiom,
! [X0,X11,X34,X32] :
( X0 = X11
| c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OAss(X34,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).
fof(f1545,plain,
spl0_168,
inference(avatar_split_clause,[],[f386,f1543]) ).
fof(f1543,plain,
( spl0_168
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f386,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1541,plain,
spl0_167,
inference(avatar_split_clause,[],[f385,f1539]) ).
fof(f1539,plain,
( spl0_167
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f385,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1537,plain,
spl0_166,
inference(avatar_split_clause,[],[f341,f1535]) ).
fof(f1535,plain,
( spl0_166
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_Divides_Odiv__class_Omod(X6,X7,tc_nat) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f341,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_Divides_Odiv__class_Omod(X6,X7,tc_nat) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f1533,plain,
spl0_165,
inference(avatar_split_clause,[],[f336,f1531]) ).
fof(f1531,plain,
( spl0_165
<=> ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X6,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f336,axiom,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X6,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1529,plain,
spl0_164,
inference(avatar_split_clause,[],[f191,f1527]) ).
fof(f1527,plain,
( spl0_164
<=> ! [X2,X8,X58] :
( X8 = X58
| c_Option_Ooption_OSome(X58,X2) != c_Option_Ooption_OSome(X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f191,axiom,
! [X2,X58,X8] :
( X8 = X58
| c_Option_Ooption_OSome(X58,X2) != c_Option_Ooption_OSome(X8,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
fof(f1525,plain,
spl0_163,
inference(avatar_split_clause,[],[f138,f1523]) ).
fof(f1523,plain,
( spl0_163
<=> ! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X7),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f138,axiom,
! [X6,X7] :
( c_HOL_Oord__class_Oless(X7,X6,tc_nat)
| ~ c_lessequals(hAPP(c_Suc,X7),X6,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
fof(f1521,plain,
spl0_162,
inference(avatar_split_clause,[],[f135,f1519]) ).
fof(f1519,plain,
( spl0_162
<=> ! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_lessequals(hAPP(c_Suc,X6),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f135,axiom,
! [X6,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| c_lessequals(hAPP(c_Suc,X6),X7,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
fof(f1517,plain,
spl0_161,
inference(avatar_split_clause,[],[f130,f1515]) ).
fof(f1515,plain,
( spl0_161
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f130,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1513,plain,
( spl0_160
| ~ spl0_1
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1474,f1419,f780,f1510]) ).
fof(f1510,plain,
( spl0_160
<=> hBOOL(hAPP(v_Procs,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1419,plain,
( spl0_150
<=> ! [X98,X2,X3] :
( hBOOL(hAPP(X98,X3))
| ~ hBOOL(c_in(X3,X98,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1474,plain,
( hBOOL(hAPP(v_Procs,v_x))
| ~ spl0_1
| ~ spl0_150 ),
inference(resolution,[],[f1420,f782]) ).
fof(f1420,plain,
( ! [X2,X3,X98] :
( ~ hBOOL(c_in(X3,X98,X2))
| hBOOL(hAPP(X98,X3)) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f1508,plain,
spl0_159,
inference(avatar_split_clause,[],[f128,f1506]) ).
fof(f1506,plain,
( spl0_159
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f128,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1504,plain,
spl0_158,
inference(avatar_split_clause,[],[f123,f1502]) ).
fof(f1502,plain,
( spl0_158
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f123,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1500,plain,
spl0_157,
inference(avatar_split_clause,[],[f66,f1498]) ).
fof(f1498,plain,
( spl0_157
<=> ! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f66,axiom,
! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1496,plain,
spl0_156,
inference(avatar_split_clause,[],[f65,f1494]) ).
fof(f1494,plain,
( spl0_156
<=> ! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,X7),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f65,axiom,
! [X6,X7] :
( ~ c_lessequals(X6,X7,tc_nat)
| c_HOL_Oord__class_Oless(X6,hAPP(c_Suc,X7),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1492,plain,
spl0_155,
inference(avatar_split_clause,[],[f47,f1490]) ).
fof(f1490,plain,
( spl0_155
<=> ! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X8,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f47,axiom,
! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X8,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1488,plain,
spl0_154,
inference(avatar_split_clause,[],[f25,f1486]) ).
fof(f1486,plain,
( spl0_154
<=> ! [X18,X19,X20,X21] :
( X18 = X20
| c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OSemi(X20,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f25,axiom,
! [X21,X18,X19,X20] :
( X18 = X20
| c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OSemi(X20,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
fof(f1484,plain,
spl0_153,
inference(avatar_split_clause,[],[f24,f1482]) ).
fof(f1482,plain,
( spl0_153
<=> ! [X20,X21,X19,X18] :
( X19 = X21
| c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OSemi(X20,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f24,axiom,
! [X21,X18,X19,X20] :
( X19 = X21
| c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OSemi(X20,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
fof(f1480,plain,
spl0_152,
inference(avatar_split_clause,[],[f12,f1478]) ).
fof(f1478,plain,
( spl0_152
<=> ! [X13,X9,X14] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X14,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f12,axiom,
! [X9,X14,X13] :
( hBOOL(hAPP(X9,X14))
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X9,X13),X14,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
fof(f1471,plain,
( spl0_151
| ~ spl0_15
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1438,f1343,f850,f1469]) ).
fof(f1343,plain,
( spl0_131
<=> ! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Ozero__class_Ozero(X2),X2) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1438,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_15
| ~ spl0_131 ),
inference(resolution,[],[f1344,f852]) ).
fof(f1344,plain,
( ! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Ozero__class_Ozero(X2),X2) = X8 )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1343]) ).
fof(f1421,plain,
spl0_150,
inference(avatar_split_clause,[],[f730,f1419]) ).
fof(f730,axiom,
! [X2,X3,X98] :
( hBOOL(hAPP(X98,X3))
| ~ hBOOL(c_in(X3,X98,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1417,plain,
spl0_149,
inference(avatar_split_clause,[],[f729,f1415]) ).
fof(f729,axiom,
! [X2,X3,X98] :
( ~ hBOOL(hAPP(X98,X3))
| hBOOL(c_in(X3,X98,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1413,plain,
spl0_148,
inference(avatar_split_clause,[],[f622,f1411]) ).
fof(f1411,plain,
( spl0_148
<=> ! [X35,X10,X11,X34,X0,X12] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OCall(X34,X35,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f622,axiom,
! [X10,X0,X11,X34,X35,X12] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OCall(X34,X35,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
fof(f1409,plain,
spl0_147,
inference(avatar_split_clause,[],[f554,f1407]) ).
fof(f1407,plain,
( spl0_147
<=> ! [X81,X8,X80,X2] : c_Power_Opower_Opower(X80,X81,X8,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X80 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f554,axiom,
! [X2,X80,X81,X8] : c_Power_Opower_Opower(X80,X81,X8,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X80,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power_Opower_Opower__0_0) ).
fof(f1405,plain,
spl0_146,
inference(avatar_split_clause,[],[f547,f1403]) ).
fof(f1403,plain,
( spl0_146
<=> ! [X2,X40,X23] : c_Fun_Ofcomp(c_Fun_Oid(X2),X40,X2,X2,X23) = X40 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f547,axiom,
! [X2,X40,X23] : c_Fun_Ofcomp(c_Fun_Oid(X2),X40,X2,X2,X23) = X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
fof(f1401,plain,
spl0_145,
inference(avatar_split_clause,[],[f546,f1399]) ).
fof(f1399,plain,
( spl0_145
<=> ! [X2,X37,X23] : c_Fun_Ofcomp(X37,c_Fun_Oid(X23),X2,X23,X23) = X37 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f546,axiom,
! [X2,X37,X23] : c_Fun_Ofcomp(X37,c_Fun_Oid(X23),X2,X23,X23) = X37,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
fof(f1397,plain,
spl0_144,
inference(avatar_split_clause,[],[f545,f1395]) ).
fof(f545,axiom,
! [X17,X15] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X17),X15),X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1393,plain,
spl0_143,
inference(avatar_split_clause,[],[f544,f1391]) ).
fof(f1391,plain,
( spl0_143
<=> ! [X17,X15] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f544,axiom,
! [X17,X15] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X17),X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1389,plain,
spl0_142,
inference(avatar_split_clause,[],[f505,f1387]) ).
fof(f1387,plain,
( spl0_142
<=> ! [X14,X13,X3,X45] :
( c_Natural_Oevalc(X13,X14,X45)
| ~ c_Natural_Oevaln(X13,X14,X3,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f505,axiom,
! [X3,X45,X14,X13] :
( c_Natural_Oevalc(X13,X14,X45)
| ~ c_Natural_Oevaln(X13,X14,X3,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_1) ).
fof(f1385,plain,
spl0_141,
inference(avatar_split_clause,[],[f481,f1383]) ).
fof(f481,axiom,
! [X6] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),c_HOL_Ozero__class_Ozero(tc_nat)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f1381,plain,
spl0_140,
inference(avatar_split_clause,[],[f480,f1379]) ).
fof(f1379,plain,
( spl0_140
<=> ! [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_140])]) ).
fof(f480,axiom,
! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X7) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f1377,plain,
spl0_139,
inference(avatar_split_clause,[],[f421,f1375]) ).
fof(f1375,plain,
( spl0_139
<=> ! [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_139])]) ).
fof(f421,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/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1373,plain,
spl0_138,
inference(avatar_split_clause,[],[f416,f1371]) ).
fof(f416,axiom,
! [X2,X8,X22] : c_Set_Oinsert(X8,X22,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f1369,plain,
spl0_137,
inference(avatar_split_clause,[],[f355,f1367]) ).
fof(f1367,plain,
( spl0_137
<=> ! [X6,X3] : c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f355,axiom,
! [X3,X6] : c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X3),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
fof(f1365,plain,
( spl0_136
| ~ spl0_60
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1289,f1230,f1040,f1363]) ).
fof(f1363,plain,
( spl0_136
<=> ! [X0] : c_lessequals(X0,hAPP(c_Suc,X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1040,plain,
( spl0_60
<=> ! [X3] : c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1230,plain,
( spl0_106
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_lessequals(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1289,plain,
( ! [X0] : c_lessequals(X0,hAPP(c_Suc,X0),tc_nat)
| ~ spl0_60
| ~ spl0_106 ),
inference(resolution,[],[f1231,f1041]) ).
fof(f1041,plain,
( ! [X3] : c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X3),tc_nat)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1231,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_lessequals(X3,X4,tc_nat) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f1361,plain,
spl0_135,
inference(avatar_split_clause,[],[f354,f1359]) ).
fof(f354,axiom,
! [X6,X7] : c_lessequals(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X7),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f1357,plain,
spl0_134,
inference(avatar_split_clause,[],[f351,f1355]) ).
fof(f351,axiom,
! [X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1353,plain,
spl0_133,
inference(avatar_split_clause,[],[f222,f1351]) ).
fof(f1351,plain,
( spl0_133
<=> ! [X9,X43,X42] :
( ~ c_Com_OWT(X42)
| ~ c_Com_OWT(X43)
| c_Com_OWT(c_Com_Ocom_OCond(X9,X42,X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f222,axiom,
! [X9,X42,X43] :
( ~ c_Com_OWT(X42)
| ~ c_Com_OWT(X43)
| c_Com_OWT(c_Com_Ocom_OCond(X9,X42,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
fof(f1349,plain,
spl0_132,
inference(avatar_split_clause,[],[f151,f1347]) ).
fof(f151,axiom,
! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X8,X8,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1345,plain,
spl0_131,
inference(avatar_split_clause,[],[f150,f1343]) ).
fof(f150,axiom,
! [X2,X8] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X8,c_HOL_Ozero__class_Ozero(X2),X2) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1341,plain,
spl0_130,
inference(avatar_split_clause,[],[f75,f1339]) ).
fof(f1339,plain,
( spl0_130
<=> ! [X2,X40,X23] : c_Fun_Ocomp(c_Fun_Oid(X23),X40,X23,X23,X2) = X40 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f75,axiom,
! [X40,X2,X23] : c_Fun_Ocomp(c_Fun_Oid(X23),X40,X23,X23,X2) = X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__o_0) ).
fof(f1337,plain,
spl0_129,
inference(avatar_split_clause,[],[f74,f1335]) ).
fof(f1335,plain,
( spl0_129
<=> ! [X2,X37,X23] : c_Fun_Ocomp(X37,c_Fun_Oid(X2),X2,X23,X2) = X37 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f74,axiom,
! [X2,X37,X23] : c_Fun_Ocomp(X37,c_Fun_Oid(X2),X2,X23,X2) = X37,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__id_0) ).
fof(f1333,plain,
spl0_128,
inference(avatar_split_clause,[],[f72,f1331]) ).
fof(f72,axiom,
! [X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),hAPP(c_Suc,X6),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1329,plain,
spl0_127,
inference(avatar_split_clause,[],[f54,f1327]) ).
fof(f1327,plain,
( spl0_127
<=> ! [X18,X11,X34,X0,X35,X19] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OCond(X11,X18,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f54,axiom,
! [X0,X11,X18,X19,X34,X35] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OCond(X11,X18,X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
fof(f1325,plain,
spl0_126,
inference(avatar_split_clause,[],[f52,f1323]) ).
fof(f1323,plain,
( spl0_126
<=> ! [X10,X11,X20,X0,X12,X21] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OCond(X0,X20,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f52,axiom,
! [X21,X10,X0,X11,X12,X20] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OCond(X0,X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
fof(f1321,plain,
( spl0_125
| ~ spl0_17
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1288,f1226,f860,f1319]) ).
fof(f1319,plain,
( spl0_125
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f860,plain,
( spl0_17
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1226,plain,
( spl0_105
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1288,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_17
| ~ spl0_105 ),
inference(resolution,[],[f1227,f862]) ).
fof(f862,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f1227,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X3,X2) = X3 )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f1317,plain,
spl0_124,
inference(avatar_split_clause,[],[f22,f1315]) ).
fof(f1315,plain,
( spl0_124
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f22,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1313,plain,
spl0_123,
inference(avatar_split_clause,[],[f21,f1311]) ).
fof(f1311,plain,
( spl0_123
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f21,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1309,plain,
spl0_122,
inference(avatar_split_clause,[],[f10,f1307]) ).
fof(f1307,plain,
( spl0_122
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f10,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1305,plain,
spl0_121,
inference(avatar_split_clause,[],[f9,f1303]) ).
fof(f1303,plain,
( spl0_121
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f9,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1295,plain,
( spl0_120
| ~ spl0_17
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1287,f1218,f860,f1293]) ).
fof(f1293,plain,
( spl0_120
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1218,plain,
( spl0_103
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1287,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_17
| ~ spl0_103 ),
inference(resolution,[],[f1219,f862]) ).
fof(f1219,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X3,X2) = X3 )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f1284,plain,
spl0_119,
inference(avatar_split_clause,[],[f733,f1282]) ).
fof(f1282,plain,
( spl0_119
<=> ! [X35,X33] :
( X33 = X35
| c_Com_Ocom_OBODY(X35) != c_Com_Ocom_OBODY(X33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f733,axiom,
! [X35,X33] :
( X33 = X35
| c_Com_Ocom_OBODY(X35) != c_Com_Ocom_OBODY(X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
fof(f1280,plain,
spl0_118,
inference(avatar_split_clause,[],[f701,f1278]) ).
fof(f1278,plain,
( spl0_118
<=> ! [X68] :
( c_Com_OWT(c_Com_Ocom_OBODY(X68))
| c_Com_Obody(X68) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f701,axiom,
! [X68] :
( c_Com_OWT(c_Com_Ocom_OBODY(X68))
| c_Com_Obody(X68) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
fof(f1276,plain,
spl0_117,
inference(avatar_split_clause,[],[f630,f1274]) ).
fof(f1274,plain,
( spl0_117
<=> ! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| c_lessequals(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f630,axiom,
! [X6,X7] :
( c_lessequals(X6,X7,tc_nat)
| c_lessequals(X7,X6,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1272,plain,
spl0_116,
inference(avatar_split_clause,[],[f540,f1270]) ).
fof(f1270,plain,
( spl0_116
<=> ! [X43,X42] :
( ~ c_Com_OWT(X42)
| ~ c_Com_OWT(X43)
| c_Com_OWT(c_Com_Ocom_OSemi(X42,X43)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f540,axiom,
! [X42,X43] :
( ~ c_Com_OWT(X42)
| ~ c_Com_OWT(X43)
| c_Com_OWT(c_Com_Ocom_OSemi(X42,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
fof(f1268,plain,
spl0_115,
inference(avatar_split_clause,[],[f516,f1266]) ).
fof(f516,axiom,
! [X2,X3,X78] : hBOOL(c_in(X3,c_Set_Oinsert(X3,X78,X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f1264,plain,
spl0_114,
inference(avatar_split_clause,[],[f509,f1262]) ).
fof(f509,axiom,
! [X2,X3] : ~ hBOOL(c_in(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f1260,plain,
spl0_113,
inference(avatar_split_clause,[],[f488,f1258]) ).
fof(f1258,plain,
( spl0_113
<=> ! [X45,X7,X14] :
( X14 = X45
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X14,X7,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f488,axiom,
! [X45,X14,X7] :
( X14 = X45
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X14,X7,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
fof(f1256,plain,
spl0_112,
inference(avatar_split_clause,[],[f472,f1254]) ).
fof(f1254,plain,
( spl0_112
<=> ! [X11,X20,X21,X0,X32] : c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OAss(X32,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f472,axiom,
! [X21,X0,X11,X32,X20] : c_Com_Ocom_OCond(X0,X20,X21) != c_Com_Ocom_OAss(X32,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I27_J_0) ).
fof(f1252,plain,
spl0_111,
inference(avatar_split_clause,[],[f470,f1250]) ).
fof(f1250,plain,
( spl0_111
<=> ! [X35,X34,X0,X18,X19] : c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OCall(X34,X35,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f470,axiom,
! [X0,X18,X19,X34,X35] : c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OCall(X34,X35,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
fof(f1248,plain,
spl0_110,
inference(avatar_split_clause,[],[f468,f1246]) ).
fof(f1246,plain,
( spl0_110
<=> ! [X18,X19,X11,X0,X1] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OCond(X11,X18,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f468,axiom,
! [X0,X11,X1,X18,X19] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OCond(X11,X18,X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
fof(f1244,plain,
spl0_109,
inference(avatar_split_clause,[],[f451,f1242]) ).
fof(f1242,plain,
( spl0_109
<=> ! [X10,X11,X12,X21,X20] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OSemi(X20,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f451,axiom,
! [X21,X10,X11,X12,X20] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OSemi(X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
fof(f1240,plain,
spl0_108,
inference(avatar_split_clause,[],[f425,f1238]) ).
fof(f1238,plain,
( spl0_108
<=> ! [X35,X34,X11,X0,X32] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OAss(X32,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f425,axiom,
! [X0,X11,X34,X35,X32] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OAss(X32,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I33_J_0) ).
fof(f1236,plain,
spl0_107,
inference(avatar_split_clause,[],[f412,f1234]) ).
fof(f1234,plain,
( spl0_107
<=> ! [X2,X24,X25] : c_Nat_Onat_Onat__rec(X24,X25,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X24 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f412,axiom,
! [X2,X24,X25] : c_Nat_Onat_Onat__rec(X24,X25,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__rec__0_0) ).
fof(f1232,plain,
spl0_106,
inference(avatar_split_clause,[],[f383,f1230]) ).
fof(f383,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_lessequals(X3,X4,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
fof(f1228,plain,
spl0_105,
inference(avatar_split_clause,[],[f380,f1226]) ).
fof(f380,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1224,plain,
spl0_104,
inference(avatar_split_clause,[],[f359,f1222]) ).
fof(f1222,plain,
( spl0_104
<=> ! [X35,X34,X11,X0,X12] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OWhile(X11,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f359,axiom,
! [X0,X11,X34,X35,X12] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OWhile(X11,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).
fof(f1220,plain,
spl0_103,
inference(avatar_split_clause,[],[f350,f1218]) ).
fof(f350,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1216,plain,
spl0_102,
inference(avatar_split_clause,[],[f267,f1214]) ).
fof(f1214,plain,
( spl0_102
<=> ! [X36,X8,X67] :
( c_Com_OWT(c_Com_Ocom_OBODY(X36))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X67,X36,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f267,axiom,
! [X36,X8,X67] :
( c_Com_OWT(c_Com_Ocom_OBODY(X36))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X67,X36,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
fof(f1212,plain,
spl0_101,
inference(avatar_split_clause,[],[f266,f1210]) ).
fof(f1210,plain,
( spl0_101
<=> ! [X67,X8,X68] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(X68))
| c_Com_OWT(c_Com_Ocom_OCall(X67,X68,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f266,axiom,
! [X68,X8,X67] :
( ~ c_Com_OWT(c_Com_Ocom_OBODY(X68))
| c_Com_OWT(c_Com_Ocom_OCall(X67,X68,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
fof(f1208,plain,
spl0_100,
inference(avatar_split_clause,[],[f261,f1206]) ).
fof(f1206,plain,
( spl0_100
<=> ! [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_100])]) ).
fof(f261,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/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1204,plain,
spl0_99,
inference(avatar_split_clause,[],[f260,f1202]) ).
fof(f1202,plain,
( spl0_99
<=> ! [X2,X37,X23] : c_Fun_Oinj__on(X37,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f260,axiom,
! [X2,X37,X23] : c_Fun_Oinj__on(X37,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f1200,plain,
spl0_98,
inference(avatar_split_clause,[],[f232,f1198]) ).
fof(f1198,plain,
( spl0_98
<=> ! [X2,X62] : c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f232,axiom,
! [X2,X62] : c_Hoare__Mirabelle_Ohoare__derivs(X62,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
fof(f1196,plain,
spl0_97,
inference(avatar_split_clause,[],[f202,f1194]) ).
fof(f1194,plain,
( spl0_97
<=> ! [X32,X11,X0,X50,X1] : c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OLocal(X50,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f202,axiom,
! [X50,X0,X11,X1,X32] : c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OLocal(X50,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I22_J_0) ).
fof(f1192,plain,
spl0_96,
inference(avatar_split_clause,[],[f189,f1190]) ).
fof(f1190,plain,
( spl0_96
<=> ! [X2,X37,X3] : c_Nat_Onat_Onat__case(X3,X37,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f189,axiom,
! [X2,X3,X37] : c_Nat_Onat_Onat__case(X3,X37,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_0) ).
fof(f1188,plain,
spl0_95,
inference(avatar_split_clause,[],[f185,f1186]) ).
fof(f1186,plain,
( spl0_95
<=> ! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f185,axiom,
! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0R_0) ).
fof(f1184,plain,
spl0_94,
inference(avatar_split_clause,[],[f184,f1182]) ).
fof(f1182,plain,
( spl0_94
<=> ! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f184,axiom,
! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0L_0) ).
fof(f1180,plain,
spl0_93,
inference(avatar_split_clause,[],[f160,f1178]) ).
fof(f1178,plain,
( spl0_93
<=> ! [X18,X19,X20,X0,X21] : c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OCond(X0,X20,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f160,axiom,
! [X21,X0,X18,X19,X20] : c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OCond(X0,X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
fof(f1176,plain,
spl0_92,
inference(avatar_split_clause,[],[f119,f1174]) ).
fof(f1174,plain,
( spl0_92
<=> ! [X47,X23,X36,X2] : hAPP(c_COMBK(X36,X2,X23),X47) = X36 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f119,axiom,
! [X2,X36,X47,X23] : hAPP(c_COMBK(X36,X2,X23),X47) = X36,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f1172,plain,
spl0_91,
inference(avatar_split_clause,[],[f11,f1170]) ).
fof(f1170,plain,
( spl0_91
<=> ! [X10,X11,X0,X12,X1] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OLocal(X10,X11,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f11,axiom,
! [X10,X0,X11,X1,X12] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OLocal(X10,X11,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
fof(f1163,plain,
spl0_90,
inference(avatar_split_clause,[],[f763,f1161]) ).
fof(f1161,plain,
( spl0_90
<=> ! [X77,X2,X67] :
( X67 = X77
| ~ c_fequal(X67,X77,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f763,axiom,
! [X2,X77,X67] :
( X67 = X77
| ~ c_fequal(X67,X77,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1159,plain,
spl0_89,
inference(avatar_split_clause,[],[f708,f1157]) ).
fof(f1157,plain,
( spl0_89
<=> ! [X2,X3] : c_Option_Othe(c_Option_Ooption_OSome(X3,X2),X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f708,axiom,
! [X2,X3] : c_Option_Othe(c_Option_Ooption_OSome(X3,X2),X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
fof(f1155,plain,
spl0_88,
inference(avatar_split_clause,[],[f690,f1153]) ).
fof(f1153,plain,
( spl0_88
<=> ! [X11,X12,X35,X10] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OBODY(X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f690,axiom,
! [X10,X11,X35,X12] : c_Com_Ocom_OLocal(X10,X11,X12) != c_Com_Ocom_OBODY(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
fof(f1151,plain,
spl0_87,
inference(avatar_split_clause,[],[f687,f1149]) ).
fof(f1149,plain,
( spl0_87
<=> ! [X34,X0,X35,X33] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OBODY(X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f687,axiom,
! [X0,X34,X35,X33] : c_Com_Ocom_OCall(X34,X35,X0) != c_Com_Ocom_OBODY(X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).
fof(f1147,plain,
spl0_86,
inference(avatar_split_clause,[],[f681,f1145]) ).
fof(f1145,plain,
( spl0_86
<=> ! [X11,X18,X19,X35] : c_Com_Ocom_OCond(X11,X18,X19) != c_Com_Ocom_OBODY(X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f681,axiom,
! [X11,X18,X19,X35] : c_Com_Ocom_OCond(X11,X18,X19) != c_Com_Ocom_OBODY(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
fof(f1143,plain,
spl0_85,
inference(avatar_split_clause,[],[f625,f1141]) ).
fof(f1141,plain,
( spl0_85
<=> ! [X9,X43,X46] :
( c_Com_OWT(X43)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X9,X43,X46)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f625,axiom,
! [X46,X9,X43] :
( c_Com_OWT(X43)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X9,X43,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
fof(f1139,plain,
spl0_84,
inference(avatar_split_clause,[],[f624,f1137]) ).
fof(f1137,plain,
( spl0_84
<=> ! [X9,X43,X46] :
( c_Com_OWT(X46)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X9,X43,X46)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f624,axiom,
! [X46,X9,X43] :
( c_Com_OWT(X46)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X9,X43,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
fof(f1135,plain,
spl0_83,
inference(avatar_split_clause,[],[f549,f1133]) ).
fof(f1133,plain,
( spl0_83
<=> ! [X18,X0,X1,X19] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OSemi(X18,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f549,axiom,
! [X0,X1,X18,X19] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OSemi(X18,X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
fof(f1131,plain,
spl0_82,
inference(avatar_split_clause,[],[f499,f1129]) ).
fof(f1129,plain,
( spl0_82
<=> ! [X45,X14] :
( X14 = X45
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,X14,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f499,axiom,
! [X45,X14] :
( X14 = X45
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,X14,X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
fof(f1127,plain,
spl0_81,
inference(avatar_split_clause,[],[f466,f1125]) ).
fof(f466,axiom,
! [X7] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
fof(f1123,plain,
spl0_80,
inference(avatar_split_clause,[],[f465,f1121]) ).
fof(f465,axiom,
! [X7] : c_Orderings_Oord__class_Omax(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
fof(f1119,plain,
spl0_79,
inference(avatar_split_clause,[],[f463,f1117]) ).
fof(f1117,plain,
( spl0_79
<=> ! [X13,X77,X8] :
( c_Com_OWT(X13)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X77,X8,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f463,axiom,
! [X8,X77,X13] :
( c_Com_OWT(X13)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X77,X8,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
fof(f1115,plain,
spl0_78,
inference(avatar_split_clause,[],[f462,f1113]) ).
fof(f1113,plain,
( spl0_78
<=> ! [X13,X77,X8] :
( ~ c_Com_OWT(X13)
| c_Com_OWT(c_Com_Ocom_OLocal(X77,X8,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f462,axiom,
! [X8,X77,X13] :
( ~ c_Com_OWT(X13)
| c_Com_OWT(c_Com_Ocom_OLocal(X77,X8,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
fof(f1111,plain,
spl0_77,
inference(avatar_split_clause,[],[f432,f1109]) ).
fof(f432,axiom,
! [X2,X3,X22] : hBOOL(hAPP(c_Set_Oinsert(X3,X22,X2),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f1107,plain,
spl0_76,
inference(avatar_split_clause,[],[f413,f1105]) ).
fof(f1105,plain,
( spl0_76
<=> ! [X32,X11,X1,X0] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OAss(X32,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f413,axiom,
! [X0,X11,X1,X32] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OAss(X32,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).
fof(f1103,plain,
spl0_75,
inference(avatar_split_clause,[],[f361,f1101]) ).
fof(f1101,plain,
( spl0_75
<=> ! [X20,X32,X11,X21] : c_Com_Ocom_OSemi(X20,X21) != c_Com_Ocom_OAss(X32,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f361,axiom,
! [X21,X11,X32,X20] : c_Com_Ocom_OSemi(X20,X21) != c_Com_Ocom_OAss(X32,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).
fof(f1099,plain,
spl0_74,
inference(avatar_split_clause,[],[f334,f1097]) ).
fof(f1097,plain,
( spl0_74
<=> ! [X2,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f334,axiom,
! [X2,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f1095,plain,
spl0_73,
inference(avatar_split_clause,[],[f308,f1093]) ).
fof(f1093,plain,
( spl0_73
<=> ! [X6,X7] : c_lessequals(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f308,axiom,
! [X6,X7] : c_lessequals(c_Divides_Odiv__class_Omod(X6,X7,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
fof(f1091,plain,
spl0_72,
inference(avatar_split_clause,[],[f277,f1089]) ).
fof(f1089,plain,
( spl0_72
<=> ! [X6,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f277,axiom,
! [X6,X7] : c_lessequals(c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1087,plain,
spl0_71,
inference(avatar_split_clause,[],[f264,f1085]) ).
fof(f264,axiom,
! [X7] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X7),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
fof(f1083,plain,
spl0_70,
inference(avatar_split_clause,[],[f173,f1081]) ).
fof(f173,axiom,
! [X6] : c_HOL_Ominus__class_Ominus(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1079,plain,
spl0_69,
inference(avatar_split_clause,[],[f172,f1077]) ).
fof(f1077,plain,
( spl0_69
<=> ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X6,X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f172,axiom,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X6,X6,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1075,plain,
spl0_68,
inference(avatar_split_clause,[],[f23,f1073]) ).
fof(f23,axiom,
! [X2,X3] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1070,plain,
spl0_67,
inference(avatar_split_clause,[],[f741,f1068]) ).
fof(f1068,plain,
( spl0_67
<=> ! [X100,X99] :
( ~ class_Orderings_Obot(X100)
| class_Orderings_Obot(tc_fun(X99,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f741,axiom,
! [X99,X100] :
( ~ class_Orderings_Obot(X100)
| class_Orderings_Obot(tc_fun(X99,X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1066,plain,
spl0_66,
inference(avatar_split_clause,[],[f740,f1064]) ).
fof(f1064,plain,
( spl0_66
<=> ! [X100,X99] :
( ~ class_Orderings_Oorder(X100)
| class_Orderings_Oorder(tc_fun(X99,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f740,axiom,
! [X99,X100] :
( ~ class_Orderings_Oorder(X100)
| class_Orderings_Oorder(tc_fun(X99,X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1062,plain,
spl0_65,
inference(avatar_split_clause,[],[f739,f1060]) ).
fof(f1060,plain,
( spl0_65
<=> ! [X100,X99] :
( ~ class_Orderings_Opreorder(X100)
| class_Orderings_Opreorder(tc_fun(X99,X100)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f739,axiom,
! [X99,X100] :
( ~ class_Orderings_Opreorder(X100)
| class_Orderings_Opreorder(tc_fun(X99,X100)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1058,plain,
spl0_64,
inference(avatar_split_clause,[],[f689,f1056]) ).
fof(f1056,plain,
( spl0_64
<=> ! [X18,X19,X35] : c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OBODY(X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f689,axiom,
! [X18,X19,X35] : c_Com_Ocom_OSemi(X18,X19) != c_Com_Ocom_OBODY(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
fof(f1054,plain,
spl0_63,
inference(avatar_split_clause,[],[f683,f1052]) ).
fof(f1052,plain,
( spl0_63
<=> ! [X32,X11,X35] : c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OBODY(X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f683,axiom,
! [X11,X35,X32] : c_Com_Ocom_OAss(X32,X11) != c_Com_Ocom_OBODY(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).
fof(f1050,plain,
spl0_62,
inference(avatar_split_clause,[],[f679,f1048]) ).
fof(f1048,plain,
( spl0_62
<=> ! [X11,X12,X35] : c_Com_Ocom_OWhile(X11,X12) != c_Com_Ocom_OBODY(X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f679,axiom,
! [X11,X35,X12] : c_Com_Ocom_OWhile(X11,X12) != c_Com_Ocom_OBODY(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
fof(f1046,plain,
spl0_61,
inference(avatar_split_clause,[],[f652,f1044]) ).
fof(f1044,plain,
( spl0_61
<=> ! [X85] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X85) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f652,axiom,
! [X85] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X85),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f1042,plain,
spl0_60,
inference(avatar_split_clause,[],[f637,f1040]) ).
fof(f637,axiom,
! [X3] : c_HOL_Oord__class_Oless(X3,hAPP(c_Suc,X3),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f1038,plain,
spl0_59,
inference(avatar_split_clause,[],[f576,f1036]) ).
fof(f1036,plain,
( spl0_59
<=> ! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f576,axiom,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1034,plain,
spl0_58,
inference(avatar_split_clause,[],[f574,f1032]) ).
fof(f1032,plain,
( spl0_58
<=> ! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f574,axiom,
! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1030,plain,
spl0_57,
inference(avatar_split_clause,[],[f543,f1028]) ).
fof(f1028,plain,
( spl0_57
<=> ! [X34,X0,X35] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X34,X35,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f543,axiom,
! [X0,X34,X35] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X34,X35,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).
fof(f1026,plain,
spl0_56,
inference(avatar_split_clause,[],[f529,f1024]) ).
fof(f1024,plain,
( spl0_56
<=> ! [X7] : ~ c_lessequals(hAPP(c_Suc,X7),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f529,axiom,
! [X7] : ~ c_lessequals(hAPP(c_Suc,X7),X7,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1022,plain,
spl0_55,
inference(avatar_split_clause,[],[f491,f1020]) ).
fof(f1020,plain,
( spl0_55
<=> ! [X2,X3] : hAPP(c_Fun_Oid(X2),X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f491,axiom,
! [X2,X3] : hAPP(c_Fun_Oid(X2),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
fof(f1018,plain,
spl0_54,
inference(avatar_split_clause,[],[f464,f1016]) ).
fof(f1016,plain,
( spl0_54
<=> ! [X20,X21,X0] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X0,X20,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f464,axiom,
! [X21,X0,X20] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X0,X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
fof(f1014,plain,
spl0_53,
inference(avatar_split_clause,[],[f458,f1012]) ).
fof(f1012,plain,
( spl0_53
<=> ! [X13,X9] :
( c_Com_OWT(X13)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X9,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f458,axiom,
! [X9,X13] :
( c_Com_OWT(X13)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X9,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
fof(f1010,plain,
spl0_52,
inference(avatar_split_clause,[],[f457,f1008]) ).
fof(f1008,plain,
( spl0_52
<=> ! [X13,X9] :
( ~ c_Com_OWT(X13)
| c_Com_OWT(c_Com_Ocom_OWhile(X9,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f457,axiom,
! [X9,X13] :
( ~ c_Com_OWT(X13)
| c_Com_OWT(c_Com_Ocom_OWhile(X9,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_While_0) ).
fof(f1006,plain,
spl0_51,
inference(avatar_split_clause,[],[f411,f1004]) ).
fof(f1004,plain,
( spl0_51
<=> ! [X43,X46] :
( c_Com_OWT(X43)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X43,X46)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f411,axiom,
! [X46,X43] :
( c_Com_OWT(X43)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X43,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
fof(f1002,plain,
spl0_50,
inference(avatar_split_clause,[],[f410,f1000]) ).
fof(f1000,plain,
( spl0_50
<=> ! [X43,X46] :
( c_Com_OWT(X46)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X43,X46)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f410,axiom,
! [X46,X43] :
( c_Com_OWT(X46)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X43,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
fof(f998,plain,
spl0_49,
inference(avatar_split_clause,[],[f348,f996]) ).
fof(f996,plain,
( spl0_49
<=> ! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f348,axiom,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f994,plain,
spl0_48,
inference(avatar_split_clause,[],[f347,f992]) ).
fof(f992,plain,
( spl0_48
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f347,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f990,plain,
spl0_47,
inference(avatar_split_clause,[],[f346,f988]) ).
fof(f988,plain,
( spl0_47
<=> ! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f346,axiom,
! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f986,plain,
spl0_46,
inference(avatar_split_clause,[],[f337,f984]) ).
fof(f984,plain,
( spl0_46
<=> ! [X50,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X50,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f337,axiom,
! [X50,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X50,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
fof(f982,plain,
spl0_45,
inference(avatar_split_clause,[],[f244,f980]) ).
fof(f980,plain,
( spl0_45
<=> ! [X2,X4] : c_Option_Ooption_ONone(X2) != c_Option_Ooption_OSome(X4,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f244,axiom,
! [X2,X4] : c_Option_Ooption_ONone(X2) != c_Option_Ooption_OSome(X4,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
fof(f978,plain,
spl0_44,
inference(avatar_split_clause,[],[f118,f976]) ).
fof(f976,plain,
( spl0_44
<=> ! [X36,X2] : hAPP(c_COMBI(X2),X36) = X36 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f118,axiom,
! [X2,X36] : hAPP(c_COMBI(X2),X36) = X36,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
fof(f974,plain,
spl0_43,
inference(avatar_split_clause,[],[f99,f972]) ).
fof(f972,plain,
( spl0_43
<=> ! [X22,X2] : c_Fun_Oinj__on(c_Fun_Oid(X2),X22,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f99,axiom,
! [X2,X22] : c_Fun_Oinj__on(c_Fun_Oid(X2),X22,X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
fof(f970,plain,
spl0_42,
inference(avatar_split_clause,[],[f32,f968]) ).
fof(f968,plain,
( spl0_42
<=> ! [X22,X2] : c_Fun_Oinj__on(c_COMBI(X2),X22,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f32,axiom,
! [X2,X22] : c_Fun_Oinj__on(c_COMBI(X2),X22,X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
fof(f966,plain,
spl0_41,
inference(avatar_split_clause,[],[f721,f964]) ).
fof(f964,plain,
( spl0_41
<=> ! [X7] : hAPP(c_Suc,X7) != X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f721,axiom,
! [X7] : hAPP(c_Suc,X7) != X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f962,plain,
spl0_40,
inference(avatar_split_clause,[],[f649,f960]) ).
fof(f960,plain,
( spl0_40
<=> ! [X88] : c_Fun_Oinj__on(c_Suc,X88,tc_nat,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f649,axiom,
! [X88] : c_Fun_Oinj__on(c_Suc,X88,tc_nat,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__Suc_0) ).
fof(f958,plain,
spl0_39,
inference(avatar_split_clause,[],[f627,f956]) ).
fof(f956,plain,
( spl0_39
<=> ! [X20,X21] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X20,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f627,axiom,
! [X21,X20] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X20,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
fof(f954,plain,
spl0_38,
inference(avatar_split_clause,[],[f409,f952]) ).
fof(f952,plain,
( spl0_38
<=> ! [X34,X0] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X34,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f409,axiom,
! [X0,X34] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X34,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).
fof(f950,plain,
spl0_37,
inference(avatar_split_clause,[],[f387,f948]) ).
fof(f948,plain,
( spl0_37
<=> ! [X7,X14] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X14,X7,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f387,axiom,
! [X7,X14] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X14,X7,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
fof(f946,plain,
spl0_36,
inference(avatar_split_clause,[],[f292,f944]) ).
fof(f292,axiom,
! [X7] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f942,plain,
spl0_35,
inference(avatar_split_clause,[],[f233,f940]) ).
fof(f940,plain,
( spl0_35
<=> ! [X0,X1] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f233,axiom,
! [X0,X1] : c_Com_Ocom_OWhile(X0,X1) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
fof(f938,plain,
spl0_34,
inference(avatar_split_clause,[],[f96,f936]) ).
fof(f96,axiom,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f934,plain,
spl0_33,
inference(avatar_split_clause,[],[f738,f932]) ).
fof(f738,axiom,
! [X3] :
( ~ hBOOL(c_in(X3,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X3),c_Option_Othe(c_Com_Obody(X3),tc_Com_Ocom),hAPP(v_Q,X3),t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f930,plain,
spl0_32,
inference(avatar_split_clause,[],[f737,f928]) ).
fof(f928,plain,
( spl0_32
<=> ! [X3] :
( ~ hBOOL(c_in(X3,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X3),c_Com_Ocom_OBODY(X3),hAPP(v_Q,X3),t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f737,axiom,
! [X3] :
( ~ hBOOL(c_in(X3,v_Procs,tc_Com_Opname))
| c_Hoare__Mirabelle_Otriple__valid(v_na,c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,X3),c_Com_Ocom_OBODY(X3),hAPP(v_Q,X3),t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f926,plain,
spl0_31,
inference(avatar_split_clause,[],[f762,f924]) ).
fof(f924,plain,
( spl0_31
<=> ! [X2,X3] : c_fequal(X3,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f762,axiom,
! [X2,X3] : c_fequal(X3,X3,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f922,plain,
spl0_30,
inference(avatar_split_clause,[],[f693,f920]) ).
fof(f920,plain,
( spl0_30
<=> ! [X35] : c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f693,axiom,
! [X35] : c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
fof(f918,plain,
spl0_29,
inference(avatar_split_clause,[],[f647,f915]) ).
fof(f915,plain,
( spl0_29
<=> c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f647,axiom,
c_Orderings_Oorder__class_Omono(c_Suc,tc_nat,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mono__Suc_0) ).
fof(f913,plain,
spl0_28,
inference(avatar_split_clause,[],[f573,f911]) ).
fof(f911,plain,
( spl0_28
<=> ! [X3] : c_lessequals(X3,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f573,axiom,
! [X3] : c_lessequals(X3,X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f909,plain,
spl0_27,
inference(avatar_split_clause,[],[f360,f907]) ).
fof(f907,plain,
( spl0_27
<=> ! [X14] : c_Natural_Oevalc(c_Com_Ocom_OSKIP,X14,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f360,axiom,
! [X14] : c_Natural_Oevalc(c_Com_Ocom_OSKIP,X14,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
fof(f905,plain,
spl0_26,
inference(avatar_split_clause,[],[f344,f903]) ).
fof(f344,axiom,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f901,plain,
spl0_25,
inference(avatar_split_clause,[],[f259,f899]) ).
fof(f899,plain,
( spl0_25
<=> ! [X8,X67] : c_Com_OWT(c_Com_Ocom_OAss(X67,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f259,axiom,
! [X8,X67] : c_Com_OWT(c_Com_Ocom_OAss(X67,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).
fof(f897,plain,
~ spl0_24,
inference(avatar_split_clause,[],[f735,f894]) ).
fof(f735,axiom,
~ c_Hoare__Mirabelle_Otriple__valid(hAPP(c_Suc,v_na),c_Hoare__Mirabelle_Otriple_Otriple(hAPP(v_P,v_x),c_Com_Ocom_OBODY(v_x),hAPP(v_Q,v_x),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f892,plain,
spl0_23,
inference(avatar_split_clause,[],[f736,f890]) ).
fof(f736,axiom,
! [X3] :
( c_Hoare__Mirabelle_Otriple__valid(v_na,X3,t_a)
| ~ hBOOL(c_in(X3,v_G,tc_Hoare__Mirabelle_Otriple(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f888,plain,
spl0_22,
inference(avatar_split_clause,[],[f761,f885]) ).
fof(f761,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f883,plain,
spl0_21,
inference(avatar_split_clause,[],[f760,f880]) ).
fof(f880,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f760,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f878,plain,
spl0_20,
inference(avatar_split_clause,[],[f759,f875]) ).
fof(f875,plain,
( spl0_20
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f759,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f873,plain,
spl0_19,
inference(avatar_split_clause,[],[f758,f870]) ).
fof(f758,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f868,plain,
spl0_18,
inference(avatar_split_clause,[],[f757,f865]) ).
fof(f865,plain,
( spl0_18
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f757,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f863,plain,
spl0_17,
inference(avatar_split_clause,[],[f756,f860]) ).
fof(f756,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f858,plain,
spl0_16,
inference(avatar_split_clause,[],[f755,f855]) ).
fof(f855,plain,
( spl0_16
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f755,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f853,plain,
spl0_15,
inference(avatar_split_clause,[],[f754,f850]) ).
fof(f754,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f848,plain,
spl0_14,
inference(avatar_split_clause,[],[f753,f845]) ).
fof(f845,plain,
( spl0_14
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f753,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f843,plain,
spl0_13,
inference(avatar_split_clause,[],[f752,f840]) ).
fof(f840,plain,
( spl0_13
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f752,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f838,plain,
spl0_12,
inference(avatar_split_clause,[],[f751,f835]) ).
fof(f835,plain,
( spl0_12
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f751,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f833,plain,
spl0_11,
inference(avatar_split_clause,[],[f750,f830]) ).
fof(f830,plain,
( spl0_11
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f750,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f828,plain,
spl0_10,
inference(avatar_split_clause,[],[f749,f825]) ).
fof(f825,plain,
( spl0_10
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f749,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f823,plain,
spl0_9,
inference(avatar_split_clause,[],[f748,f820]) ).
fof(f820,plain,
( spl0_9
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f748,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f818,plain,
spl0_8,
inference(avatar_split_clause,[],[f747,f815]) ).
fof(f815,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f747,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f813,plain,
spl0_7,
inference(avatar_split_clause,[],[f746,f810]) ).
fof(f810,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f746,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f808,plain,
spl0_6,
inference(avatar_split_clause,[],[f745,f805]) ).
fof(f805,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f745,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f803,plain,
spl0_5,
inference(avatar_split_clause,[],[f744,f800]) ).
fof(f800,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f744,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f798,plain,
spl0_4,
inference(avatar_split_clause,[],[f743,f795]) ).
fof(f795,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f743,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f793,plain,
spl0_3,
inference(avatar_split_clause,[],[f742,f790]) ).
fof(f790,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f742,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f788,plain,
spl0_2,
inference(avatar_split_clause,[],[f255,f785]) ).
fof(f785,plain,
( spl0_2
<=> c_Com_OWT(c_Com_Ocom_OSKIP) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f255,axiom,
c_Com_OWT(c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
fof(f783,plain,
spl0_1,
inference(avatar_split_clause,[],[f734,f780]) ).
fof(f734,axiom,
hBOOL(c_in(v_x,v_Procs,tc_Com_Opname)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV854-1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 09:24:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (2300)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.40 % (2303)WARNING: value z3 for option sas not known
% 0.20/0.40 % (2302)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 % (2301)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.40 % (2304)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.40 % (2305)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 % (2306)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)
% 0.20/0.40 % (2303)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 % (2307)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)
% 0.20/0.50 TRYING [1]
% 0.20/0.52 TRYING [2]
% 1.83/0.70 TRYING [1]
% 1.83/0.71 % (2305)First to succeed.
% 2.50/0.73 % (2305)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2300"
% 2.50/0.73 % (2305)Refutation found. Thanks to Tanya!
% 2.50/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.50/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/0.74 % (2305)------------------------------
% 2.50/0.74 % (2305)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.50/0.74 % (2305)Termination reason: Refutation
% 2.50/0.74
% 2.50/0.74 % (2305)Memory used [KB]: 6138
% 2.50/0.74 % (2305)Time elapsed: 0.327 s
% 2.50/0.74 % (2305)Instructions burned: 827 (million)
% 2.50/0.74 % (2300)Success in time 0.372 s
%------------------------------------------------------------------------------