TSTP Solution File: SWV840-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV840-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:07:12 EDT 2024
% Result : Unsatisfiable 1.62s 0.62s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 779
% Syntax : Number of formulae : 1683 ( 512 unt; 0 def)
% Number of atoms : 4074 ( 736 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 4205 (1814 ~;1961 |; 0 &)
% ( 430 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 450 ( 448 usr; 431 prp; 0-9 aty)
% Number of functors : 75 ( 75 usr; 15 con; 0-10 aty)
% Number of variables : 5047 (5047 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5876,plain,
$false,
inference(avatar_sat_refutation,[],[f808,f813,f818,f823,f828,f833,f838,f843,f848,f853,f858,f863,f868,f873,f878,f883,f888,f893,f897,f901,f905,f909,f913,f917,f921,f925,f929,f933,f937,f941,f945,f949,f953,f957,f961,f965,f969,f973,f977,f981,f985,f989,f993,f997,f1001,f1005,f1009,f1014,f1018,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1050,f1054,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1088,f1092,f1096,f1100,f1104,f1108,f1112,f1116,f1120,f1124,f1128,f1132,f1136,f1144,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1179,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1211,f1215,f1219,f1238,f1250,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1362,f1366,f1370,f1374,f1378,f1382,f1413,f1437,f1441,f1445,f1449,f1453,f1457,f1461,f1465,f1469,f1473,f1477,f1481,f1485,f1489,f1493,f1497,f1501,f1561,f1571,f1575,f1579,f1583,f1587,f1597,f1601,f1605,f1609,f1613,f1617,f1621,f1625,f1629,f1633,f1642,f1714,f1818,f1822,f1826,f1833,f1837,f1841,f1845,f1849,f1853,f1858,f1864,f1871,f1876,f1880,f1884,f1888,f1892,f1896,f1900,f1904,f1908,f1912,f2018,f2050,f2054,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2199,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2331,f2398,f2407,f2412,f2417,f2421,f2425,f2429,f2433,f2437,f2441,f2445,f2449,f2453,f2457,f2461,f2465,f2469,f2473,f2477,f2481,f2485,f2489,f2493,f2497,f2501,f2505,f2570,f2763,f2774,f2778,f2782,f2786,f2790,f2794,f2798,f2803,f2807,f2811,f2815,f2819,f2823,f3021,f3025,f3029,f3065,f3069,f3073,f3077,f3121,f3125,f3129,f3133,f3137,f3141,f3145,f3149,f3153,f3157,f3165,f3169,f3173,f3177,f3334,f3338,f3342,f3346,f3350,f3428,f3432,f3436,f3440,f3444,f3448,f3452,f3456,f3460,f3464,f3468,f3473,f3487,f3492,f3500,f3505,f3618,f3648,f3652,f3656,f3660,f3664,f3668,f3672,f3676,f3680,f3685,f3716,f3721,f3992,f4026,f4030,f4035,f4048,f4052,f4056,f4060,f4064,f4069,f4138,f4203,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4509,f4515,f4521,f4525,f4530,f4568,f4573,f4610,f4616,f4634,f4638,f4642,f4646,f4651,f4666,f4671,f4693,f4751,f4757,f4777,f4782,f4787,f4792,f4797,f4801,f4902,f4907,f4924,f4929,f4946,f4951,f4982,f4988,f4999,f5004,f5065,f5071,f5189,f5217,f5247,f5252,f5292,f5298,f5303,f5309,f5315,f5319,f5338,f5343,f5375,f5380,f5402,f5410,f5445,f5453,f5459,f5471,f5477,f5489,f5495,f5499,f5511,f5517,f5529,f5535,f5546,f5552,f5572,f5578,f5592,f5598,f5608,f5614,f5624,f5630,f5634,f5648,f5654,f5668,f5674,f5688,f5695,f5724,f5731,f5743,f5750,f5776,f5783,f5795,f5799,f5804,f5820,f5872]) ).
fof(f5872,plain,
( spl0_225
| ~ spl0_338 ),
inference(avatar_contradiction_clause,[],[f5836]) ).
fof(f5836,plain,
( $false
| spl0_225
| ~ spl0_338 ),
inference(resolution,[],[f4245,f2416]) ).
fof(f2416,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G,t_a)
| spl0_225 ),
inference(avatar_component_clause,[],[f2414]) ).
fof(f2414,plain,
( spl0_225
<=> c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f4245,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0,X2)
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f4244]) ).
fof(f4244,plain,
( spl0_338
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f5820,plain,
spl0_430,
inference(avatar_split_clause,[],[f235,f5818]) ).
fof(f5818,plain,
( spl0_430
<=> ! [X0,X75,X74,X45,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f235,axiom,
! [X0,X7,X45,X74,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OBody_0) ).
fof(f5804,plain,
( spl0_429
| ~ spl0_120
| ~ spl0_287
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f5800,f5797,f3344,f1344,f5802]) ).
fof(f5802,plain,
( spl0_429
<=> ! [X0,X75,X5,X74,X45,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5))),X0)
| ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f1344,plain,
( spl0_120
<=> ! [X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f3344,plain,
( spl0_287
<=> ! [X6,X0] : hAPP(c_fequal(X0),X6) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f5797,plain,
( spl0_428
<=> ! [X0,X75,X5,X74,X45,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5))),X0)
| ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f5800,plain,
( ! [X0,X7,X45,X5,X74,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5))),X0)
| ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_428 ),
inference(forward_demodulation,[],[f5798,f3370]) ).
fof(f3370,plain,
( ! [X0,X1] : hAPP(c_fequal(X0),X1) = hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1)
| ~ spl0_120
| ~ spl0_287 ),
inference(superposition,[],[f3345,f1345]) ).
fof(f1345,plain,
( ! [X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f3345,plain,
( ! [X0,X6] : hAPP(c_fequal(X0),X6) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f3344]) ).
fof(f5798,plain,
( ! [X0,X7,X45,X5,X74,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5))),X0)
| ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f5797]) ).
fof(f5799,plain,
spl0_428,
inference(avatar_split_clause,[],[f727,f5797]) ).
fof(f727,plain,
! [X0,X7,X45,X5,X74,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5))),X0)
| ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
inference(forward_demodulation,[],[f726,f91]) ).
fof(f91,axiom,
! [X0,X7] : c_Collect(X7,X0) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f726,plain,
! [X0,X7,X45,X5,X74,X75] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5))),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
inference(forward_demodulation,[],[f546,f201]) ).
fof(f201,axiom,
! [X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f546,plain,
! [X0,X7,X45,X5,X74,X75] :
( ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5))),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
inference(definition_unfolding,[],[f359,f149]) ).
fof(f149,axiom,
! [X0,X6,X9] : c_Set_Oinsert(X6,X9,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X9,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
fof(f359,axiom,
! [X0,X7,X45,X5,X74,X75] :
( ~ hBOOL(c_in(X5,X75,tc_Com_Opname))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),hAPP(X7,X5)),hAPP(c_Com_Ocom_OBODY,X5)),hAPP(X45,X5)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X74,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0))),X45,tc_Com_Opname,tc_fun(X0,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X75,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body1_0) ).
fof(f5795,plain,
( spl0_427
| ~ spl0_384
| ~ spl0_424 ),
inference(avatar_split_clause,[],[f5751,f5748,f5313,f5793]) ).
fof(f5793,plain,
( spl0_427
<=> ! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f5313,plain,
( spl0_384
<=> ! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f5748,plain,
( spl0_424
<=> ! [X0,X5,X74,X45,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f5751,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) )
| ~ spl0_384
| ~ spl0_424 ),
inference(resolution,[],[f5749,f5314]) ).
fof(f5314,plain,
( ! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) )
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f5313]) ).
fof(f5749,plain,
( ! [X0,X7,X45,X5,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) )
| ~ spl0_424 ),
inference(avatar_component_clause,[],[f5748]) ).
fof(f5783,plain,
( spl0_426
| ~ spl0_120
| ~ spl0_287
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f5779,f5774,f3344,f1344,f5781]) ).
fof(f5781,plain,
( spl0_426
<=> ! [X69,X11,X0,X23,X74,X45,X7] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f5774,plain,
( spl0_425
<=> ! [X74,X11,X0,X23,X69,X45,X7] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f5779,plain,
( ! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_425 ),
inference(forward_demodulation,[],[f5778,f3370]) ).
fof(f5778,plain,
( ! [X0,X11,X69,X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_425 ),
inference(forward_demodulation,[],[f5777,f3370]) ).
fof(f5777,plain,
( ! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_425 ),
inference(forward_demodulation,[],[f5775,f3370]) ).
fof(f5775,plain,
( ! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0) )
| ~ spl0_425 ),
inference(avatar_component_clause,[],[f5774]) ).
fof(f5776,plain,
spl0_425,
inference(avatar_split_clause,[],[f790,f5774]) ).
fof(f790,plain,
! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0) ),
inference(forward_demodulation,[],[f789,f91]) ).
fof(f789,plain,
! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0) ),
inference(forward_demodulation,[],[f788,f201]) ).
fof(f788,plain,
! [X0,X11,X69,X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f787,f91]) ).
fof(f787,plain,
! [X0,X11,X69,X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f786,f201]) ).
fof(f786,plain,
! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f785,f91]) ).
fof(f785,plain,
! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f566,f201]) ).
fof(f566,plain,
! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(definition_unfolding,[],[f366,f149,f149,f149]) ).
fof(f366,axiom,
! [X0,X11,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OCond(X11,X23,X69)),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),X69),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OIf_0) ).
fof(f5750,plain,
( spl0_424
| ~ spl0_120
| ~ spl0_287
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f5746,f5741,f3344,f1344,f5748]) ).
fof(f5741,plain,
( spl0_423
<=> ! [X0,X5,X74,X45,X7] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f5746,plain,
( ! [X0,X7,X45,X5,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_423 ),
inference(forward_demodulation,[],[f5745,f3370]) ).
fof(f5745,plain,
( ! [X0,X7,X45,X5,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_423 ),
inference(forward_demodulation,[],[f5744,f3370]) ).
fof(f5744,plain,
( ! [X0,X7,X45,X5,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_423 ),
inference(forward_demodulation,[],[f5742,f3370]) ).
fof(f5742,plain,
( ! [X0,X7,X45,X5,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) )
| ~ spl0_423 ),
inference(avatar_component_clause,[],[f5741]) ).
fof(f5743,plain,
spl0_423,
inference(avatar_split_clause,[],[f692,f5741]) ).
fof(f692,plain,
! [X0,X7,X45,X5,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) ),
inference(forward_demodulation,[],[f691,f91]) ).
fof(f691,plain,
! [X0,X7,X45,X5,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) ),
inference(forward_demodulation,[],[f690,f91]) ).
fof(f690,plain,
! [X0,X7,X45,X5,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0) ),
inference(forward_demodulation,[],[f689,f201]) ).
fof(f689,plain,
! [X0,X7,X45,X5,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f688,f91]) ).
fof(f688,plain,
! [X0,X7,X45,X5,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f537,f201]) ).
fof(f537,plain,
! [X0,X7,X45,X5,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(definition_unfolding,[],[f431,f149,f149,f149]) ).
fof(f431,axiom,
! [X0,X7,X45,X5,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),X74,tc_Hoare__Mirabelle_Otriple(X0)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).
fof(f5731,plain,
( spl0_422
| ~ spl0_120
| ~ spl0_287
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f5727,f5722,f3344,f1344,f5729]) ).
fof(f5729,plain,
( spl0_422
<=> ! [X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f5722,plain,
( spl0_421
<=> ! [X7,X23,X74,X45] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f5727,plain,
( ! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),t_a) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_421 ),
inference(forward_demodulation,[],[f5726,f3370]) ).
fof(f5726,plain,
( ! [X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_421 ),
inference(forward_demodulation,[],[f5725,f3370]) ).
fof(f5725,plain,
( ! [X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_421 ),
inference(forward_demodulation,[],[f5723,f3370]) ).
fof(f5723,plain,
( ! [X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a) )
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f5722]) ).
fof(f5724,plain,
spl0_421,
inference(avatar_split_clause,[],[f687,f5722]) ).
fof(f687,plain,
! [X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a) ),
inference(forward_demodulation,[],[f686,f91]) ).
fof(f686,plain,
! [X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a) ),
inference(forward_demodulation,[],[f685,f201]) ).
fof(f685,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f684,f91]) ).
fof(f684,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f536,f201]) ).
fof(f536,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a))),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f358,f149,f149]) ).
fof(f358,axiom,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X23),c_COMBK(hAPP(X45,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_1) ).
fof(f5695,plain,
( spl0_420
| ~ spl0_120
| ~ spl0_287
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f5691,f5686,f3344,f1344,f5693]) ).
fof(f5693,plain,
( spl0_420
<=> ! [X69,X47,X0,X23,X74,X45,X7] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f5686,plain,
( spl0_419
<=> ! [X74,X47,X0,X23,X69,X45,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f5691,plain,
( ! [X0,X47,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_419 ),
inference(forward_demodulation,[],[f5690,f3370]) ).
fof(f5690,plain,
( ! [X0,X47,X69,X45,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_419 ),
inference(forward_demodulation,[],[f5689,f3370]) ).
fof(f5689,plain,
( ! [X0,X47,X69,X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_419 ),
inference(forward_demodulation,[],[f5687,f3370]) ).
fof(f5687,plain,
( ! [X0,X47,X69,X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f5686]) ).
fof(f5688,plain,
spl0_419,
inference(avatar_split_clause,[],[f784,f5686]) ).
fof(f784,plain,
! [X0,X47,X69,X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0) ),
inference(forward_demodulation,[],[f783,f91]) ).
fof(f783,plain,
! [X0,X47,X69,X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0) ),
inference(forward_demodulation,[],[f782,f201]) ).
fof(f782,plain,
! [X0,X47,X69,X45,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f781,f91]) ).
fof(f781,plain,
! [X0,X47,X69,X45,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f780,f201]) ).
fof(f780,plain,
! [X0,X47,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f779,f91]) ).
fof(f779,plain,
! [X0,X47,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f565,f201]) ).
fof(f565,plain,
! [X0,X47,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(definition_unfolding,[],[f417,f149,f149,f149]) ).
fof(f417,axiom,
! [X0,X47,X69,X7,X45,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X45),X69),X47),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSemi(X23,X69)),X47),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).
fof(f5674,plain,
( spl0_418
| ~ spl0_120
| ~ spl0_287
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f5670,f5666,f3344,f1344,f5672]) ).
fof(f5672,plain,
( spl0_418
<=> ! [X93,X45,X7,X23,X74,X43,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f5666,plain,
( spl0_417
<=> ! [X93,X43,X7,X23,X74,X45,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f5670,plain,
( ! [X1,X7,X45,X23,X74,X43,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_417 ),
inference(forward_demodulation,[],[f5669,f3370]) ).
fof(f5669,plain,
( ! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_417 ),
inference(forward_demodulation,[],[f5667,f3370]) ).
fof(f5667,plain,
( ! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_417 ),
inference(avatar_component_clause,[],[f5666]) ).
fof(f5668,plain,
spl0_417,
inference(avatar_split_clause,[],[f803,f5666]) ).
fof(f803,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f802,f91]) ).
fof(f802,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f801,f201]) ).
fof(f801,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f800,f91]) ).
fof(f800,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f570,f201]) ).
fof(f570,plain,
! [X1,X7,X45,X23,X74,X93,X43] :
( ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f397,f149,f149]) ).
fof(f397,axiom,
! [X1,X7,X45,X23,X74,X93,X43] :
( ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).
fof(f5654,plain,
( spl0_416
| ~ spl0_120
| ~ spl0_287
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f5650,f5646,f3344,f1344,f5652]) ).
fof(f5652,plain,
( spl0_416
<=> ! [X93,X45,X7,X23,X74,X43,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f5646,plain,
( spl0_415
<=> ! [X93,X43,X7,X23,X74,X45,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f5650,plain,
( ! [X1,X7,X45,X23,X74,X43,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_415 ),
inference(forward_demodulation,[],[f5649,f3370]) ).
fof(f5649,plain,
( ! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_415 ),
inference(forward_demodulation,[],[f5647,f3370]) ).
fof(f5647,plain,
( ! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_415 ),
inference(avatar_component_clause,[],[f5646]) ).
fof(f5648,plain,
spl0_415,
inference(avatar_split_clause,[],[f799,f5646]) ).
fof(f799,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f798,f91]) ).
fof(f798,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f797,f201]) ).
fof(f797,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f796,f91]) ).
fof(f796,plain,
! [X1,X7,X45,X23,X74,X43,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f569,f201]) ).
fof(f569,plain,
! [X1,X7,X45,X23,X74,X93,X43] :
( ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f399,f149,f149]) ).
fof(f399,axiom,
! [X1,X7,X45,X23,X74,X93,X43] :
( ~ hBOOL(hAPP(hAPP(X1,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| hBOOL(hAPP(hAPP(X43,X93),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(f5634,plain,
( spl0_414
| ~ spl0_120
| ~ spl0_287
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f5626,f5622,f3344,f1344,f5632]) ).
fof(f5632,plain,
( spl0_414
<=> ! [X93,X95,X7,X23,X74,X45,X94] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f5622,plain,
( spl0_412
<=> ! [X93,X95,X7,X23,X74,X45,X94] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f5626,plain,
( ! [X7,X45,X94,X95,X23,X74,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_412 ),
inference(forward_demodulation,[],[f5625,f3370]) ).
fof(f5625,plain,
( ! [X7,X45,X94,X95,X23,X74,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_412 ),
inference(forward_demodulation,[],[f5623,f3370]) ).
fof(f5623,plain,
( ! [X7,X45,X94,X95,X23,X74,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) )
| ~ spl0_412 ),
inference(avatar_component_clause,[],[f5622]) ).
fof(f5630,plain,
( spl0_413
| ~ spl0_144
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f5568,f5497,f1487,f5628]) ).
fof(f5628,plain,
( spl0_413
<=> ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f1487,plain,
( spl0_144
<=> ! [X0,X74,X90,X92] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,X90,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X92,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f5497,plain,
( spl0_399
<=> ! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f5568,plain,
( ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_144
| ~ spl0_399 ),
inference(resolution,[],[f5498,f1488]) ).
fof(f1488,plain,
( ! [X90,X0,X92,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,X90,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X92,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1487]) ).
fof(f5498,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f5497]) ).
fof(f5624,plain,
spl0_412,
inference(avatar_split_clause,[],[f795,f5622]) ).
fof(f795,plain,
! [X7,X45,X94,X95,X23,X74,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ),
inference(forward_demodulation,[],[f794,f91]) ).
fof(f794,plain,
! [X7,X45,X94,X95,X23,X74,X93] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ),
inference(forward_demodulation,[],[f793,f201]) ).
fof(f793,plain,
! [X7,X45,X94,X95,X23,X74,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f792,f91]) ).
fof(f792,plain,
! [X7,X45,X94,X95,X23,X74,X93] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f568,f201]) ).
fof(f568,plain,
! [X7,X45,X94,X95,X23,X74,X93] :
( ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f398,f149,f149]) ).
fof(f398,axiom,
! [X7,X45,X94,X95,X23,X74,X93] :
( ~ hBOOL(hAPP(hAPP(X95,X93),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| hBOOL(hAPP(hAPP(X94,X93),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).
fof(f5614,plain,
( spl0_411
| ~ spl0_120
| ~ spl0_287
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f5610,f5606,f3344,f1344,f5612]) ).
fof(f5612,plain,
( spl0_411
<=> ! [X45,X7,X23,X74,X43,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f5606,plain,
( spl0_410
<=> ! [X43,X7,X23,X74,X45,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f5610,plain,
( ! [X1,X7,X45,X23,X74,X43] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_410 ),
inference(forward_demodulation,[],[f5609,f3370]) ).
fof(f5609,plain,
( ! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_410 ),
inference(forward_demodulation,[],[f5607,f3370]) ).
fof(f5607,plain,
( ! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f5606]) ).
fof(f5608,plain,
spl0_410,
inference(avatar_split_clause,[],[f778,f5606]) ).
fof(f778,plain,
! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f777,f91]) ).
fof(f777,plain,
! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f776,f201]) ).
fof(f776,plain,
! [X1,X45,X7,X23,X74,X43] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f775,f91]) ).
fof(f775,plain,
! [X1,X45,X7,X23,X74,X43] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f564,f201]) ).
fof(f564,plain,
! [X1,X45,X7,X23,X74,X43] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f401,f149,f149]) ).
fof(f401,axiom,
! [X1,X45,X7,X23,X74,X43] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(f5598,plain,
( spl0_409
| ~ spl0_120
| ~ spl0_287
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f5594,f5590,f3344,f1344,f5596]) ).
fof(f5596,plain,
( spl0_409
<=> ! [X45,X7,X23,X74,X43,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f5590,plain,
( spl0_408
<=> ! [X43,X7,X23,X74,X45,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f5594,plain,
( ! [X1,X7,X45,X23,X74,X43] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_408 ),
inference(forward_demodulation,[],[f5593,f3370]) ).
fof(f5593,plain,
( ! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_408 ),
inference(forward_demodulation,[],[f5591,f3370]) ).
fof(f5591,plain,
( ! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) )
| ~ spl0_408 ),
inference(avatar_component_clause,[],[f5590]) ).
fof(f5592,plain,
spl0_408,
inference(avatar_split_clause,[],[f774,f5590]) ).
fof(f774,plain,
! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f773,f91]) ).
fof(f773,plain,
! [X1,X7,X45,X23,X74,X43] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43))) ),
inference(forward_demodulation,[],[f772,f201]) ).
fof(f772,plain,
! [X1,X45,X7,X23,X74,X43] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f771,f91]) ).
fof(f771,plain,
! [X1,X45,X7,X23,X74,X43] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f563,f201]) ).
fof(f563,plain,
! [X1,X45,X7,X23,X74,X43] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f406,f149,f149]) ).
fof(f406,axiom,
! [X1,X45,X7,X23,X74,X43] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X74,X7,X45,X23,X1,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X1),X23),X43),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).
fof(f5578,plain,
( spl0_407
| ~ spl0_120
| ~ spl0_287
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f5574,f5570,f3344,f1344,f5576]) ).
fof(f5576,plain,
( spl0_407
<=> ! [X95,X7,X23,X74,X45,X94] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f5570,plain,
( spl0_406
<=> ! [X95,X7,X23,X74,X45,X94] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f5574,plain,
( ! [X7,X45,X94,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_406 ),
inference(forward_demodulation,[],[f5573,f3370]) ).
fof(f5573,plain,
( ! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_406 ),
inference(forward_demodulation,[],[f5571,f3370]) ).
fof(f5571,plain,
( ! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94))) )
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f5570]) ).
fof(f5572,plain,
spl0_406,
inference(avatar_split_clause,[],[f770,f5570]) ).
fof(f770,plain,
! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94))) ),
inference(forward_demodulation,[],[f769,f91]) ).
fof(f769,plain,
! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94))) ),
inference(forward_demodulation,[],[f768,f201]) ).
fof(f768,plain,
! [X7,X45,X94,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f767,f91]) ).
fof(f767,plain,
! [X7,X45,X94,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f562,f201]) ).
fof(f562,plain,
! [X7,X45,X94,X95,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f404,f149,f149]) ).
fof(f404,axiom,
! [X7,X45,X94,X95,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__2(X7,X95,X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).
fof(f5552,plain,
( spl0_405
| ~ spl0_120
| ~ spl0_287
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f5548,f5544,f3344,f1344,f5550]) ).
fof(f5550,plain,
( spl0_405
<=> ! [X95,X7,X23,X74,X45,X94] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f5544,plain,
( spl0_404
<=> ! [X95,X7,X23,X74,X45,X94] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f5548,plain,
( ! [X7,X45,X94,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_404 ),
inference(forward_demodulation,[],[f5547,f3370]) ).
fof(f5547,plain,
( ! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_404 ),
inference(forward_demodulation,[],[f5545,f3370]) ).
fof(f5545,plain,
( ! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) )
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f5544]) ).
fof(f5546,plain,
spl0_404,
inference(avatar_split_clause,[],[f766,f5544]) ).
fof(f766,plain,
! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ),
inference(forward_demodulation,[],[f765,f91]) ).
fof(f765,plain,
! [X7,X45,X94,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94))) ),
inference(forward_demodulation,[],[f764,f201]) ).
fof(f764,plain,
! [X45,X7,X94,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f763,f91]) ).
fof(f763,plain,
! [X45,X7,X94,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f561,f201]) ).
fof(f561,plain,
! [X45,X7,X94,X95,X23,X74] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f408,f149,f149]) ).
fof(f408,axiom,
! [X45,X7,X94,X95,X23,X74] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X7,X95,X45,X94)),v_sko__Hoare__Mirabelle__Xconseq12__3(X7,X95,X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X94),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).
fof(f5535,plain,
( spl0_403
| ~ spl0_120
| ~ spl0_287
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5531,f5527,f3344,f1344,f5533]) ).
fof(f5533,plain,
( spl0_403
<=> ! [X11,X0,X23,X74,X7] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f5527,plain,
( spl0_402
<=> ! [X11,X0,X23,X74,X7] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f5531,plain,
( ! [X0,X11,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_402 ),
inference(forward_demodulation,[],[f5530,f3370]) ).
fof(f5530,plain,
( ! [X0,X11,X7,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_402 ),
inference(forward_demodulation,[],[f5528,f3370]) ).
fof(f5528,plain,
( ! [X0,X11,X7,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f5527]) ).
fof(f5529,plain,
spl0_402,
inference(avatar_split_clause,[],[f696,f5527]) ).
fof(f696,plain,
! [X0,X11,X7,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0) ),
inference(forward_demodulation,[],[f695,f91]) ).
fof(f695,plain,
! [X0,X11,X7,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0) ),
inference(forward_demodulation,[],[f694,f201]) ).
fof(f694,plain,
! [X0,X11,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f693,f91]) ).
fof(f693,plain,
! [X0,X11,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f538,f201]) ).
fof(f538,plain,
! [X0,X11,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0))),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(definition_unfolding,[],[f365,f149,f149]) ).
fof(f365,axiom,
! [X0,X11,X7,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),c_Hoare__Mirabelle_Opeek__and(X7,X11,X0)),X23),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OWhile(X11,X23)),c_Hoare__Mirabelle_Opeek__and(X7,c_Fun_Ocomp(c_Not,X11,tc_bool,tc_bool,tc_Com_Ostate),X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Loop_0) ).
fof(f5517,plain,
( spl0_401
| ~ spl0_120
| ~ spl0_287
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f5513,f5509,f3344,f1344,f5515]) ).
fof(f5515,plain,
( spl0_401
<=> ! [X95,X7,X23,X74,X45] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f5509,plain,
( spl0_400
<=> ! [X95,X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f5513,plain,
( ! [X45,X7,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_400 ),
inference(forward_demodulation,[],[f5512,f3370]) ).
fof(f5512,plain,
( ! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_400 ),
inference(forward_demodulation,[],[f5510,f3370]) ).
fof(f5510,plain,
( ! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f5509]) ).
fof(f5511,plain,
spl0_400,
inference(avatar_split_clause,[],[f762,f5509]) ).
fof(f762,plain,
! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ),
inference(forward_demodulation,[],[f761,f91]) ).
fof(f761,plain,
! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ),
inference(forward_demodulation,[],[f760,f201]) ).
fof(f760,plain,
! [X45,X7,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f759,f91]) ).
fof(f759,plain,
! [X45,X7,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f560,f201]) ).
fof(f560,plain,
! [X7,X45,X95,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f405,f149,f149]) ).
fof(f405,axiom,
! [X7,X45,X95,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).
fof(f5499,plain,
( spl0_399
| ~ spl0_62
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f5413,f5313,f1070,f5497]) ).
fof(f1070,plain,
( spl0_62
<=> ! [X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X8,tc_fun(X0,tc_bool)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f5413,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) )
| ~ spl0_62
| ~ spl0_384 ),
inference(superposition,[],[f5314,f1071]) ).
fof(f1071,plain,
( ! [X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X8,tc_fun(X0,tc_bool)) = X8
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f5495,plain,
( spl0_398
| ~ spl0_120
| ~ spl0_287
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f5491,f5487,f3344,f1344,f5493]) ).
fof(f5493,plain,
( spl0_398
<=> ! [X7,X23,X74,X45,X94] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f5487,plain,
( spl0_397
<=> ! [X7,X23,X74,X45,X94] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f5491,plain,
( ! [X7,X45,X94,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_397 ),
inference(forward_demodulation,[],[f5490,f3370]) ).
fof(f5490,plain,
( ! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_397 ),
inference(forward_demodulation,[],[f5488,f3370]) ).
fof(f5488,plain,
( ! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) )
| ~ spl0_397 ),
inference(avatar_component_clause,[],[f5487]) ).
fof(f5489,plain,
spl0_397,
inference(avatar_split_clause,[],[f758,f5487]) ).
fof(f758,plain,
! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ),
inference(forward_demodulation,[],[f757,f91]) ).
fof(f757,plain,
! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ),
inference(forward_demodulation,[],[f756,f201]) ).
fof(f756,plain,
! [X7,X45,X94,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f755,f91]) ).
fof(f755,plain,
! [X7,X45,X94,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f559,f201]) ).
fof(f559,plain,
! [X45,X7,X94,X23,X74] :
( hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f403,f149,f149]) ).
fof(f403,axiom,
! [X45,X7,X94,X23,X74] :
( hBOOL(hAPP(hAPP(X94,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_0) ).
fof(f5477,plain,
( spl0_396
| ~ spl0_120
| ~ spl0_287
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f5473,f5469,f3344,f1344,f5475]) ).
fof(f5475,plain,
( spl0_396
<=> ! [X7,X23,X74,X45,X94] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f5469,plain,
( spl0_395
<=> ! [X7,X23,X74,X45,X94] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f5473,plain,
( ! [X7,X45,X94,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_395 ),
inference(forward_demodulation,[],[f5472,f3370]) ).
fof(f5472,plain,
( ! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_395 ),
inference(forward_demodulation,[],[f5470,f3370]) ).
fof(f5470,plain,
( ! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) )
| ~ spl0_395 ),
inference(avatar_component_clause,[],[f5469]) ).
fof(f5471,plain,
spl0_395,
inference(avatar_split_clause,[],[f754,f5469]) ).
fof(f754,plain,
! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ),
inference(forward_demodulation,[],[f753,f91]) ).
fof(f753,plain,
! [X7,X45,X94,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94))) ),
inference(forward_demodulation,[],[f752,f201]) ).
fof(f752,plain,
! [X7,X45,X94,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f751,f91]) ).
fof(f751,plain,
! [X7,X45,X94,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f558,f201]) ).
fof(f558,plain,
! [X45,X7,X94,X23,X74] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f409,f149,f149]) ).
fof(f409,axiom,
! [X45,X7,X94,X23,X74] :
( ~ hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq2__1(X45,X94)),v_sko__Hoare__Mirabelle__Xconseq2__2(X45,X94)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X94),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_1) ).
fof(f5459,plain,
( spl0_394
| ~ spl0_120
| ~ spl0_287
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f5455,f5451,f3344,f1344,f5457]) ).
fof(f5457,plain,
( spl0_394
<=> ! [X95,X7,X23,X74,X45] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f5451,plain,
( spl0_393
<=> ! [X95,X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f5455,plain,
( ! [X45,X7,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_393 ),
inference(forward_demodulation,[],[f5454,f3370]) ).
fof(f5454,plain,
( ! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_393 ),
inference(forward_demodulation,[],[f5452,f3370]) ).
fof(f5452,plain,
( ! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) )
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f5451]) ).
fof(f5453,plain,
spl0_393,
inference(avatar_split_clause,[],[f750,f5451]) ).
fof(f750,plain,
! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ),
inference(forward_demodulation,[],[f749,f91]) ).
fof(f749,plain,
! [X7,X45,X95,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95))) ),
inference(forward_demodulation,[],[f748,f201]) ).
fof(f748,plain,
! [X45,X7,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f747,f91]) ).
fof(f747,plain,
! [X45,X7,X95,X23,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(forward_demodulation,[],[f557,f201]) ).
fof(f557,plain,
! [X7,X45,X95,X23,X74] :
( ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f407,f149,f149]) ).
fof(f407,axiom,
! [X7,X45,X95,X23,X74] :
( ~ hBOOL(hAPP(hAPP(X95,v_sko__Hoare__Mirabelle__Xconseq1__1(X7,X95)),v_sko__Hoare__Mirabelle__Xconseq1__2(X7,X95)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X95),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).
fof(f5445,plain,
spl0_392,
inference(avatar_split_clause,[],[f708,f5443]) ).
fof(f5443,plain,
( spl0_392
<=> ! [X6,X11,X0,X23,X69] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X11 = X69
| X6 = X69 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f708,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X11 = X69
| X6 = X69 ),
inference(forward_demodulation,[],[f707,f91]) ).
fof(f707,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X11 = X69
| X6 = X69 ),
inference(forward_demodulation,[],[f706,f91]) ).
fof(f706,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X11 = X69
| X6 = X69 ),
inference(forward_demodulation,[],[f705,f201]) ).
fof(f705,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X11 = X69
| X6 = X69 ),
inference(forward_demodulation,[],[f704,f91]) ).
fof(f704,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X11 = X69
| X6 = X69 ),
inference(forward_demodulation,[],[f703,f91]) ).
fof(f703,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),X0),tc_fun(X0,tc_bool))
| X11 = X69
| X6 = X69 ),
inference(forward_demodulation,[],[f540,f201]) ).
fof(f540,plain,
! [X0,X11,X6,X69,X23] :
( X11 = X69
| X6 = X69
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f426,f149,f149,f149,f149]) ).
fof(f426,axiom,
! [X0,X11,X6,X69,X23] :
( X11 = X69
| X6 = X69
| c_Set_Oinsert(X6,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X23,c_Set_Oinsert(X69,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
fof(f5410,plain,
( spl0_391
| ~ spl0_120
| ~ spl0_287
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f5406,f5400,f3344,f1344,f5408]) ).
fof(f5408,plain,
( spl0_391
<=> ! [X6,X11,X0,X23,X69] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X23),hAPP(c_fequal(X0),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f5400,plain,
( spl0_390
<=> ! [X6,X11,X0,X23,X69] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f5406,plain,
( ! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X23),hAPP(c_fequal(X0),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_390 ),
inference(forward_demodulation,[],[f5405,f3370]) ).
fof(f5405,plain,
( ! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X23),hAPP(c_fequal(X0),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_390 ),
inference(forward_demodulation,[],[f5404,f3370]) ).
fof(f5404,plain,
( ! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X23),hAPP(c_fequal(X0),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_390 ),
inference(forward_demodulation,[],[f5403,f3370]) ).
fof(f5403,plain,
( ! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_fequal(X0),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_390 ),
inference(forward_demodulation,[],[f5401,f3370]) ).
fof(f5401,plain,
( ! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f5400]) ).
fof(f5402,plain,
spl0_390,
inference(avatar_split_clause,[],[f702,f5400]) ).
fof(f702,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ),
inference(forward_demodulation,[],[f701,f91]) ).
fof(f701,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ),
inference(forward_demodulation,[],[f700,f91]) ).
fof(f700,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ),
inference(forward_demodulation,[],[f699,f201]) ).
fof(f699,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ),
inference(forward_demodulation,[],[f698,f91]) ).
fof(f698,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ),
inference(forward_demodulation,[],[f697,f91]) ).
fof(f697,plain,
! [X0,X11,X6,X69,X23] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),X0),tc_fun(X0,tc_bool))
| X6 = X23
| X11 = X23 ),
inference(forward_demodulation,[],[f539,f201]) ).
fof(f539,plain,
! [X0,X11,X6,X69,X23] :
( X6 = X23
| X11 = X23
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X69),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f427,f149,f149,f149,f149]) ).
fof(f427,axiom,
! [X0,X11,X6,X69,X23] :
( X6 = X23
| X11 = X23
| c_Set_Oinsert(X6,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X23,c_Set_Oinsert(X69,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
fof(f5380,plain,
( spl0_389
| ~ spl0_120
| ~ spl0_287
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f5376,f5373,f3344,f1344,f5378]) ).
fof(f5378,plain,
( spl0_389
<=> ! [X0,X8,X9,X1] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f5373,plain,
( spl0_388
<=> ! [X0,X8,X9,X1] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f5376,plain,
( ! [X0,X1,X8,X9] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_388 ),
inference(forward_demodulation,[],[f5374,f3370]) ).
fof(f5374,plain,
( ! [X0,X1,X8,X9] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f5373]) ).
fof(f5375,plain,
spl0_388,
inference(avatar_split_clause,[],[f652,f5373]) ).
fof(f652,plain,
! [X0,X1,X8,X9] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) ),
inference(forward_demodulation,[],[f521,f91]) ).
fof(f521,plain,
! [X0,X1,X8,X9] :
( hBOOL(c_in(X1,X9,X0))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f170,f149,f149]) ).
fof(f170,axiom,
! [X0,X1,X8,X9] :
( hBOOL(c_in(X1,X9,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X8,X0),X9,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
fof(f5343,plain,
( spl0_387
| ~ spl0_120
| ~ spl0_287
| ~ spl0_386 ),
inference(avatar_split_clause,[],[f5339,f5336,f3344,f1344,f5341]) ).
fof(f5341,plain,
( spl0_387
<=> ! [X0,X8,X9,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X9,tc_fun(X0,tc_bool))
| X8 = X9
| hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f5336,plain,
( spl0_386
<=> ! [X0,X8,X9,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X9,tc_fun(X0,tc_bool))
| X8 = X9
| hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f5339,plain,
( ! [X0,X1,X8,X9] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X9,tc_fun(X0,tc_bool))
| X8 = X9
| hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_386 ),
inference(forward_demodulation,[],[f5337,f3370]) ).
fof(f5337,plain,
( ! [X0,X1,X8,X9] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X9,tc_fun(X0,tc_bool))
| X8 = X9
| hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_386 ),
inference(avatar_component_clause,[],[f5336]) ).
fof(f5338,plain,
spl0_386,
inference(avatar_split_clause,[],[f791,f5336]) ).
fof(f791,plain,
! [X0,X1,X8,X9] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X9,tc_fun(X0,tc_bool))
| X8 = X9
| hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X9,X0)) ),
inference(forward_demodulation,[],[f567,f91]) ).
fof(f567,plain,
! [X0,X1,X8,X9] :
( X8 = X9
| hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X9,X0))
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X9,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f233,f149,f149]) ).
fof(f233,axiom,
! [X0,X1,X8,X9] :
( X8 = X9
| hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(X1,X9,X0))
| c_Set_Oinsert(X1,X8,X0) != c_Set_Oinsert(X1,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f5319,plain,
( spl0_385
| ~ spl0_120
| ~ spl0_287
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5311,f5307,f3344,f1344,f5317]) ).
fof(f5317,plain,
( spl0_385
<=> ! [X38,X0,X74,X90] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X38),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f5307,plain,
( spl0_383
<=> ! [X38,X0,X74,X90] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f5311,plain,
( ! [X38,X0,X90,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X38),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_383 ),
inference(forward_demodulation,[],[f5310,f3370]) ).
fof(f5310,plain,
( ! [X38,X0,X90,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),X38),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_383 ),
inference(forward_demodulation,[],[f5308,f3370]) ).
fof(f5308,plain,
( ! [X38,X0,X90,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f5307]) ).
fof(f5315,plain,
( spl0_384
| ~ spl0_120
| ~ spl0_201
| ~ spl0_287
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f5212,f4136,f3344,f2097,f1344,f5313]) ).
fof(f2097,plain,
( spl0_201
<=> ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f4136,plain,
( spl0_329
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f5212,plain,
( ! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) )
| ~ spl0_120
| ~ spl0_201
| ~ spl0_287
| ~ spl0_329 ),
inference(forward_demodulation,[],[f5192,f3370]) ).
fof(f5192,plain,
( ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_201
| ~ spl0_329 ),
inference(resolution,[],[f4137,f2098]) ).
fof(f2098,plain,
( ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2097]) ).
fof(f4137,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1,X2)
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f4136]) ).
fof(f5309,plain,
spl0_383,
inference(avatar_split_clause,[],[f725,f5307]) ).
fof(f725,plain,
! [X38,X0,X90,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) ),
inference(forward_demodulation,[],[f724,f91]) ).
fof(f724,plain,
! [X38,X0,X90,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),tc_Hoare__Mirabelle_Otriple(X0)),X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) ),
inference(forward_demodulation,[],[f723,f201]) ).
fof(f723,plain,
! [X38,X0,X90,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f545,f91]) ).
fof(f545,plain,
! [X38,X90,X0,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),tc_Hoare__Mirabelle_Otriple(X0)),X90,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),X38),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
inference(definition_unfolding,[],[f418,f149,f149]) ).
fof(f418,axiom,
! [X38,X90,X0,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(X38,X90,tc_Hoare__Mirabelle_Otriple(X0)),X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(X38,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
fof(f5303,plain,
spl0_382,
inference(avatar_split_clause,[],[f675,f5301]) ).
fof(f5301,plain,
( spl0_382
<=> ! [X0,X11,X18,X19,X16,X14,X6,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),X11) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f675,plain,
! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),X11) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f674,f91]) ).
fof(f674,plain,
! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),X11) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f673,f91]) ).
fof(f673,plain,
! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),X11) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f532,f201]) ).
fof(f532,plain,
! [X0,X11,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(hAPP(X17,X6),X11) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f382,f149,f149]) ).
fof(f382,axiom,
! [X0,X11,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X13,c_Set_Oinsert(X6,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) = hAPP(hAPP(X17,X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
fof(f5298,plain,
( spl0_381
| ~ spl0_120
| ~ spl0_287
| ~ spl0_380 ),
inference(avatar_split_clause,[],[f5294,f5290,f3344,f1344,f5296]) ).
fof(f5296,plain,
( spl0_381
<=> ! [X0,X11,X18,X19,X16,X14,X6,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f5290,plain,
( spl0_380
<=> ! [X0,X11,X18,X19,X16,X14,X6,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f5294,plain,
( ! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_380 ),
inference(forward_demodulation,[],[f5293,f3370]) ).
fof(f5293,plain,
( ! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_380 ),
inference(forward_demodulation,[],[f5291,f3370]) ).
fof(f5291,plain,
( ! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_380 ),
inference(avatar_component_clause,[],[f5290]) ).
fof(f5292,plain,
spl0_380,
inference(avatar_split_clause,[],[f672,f5290]) ).
fof(f672,plain,
! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f671,f91]) ).
fof(f671,plain,
! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f670,f91]) ).
fof(f670,plain,
! [X0,X11,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f531,f201]) ).
fof(f531,plain,
! [X0,X11,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(hAPP(X16,X6),X11) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f383,f149,f149]) ).
fof(f383,axiom,
! [X0,X11,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X12,c_Set_Oinsert(X6,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) = hAPP(hAPP(X16,X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
fof(f5252,plain,
( spl0_379
| ~ spl0_120
| ~ spl0_287
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5248,f5245,f3344,f1344,f5250]) ).
fof(f5250,plain,
( spl0_379
<=> ! [X9,X0,X6,X8] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,hAPP(c_fequal(X0),X6),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f5245,plain,
( spl0_378
<=> ! [X9,X0,X6,X8] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f5248,plain,
( ! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,hAPP(c_fequal(X0),X6),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ spl0_120
| ~ spl0_287
| ~ spl0_378 ),
inference(forward_demodulation,[],[f5246,f3370]) ).
fof(f5246,plain,
( ! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f5245]) ).
fof(f5247,plain,
spl0_378,
inference(avatar_split_clause,[],[f612,f5245]) ).
fof(f612,plain,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f611,f91]) ).
fof(f611,plain,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f499,f201]) ).
fof(f499,plain,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f384,f149,f149]) ).
fof(f384,axiom,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X6,X9,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
fof(f5217,plain,
( spl0_377
| ~ spl0_120
| ~ spl0_287
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f5190,f5187,f3344,f1344,f5215]) ).
fof(f5215,plain,
( spl0_377
<=> ! [X9,X0,X6,X8] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X6),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f5187,plain,
( spl0_376
<=> ! [X9,X0,X6,X8] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f5190,plain,
( ! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),hAPP(c_fequal(X0),X6),tc_fun(X0,tc_bool))
| ~ spl0_120
| ~ spl0_287
| ~ spl0_376 ),
inference(forward_demodulation,[],[f5188,f3370]) ).
fof(f5188,plain,
( ! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),tc_fun(X0,tc_bool))
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f5187]) ).
fof(f5189,plain,
spl0_376,
inference(avatar_split_clause,[],[f610,f5187]) ).
fof(f610,plain,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f609,f91]) ).
fof(f609,plain,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f498,f201]) ).
fof(f498,plain,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f385,f149,f149]) ).
fof(f385,axiom,
! [X0,X8,X6,X9] : c_HOL_Ominus__class_Ominus(X8,c_Set_Oinsert(X6,X9,X0),tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
fof(f5071,plain,
( spl0_375
| ~ spl0_120
| ~ spl0_287
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f5067,f5063,f3344,f1344,f5069]) ).
fof(f5069,plain,
( spl0_375
<=> ! [X24,X0,X31,X6,X9] : c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X24),X6),X9,tc_fun(X24,tc_bool)),X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),hAPP(X31,X6)),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f5063,plain,
( spl0_374
<=> ! [X24,X9,X0,X31,X6] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X31,X6)),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X9,tc_fun(X24,tc_bool)),X24,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f5067,plain,
( ! [X31,X0,X6,X9,X24] : c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X24),X6),X9,tc_fun(X24,tc_bool)),X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),hAPP(X31,X6)),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool))
| ~ spl0_120
| ~ spl0_287
| ~ spl0_374 ),
inference(forward_demodulation,[],[f5066,f3370]) ).
fof(f5066,plain,
( ! [X31,X0,X6,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X31,X6)),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X24),X6),X9,tc_fun(X24,tc_bool)),X24,X0)
| ~ spl0_120
| ~ spl0_287
| ~ spl0_374 ),
inference(forward_demodulation,[],[f5064,f3370]) ).
fof(f5064,plain,
( ! [X31,X0,X6,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X31,X6)),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X9,tc_fun(X24,tc_bool)),X24,X0)
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f5063]) ).
fof(f5065,plain,
spl0_374,
inference(avatar_split_clause,[],[f597,f5063]) ).
fof(f597,plain,
! [X31,X0,X6,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X31,X6)),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)) = c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X9,tc_fun(X24,tc_bool)),X24,X0),
inference(forward_demodulation,[],[f596,f91]) ).
fof(f596,plain,
! [X31,X0,X6,X9,X24] : c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X24),X9,tc_fun(X24,tc_bool)),X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X31,X6)),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f490,f91]) ).
fof(f490,plain,
! [X31,X0,X6,X9,X24] : c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X24),X9,tc_fun(X24,tc_bool)),X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),hAPP(X31,X6)),X0),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f221,f149,f149]) ).
fof(f221,axiom,
! [X31,X0,X6,X9,X24] : c_Set_Oimage(X31,c_Set_Oinsert(X6,X9,X24),X24,X0) = c_Set_Oinsert(hAPP(X31,X6),c_Set_Oimage(X31,X9,X24,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f5004,plain,
( spl0_373
| ~ spl0_120
| ~ spl0_287
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f5000,f4997,f3344,f1344,f5002]) ).
fof(f5002,plain,
( spl0_373
<=> ! [X10,X0,X6,X73] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X10,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X10,X73,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f4997,plain,
( spl0_372
<=> ! [X10,X0,X6,X73] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X10,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X10,X73,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f5000,plain,
( ! [X10,X0,X73,X6] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X10,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X10,X73,tc_fun(X0,tc_bool)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_372 ),
inference(forward_demodulation,[],[f4998,f3370]) ).
fof(f4998,plain,
( ! [X10,X0,X73,X6] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X10,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X10,X73,tc_fun(X0,tc_bool)) )
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f4997]) ).
fof(f4999,plain,
spl0_372,
inference(avatar_split_clause,[],[f654,f4997]) ).
fof(f654,plain,
! [X10,X0,X73,X6] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X10,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ c_lessequals(X10,X73,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f523,f91]) ).
fof(f523,plain,
! [X10,X73,X0,X6] :
( ~ c_lessequals(X10,X73,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X10,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f218,f149,f149]) ).
fof(f218,axiom,
! [X10,X73,X0,X6] :
( ~ c_lessequals(X10,X73,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X6,X10,X0),c_Set_Oinsert(X6,X73,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f4988,plain,
( spl0_371
| ~ spl0_120
| ~ spl0_287
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f4984,f4980,f3344,f1344,f4986]) ).
fof(f4986,plain,
( spl0_371
<=> ! [X6,X0,X11] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X6 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f4980,plain,
( spl0_370
<=> ! [X6,X0,X11] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X6 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f4984,plain,
( ! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X6 = X11 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_370 ),
inference(forward_demodulation,[],[f4983,f3370]) ).
fof(f4983,plain,
( ! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X6 = X11 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_370 ),
inference(forward_demodulation,[],[f4981,f3370]) ).
fof(f4981,plain,
( ! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X6 = X11 )
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f4980]) ).
fof(f4982,plain,
spl0_370,
inference(avatar_split_clause,[],[f632,f4980]) ).
fof(f632,plain,
! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X6 = X11 ),
inference(forward_demodulation,[],[f631,f91]) ).
fof(f631,plain,
! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| X6 = X11 ),
inference(forward_demodulation,[],[f509,f91]) ).
fof(f509,plain,
! [X0,X11,X6] :
( X6 = X11
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f437,f149,f149]) ).
fof(f437,axiom,
! [X0,X11,X6] :
( X6 = X11
| c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f4951,plain,
( spl0_369
| ~ spl0_120
| ~ spl0_287
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f4947,f4944,f3344,f1344,f4949]) ).
fof(f4949,plain,
( spl0_369
<=> ! [X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f4944,plain,
( spl0_368
<=> ! [X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f4947,plain,
( ! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_368 ),
inference(forward_demodulation,[],[f4945,f3370]) ).
fof(f4945,plain,
( ! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23))) )
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f4944]) ).
fof(f4946,plain,
spl0_368,
inference(avatar_split_clause,[],[f683,f4944]) ).
fof(f683,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23))) ),
inference(forward_demodulation,[],[f682,f91]) ).
fof(f682,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23))) ),
inference(forward_demodulation,[],[f535,f201]) ).
fof(f535,plain,
! [X7,X45,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f400,f149]) ).
fof(f400,axiom,
! [X7,X45,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X74,X7,X45,X23)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(f4929,plain,
( spl0_367
| ~ spl0_120
| ~ spl0_287
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f4925,f4922,f3344,f1344,f4927]) ).
fof(f4927,plain,
( spl0_367
<=> ! [X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f4922,plain,
( spl0_366
<=> ! [X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f4925,plain,
( ! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_366 ),
inference(forward_demodulation,[],[f4923,f3370]) ).
fof(f4923,plain,
( ! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23))) )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f4922]) ).
fof(f4924,plain,
spl0_366,
inference(avatar_split_clause,[],[f681,f4922]) ).
fof(f681,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23))) ),
inference(forward_demodulation,[],[f680,f91]) ).
fof(f680,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23))) ),
inference(forward_demodulation,[],[f534,f201]) ).
fof(f534,plain,
! [X7,X45,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f410,f149]) ).
fof(f410,axiom,
! [X7,X45,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xescape__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X74,X7,X45,X23)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).
fof(f4907,plain,
( spl0_365
| ~ spl0_120
| ~ spl0_287
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f4903,f4900,f3344,f1344,f4905]) ).
fof(f4905,plain,
( spl0_365
<=> ! [X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f4900,plain,
( spl0_364
<=> ! [X7,X23,X74,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f4903,plain,
( ! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23))) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_364 ),
inference(forward_demodulation,[],[f4901,f3370]) ).
fof(f4901,plain,
( ! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23))) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f4900]) ).
fof(f4902,plain,
spl0_364,
inference(avatar_split_clause,[],[f679,f4900]) ).
fof(f679,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23))) ),
inference(forward_demodulation,[],[f678,f91]) ).
fof(f678,plain,
! [X7,X45,X23,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23))) ),
inference(forward_demodulation,[],[f533,f201]) ).
fof(f533,plain,
! [X7,X45,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
inference(definition_unfolding,[],[f402,f149]) ).
fof(f402,axiom,
! [X7,X45,X23,X74] :
( hBOOL(hAPP(hAPP(X7,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X74,X7,X45,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X74,X7,X45,X23)))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_0) ).
fof(f4801,plain,
( spl0_363
| ~ spl0_5
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f4694,f3340,f825,f4799]) ).
fof(f4799,plain,
( spl0_363
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f825,plain,
( spl0_5
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f3340,plain,
( spl0_286
<=> ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f4694,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,tc_nat)) = X0
| ~ spl0_5
| ~ spl0_286 ),
inference(resolution,[],[f3341,f827]) ).
fof(f827,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f3341,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0 )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f3340]) ).
fof(f4797,plain,
( spl0_362
| ~ spl0_120
| ~ spl0_287
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4793,f4790,f3344,f1344,f4795]) ).
fof(f4795,plain,
( spl0_362
<=> ! [X24,X0,X6,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X24),X6),X8,tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f4790,plain,
( spl0_361
<=> ! [X24,X0,X6,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X8,tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f4793,plain,
( ! [X0,X8,X6,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X24),X6),X8,tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool))
| ~ spl0_120
| ~ spl0_287
| ~ spl0_361 ),
inference(forward_demodulation,[],[f4791,f3370]) ).
fof(f4791,plain,
( ! [X0,X8,X6,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X8,tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool))
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f4790]) ).
fof(f4792,plain,
spl0_361,
inference(avatar_split_clause,[],[f608,f4790]) ).
fof(f608,plain,
! [X0,X8,X6,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X8,tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f497,f91]) ).
fof(f497,plain,
! [X0,X8,X6,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X6),X24),X8,tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f269,f149]) ).
fof(f269,axiom,
! [X0,X8,X6,X9,X24] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(X6,X8,X24),X9,X24,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
fof(f4787,plain,
spl0_360,
inference(avatar_split_clause,[],[f669,f4785]) ).
fof(f4785,plain,
( spl0_360
<=> ! [X0,X18,X8,X19,X16,X14,X6,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),hAPP(X12,X8)) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f669,plain,
! [X0,X18,X8,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X16,X6),hAPP(X12,X8)) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f530,f91]) ).
fof(f530,plain,
! [X0,X18,X8,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(hAPP(X16,X6),hAPP(X12,X8)) = hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X8,tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f223,f149]) ).
fof(f223,axiom,
! [X0,X18,X8,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X12,c_Set_Oinsert(X6,X8,X0)) = hAPP(hAPP(X16,X6),hAPP(X12,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
fof(f4782,plain,
( spl0_359
| ~ spl0_120
| ~ spl0_287
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4778,f4775,f3344,f1344,f4780]) ).
fof(f4780,plain,
( spl0_359
<=> ! [X0,X18,X8,X19,X16,X14,X6,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),hAPP(X13,X8)) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X8,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f4775,plain,
( spl0_358
<=> ! [X0,X18,X8,X19,X16,X14,X6,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),hAPP(X13,X8)) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f4778,plain,
( ! [X0,X18,X8,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),hAPP(X13,X8)) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X8,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_358 ),
inference(forward_demodulation,[],[f4776,f3370]) ).
fof(f4776,plain,
( ! [X0,X18,X8,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),hAPP(X13,X8)) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f4775]) ).
fof(f4777,plain,
spl0_358,
inference(avatar_split_clause,[],[f668,f4775]) ).
fof(f668,plain,
! [X0,X18,X8,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(hAPP(X17,X6),hAPP(X13,X8)) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f529,f91]) ).
fof(f529,plain,
! [X0,X18,X8,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(hAPP(X17,X6),hAPP(X13,X8)) = hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X8,tc_fun(X0,tc_bool))) ),
inference(definition_unfolding,[],[f222,f149]) ).
fof(f222,axiom,
! [X0,X18,X8,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X13,c_Set_Oinsert(X6,X8,X0)) = hAPP(hAPP(X17,X6),hAPP(X13,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
fof(f4757,plain,
( spl0_357
| ~ spl0_120
| ~ spl0_122
| ~ spl0_123
| ~ spl0_287
| ~ spl0_333
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f4753,f4749,f4224,f3344,f1356,f1352,f1344,f4755]) ).
fof(f4755,plain,
( spl0_357
<=> ! [X0,X1,X8] :
( c_HOL_Ominus__class_Ominus(X8,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)) = X8
| hBOOL(c_in(X1,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f1352,plain,
( spl0_122
<=> ! [X9,X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1356,plain,
( spl0_123
<=> ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X8,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f4224,plain,
( spl0_333
<=> ! [X10,X0,X9,X8] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X8,X10,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4749,plain,
( spl0_356
<=> ! [X0,X1,X8] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X8
| hBOOL(c_in(X1,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f4753,plain,
( ! [X0,X1,X8] :
( c_HOL_Ominus__class_Ominus(X8,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool)) = X8
| hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_120
| ~ spl0_122
| ~ spl0_123
| ~ spl0_287
| ~ spl0_333
| ~ spl0_356 ),
inference(forward_demodulation,[],[f4752,f3370]) ).
fof(f4752,plain,
( ! [X0,X1,X8] :
( c_HOL_Ominus__class_Ominus(X8,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X8
| hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_122
| ~ spl0_123
| ~ spl0_333
| ~ spl0_356 ),
inference(forward_demodulation,[],[f4750,f4364]) ).
fof(f4364,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ spl0_122
| ~ spl0_123
| ~ spl0_333 ),
inference(forward_demodulation,[],[f4317,f1353]) ).
fof(f1353,plain,
( ! [X0,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = X9
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1352]) ).
fof(f4317,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_123
| ~ spl0_333 ),
inference(superposition,[],[f4225,f1357]) ).
fof(f1357,plain,
( ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X8,X8,tc_fun(X0,tc_bool))
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1356]) ).
fof(f4225,plain,
( ! [X10,X0,X8,X9] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X8,X10,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f4224]) ).
fof(f4750,plain,
( ! [X0,X1,X8] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X8
| hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f4749]) ).
fof(f4751,plain,
spl0_356,
inference(avatar_split_clause,[],[f651,f4749]) ).
fof(f651,plain,
! [X0,X1,X8] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool)) = X8
| hBOOL(c_in(X1,X8,X0)) ),
inference(forward_demodulation,[],[f650,f91]) ).
fof(f650,plain,
! [X0,X1,X8] :
( c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),tc_fun(X0,tc_bool)) = X8
| hBOOL(c_in(X1,X8,X0)) ),
inference(forward_demodulation,[],[f520,f201]) ).
fof(f520,plain,
! [X0,X1,X8] :
( hBOOL(c_in(X1,X8,X0))
| c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
inference(definition_unfolding,[],[f217,f149,f149]) ).
fof(f217,axiom,
! [X0,X1,X8] :
( hBOOL(c_in(X1,X8,X0))
| c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X8,X0),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
fof(f4693,plain,
spl0_355,
inference(avatar_split_clause,[],[f324,f4691]) ).
fof(f4691,plain,
( spl0_355
<=> ! [X24,X0,X9,X8,X30] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X24,tc_bool)),X30,X24,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X30,X24,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,X30,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f324,axiom,
! [X0,X8,X9,X24,X30] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X24,tc_bool)),X30,X24,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X30,X24,tc_fun(X0,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X9,X30,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
fof(f4671,plain,
( spl0_354
| ~ spl0_120
| ~ spl0_287
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4667,f4664,f3344,f1344,f4669]) ).
fof(f4669,plain,
( spl0_354
<=> ! [X0,X8,X9,X1] :
( c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f4664,plain,
( spl0_353
<=> ! [X0,X8,X9,X1] :
( c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f4667,plain,
( ! [X0,X1,X8,X9] :
( c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_353 ),
inference(forward_demodulation,[],[f4665,f3370]) ).
fof(f4665,plain,
( ! [X0,X1,X8,X9] :
( c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4664]) ).
fof(f4666,plain,
spl0_353,
inference(avatar_split_clause,[],[f642,f4664]) ).
fof(f642,plain,
! [X0,X1,X8,X9] :
( c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0)) ),
inference(forward_demodulation,[],[f515,f91]) ).
fof(f515,plain,
! [X0,X1,X8,X9] :
( ~ hBOOL(c_in(X1,X9,X0))
| c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f80,f149]) ).
fof(f80,axiom,
! [X0,X1,X8,X9] :
( ~ hBOOL(c_in(X1,X9,X0))
| c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Set_Oinsert(X1,X8,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
fof(f4651,plain,
( spl0_352
| ~ spl0_120
| ~ spl0_287
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4647,f4644,f3344,f1344,f4649]) ).
fof(f4649,plain,
( spl0_352
<=> ! [X24,X0,X31,X8,X1] :
( c_Set_Oimage(X31,X8,X0,X24) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X24),hAPP(X31,X1)),c_Set_Oimage(X31,X8,X0,X24),tc_fun(X24,tc_bool))
| ~ hBOOL(c_in(X1,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f4644,plain,
( spl0_351
<=> ! [X24,X0,X31,X8,X1] :
( c_Set_Oimage(X31,X8,X0,X24) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),hAPP(X31,X1)),c_Set_Oimage(X31,X8,X0,X24),tc_fun(X24,tc_bool))
| ~ hBOOL(c_in(X1,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f4647,plain,
( ! [X31,X0,X1,X8,X24] :
( c_Set_Oimage(X31,X8,X0,X24) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X24),hAPP(X31,X1)),c_Set_Oimage(X31,X8,X0,X24),tc_fun(X24,tc_bool))
| ~ hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_351 ),
inference(forward_demodulation,[],[f4645,f3370]) ).
fof(f4645,plain,
( ! [X31,X0,X1,X8,X24] :
( c_Set_Oimage(X31,X8,X0,X24) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),hAPP(X31,X1)),c_Set_Oimage(X31,X8,X0,X24),tc_fun(X24,tc_bool))
| ~ hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f4644]) ).
fof(f4646,plain,
spl0_351,
inference(avatar_split_clause,[],[f641,f4644]) ).
fof(f641,plain,
! [X31,X0,X1,X8,X24] :
( c_Set_Oimage(X31,X8,X0,X24) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),hAPP(X31,X1)),c_Set_Oimage(X31,X8,X0,X24),tc_fun(X24,tc_bool))
| ~ hBOOL(c_in(X1,X8,X0)) ),
inference(forward_demodulation,[],[f514,f91]) ).
fof(f514,plain,
! [X31,X0,X1,X8,X24] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_Set_Oimage(X31,X8,X0,X24) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),hAPP(X31,X1)),X24),c_Set_Oimage(X31,X8,X0,X24),tc_fun(X24,tc_bool)) ),
inference(definition_unfolding,[],[f35,f149]) ).
fof(f35,axiom,
! [X31,X0,X1,X8,X24] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_Set_Oimage(X31,X8,X0,X24) = c_Set_Oinsert(hAPP(X31,X1),c_Set_Oimage(X31,X8,X0,X24),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
fof(f4642,plain,
spl0_350,
inference(avatar_split_clause,[],[f413,f4640]) ).
fof(f4640,plain,
( spl0_350
<=> ! [X40,X0,X5,X45,X7] :
( ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X40),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),X0)
| c_Hoare__Mirabelle_Otriple__valid(X40,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f413,axiom,
! [X40,X0,X7,X45,X5] :
( ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X40),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),X0)
| c_Hoare__Mirabelle_Otriple__valid(X40,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_1) ).
fof(f4638,plain,
( spl0_349
| ~ spl0_19
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1913,f1816,f895,f4636]) ).
fof(f4636,plain,
( spl0_349
<=> ! [X2,X0,X1] :
( ~ c_Natural_Oevalc(X0,X1,X2)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(X0,c_Com_Ocom_OSKIP),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f895,plain,
( spl0_19
<=> ! [X37] : c_Natural_Oevalc(c_Com_Ocom_OSKIP,X37,X37) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1816,plain,
( spl0_166
<=> ! [X35,X33,X34,X36,X32] :
( ~ c_Natural_Oevalc(X32,X34,X36)
| ~ c_Natural_Oevalc(X33,X36,X35)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(X32,X33),X34,X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1913,plain,
( ! [X2,X0,X1] :
( ~ c_Natural_Oevalc(X0,X1,X2)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(X0,c_Com_Ocom_OSKIP),X1,X2) )
| ~ spl0_19
| ~ spl0_166 ),
inference(resolution,[],[f1817,f896]) ).
fof(f896,plain,
( ! [X37] : c_Natural_Oevalc(c_Com_Ocom_OSKIP,X37,X37)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f1817,plain,
( ! [X36,X34,X35,X32,X33] :
( ~ c_Natural_Oevalc(X33,X36,X35)
| ~ c_Natural_Oevalc(X32,X34,X36)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(X32,X33),X34,X35) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f4634,plain,
spl0_348,
inference(avatar_split_clause,[],[f412,f4632]) ).
fof(f4632,plain,
( spl0_348
<=> ! [X40,X0,X5,X45,X7] :
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X40),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X40,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f412,axiom,
! [X40,X0,X7,X45,X5] :
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(X40),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X40,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5))),X45),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).
fof(f4616,plain,
( spl0_347
| ~ spl0_120
| ~ spl0_287
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4612,f4608,f3344,f1344,f4614]) ).
fof(f4614,plain,
( spl0_347
<=> ! [X0,X1,X8] :
( hAPP(c_fequal(X0),X1) = X8
| ~ c_lessequals(X8,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f4608,plain,
( spl0_346
<=> ! [X0,X1,X8] :
( ~ c_lessequals(X8,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f4612,plain,
( ! [X0,X1,X8] :
( hAPP(c_fequal(X0),X1) = X8
| ~ c_lessequals(X8,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_346 ),
inference(forward_demodulation,[],[f4611,f3370]) ).
fof(f4611,plain,
( ! [X0,X1,X8] :
( ~ c_lessequals(X8,hAPP(c_fequal(X0),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8 )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_346 ),
inference(forward_demodulation,[],[f4609,f3370]) ).
fof(f4609,plain,
( ! [X0,X1,X8] :
( ~ c_lessequals(X8,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8 )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f4608]) ).
fof(f4610,plain,
spl0_346,
inference(avatar_split_clause,[],[f746,f4608]) ).
fof(f746,plain,
! [X0,X1,X8] :
( ~ c_lessequals(X8,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8 ),
inference(forward_demodulation,[],[f745,f91]) ).
fof(f745,plain,
! [X0,X1,X8] :
( ~ c_lessequals(X8,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),tc_fun(X0,tc_bool))
| hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8 ),
inference(forward_demodulation,[],[f744,f201]) ).
fof(f744,plain,
! [X0,X1,X8] :
( hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f743,f91]) ).
fof(f743,plain,
! [X0,X1,X8] :
( c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f556,f201]) ).
fof(f556,plain,
! [X0,X1,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8
| ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f372,f149,f149]) ).
fof(f372,axiom,
! [X0,X1,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X8
| ~ c_lessequals(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f4573,plain,
( spl0_345
| ~ spl0_120
| ~ spl0_287
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4569,f4566,f3344,f1344,f4571]) ).
fof(f4571,plain,
( spl0_345
<=> ! [X0,X8,X9,X1] :
( ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f4566,plain,
( spl0_344
<=> ! [X0,X8,X9,X1] :
( ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f4569,plain,
( ! [X0,X1,X8,X9] :
( ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_344 ),
inference(forward_demodulation,[],[f4567,f3370]) ).
fof(f4567,plain,
( ! [X0,X1,X8,X9] :
( ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool)) )
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f4566]) ).
fof(f4568,plain,
spl0_344,
inference(avatar_split_clause,[],[f740,f4566]) ).
fof(f740,plain,
! [X0,X1,X8,X9] :
( ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X8,X0))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f553,f91]) ).
fof(f553,plain,
! [X0,X1,X8,X9] :
( hBOOL(c_in(X1,X8,X0))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f37,f149]) ).
fof(f37,axiom,
! [X0,X1,X8,X9] :
( hBOOL(c_in(X1,X8,X0))
| c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X8,c_Set_Oinsert(X1,X9,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
fof(f4530,plain,
( spl0_343
| ~ spl0_120
| ~ spl0_287
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4526,f4523,f3344,f1344,f4528]) ).
fof(f4528,plain,
( spl0_343
<=> ! [X0,X8,X9,X1] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f4523,plain,
( spl0_342
<=> ! [X0,X8,X9,X1] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f4526,plain,
( ! [X0,X1,X8,X9] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_342 ),
inference(forward_demodulation,[],[f4524,f3370]) ).
fof(f4524,plain,
( ! [X0,X1,X8,X9] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4523]) ).
fof(f4525,plain,
spl0_342,
inference(avatar_split_clause,[],[f728,f4523]) ).
fof(f728,plain,
! [X0,X1,X8,X9] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| ~ hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[],[f547,f91]) ).
fof(f547,plain,
! [X0,X1,X8,X9] :
( ~ hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f281,f149]) ).
fof(f281,axiom,
! [X0,X1,X8,X9] :
( ~ hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X1,X8,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f4521,plain,
( spl0_341
| ~ spl0_116
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1428,f1372,f1328,f4519]) ).
fof(f4519,plain,
( spl0_341
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f1328,plain,
( spl0_116
<=> ! [X9,X0,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1372,plain,
( spl0_127
<=> ! [X0,X74,X90] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| ~ c_lessequals(X90,X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1428,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2)
| ~ spl0_116
| ~ spl0_127 ),
inference(resolution,[],[f1373,f1329]) ).
fof(f1329,plain,
( ! [X0,X8,X9] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool))
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f1373,plain,
( ! [X90,X0,X74] :
( ~ c_lessequals(X90,X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1372]) ).
fof(f4515,plain,
( spl0_340
| ~ spl0_120
| ~ spl0_287
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4511,f4507,f3344,f1344,f4513]) ).
fof(f4513,plain,
( spl0_340
<=> ! [X6,X0,X11] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f4507,plain,
( spl0_339
<=> ! [X6,X0,X11] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f4511,plain,
( ! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_339 ),
inference(forward_demodulation,[],[f4510,f3370]) ).
fof(f4510,plain,
( ! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_fequal(X0),X11),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_339 ),
inference(forward_demodulation,[],[f4508,f3370]) ).
fof(f4508,plain,
( ! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f4507]) ).
fof(f4509,plain,
spl0_339,
inference(avatar_split_clause,[],[f624,f4507]) ).
fof(f624,plain,
! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f623,f91]) ).
fof(f623,plain,
! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f622,f91]) ).
fof(f622,plain,
! [X0,X11,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f505,f201]) ).
fof(f505,plain,
! [X0,X11,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) ),
inference(definition_unfolding,[],[f215,f149,f149]) ).
fof(f215,axiom,
! [X0,X11,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Set_Oinsert(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
fof(f4246,plain,
( spl0_338
| ~ spl0_115
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1419,f1372,f1324,f4244]) ).
fof(f1324,plain,
( spl0_115
<=> ! [X9,X0,X8] : c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1419,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X0,X2)
| ~ spl0_115
| ~ spl0_127 ),
inference(resolution,[],[f1373,f1325]) ).
fof(f1325,plain,
( ! [X0,X8,X9] : c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1324]) ).
fof(f4242,plain,
spl0_337,
inference(avatar_split_clause,[],[f322,f4240]) ).
fof(f4240,plain,
( spl0_337
<=> ! [X31,X41,X83,X0,X1,X81,X84,X46,X24,X85,X61] :
( hAPP(X31,hAPP(X61,X1)) != hAPP(X83,hAPP(X84,X41))
| hAPP(c_Fun_Ocomp(X31,X61,X24,X0,X46),X1) = hAPP(c_Fun_Ocomp(X83,X84,X81,X0,X85),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f322,axiom,
! [X31,X41,X83,X0,X46,X1,X81,X84,X24,X85,X61] :
( hAPP(X31,hAPP(X61,X1)) != hAPP(X83,hAPP(X84,X41))
| hAPP(c_Fun_Ocomp(X31,X61,X24,X0,X46),X1) = hAPP(c_Fun_Ocomp(X83,X84,X81,X0,X85),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
fof(f4238,plain,
spl0_336,
inference(avatar_split_clause,[],[f277,f4236]) ).
fof(f4236,plain,
( spl0_336
<=> ! [X9,X0,X10,X73,X8] :
( ~ c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X73,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X10,X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f277,axiom,
! [X10,X0,X73,X8,X9] :
( ~ c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X73,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X10,X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f4234,plain,
spl0_335,
inference(avatar_split_clause,[],[f265,f4232]) ).
fof(f4232,plain,
( spl0_335
<=> ! [X37,X40,X7,X77,X23,X45,X79] :
( ~ c_Natural_Oevaln(X23,X37,X40,X77)
| ~ hBOOL(hAPP(hAPP(X7,X79),X37))
| hBOOL(hAPP(hAPP(X45,X79),X77))
| ~ c_Hoare__Mirabelle_Otriple__valid(X40,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f265,axiom,
! [X40,X37,X79,X7,X45,X77,X23] :
( ~ c_Natural_Oevaln(X23,X37,X40,X77)
| ~ hBOOL(hAPP(hAPP(X7,X79),X37))
| hBOOL(hAPP(hAPP(X45,X79),X77))
| ~ c_Hoare__Mirabelle_Otriple__valid(X40,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X23),X45),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__def2_0) ).
fof(f4230,plain,
spl0_334,
inference(avatar_split_clause,[],[f242,f4228]) ).
fof(f4228,plain,
( spl0_334
<=> ! [X10,X0,X9,X73,X8] :
( ~ c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(X73,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X10,X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f242,axiom,
! [X10,X0,X73,X8,X9] :
( ~ c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(X73,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X10,X73,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
fof(f4226,plain,
spl0_333,
inference(avatar_split_clause,[],[f146,f4224]) ).
fof(f146,axiom,
! [X10,X0,X8,X9] : c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X8,X10,tc_fun(X0,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
fof(f4222,plain,
spl0_332,
inference(avatar_split_clause,[],[f43,f4220]) ).
fof(f4220,plain,
( spl0_332
<=> ! [X24,X0,X31,X9,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X31,X8,X24,X0),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X31,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X24,tc_bool)),X24,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f43,axiom,
! [X31,X0,X8,X9,X24] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(X31,X8,X24,X0),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)),c_Set_Oimage(X31,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X24,tc_bool)),X24,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
fof(f4218,plain,
spl0_331,
inference(avatar_split_clause,[],[f18,f4216]) ).
fof(f4216,plain,
( spl0_331
<=> ! [X0,X18,X19,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| c_Complete__Lattice_Ocomplete__lattice(X12,X13,c_COMBC(X14,X0,X0,tc_bool),c_COMBC(X15,X0,X0,tc_bool),X16,X17,X18,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f18,axiom,
! [X0,X18,X19,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| c_Complete__Lattice_Ocomplete__lattice(X12,X13,c_COMBC(X14,X0,X0,tc_bool),c_COMBC(X15,X0,X0,tc_bool),X16,X17,X18,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
fof(f4203,plain,
spl0_330,
inference(avatar_split_clause,[],[f108,f4201]) ).
fof(f4201,plain,
( spl0_330
<=> ! [X24,X0,X67,X8,X68] :
( ~ hBOOL(c_in(X68,X67,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X67,X8,X0,tc_fun(X24,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X8,X68),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X67,X8,X0,tc_fun(X24,tc_bool)),tc_fun(X24,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f108,axiom,
! [X0,X68,X8,X24,X67] :
( ~ hBOOL(c_in(X68,X67,X0))
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X67,X8,X0,tc_fun(X24,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X8,X68),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X67,X8,X0,tc_fun(X24,tc_bool)),tc_fun(X24,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
fof(f4138,plain,
( spl0_329
| ~ spl0_114
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1418,f1372,f1320,f4136]) ).
fof(f1320,plain,
( spl0_114
<=> ! [X9,X0,X8] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1418,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X1,X2)
| ~ spl0_114
| ~ spl0_127 ),
inference(resolution,[],[f1373,f1321]) ).
fof(f1321,plain,
( ! [X0,X8,X9] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f4069,plain,
( spl0_328
| ~ spl0_120
| ~ spl0_287
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f4065,f4062,f3344,f1344,f4067]) ).
fof(f4067,plain,
( spl0_328
<=> ! [X11,X0,X6,X8] :
( ~ hBOOL(c_in(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X11),X8,tc_fun(X0,tc_bool)),X0))
| X6 = X11
| hBOOL(c_in(X6,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f4062,plain,
( spl0_327
<=> ! [X11,X0,X6,X8] :
( ~ hBOOL(c_in(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X8,tc_fun(X0,tc_bool)),X0))
| X6 = X11
| hBOOL(c_in(X6,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f4065,plain,
( ! [X0,X11,X8,X6] :
( ~ hBOOL(c_in(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X11),X8,tc_fun(X0,tc_bool)),X0))
| X6 = X11
| hBOOL(c_in(X6,X8,X0)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_327 ),
inference(forward_demodulation,[],[f4063,f3370]) ).
fof(f4063,plain,
( ! [X0,X11,X8,X6] :
( ~ hBOOL(c_in(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X8,tc_fun(X0,tc_bool)),X0))
| X6 = X11
| hBOOL(c_in(X6,X8,X0)) )
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f4062]) ).
fof(f4064,plain,
spl0_327,
inference(avatar_split_clause,[],[f722,f4062]) ).
fof(f722,plain,
! [X0,X11,X8,X6] :
( ~ hBOOL(c_in(X6,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X8,tc_fun(X0,tc_bool)),X0))
| X6 = X11
| hBOOL(c_in(X6,X8,X0)) ),
inference(forward_demodulation,[],[f544,f91]) ).
fof(f544,plain,
! [X0,X11,X8,X6] :
( X6 = X11
| hBOOL(c_in(X6,X8,X0))
| ~ hBOOL(c_in(X6,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X11),X0),X8,tc_fun(X0,tc_bool)),X0)) ),
inference(definition_unfolding,[],[f224,f149]) ).
fof(f224,axiom,
! [X0,X11,X8,X6] :
( X6 = X11
| hBOOL(c_in(X6,X8,X0))
| ~ hBOOL(c_in(X6,c_Set_Oinsert(X11,X8,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f4060,plain,
spl0_326,
inference(avatar_split_clause,[],[f332,f4058]) ).
fof(f4058,plain,
( spl0_326
<=> ! [X24,X0,X31,X9,X8] : c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X24,tc_bool)),X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X31,X8,X24,X0),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f332,axiom,
! [X31,X0,X8,X9,X24] : c_Set_Oimage(X31,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X24,tc_bool)),X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X31,X8,X24,X0),c_Set_Oimage(X31,X9,X24,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
fof(f4056,plain,
spl0_325,
inference(avatar_split_clause,[],[f326,f4054]) ).
fof(f4054,plain,
( spl0_325
<=> ! [X10,X0,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X10,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f326,axiom,
! [X10,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X10,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
fof(f4052,plain,
spl0_324,
inference(avatar_split_clause,[],[f136,f4050]) ).
fof(f4050,plain,
( spl0_324
<=> ! [X24,X0,X8,X9,X1] :
( ~ hBOOL(c_in(X1,X8,X24))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X9,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f136,axiom,
! [X0,X1,X8,X9,X24] :
( ~ hBOOL(c_in(X1,X8,X24))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(X9,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
fof(f4048,plain,
spl0_323,
inference(avatar_split_clause,[],[f104,f4046]) ).
fof(f4046,plain,
( spl0_323
<=> ! [X24,X0,X8,X9,X67,X1] :
( ~ hBOOL(c_in(X1,X67,X24))
| c_lessequals(hAPP(X8,X1),X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X67,X8,X24,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f104,axiom,
! [X0,X1,X8,X9,X24,X67] :
( ~ hBOOL(c_in(X1,X67,X24))
| c_lessequals(hAPP(X8,X1),X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X67,X8,X24,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
fof(f4035,plain,
( spl0_322
| ~ spl0_120
| ~ spl0_287
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4031,f4028,f3344,f1344,f4033]) ).
fof(f4033,plain,
( spl0_322
<=> ! [X6,X0,X8] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X8,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f4028,plain,
( spl0_321
<=> ! [X6,X0,X8] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f4031,plain,
( ! [X0,X8,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X6),X8,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_321 ),
inference(forward_demodulation,[],[f4029,f3370]) ).
fof(f4029,plain,
( ! [X0,X8,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f4028]) ).
fof(f4030,plain,
spl0_321,
inference(avatar_split_clause,[],[f621,f4028]) ).
fof(f621,plain,
! [X0,X8,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)),X0)
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f504,f91]) ).
fof(f504,plain,
! [X0,X8,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) = c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X8,tc_fun(X0,tc_bool)),X0) ),
inference(definition_unfolding,[],[f95,f149]) ).
fof(f95,axiom,
! [X0,X8,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,X8,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
fof(f4026,plain,
spl0_320,
inference(avatar_split_clause,[],[f321,f4024]) ).
fof(f4024,plain,
( spl0_320
<=> ! [X70,X0,X11,X81,X6,X69,X46,X24,X23] :
( hAPP(X6,hAPP(X11,X70)) = hAPP(X23,hAPP(X69,X70))
| c_Fun_Ocomp(X6,X11,X46,X24,X0) != c_Fun_Ocomp(X23,X69,X81,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f321,axiom,
! [X70,X46,X11,X0,X81,X6,X69,X24,X23] :
( hAPP(X6,hAPP(X11,X70)) = hAPP(X23,hAPP(X69,X70))
| c_Fun_Ocomp(X6,X11,X46,X24,X0) != c_Fun_Ocomp(X23,X69,X81,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
fof(f3992,plain,
( spl0_319
| ~ spl0_262
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f3373,f3344,f2821,f3990]) ).
fof(f3990,plain,
( spl0_319
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_fequal(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2821,plain,
( spl0_262
<=> ! [X6,X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f3373,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != hAPP(c_fequal(X0),X1)
| ~ spl0_262
| ~ spl0_287 ),
inference(superposition,[],[f2822,f3345]) ).
fof(f2822,plain,
( ! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool))
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2821]) ).
fof(f3721,plain,
( spl0_318
| ~ spl0_120
| ~ spl0_287
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f3717,f3714,f3344,f1344,f3719]) ).
fof(f3719,plain,
( spl0_318
<=> ! [X0,X8,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),X8,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X8,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f3714,plain,
( spl0_317
<=> ! [X0,X8,X2,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X8,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X8,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f3717,plain,
( ! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X2),X8,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X8,X1)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_317 ),
inference(forward_demodulation,[],[f3715,f3370]) ).
fof(f3715,plain,
( ! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X8,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X8,X1)) )
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3714]) ).
fof(f3716,plain,
spl0_317,
inference(avatar_split_clause,[],[f721,f3714]) ).
fof(f721,plain,
! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X8,tc_fun(X0,tc_bool)),X1))
| X1 = X2
| hBOOL(hAPP(X8,X1)) ),
inference(forward_demodulation,[],[f543,f91]) ).
fof(f543,plain,
! [X2,X0,X1,X8] :
( X1 = X2
| hBOOL(hAPP(X8,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),X0),X8,tc_fun(X0,tc_bool)),X1)) ),
inference(definition_unfolding,[],[f432,f149]) ).
fof(f432,axiom,
! [X2,X0,X1,X8] :
( X1 = X2
| hBOOL(hAPP(X8,X1))
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X8,X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f3685,plain,
( spl0_316
| ~ spl0_120
| ~ spl0_287
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3681,f3678,f3344,f1344,f3683]) ).
fof(f3683,plain,
( spl0_316
<=> ! [X0,X8,X9,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f3678,plain,
( spl0_315
<=> ! [X0,X8,X9,X1] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3681,plain,
( ! [X0,X1,X8,X9] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(X0),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_315 ),
inference(forward_demodulation,[],[f3679,f3370]) ).
fof(f3679,plain,
( ! [X0,X1,X8,X9] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3678]) ).
fof(f3680,plain,
spl0_315,
inference(avatar_split_clause,[],[f649,f3678]) ).
fof(f649,plain,
! [X0,X1,X8,X9] :
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool))
| hBOOL(c_in(X1,X9,X0)) ),
inference(forward_demodulation,[],[f519,f91]) ).
fof(f519,plain,
! [X0,X1,X8,X9] :
( hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f31,f149]) ).
fof(f31,axiom,
! [X0,X1,X8,X9] :
( hBOOL(c_in(X1,X9,X0))
| ~ c_lessequals(c_Set_Oinsert(X1,X8,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f3676,plain,
spl0_314,
inference(avatar_split_clause,[],[f278,f3674]) ).
fof(f3674,plain,
( spl0_314
<=> ! [X24,X81,X0,X31,X80,X61,X46] : c_Fun_Ocomp(X31,c_Fun_Ocomp(X61,X80,X81,X46,X0),X46,X24,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X31,X61,X46,X24,X81),X80,X81,X24,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f278,axiom,
! [X31,X46,X80,X0,X81,X24,X61] : c_Fun_Ocomp(X31,c_Fun_Ocomp(X61,X80,X81,X46,X0),X46,X24,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X31,X61,X46,X24,X81),X80,X81,X24,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f3672,plain,
spl0_313,
inference(avatar_split_clause,[],[f151,f3670]) ).
fof(f3670,plain,
( spl0_313
<=> ! [X0,X18,X8,X19,X1,X16,X14,X17,X15,X12,X13] :
( ~ hBOOL(c_in(X1,X8,X0))
| hBOOL(hAPP(hAPP(X14,X1),hAPP(X12,X8)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f151,axiom,
! [X0,X1,X8,X19,X18,X16,X14,X17,X15,X12,X13] :
( ~ hBOOL(c_in(X1,X8,X0))
| hBOOL(hAPP(hAPP(X14,X1),hAPP(X12,X8)))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
fof(f3668,plain,
spl0_312,
inference(avatar_split_clause,[],[f150,f3666]) ).
fof(f3666,plain,
( spl0_312
<=> ! [X0,X18,X8,X19,X1,X16,X14,X17,X15,X12,X13] :
( ~ hBOOL(c_in(X1,X8,X0))
| hBOOL(hAPP(hAPP(X14,hAPP(X13,X8)),X1))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f150,axiom,
! [X0,X1,X8,X19,X18,X16,X14,X17,X15,X12,X13] :
( ~ hBOOL(c_in(X1,X8,X0))
| hBOOL(hAPP(hAPP(X14,hAPP(X13,X8)),X1))
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
fof(f3664,plain,
spl0_311,
inference(avatar_split_clause,[],[f140,f3662]) ).
fof(f3662,plain,
( spl0_311
<=> ! [X24,X11,X0,X8,X9,X1] :
( ~ hBOOL(c_in(X1,X8,X24))
| ~ hBOOL(c_in(X11,hAPP(X9,X1),X0))
| hBOOL(c_in(X11,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f140,axiom,
! [X0,X11,X1,X8,X9,X24] :
( ~ hBOOL(c_in(X1,X8,X24))
| ~ hBOOL(c_in(X11,hAPP(X9,X1),X0))
| hBOOL(c_in(X11,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X24,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
fof(f3660,plain,
spl0_310,
inference(avatar_split_clause,[],[f53,f3658]) ).
fof(f3658,plain,
( spl0_310
<=> ! [X35,X23,X34,X11,X40,X36] :
( ~ hBOOL(hAPP(X11,X34))
| ~ c_Natural_Oevaln(X23,X34,X40,X36)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X36,X40,X35)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X34,X40,X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f53,axiom,
! [X40,X11,X36,X34,X35,X23] :
( ~ hBOOL(hAPP(X11,X34))
| ~ c_Natural_Oevaln(X23,X34,X40,X36)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X36,X40,X35)
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X34,X40,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).
fof(f3656,plain,
spl0_309,
inference(avatar_split_clause,[],[f41,f3654]) ).
fof(f3654,plain,
( spl0_309
<=> ! [X10,X0,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X8,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f41,axiom,
! [X10,X0,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,c_Lattices_Oupper__semilattice__class_Osup(X8,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f3652,plain,
spl0_308,
inference(avatar_split_clause,[],[f40,f3650]) ).
fof(f3650,plain,
( spl0_308
<=> ! [X10,X0,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f40,axiom,
! [X10,X0,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f3648,plain,
spl0_307,
inference(avatar_split_clause,[],[f7,f3646]) ).
fof(f3646,plain,
( spl0_307
<=> ! [X10,X0,X9,X8] :
( ~ c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f7,axiom,
! [X10,X0,X8,X9] :
( ~ c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
fof(f3618,plain,
( spl0_305
| spl0_306
| ~ spl0_120
| ~ spl0_201
| ~ spl0_287
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3424,f3348,f3344,f2097,f1344,f3616,f3613]) ).
fof(f3613,plain,
( spl0_305
<=> ! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),c_Com_Ocom_OSKIP),X0)),v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f3616,plain,
( spl0_306
<=> ! [X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f3348,plain,
( spl0_288
<=> ! [X0,X7,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSKIP),X7)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f3424,plain,
( ! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),c_Com_Ocom_OSKIP),X0)),v_G,t_a) )
| ~ spl0_120
| ~ spl0_201
| ~ spl0_287
| ~ spl0_288 ),
inference(forward_demodulation,[],[f3423,f3370]) ).
fof(f3423,plain,
( ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),c_Com_Ocom_OSKIP),X0)),v_G,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_120
| ~ spl0_201
| ~ spl0_287
| ~ spl0_288 ),
inference(forward_demodulation,[],[f3422,f3370]) ).
fof(f3422,plain,
( ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X0),c_Com_Ocom_OSKIP),X0)),v_G,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_201
| ~ spl0_288 ),
inference(resolution,[],[f3349,f2098]) ).
fof(f3349,plain,
( ! [X0,X7,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSKIP),X7)),X0)
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3348]) ).
fof(f3505,plain,
( spl0_304
| ~ spl0_120
| ~ spl0_287
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3501,f3498,f3344,f1344,f3503]) ).
fof(f3503,plain,
( spl0_304
<=> ! [X19,X0,X18,X6,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,hAPP(c_fequal(X0),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f3498,plain,
( spl0_303
<=> ! [X19,X0,X18,X6,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f3501,plain,
( ! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,hAPP(c_fequal(X0),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_303 ),
inference(forward_demodulation,[],[f3499,f3370]) ).
fof(f3499,plain,
( ! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f3498]) ).
fof(f3500,plain,
spl0_303,
inference(avatar_split_clause,[],[f667,f3498]) ).
fof(f667,plain,
! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f666,f91]) ).
fof(f666,plain,
! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f528,f201]) ).
fof(f528,plain,
! [X0,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X13,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) = X6 ),
inference(definition_unfolding,[],[f374,f149]) ).
fof(f374,axiom,
! [X0,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X13,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
fof(f3492,plain,
( spl0_302
| ~ spl0_120
| ~ spl0_287
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f3488,f3485,f3344,f1344,f3490]) ).
fof(f3490,plain,
( spl0_302
<=> ! [X19,X0,X18,X6,X16,X14,X17,X15,X12,X13] :
( hAPP(X12,hAPP(c_fequal(X0),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3485,plain,
( spl0_301
<=> ! [X19,X0,X18,X6,X16,X14,X17,X15,X12,X13] :
( hAPP(X12,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f3488,plain,
( ! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X12,hAPP(c_fequal(X0),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_301 ),
inference(forward_demodulation,[],[f3486,f3370]) ).
fof(f3486,plain,
( ! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X12,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f3487,plain,
spl0_301,
inference(avatar_split_clause,[],[f665,f3485]) ).
fof(f665,plain,
! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X12,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f664,f91]) ).
fof(f664,plain,
! [X0,X18,X6,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X12,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0)) = X6
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
inference(forward_demodulation,[],[f527,f201]) ).
fof(f527,plain,
! [X0,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X12,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))) = X6 ),
inference(definition_unfolding,[],[f375,f149]) ).
fof(f375,axiom,
! [X0,X18,X19,X6,X16,X14,X17,X15,X12,X13] :
( ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0)
| hAPP(X12,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
fof(f3473,plain,
( spl0_300
| ~ spl0_120
| ~ spl0_287
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3469,f3466,f3344,f1344,f3471]) ).
fof(f3471,plain,
( spl0_300
<=> ! [X24,X0,X23,X8,X1] :
( c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = hAPP(c_fequal(X24),X23)
| ~ hBOOL(c_in(X1,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3466,plain,
( spl0_299
<=> ! [X24,X0,X23,X8,X1] :
( c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X23)
| ~ hBOOL(c_in(X1,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f3469,plain,
( ! [X0,X1,X8,X24,X23] :
( c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = hAPP(c_fequal(X24),X23)
| ~ hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_120
| ~ spl0_287
| ~ spl0_299 ),
inference(forward_demodulation,[],[f3467,f3370]) ).
fof(f3467,plain,
( ! [X0,X1,X8,X24,X23] :
( c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X23)
| ~ hBOOL(c_in(X1,X8,X0)) )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3466]) ).
fof(f3468,plain,
spl0_299,
inference(avatar_split_clause,[],[f644,f3466]) ).
fof(f644,plain,
! [X0,X1,X8,X24,X23] :
( c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X23)
| ~ hBOOL(c_in(X1,X8,X0)) ),
inference(forward_demodulation,[],[f643,f91]) ).
fof(f643,plain,
! [X0,X1,X8,X24,X23] :
( c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = c_Collect(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X23),X24)
| ~ hBOOL(c_in(X1,X8,X0)) ),
inference(forward_demodulation,[],[f516,f201]) ).
fof(f516,plain,
! [X0,X1,X8,X24,X23] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X24),X24,X24,tc_bool),X23),X24),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),tc_fun(X24,tc_bool)) ),
inference(definition_unfolding,[],[f70,f149]) ).
fof(f70,axiom,
! [X0,X1,X8,X24,X23] :
( ~ hBOOL(c_in(X1,X8,X0))
| c_Set_Oimage(c_COMBK(X23,X24,X0),X8,X0,X24) = c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
fof(f3464,plain,
spl0_298,
inference(avatar_split_clause,[],[f320,f3462]) ).
fof(f3462,plain,
( spl0_298
<=> ! [X50,X51,X28,X59,X0,X56,X54,X55,X52,X53,X60,X49] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OCond(X28,X59,X60),X0) = hAPP(hAPP(hAPP(X53,X28),X59),X60) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f320,axiom,
! [X50,X51,X28,X59,X49,X0,X56,X54,X55,X52,X53,X60] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OCond(X28,X59,X60),X0) = hAPP(hAPP(hAPP(X53,X28),X59),X60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).
fof(f3460,plain,
spl0_297,
inference(avatar_split_clause,[],[f275,f3458]) ).
fof(f3458,plain,
( spl0_297
<=> ! [X28,X51,X29,X0,X52,X56,X54,X55,X27,X50,X53,X49] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OLocal(X27,X28,X29),X0) = hAPP(hAPP(hAPP(X51,X27),X28),X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f275,axiom,
! [X50,X51,X28,X29,X49,X0,X56,X54,X55,X52,X27,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OLocal(X27,X28,X29),X0) = hAPP(hAPP(hAPP(X51,X27),X28),X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).
fof(f3456,plain,
spl0_296,
inference(avatar_split_clause,[],[f177,f3454]) ).
fof(f3454,plain,
( spl0_296
<=> ! [X10,X0,X9,X8] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f177,axiom,
! [X10,X0,X8,X9] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool))
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
fof(f3452,plain,
spl0_295,
inference(avatar_split_clause,[],[f176,f3450]) ).
fof(f3450,plain,
( spl0_295
<=> ! [X10,X0,X9,X8] :
( ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f176,axiom,
! [X10,X0,X8,X9] :
( ~ c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X9,X10,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
fof(f3448,plain,
spl0_294,
inference(avatar_split_clause,[],[f119,f3446]) ).
fof(f3446,plain,
( spl0_294
<=> ! [X23,X11,X0,X6,X69] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X11,X0)
| c_lessequals(X23,X6,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f119,axiom,
! [X0,X11,X6,X69,X23] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X11,X0)
| c_lessequals(X23,X6,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
fof(f3444,plain,
( spl0_293
| ~ spl0_245
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f3374,f3344,f2495,f3442]) ).
fof(f3442,plain,
( spl0_293
<=> ! [X0,X1] : hBOOL(c_in(X1,hAPP(c_fequal(X0),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2495,plain,
( spl0_245
<=> ! [X0,X1,X8] : hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3374,plain,
( ! [X0,X1] : hBOOL(c_in(X1,hAPP(c_fequal(X0),X1),X0))
| ~ spl0_245
| ~ spl0_287 ),
inference(superposition,[],[f2496,f3345]) ).
fof(f2496,plain,
( ! [X0,X1,X8] : hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X0))
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2495]) ).
fof(f3440,plain,
spl0_292,
inference(avatar_split_clause,[],[f118,f3438]) ).
fof(f3438,plain,
( spl0_292
<=> ! [X23,X11,X0,X6,X69] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X11,X0)
| c_lessequals(X11,X69,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f118,axiom,
! [X0,X11,X6,X69,X23] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X11,X0)
| c_lessequals(X11,X69,X0)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
fof(f3436,plain,
spl0_291,
inference(avatar_split_clause,[],[f117,f3434]) ).
fof(f3434,plain,
( spl0_291
<=> ! [X23,X11,X0,X6,X69] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X23,X6,X0)
| ~ c_lessequals(X11,X69,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f117,axiom,
! [X0,X11,X6,X69,X23] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X23,X6,X0)
| ~ c_lessequals(X11,X69,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
fof(f3432,plain,
spl0_290,
inference(avatar_split_clause,[],[f71,f3430]) ).
fof(f3430,plain,
( spl0_290
<=> ! [X24,X31,X0,X8,X9,X1] :
( ~ hBOOL(c_in(X1,X8,X24))
| hBOOL(c_in(hAPP(X31,X1),X9,X0))
| ~ c_lessequals(c_Set_Oimage(X31,X8,X24,X0),X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f71,axiom,
! [X31,X0,X1,X8,X9,X24] :
( ~ hBOOL(c_in(X1,X8,X24))
| hBOOL(c_in(hAPP(X31,X1),X9,X0))
| ~ c_lessequals(c_Set_Oimage(X31,X8,X24,X0),X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
fof(f3428,plain,
spl0_289,
inference(avatar_split_clause,[],[f65,f3426]) ).
fof(f3426,plain,
( spl0_289
<=> ! [X28,X51,X58,X0,X49,X56,X54,X57,X55,X52,X50,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OCall(X57,X58,X28),X0) = hAPP(hAPP(hAPP(X56,X57),X58),X28) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f65,axiom,
! [X50,X51,X58,X28,X0,X49,X56,X54,X57,X55,X52,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OCall(X57,X58,X28),X0) = hAPP(hAPP(hAPP(X56,X57),X58),X28),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).
fof(f3350,plain,
spl0_288,
inference(avatar_split_clause,[],[f601,f3348]) ).
fof(f601,plain,
! [X0,X7,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSKIP),X7)),X0),
inference(forward_demodulation,[],[f600,f91]) ).
fof(f600,plain,
! [X0,X7,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSKIP),X7)),tc_Hoare__Mirabelle_Otriple(X0)),X0),
inference(forward_demodulation,[],[f493,f201]) ).
fof(f493,plain,
! [X0,X7,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(X0)),tc_Hoare__Mirabelle_Otriple(X0),tc_Hoare__Mirabelle_Otriple(X0),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSKIP),X7)),tc_Hoare__Mirabelle_Otriple(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0),
inference(definition_unfolding,[],[f416,f149]) ).
fof(f416,axiom,
! [X0,X7,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),c_Com_Ocom_OSKIP),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),tc_Hoare__Mirabelle_Otriple(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
fof(f3346,plain,
spl0_287,
inference(avatar_split_clause,[],[f590,f3344]) ).
fof(f590,plain,
! [X0,X6] : hAPP(c_fequal(X0),X6) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f589,f91]) ).
fof(f589,plain,
! [X0,X6] : c_Collect(hAPP(c_fequal(X0),X6),X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f485,f91]) ).
fof(f485,plain,
! [X0,X6] : c_Collect(hAPP(c_fequal(X0),X6),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f371,f149]) ).
fof(f371,axiom,
! [X0,X6] : c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Collect(hAPP(c_fequal(X0),X6),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f3342,plain,
( spl0_286
| ~ spl0_40
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f1139,f1066,f979,f3340]) ).
fof(f979,plain,
( spl0_40
<=> ! [X98,X99] :
( ~ class_Lattices_Olattice(X99)
| class_Lattices_Oupper__semilattice(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1066,plain,
( spl0_61
<=> ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1139,plain,
( ! [X2,X0,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
| ~ class_Lattices_Olattice(X2) )
| ~ spl0_40
| ~ spl0_61 ),
inference(resolution,[],[f1067,f980]) ).
fof(f980,plain,
( ! [X98,X99] :
( class_Lattices_Oupper__semilattice(tc_fun(X98,X99))
| ~ class_Lattices_Olattice(X99) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f1067,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f3338,plain,
spl0_285,
inference(avatar_split_clause,[],[f367,f3336]) ).
fof(f3336,plain,
( spl0_285
<=> ! [X37,X40,X7,X36] :
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X7),X37,X40,X36)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X7)),X37,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X7,X40,X37,X36),X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f367,axiom,
! [X40,X36,X37,X7] :
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X7),X37,X40,X36)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X7)),X37,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X7,X40,X37,X36),X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
fof(f3334,plain,
spl0_284,
inference(avatar_split_clause,[],[f165,f3332]) ).
fof(f3332,plain,
( spl0_284
<=> ! [X8,X11,X0,X9,X1,X24] :
( ~ hBOOL(c_in(X1,X8,X0))
| ~ hBOOL(hAPP(hAPP(X9,X1),X11))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X0,tc_fun(X24,tc_bool)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f165,axiom,
! [X0,X11,X1,X8,X9,X24] :
( ~ hBOOL(c_in(X1,X8,X0))
| ~ hBOOL(hAPP(hAPP(X9,X1),X11))
| hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X0,tc_fun(X24,tc_bool)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
fof(f3177,plain,
spl0_283,
inference(avatar_split_clause,[],[f638,f3175]) ).
fof(f3175,plain,
( spl0_283
<=> ! [X6,X0,X8] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)) = X8
| ~ hBOOL(c_in(X6,X8,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f638,plain,
! [X0,X8,X6] :
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)) = X8
| ~ hBOOL(c_in(X6,X8,X0)) ),
inference(forward_demodulation,[],[f511,f91]) ).
fof(f511,plain,
! [X0,X8,X6] :
( ~ hBOOL(c_in(X6,X8,X0))
| c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X8,tc_fun(X0,tc_bool)) = X8 ),
inference(definition_unfolding,[],[f234,f149]) ).
fof(f234,axiom,
! [X0,X8,X6] :
( ~ hBOOL(c_in(X6,X8,X0))
| c_Set_Oinsert(X6,X8,X0) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f3173,plain,
spl0_282,
inference(avatar_split_clause,[],[f424,f3171]) ).
fof(f3171,plain,
( spl0_282
<=> ! [X88,X97,X64,X0,X29,X89,X96] :
( X88 = X96
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X88),X29),X89) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X96),X64),X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f424,axiom,
! [X0,X29,X88,X89,X96,X97,X64] :
( X88 = X96
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X88),X29),X89) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X96),X64),X97) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
fof(f3169,plain,
spl0_281,
inference(avatar_split_clause,[],[f423,f3167]) ).
fof(f3167,plain,
( spl0_281
<=> ! [X88,X97,X64,X0,X29,X89,X96] :
( X29 = X64
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X88),X29),X89) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X96),X64),X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f423,axiom,
! [X29,X0,X88,X89,X96,X97,X64] :
( X29 = X64
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X88),X29),X89) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X96),X64),X97) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
fof(f3165,plain,
spl0_280,
inference(avatar_split_clause,[],[f422,f3163]) ).
fof(f3163,plain,
( spl0_280
<=> ! [X88,X97,X64,X0,X29,X89,X96] :
( X89 = X97
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X88),X29),X89) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X96),X64),X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f422,axiom,
! [X0,X29,X88,X89,X96,X97,X64] :
( X89 = X97
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X88),X29),X89) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X96),X64),X97) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
fof(f3157,plain,
spl0_279,
inference(avatar_split_clause,[],[f353,f3155]) ).
fof(f3155,plain,
( spl0_279
<=> ! [X24,X88,X0,X29,X49,X89] : hAPP(hAPP(hAPP(X49,X88),X29),X89) = c_Hoare__Mirabelle_Otriple_Otriple__case(X49,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X24),X88),X29),X89),X24,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f353,axiom,
! [X29,X49,X0,X88,X89,X24] : hAPP(hAPP(hAPP(X49,X88),X29),X89) = c_Hoare__Mirabelle_Otriple_Otriple__case(X49,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X24),X88),X29),X89),X24,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).
fof(f3153,plain,
spl0_278,
inference(avatar_split_clause,[],[f352,f3151]) ).
fof(f3151,plain,
( spl0_278
<=> ! [X24,X88,X0,X29,X49,X89] : hAPP(hAPP(hAPP(X49,X88),X29),X89) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X49,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X24),X88),X29),X89),X24,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f352,axiom,
! [X29,X49,X0,X88,X89,X24] : hAPP(hAPP(hAPP(X49,X88),X29),X89) = c_Hoare__Mirabelle_Otriple_Otriple__rec(X49,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X24),X88),X29),X89),X24,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).
fof(f3149,plain,
spl0_277,
inference(avatar_split_clause,[],[f329,f3147]) ).
fof(f3147,plain,
( spl0_277
<=> ! [X24,X0,X31,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oimage(X31,X8,X0,X24),c_Set_Oimage(X31,X9,X0,X24),tc_fun(X24,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f329,axiom,
! [X31,X0,X8,X9,X24] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oimage(X31,X8,X0,X24),c_Set_Oimage(X31,X9,X0,X24),tc_fun(X24,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
fof(f3145,plain,
spl0_276,
inference(avatar_split_clause,[],[f292,f3143]) ).
fof(f3143,plain,
( spl0_276
<=> ! [X0,X24,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),X24),X24,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f292,axiom,
! [X0,X8,X24] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool),X24),X24,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
fof(f3141,plain,
spl0_275,
inference(avatar_split_clause,[],[f288,f3139]) ).
fof(f3139,plain,
( spl0_275
<=> ! [X24,X82,X0,X31,X61,X46] : c_Set_Oimage(c_Fun_Ocomp(X31,X61,X46,X0,X24),X82,X24,X0) = c_Set_Oimage(X31,c_Set_Oimage(X61,X82,X24,X46),X46,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f288,axiom,
! [X31,X82,X46,X0,X24,X61] : c_Set_Oimage(c_Fun_Ocomp(X31,X61,X46,X0,X24),X82,X24,X0) = c_Set_Oimage(X31,c_Set_Oimage(X61,X82,X24,X46),X46,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__compose_0) ).
fof(f3137,plain,
spl0_274,
inference(avatar_split_clause,[],[f282,f3135]) ).
fof(f3135,plain,
( spl0_274
<=> ! [X24,X0,X31,X61,X8,X46] : c_Set_Oimage(X31,c_Set_Oimage(X61,X8,X46,X24),X24,X0) = c_Set_Oimage(c_COMBB(X31,X61,X24,X0,X46),X8,X46,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f282,axiom,
! [X31,X46,X0,X8,X24,X61] : c_Set_Oimage(X31,c_Set_Oimage(X61,X8,X46,X24),X24,X0) = c_Set_Oimage(c_COMBB(X31,X61,X24,X0,X46),X8,X46,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
fof(f3133,plain,
spl0_273,
inference(avatar_split_clause,[],[f134,f3131]) ).
fof(f3131,plain,
( spl0_273
<=> ! [X23,X0,X9,X8] :
( hBOOL(c_in(X23,X9,X0))
| hBOOL(c_in(X23,X8,X0))
| ~ hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f134,axiom,
! [X0,X8,X9,X23] :
( hBOOL(c_in(X23,X9,X0))
| hBOOL(c_in(X23,X8,X0))
| ~ hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f3129,plain,
spl0_272,
inference(avatar_split_clause,[],[f50,f3127]) ).
fof(f3127,plain,
( spl0_272
<=> ! [X35,X23,X34,X11,X36] :
( ~ hBOOL(hAPP(X11,X34))
| ~ c_Natural_Oevalc(X23,X34,X36)
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X36,X35)
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X34,X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f50,axiom,
! [X11,X36,X34,X35,X23] :
( ~ hBOOL(hAPP(X11,X34))
| ~ c_Natural_Oevalc(X23,X34,X36)
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X36,X35)
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X34,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
fof(f3125,plain,
spl0_271,
inference(avatar_split_clause,[],[f32,f3123]) ).
fof(f3123,plain,
( spl0_271
<=> ! [X24,X0,X23,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,c_COMBK(X23,tc_fun(X0,tc_bool),X24),X24,tc_fun(X0,tc_bool)) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f32,axiom,
! [X0,X8,X24,X23] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,c_COMBK(X23,tc_fun(X0,tc_bool),X24),X24,tc_fun(X0,tc_bool)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_1) ).
fof(f3121,plain,
spl0_270,
inference(avatar_split_clause,[],[f28,f3119]) ).
fof(f3119,plain,
( spl0_270
<=> ! [X23,X0,X9,X8] :
( ~ hBOOL(c_in(X23,X8,X0))
| hBOOL(c_in(X23,X9,X0))
| hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f28,axiom,
! [X0,X8,X9,X23] :
( ~ hBOOL(c_in(X23,X8,X0))
| hBOOL(c_in(X23,X9,X0))
| hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
fof(f3077,plain,
spl0_269,
inference(avatar_split_clause,[],[f663,f3075]) ).
fof(f3075,plain,
( spl0_269
<=> ! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f663,plain,
! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1)) ),
inference(forward_demodulation,[],[f662,f91]) ).
fof(f662,plain,
! [X2,X0,X1] :
( c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X0) = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1)) ),
inference(forward_demodulation,[],[f661,f201]) ).
fof(f661,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X2),X1))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X2 ),
inference(forward_demodulation,[],[f660,f58]) ).
fof(f58,axiom,
! [X46,X0,X47,X7,X45,X24] : hAPP(hAPP(c_COMBC(X7,X24,X46,X0),X45),X47) = hAPP(hAPP(X7,X47),X45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f660,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X2 ),
inference(forward_demodulation,[],[f659,f91]) ).
fof(f659,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X2 ),
inference(forward_demodulation,[],[f526,f201]) ).
fof(f526,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X2 ),
inference(definition_unfolding,[],[f388,f149,f149]) ).
fof(f388,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X2))
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
fof(f3073,plain,
spl0_268,
inference(avatar_split_clause,[],[f657,f3071]) ).
fof(f3071,plain,
( spl0_268
<=> ! [X24,X0,X23,X8] :
( c_Set_Oimage(c_COMBK(X23,X0,X24),X8,X24,X0) = hAPP(c_fequal(X0),X23)
| c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f657,plain,
! [X0,X8,X24,X23] :
( c_Set_Oimage(c_COMBK(X23,X0,X24),X8,X24,X0) = hAPP(c_fequal(X0),X23)
| c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8 ),
inference(forward_demodulation,[],[f656,f590]) ).
fof(f656,plain,
! [X0,X8,X24,X23] :
( c_Set_Oimage(c_COMBK(X23,X0,X24),X8,X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8 ),
inference(forward_demodulation,[],[f524,f91]) ).
fof(f524,plain,
! [X0,X8,X24,X23] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8
| c_Set_Oimage(c_COMBK(X23,X0,X24),X8,X24,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X23),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f214,f149]) ).
fof(f214,axiom,
! [X0,X8,X24,X23] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8
| c_Set_Oimage(c_COMBK(X23,X0,X24),X8,X24,X0) = c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
fof(f3069,plain,
spl0_267,
inference(avatar_split_clause,[],[f276,f3067]) ).
fof(f3067,plain,
( spl0_267
<=> ! [X28,X51,X29,X0,X49,X56,X54,X55,X52,X50,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OWhile(X28,X29),X0) = hAPP(hAPP(X54,X28),X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f276,axiom,
! [X50,X51,X28,X29,X49,X0,X56,X54,X55,X52,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OWhile(X28,X29),X0) = hAPP(hAPP(X54,X28),X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).
fof(f3065,plain,
spl0_266,
inference(avatar_split_clause,[],[f147,f3063]) ).
fof(f3063,plain,
( spl0_266
<=> ! [X50,X51,X59,X0,X56,X54,X55,X52,X53,X60,X49] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OSemi(X59,X60),X0) = hAPP(hAPP(X52,X59),X60) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f147,axiom,
! [X50,X51,X59,X49,X0,X56,X54,X55,X52,X53,X60] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OSemi(X59,X60),X0) = hAPP(hAPP(X52,X59),X60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).
fof(f3029,plain,
spl0_265,
inference(avatar_split_clause,[],[f145,f3027]) ).
fof(f3027,plain,
( spl0_265
<=> ! [X9,X24,X8] :
( ~ class_HOL_Ominus(X24)
| hAPP(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(t_a,X24)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X8,v_x),hAPP(X9,v_x),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f145,axiom,
! [X8,X9,X24] :
( ~ class_HOL_Ominus(X24)
| hAPP(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(t_a,X24)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X8,v_x),hAPP(X9,v_x),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
fof(f3025,plain,
spl0_264,
inference(avatar_split_clause,[],[f79,f3023]) ).
fof(f3023,plain,
( spl0_264
<=> ! [X24,X9,X0,X6,X8] :
( ~ hBOOL(c_in(X6,X8,X0))
| c_lessequals(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X0,tc_fun(X24,tc_bool)),tc_fun(X24,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f79,axiom,
! [X0,X8,X6,X9,X24] :
( ~ hBOOL(c_in(X6,X8,X0))
| c_lessequals(hAPP(X9,X6),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X9,X0,tc_fun(X24,tc_bool)),tc_fun(X24,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
fof(f3021,plain,
spl0_263,
inference(avatar_split_clause,[],[f69,f3019]) ).
fof(f3019,plain,
( spl0_263
<=> ! [X61,X24,X31] :
( ~ class_Lattices_Olattice(X24)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X31,X61,tc_fun(t_a,X24)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X31,v_x),hAPP(X61,v_x),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f69,axiom,
! [X31,X24,X61] :
( ~ class_Lattices_Olattice(X24)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X31,X61,tc_fun(t_a,X24)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(X31,v_x),hAPP(X61,v_x),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
fof(f2823,plain,
spl0_262,
inference(avatar_split_clause,[],[f575,f2821]) ).
fof(f575,plain,
! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X8,tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f476,f91]) ).
fof(f476,plain,
! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X8,tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f421,f149]) ).
fof(f421,axiom,
! [X0,X8,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X6,X8,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f2819,plain,
spl0_261,
inference(avatar_split_clause,[],[f368,f2817]) ).
fof(f2817,plain,
( spl0_261
<=> ! [X5,X34,X40,X36] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X5),X34,c_Suc(X40),X36)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5)),X34,X40,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f368,axiom,
! [X40,X36,X34,X5] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X5),X34,c_Suc(X40),X36)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5)),X34,X40,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
fof(f2815,plain,
spl0_260,
inference(avatar_split_clause,[],[f331,f2813]) ).
fof(f2813,plain,
( spl0_260
<=> ! [X38,X40,X11,X33,X39,X37] :
( c_Natural_Oevaln(X39,X37,X40,X38)
| c_Natural_Oevaln(X33,X37,X40,X38)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X33,X39),X37,X40,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f331,axiom,
! [X40,X38,X39,X11,X37,X33] :
( c_Natural_Oevaln(X39,X37,X40,X38)
| c_Natural_Oevaln(X33,X37,X40,X38)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X33,X39),X37,X40,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).
fof(f2811,plain,
spl0_259,
inference(avatar_split_clause,[],[f312,f2809]) ).
fof(f2809,plain,
( spl0_259
<=> ! [X10,X0,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| c_lessequals(X8,X10,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f312,axiom,
! [X10,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| c_lessequals(X8,X10,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f2807,plain,
spl0_258,
inference(avatar_split_clause,[],[f190,f2805]) ).
fof(f2805,plain,
( spl0_258
<=> ! [X15,X18,X16,X0,X14,X13,X12,X17,X19] :
( hAPP(X12,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X19
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f190,axiom,
! [X0,X18,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X12,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X19
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
fof(f2803,plain,
( spl0_257
| ~ spl0_10
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1432,f1380,f850,f2800]) ).
fof(f2800,plain,
( spl0_257
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f850,plain,
( spl0_10
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1380,plain,
( spl0_129
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1432,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_10
| ~ spl0_129 ),
inference(resolution,[],[f1381,f852]) ).
fof(f852,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f1381,plain,
( ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1380]) ).
fof(f2798,plain,
spl0_256,
inference(avatar_split_clause,[],[f189,f2796]) ).
fof(f2796,plain,
( spl0_256
<=> ! [X0,X18,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X18
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f189,axiom,
! [X0,X18,X19,X16,X14,X17,X15,X12,X13] :
( hAPP(X13,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = X18
| ~ c_Complete__Lattice_Ocomplete__lattice(X13,X12,X14,X15,X17,X16,X19,X18,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
fof(f2794,plain,
spl0_255,
inference(avatar_split_clause,[],[f159,f2792]) ).
fof(f2792,plain,
( spl0_255
<=> ! [X9,X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f159,axiom,
! [X0,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f2790,plain,
spl0_254,
inference(avatar_split_clause,[],[f143,f2788]) ).
fof(f2788,plain,
( spl0_254
<=> ! [X9,X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f143,axiom,
! [X0,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
fof(f2786,plain,
spl0_253,
inference(avatar_split_clause,[],[f142,f2784]) ).
fof(f2784,plain,
( spl0_253
<=> ! [X9,X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f142,axiom,
! [X0,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(X9,X8,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
fof(f2782,plain,
spl0_252,
inference(avatar_split_clause,[],[f128,f2780]) ).
fof(f2780,plain,
( spl0_252
<=> ! [X23,X11,X0,X6,X69] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X6,X11,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f128,axiom,
! [X0,X11,X6,X69,X23] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X6,X11,X0)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0),c_SetInterval_Oord__class_OatLeastAtMost(X23,X69,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
fof(f2778,plain,
spl0_251,
inference(avatar_split_clause,[],[f54,f2776]) ).
fof(f2776,plain,
( spl0_251
<=> ! [X9,X0,X8] : c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f54,axiom,
! [X0,X8,X9] : c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
fof(f2774,plain,
spl0_250,
inference(avatar_split_clause,[],[f33,f2772]) ).
fof(f2772,plain,
( spl0_250
<=> ! [X24,X0,X30,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,c_COMBK(X30,X24,X0),X0,X24) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f33,axiom,
! [X0,X8,X24,X30] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,c_COMBK(X30,X24,X0),X0,X24) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).
fof(f2763,plain,
( spl0_249
| ~ spl0_16
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1430,f1376,f880,f2760]) ).
fof(f2760,plain,
( spl0_249
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f880,plain,
( spl0_16
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1376,plain,
( spl0_128
<=> ! [X24] :
( ~ class_Orderings_Obot(X24)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X24)),v_x) = c_Orderings_Obot__class_Obot(X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1430,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ spl0_16
| ~ spl0_128 ),
inference(resolution,[],[f1377,f882]) ).
fof(f882,plain,
( class_Orderings_Obot(tc_bool)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f1377,plain,
( ! [X24] :
( ~ class_Orderings_Obot(X24)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X24)),v_x) = c_Orderings_Obot__class_Obot(X24) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f2570,plain,
( spl0_248
| ~ spl0_7
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1429,f1376,f835,f2567]) ).
fof(f2567,plain,
( spl0_248
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f835,plain,
( spl0_7
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1429,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_nat)),v_x) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_7
| ~ spl0_128 ),
inference(resolution,[],[f1377,f837]) ).
fof(f837,plain,
( class_Orderings_Obot(tc_nat)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f2505,plain,
spl0_247,
inference(avatar_split_clause,[],[f630,f2503]) ).
fof(f2503,plain,
( spl0_247
<=> ! [X31,X11,X0,X6] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X11))
| X6 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f630,plain,
! [X31,X0,X11,X6] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X11))
| X6 = X11 ),
inference(forward_demodulation,[],[f629,f91]) ).
fof(f629,plain,
! [X31,X0,X11,X6] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0),X11))
| X6 = X11 ),
inference(forward_demodulation,[],[f508,f201]) ).
fof(f508,plain,
! [X31,X0,X11,X6] :
( X6 = X11
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0),X11)) ),
inference(definition_unfolding,[],[f386,f149]) ).
fof(f386,axiom,
! [X31,X0,X11,X6] :
( X6 = X11
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
fof(f2501,plain,
( spl0_246
| ~ spl0_11
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1387,f1336,f855,f2499]) ).
fof(f2499,plain,
( spl0_246
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f855,plain,
( spl0_11
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1336,plain,
( spl0_118
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1387,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool)
| ~ spl0_11
| ~ spl0_118 ),
inference(resolution,[],[f1337,f857]) ).
fof(f857,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f855]) ).
fof(f1337,plain,
( ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1336]) ).
fof(f2497,plain,
spl0_245,
inference(avatar_split_clause,[],[f572,f2495]) ).
fof(f572,plain,
! [X0,X1,X8] : hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X0)),
inference(forward_demodulation,[],[f473,f91]) ).
fof(f473,plain,
! [X0,X1,X8] : hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),X0)),
inference(definition_unfolding,[],[f230,f149]) ).
fof(f230,axiom,
! [X0,X1,X8] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X8,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
fof(f2493,plain,
spl0_244,
inference(avatar_split_clause,[],[f347,f2491]) ).
fof(f2491,plain,
( spl0_244
<=> ! [X50,X51,X58,X0,X49,X56,X54,X55,X52,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,hAPP(c_Com_Ocom_OBODY,X58),X0) = hAPP(X55,X58) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f347,axiom,
! [X50,X51,X58,X0,X49,X56,X54,X55,X52,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,hAPP(c_Com_Ocom_OBODY,X58),X0) = hAPP(X55,X58),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).
fof(f2489,plain,
spl0_243,
inference(avatar_split_clause,[],[f303,f2487]) ).
fof(f2487,plain,
( spl0_243
<=> ! [X9,X0,X8,X10] :
( c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f303,axiom,
! [X10,X0,X8,X9] :
( c_lessequals(X9,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f2485,plain,
spl0_242,
inference(avatar_split_clause,[],[f302,f2483]) ).
fof(f2483,plain,
( spl0_242
<=> ! [X10,X0,X9,X8] :
( c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f302,axiom,
! [X10,X0,X8,X9] :
( c_lessequals(X8,X10,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X10,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f2481,plain,
spl0_241,
inference(avatar_split_clause,[],[f244,f2479]) ).
fof(f2479,plain,
( spl0_241
<=> ! [X37,X33,X40,X11,X36,X32] :
( hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevaln(X33,X37,X40,X36)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X32,X33),X37,X40,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f244,axiom,
! [X40,X11,X36,X37,X32,X33] :
( hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevaln(X33,X37,X40,X36)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X32,X33),X37,X40,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).
fof(f2477,plain,
spl0_240,
inference(avatar_split_clause,[],[f243,f2475]) ).
fof(f2475,plain,
( spl0_240
<=> ! [X38,X40,X11,X33,X39,X37] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevaln(X39,X37,X40,X38)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X33,X39),X37,X40,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f243,axiom,
! [X40,X38,X39,X11,X37,X33] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevaln(X39,X37,X40,X38)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X33,X39),X37,X40,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).
fof(f2473,plain,
spl0_239,
inference(avatar_split_clause,[],[f210,f2471]) ).
fof(f2471,plain,
( spl0_239
<=> ! [X9,X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f210,axiom,
! [X0,X8,X9] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f2469,plain,
spl0_238,
inference(avatar_split_clause,[],[f209,f2467]) ).
fof(f2467,plain,
( spl0_238
<=> ! [X9,X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X9
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f209,axiom,
! [X0,X8,X9] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X9
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f2465,plain,
spl0_237,
inference(avatar_split_clause,[],[f138,f2463]) ).
fof(f2463,plain,
( spl0_237
<=> ! [X24,X0,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f138,axiom,
! [X0,X8,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
fof(f2461,plain,
spl0_236,
inference(avatar_split_clause,[],[f137,f2459]) ).
fof(f2459,plain,
( spl0_236
<=> ! [X24,X0,X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X8,X24,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f137,axiom,
! [X0,X8,X9,X24] : c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X8,X24,tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
fof(f2457,plain,
spl0_235,
inference(avatar_split_clause,[],[f129,f2455]) ).
fof(f2455,plain,
( spl0_235
<=> ! [X0,X8,X9,X1] :
( hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(X8,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f129,axiom,
! [X0,X1,X8,X9] :
( hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(X8,X1))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f2453,plain,
spl0_234,
inference(avatar_split_clause,[],[f78,f2451]) ).
fof(f2451,plain,
( spl0_234
<=> ! [X62,X0,X30,X8,X24] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24)
| ~ hBOOL(c_in(X62,X8,X0))
| c_lessequals(hAPP(X30,X62),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X30,X0,X24),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f78,axiom,
! [X0,X8,X62,X24,X30] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X24)
| ~ hBOOL(c_in(X62,X8,X0))
| c_lessequals(hAPP(X30,X62),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X30,X0,X24),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
fof(f2449,plain,
spl0_233,
inference(avatar_split_clause,[],[f64,f2447]) ).
fof(f2447,plain,
( spl0_233
<=> ! [X37,X33,X40,X11,X36,X32] :
( ~ hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevaln(X32,X37,X40,X36)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X32,X33),X37,X40,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f64,axiom,
! [X40,X11,X36,X37,X32,X33] :
( ~ hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevaln(X32,X37,X40,X36)
| c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X32,X33),X37,X40,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).
fof(f2445,plain,
spl0_232,
inference(avatar_split_clause,[],[f63,f2443]) ).
fof(f2443,plain,
( spl0_232
<=> ! [X38,X40,X11,X33,X39,X37] :
( ~ hBOOL(hAPP(X11,X37))
| c_Natural_Oevaln(X33,X37,X40,X38)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X33,X39),X37,X40,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f63,axiom,
! [X40,X38,X39,X11,X37,X33] :
( ~ hBOOL(hAPP(X11,X37))
| c_Natural_Oevaln(X33,X37,X40,X38)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(X11,X33,X39),X37,X40,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).
fof(f2441,plain,
spl0_231,
inference(avatar_split_clause,[],[f62,f2439]) ).
fof(f2439,plain,
( spl0_231
<=> ! [X24,X0,X9,X8] : c_HOL_Ominus__class_Ominus(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f62,axiom,
! [X0,X8,X9,X24] : c_HOL_Ominus__class_Ominus(X8,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X9,X24,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
fof(f2437,plain,
spl0_230,
inference(avatar_split_clause,[],[f47,f2435]) ).
fof(f2435,plain,
( spl0_230
<=> ! [X35,X33,X34,X40,X36,X32] :
( ~ c_Natural_Oevaln(X32,X34,X40,X36)
| ~ c_Natural_Oevaln(X33,X36,X40,X35)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X32,X33),X34,X40,X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f47,axiom,
! [X40,X36,X34,X35,X32,X33] :
( ~ c_Natural_Oevaln(X32,X34,X40,X36)
| ~ c_Natural_Oevaln(X33,X36,X40,X35)
| c_Natural_Oevaln(c_Com_Ocom_OSemi(X32,X33),X34,X40,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
fof(f2433,plain,
spl0_229,
inference(avatar_split_clause,[],[f14,f2431]) ).
fof(f2431,plain,
( spl0_229
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
fof(f2429,plain,
spl0_228,
inference(avatar_split_clause,[],[f4,f2427]) ).
fof(f2427,plain,
( spl0_228
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f2425,plain,
spl0_227,
inference(avatar_split_clause,[],[f3,f2423]) ).
fof(f2423,plain,
( spl0_227
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f2421,plain,
spl0_226,
inference(avatar_split_clause,[],[f2,f2419]) ).
fof(f2419,plain,
( spl0_226
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f2417,plain,
( ~ spl0_225
| ~ spl0_188
| spl0_223 ),
inference(avatar_split_clause,[],[f2408,f2404,f2016,f2414]) ).
fof(f2016,plain,
( spl0_188
<=> ! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f2404,plain,
( spl0_223
<=> c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2408,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G,t_a)
| ~ spl0_188
| spl0_223 ),
inference(resolution,[],[f2406,f2017]) ).
fof(f2017,plain,
( ! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f2016]) ).
fof(f2406,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| spl0_223 ),
inference(avatar_component_clause,[],[f2404]) ).
fof(f2412,plain,
spl0_224,
inference(avatar_split_clause,[],[f1,f2410]) ).
fof(f2410,plain,
( spl0_224
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f2407,plain,
( ~ spl0_223
| ~ spl0_22
| ~ spl0_120
| ~ spl0_153
| spl0_222 ),
inference(avatar_split_clause,[],[f2402,f2395,f1585,f1344,f907,f2404]) ).
fof(f907,plain,
( spl0_22
<=> ! [X0,X7] : c_Collect(X7,X0) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1585,plain,
( spl0_153
<=> ! [X9,X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f2395,plain,
( spl0_222
<=> c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2402,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ spl0_22
| ~ spl0_120
| ~ spl0_153
| spl0_222 ),
inference(forward_demodulation,[],[f2401,f908]) ).
fof(f908,plain,
( ! [X0,X7] : c_Collect(X7,X0) = X7
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f2401,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(v_G,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ spl0_22
| ~ spl0_120
| ~ spl0_153
| spl0_222 ),
inference(forward_demodulation,[],[f2400,f1586]) ).
fof(f1586,plain,
( ! [X0,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_fun(X0,tc_bool))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1585]) ).
fof(f2400,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ spl0_22
| ~ spl0_120
| spl0_222 ),
inference(forward_demodulation,[],[f2399,f908]) ).
fof(f2399,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ spl0_120
| spl0_222 ),
inference(forward_demodulation,[],[f2397,f1345]) ).
fof(f2397,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| spl0_222 ),
inference(avatar_component_clause,[],[f2395]) ).
fof(f2398,plain,
~ spl0_222,
inference(avatar_split_clause,[],[f471,f2395]) ).
fof(f471,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),v_G,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference(definition_unfolding,[],[f441,f149,f149]) ).
fof(f441,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q),v_G,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2331,plain,
( spl0_221
| ~ spl0_2
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1386,f1336,f810,f2329]) ).
fof(f2329,plain,
( spl0_221
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f810,plain,
( spl0_2
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1386,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
| ~ spl0_2
| ~ spl0_118 ),
inference(resolution,[],[f1337,f812]) ).
fof(f812,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f2305,plain,
spl0_220,
inference(avatar_split_clause,[],[f595,f2303]) ).
fof(f2303,plain,
( spl0_220
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f595,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0)),X1)),
inference(forward_demodulation,[],[f594,f58]) ).
fof(f594,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0))),
inference(forward_demodulation,[],[f593,f91]) ).
fof(f593,plain,
! [X0,X1] : hBOOL(hAPP(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X0))),
inference(forward_demodulation,[],[f489,f201]) ).
fof(f489,plain,
! [X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0))),
inference(definition_unfolding,[],[f377,f149,f149]) ).
fof(f377,axiom,
! [X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
fof(f2301,plain,
spl0_219,
inference(avatar_split_clause,[],[f571,f2299]) ).
fof(f2299,plain,
( spl0_219
<=> ! [X0,X1,X8] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f571,plain,
! [X0,X1,X8] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X8,tc_fun(X0,tc_bool)),X1)),
inference(forward_demodulation,[],[f472,f91]) ).
fof(f472,plain,
! [X0,X1,X8] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X8,tc_fun(X0,tc_bool)),X1)),
inference(definition_unfolding,[],[f419,f149]) ).
fof(f419,axiom,
! [X0,X1,X8] : hBOOL(hAPP(c_Set_Oinsert(X1,X8,X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f2297,plain,
spl0_218,
inference(avatar_split_clause,[],[f310,f2295]) ).
fof(f2295,plain,
( spl0_218
<=> ! [X38,X0,X9,X8] :
( ~ hBOOL(c_in(X38,X8,X0))
| hBOOL(c_in(X38,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f310,axiom,
! [X38,X0,X8,X9] :
( ~ hBOOL(c_in(X38,X8,X0))
| hBOOL(c_in(X38,X9,X0))
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
fof(f2293,plain,
spl0_217,
inference(avatar_split_clause,[],[f188,f2291]) ).
fof(f2291,plain,
( spl0_217
<=> ! [X24,X0,X31,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X31,X8,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f188,axiom,
! [X31,X0,X8,X24] :
( c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) = X8
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oimage(X31,X8,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
fof(f2289,plain,
spl0_216,
inference(avatar_split_clause,[],[f181,f2287]) ).
fof(f2287,plain,
( spl0_216
<=> ! [X61,X0,X31,X1,X24] :
( ~ class_HOL_Oord(X24)
| ~ c_lessequals(X31,X61,tc_fun(X0,X24))
| c_lessequals(hAPP(X31,X1),hAPP(X61,X1),X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f181,axiom,
! [X31,X0,X1,X24,X61] :
( ~ class_HOL_Oord(X24)
| ~ c_lessequals(X31,X61,tc_fun(X0,X24))
| c_lessequals(hAPP(X31,X1),hAPP(X61,X1),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f2285,plain,
spl0_215,
inference(avatar_split_clause,[],[f175,f2283]) ).
fof(f2283,plain,
( spl0_215
<=> ! [X24,X31,X0,X8,X1] :
( ~ hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(hAPP(X31,X1),c_Set_Oimage(X31,X8,X0,X24),X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f175,axiom,
! [X31,X0,X1,X8,X24] :
( ~ hBOOL(c_in(X1,X8,X0))
| hBOOL(c_in(hAPP(X31,X1),c_Set_Oimage(X31,X8,X0,X24),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
fof(f2281,plain,
spl0_214,
inference(avatar_split_clause,[],[f55,f2279]) ).
fof(f2279,plain,
( spl0_214
<=> ! [X24,X47,X0,X46,X45,X7] : hAPP(c_COMBS(X7,X45,X24,X46,X0),X47) = hAPP(hAPP(X7,X47),hAPP(X45,X47)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f55,axiom,
! [X46,X0,X47,X7,X45,X24] : hAPP(c_COMBS(X7,X45,X24,X46,X0),X47) = hAPP(hAPP(X7,X47),hAPP(X45,X47)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
fof(f2199,plain,
( spl0_212
| ~ spl0_213
| ~ spl0_78
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2141,f2097,f1134,f2196,f2193]) ).
fof(f2193,plain,
( spl0_212
<=> ! [X0] : c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2196,plain,
( spl0_213
<=> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1134,plain,
( spl0_78
<=> ! [X0,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f2141,plain,
( ! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_78
| ~ spl0_201 ),
inference(resolution,[],[f2098,f1135]) ).
fof(f1135,plain,
( ! [X0,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f2139,plain,
spl0_211,
inference(avatar_split_clause,[],[f628,f2137]) ).
fof(f2137,plain,
( spl0_211
<=> ! [X6,X0,X11] :
( ~ hBOOL(c_in(X11,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0))
| X6 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f628,plain,
! [X0,X11,X6] :
( ~ hBOOL(c_in(X11,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0))
| X6 = X11 ),
inference(forward_demodulation,[],[f627,f91]) ).
fof(f627,plain,
! [X0,X11,X6] :
( ~ hBOOL(c_in(X11,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0))
| X6 = X11 ),
inference(forward_demodulation,[],[f507,f201]) ).
fof(f507,plain,
! [X0,X11,X6] :
( X6 = X11
| ~ hBOOL(c_in(X11,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0)) ),
inference(definition_unfolding,[],[f389,f149]) ).
fof(f389,axiom,
! [X0,X11,X6] :
( X6 = X11
| ~ hBOOL(c_in(X11,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f2135,plain,
spl0_210,
inference(avatar_split_clause,[],[f626,f2133]) ).
fof(f2133,plain,
( spl0_210
<=> ! [X6,X0] :
( hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X6,X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f626,plain,
! [X0,X6] :
( hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X6,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(forward_demodulation,[],[f625,f91]) ).
fof(f625,plain,
! [X0,X6] :
( c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X6,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(forward_demodulation,[],[f506,f201]) ).
fof(f506,plain,
! [X0,X6] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_Oord__class_OatLeastAtMost(X6,X6,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f393,f149]) ).
fof(f393,axiom,
! [X0,X6] :
( ~ class_Orderings_Oorder(X0)
| c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
fof(f2131,plain,
spl0_209,
inference(avatar_split_clause,[],[f586,f2129]) ).
fof(f2129,plain,
( spl0_209
<=> ! [X6,X0,X31] : c_The(c_Finite__Set_Ofold1Set(X31,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f586,plain,
! [X31,X0,X6] : c_The(c_Finite__Set_Ofold1Set(X31,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0) = X6,
inference(forward_demodulation,[],[f585,f91]) ).
fof(f585,plain,
! [X31,X0,X6] : c_The(c_Finite__Set_Ofold1Set(X31,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0),X0) = X6,
inference(forward_demodulation,[],[f483,f201]) ).
fof(f483,plain,
! [X31,X0,X6] : c_The(c_Finite__Set_Ofold1Set(X31,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0),X0) = X6,
inference(definition_unfolding,[],[f390,f76,f149]) ).
fof(f76,axiom,
! [X31,X0,X8] : c_Finite__Set_Ofold1(X31,X8,X0) = c_The(c_Finite__Set_Ofold1Set(X31,X8,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).
fof(f390,axiom,
! [X31,X0,X6] : c_Finite__Set_Ofold1(X31,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
fof(f2127,plain,
spl0_208,
inference(avatar_split_clause,[],[f415,f2125]) ).
fof(f2125,plain,
( spl0_208
<=> ! [X36,X37,X7] :
( ~ c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X7),X37,X36)
| c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X7)),X37,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f415,axiom,
! [X36,X37,X7] :
( ~ c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X7),X37,X36)
| c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X7)),X37,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
fof(f2123,plain,
spl0_207,
inference(avatar_split_clause,[],[f414,f2121]) ).
fof(f2121,plain,
( spl0_207
<=> ! [X34,X36,X5] :
( c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X5),X34,X36)
| ~ c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5)),X34,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f414,axiom,
! [X36,X34,X5] :
( c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,X5),X34,X36)
| ~ c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X5)),X34,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
fof(f2119,plain,
spl0_206,
inference(avatar_split_clause,[],[f355,f2117]) ).
fof(f2117,plain,
( spl0_206
<=> ! [X0,X74,X90,X92] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,X90,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| ~ c_lessequals(X92,X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f355,axiom,
! [X90,X0,X92,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,X90,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| ~ c_lessequals(X92,X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_thin_0) ).
fof(f2115,plain,
spl0_205,
inference(avatar_split_clause,[],[f354,f2113]) ).
fof(f2113,plain,
( spl0_205
<=> ! [X74,X0,X91,X90] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X91,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| ~ c_lessequals(X90,X91,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f354,axiom,
! [X0,X90,X91,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X91,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| ~ c_lessequals(X90,X91,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weaken_0) ).
fof(f2111,plain,
spl0_204,
inference(avatar_split_clause,[],[f334,f2109]) ).
fof(f2109,plain,
( spl0_204
<=> ! [X38,X11,X33,X39,X37] :
( c_Natural_Oevalc(X39,X37,X38)
| c_Natural_Oevalc(X33,X37,X38)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X33,X39),X37,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f334,axiom,
! [X38,X39,X11,X37,X33] :
( c_Natural_Oevalc(X39,X37,X38)
| c_Natural_Oevalc(X33,X37,X38)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X33,X39),X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
fof(f2107,plain,
spl0_203,
inference(avatar_split_clause,[],[f319,f2105]) ).
fof(f2105,plain,
( spl0_203
<=> ! [X6,X0,X11] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X11,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f319,axiom,
! [X0,X11,X6] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X11,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
fof(f2103,plain,
spl0_202,
inference(avatar_split_clause,[],[f291,f2101]) ).
fof(f2101,plain,
( spl0_202
<=> ! [X23,X0,X9,X8] :
( ~ hBOOL(c_in(X23,X8,X0))
| hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f291,axiom,
! [X0,X8,X9,X23] :
( ~ hBOOL(c_in(X23,X8,X0))
| hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f2099,plain,
( spl0_201
| ~ spl0_144
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2055,f2016,f1487,f2097]) ).
fof(f2055,plain,
( ! [X0,X1] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_144
| ~ spl0_188 ),
inference(resolution,[],[f2017,f1488]) ).
fof(f2095,plain,
spl0_200,
inference(avatar_split_clause,[],[f290,f2093]) ).
fof(f2093,plain,
( spl0_200
<=> ! [X23,X0,X9,X8] :
( ~ hBOOL(c_in(X23,X9,X0))
| hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f290,axiom,
! [X0,X8,X9,X23] :
( ~ hBOOL(c_in(X23,X9,X0))
| hBOOL(c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f2091,plain,
spl0_199,
inference(avatar_split_clause,[],[f273,f2089]) ).
fof(f2089,plain,
( spl0_199
<=> ! [X6,X0,X11] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X6,X11,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f273,axiom,
! [X0,X11,X6] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X6,X11,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X6,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
fof(f2087,plain,
spl0_198,
inference(avatar_split_clause,[],[f268,f2085]) ).
fof(f2085,plain,
( spl0_198
<=> ! [X37,X33,X11,X36,X32] :
( ~ c_Natural_Oevalc(X33,X37,X36)
| hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X32,X33),X37,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f268,axiom,
! [X36,X11,X37,X32,X33] :
( ~ c_Natural_Oevalc(X33,X37,X36)
| hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X32,X33),X37,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
fof(f2083,plain,
spl0_197,
inference(avatar_split_clause,[],[f267,f2081]) ).
fof(f2081,plain,
( spl0_197
<=> ! [X38,X11,X33,X39,X37] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(X39,X37,X38)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X33,X39),X37,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f267,axiom,
! [X38,X39,X11,X37,X33] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(X39,X37,X38)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X33,X39),X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
fof(f2079,plain,
spl0_196,
inference(avatar_split_clause,[],[f249,f2077]) ).
fof(f2077,plain,
( spl0_196
<=> ! [X9,X0,X8] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f249,axiom,
! [X0,X8,X9] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
fof(f2075,plain,
spl0_195,
inference(avatar_split_clause,[],[f197,f2073]) ).
fof(f2073,plain,
( spl0_195
<=> ! [X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| ~ c_lessequals(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f197,axiom,
! [X0,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X8
| ~ c_lessequals(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2071,plain,
spl0_194,
inference(avatar_split_clause,[],[f169,f2069]) ).
fof(f2069,plain,
( spl0_194
<=> ! [X37,X40,X7,X36] :
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X7),X37,X40,X36)
| c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X7,X40,X37,X36)) = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f169,axiom,
! [X40,X36,X37,X7] :
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X7),X37,X40,X36)
| c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(X7,X40,X37,X36)) = X40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
fof(f2067,plain,
spl0_193,
inference(avatar_split_clause,[],[f103,f2065]) ).
fof(f2065,plain,
( spl0_193
<=> ! [X23,X0,X9,X8] :
( ~ hBOOL(c_in(X23,X9,X0))
| ~ hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f103,axiom,
! [X0,X8,X9,X23] :
( ~ hBOOL(c_in(X23,X9,X0))
| ~ hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
fof(f2063,plain,
spl0_192,
inference(avatar_split_clause,[],[f101,f2061]) ).
fof(f2061,plain,
( spl0_192
<=> ! [X23,X0,X9,X8] :
( hBOOL(c_in(X23,X8,X0))
| ~ hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f101,axiom,
! [X0,X8,X9,X23] :
( hBOOL(c_in(X23,X8,X0))
| ~ hBOOL(c_in(X23,c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
fof(f2059,plain,
spl0_191,
inference(avatar_split_clause,[],[f58,f2057]) ).
fof(f2057,plain,
( spl0_191
<=> ! [X24,X47,X0,X46,X45,X7] : hAPP(hAPP(c_COMBC(X7,X24,X46,X0),X45),X47) = hAPP(hAPP(X7,X47),X45) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2054,plain,
spl0_190,
inference(avatar_split_clause,[],[f45,f2052]) ).
fof(f2052,plain,
( spl0_190
<=> ! [X37,X33,X11,X36,X32] :
( ~ hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevalc(X32,X37,X36)
| c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X32,X33),X37,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f45,axiom,
! [X11,X36,X37,X32,X33] :
( ~ hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevalc(X32,X37,X36)
| c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X32,X33),X37,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
fof(f2050,plain,
spl0_189,
inference(avatar_split_clause,[],[f44,f2048]) ).
fof(f2048,plain,
( spl0_189
<=> ! [X38,X11,X33,X39,X37] :
( ~ hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(X33,X37,X38)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X33,X39),X37,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f44,axiom,
! [X38,X39,X11,X37,X33] :
( ~ hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(X33,X37,X38)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(X11,X33,X39),X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
fof(f2018,plain,
( spl0_188
| ~ spl0_100
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1565,f1487,f1254,f2016]) ).
fof(f1254,plain,
( spl0_100
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1565,plain,
( ! [X0] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,v_G,t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a) )
| ~ spl0_100
| ~ spl0_144 ),
inference(resolution,[],[f1488,f1256]) ).
fof(f1256,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1254]) ).
fof(f1912,plain,
spl0_187,
inference(avatar_split_clause,[],[f620,f1910]) ).
fof(f1910,plain,
( spl0_187
<=> ! [X6,X0] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f620,plain,
! [X0,X6] :
( c_Complete__Lattice_OSup__class_OSup(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f619,f91]) ).
fof(f619,plain,
! [X0,X6] :
( c_Complete__Lattice_OSup__class_OSup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0) = X6
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f503,f201]) ).
fof(f503,plain,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X6 ),
inference(definition_unfolding,[],[f376,f149]) ).
fof(f376,axiom,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
fof(f1908,plain,
spl0_186,
inference(avatar_split_clause,[],[f618,f1906]) ).
fof(f1906,plain,
( spl0_186
<=> ! [X6,X0] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f618,plain,
! [X0,X6] :
( c_Complete__Lattice_OInf__class_OInf(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f617,f91]) ).
fof(f617,plain,
! [X0,X6] :
( c_Complete__Lattice_OInf__class_OInf(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0) = X6
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(forward_demodulation,[],[f502,f201]) ).
fof(f502,plain,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X6 ),
inference(definition_unfolding,[],[f396,f149]) ).
fof(f396,axiom,
! [X0,X6] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
fof(f1904,plain,
spl0_185,
inference(avatar_split_clause,[],[f616,f1902]) ).
fof(f1902,plain,
( spl0_185
<=> ! [X6,X0] :
( c_Finite__Set_Olinorder__class_OMin(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f616,plain,
! [X0,X6] :
( c_Finite__Set_Olinorder__class_OMin(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f615,f91]) ).
fof(f615,plain,
! [X0,X6] :
( c_Finite__Set_Olinorder__class_OMin(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0) = X6
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f501,f201]) ).
fof(f501,plain,
! [X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMin(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X6 ),
inference(definition_unfolding,[],[f380,f149]) ).
fof(f380,axiom,
! [X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
fof(f1900,plain,
spl0_184,
inference(avatar_split_clause,[],[f614,f1898]) ).
fof(f1898,plain,
( spl0_184
<=> ! [X6,X0] :
( c_Finite__Set_Olinorder__class_OMax(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f614,plain,
! [X0,X6] :
( c_Finite__Set_Olinorder__class_OMax(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0) = X6
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f613,f91]) ).
fof(f613,plain,
! [X0,X6] :
( c_Finite__Set_Olinorder__class_OMax(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),X0) = X6
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_demodulation,[],[f500,f201]) ).
fof(f500,plain,
! [X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X6),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X6 ),
inference(definition_unfolding,[],[f391,f149]) ).
fof(f391,axiom,
! [X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
fof(f1896,plain,
spl0_183,
inference(avatar_split_clause,[],[f588,f1894]) ).
fof(f1894,plain,
( spl0_183
<=> ! [X0,X1,X31] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f588,plain,
! [X31,X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X1)),
inference(forward_demodulation,[],[f587,f91]) ).
fof(f587,plain,
! [X31,X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X0),X1)),
inference(forward_demodulation,[],[f484,f201]) ).
fof(f484,plain,
! [X31,X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0),X1)),
inference(definition_unfolding,[],[f379,f149]) ).
fof(f379,axiom,
! [X31,X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
fof(f1892,plain,
spl0_182,
inference(avatar_split_clause,[],[f349,f1890]) ).
fof(f1890,plain,
( spl0_182
<=> ! [X0,X5,X45,X7] : c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f349,axiom,
! [X0,X7,X45,X5] : c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X0),X7),hAPP(c_Com_Ocom_OBODY,X5)),X45),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Body__triple__valid__0_0) ).
fof(f1888,plain,
spl0_181,
inference(avatar_split_clause,[],[f323,f1886]) ).
fof(f1886,plain,
( spl0_181
<=> ! [X38,X40,X11,X23,X37] :
( X37 = X38
| hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X37,X40,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f323,axiom,
! [X40,X38,X11,X37,X23] :
( X37 = X38
| hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X37,X40,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).
fof(f1884,plain,
spl0_180,
inference(avatar_split_clause,[],[f313,f1882]) ).
fof(f1882,plain,
( spl0_180
<=> ! [X0,X7,X45,X1] :
( ~ hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(X45,X1))
| ~ c_lessequals(X7,X45,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f313,axiom,
! [X0,X1,X7,X45] :
( ~ hBOOL(hAPP(X7,X1))
| hBOOL(hAPP(X45,X1))
| ~ c_lessequals(X7,X45,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f1880,plain,
spl0_179,
inference(avatar_split_clause,[],[f305,f1878]) ).
fof(f1878,plain,
( spl0_179
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f305,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(X1,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f1876,plain,
( ~ spl0_178
| ~ spl0_71
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1865,f1861,f1106,f1873]) ).
fof(f1873,plain,
( spl0_178
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1106,plain,
( spl0_71
<=> ! [X0,X1] : ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1861,plain,
( spl0_176
<=> 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_176])]) ).
fof(f1865,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_71
| ~ spl0_176 ),
inference(superposition,[],[f1107,f1863]) ).
fof(f1863,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_176 ),
inference(avatar_component_clause,[],[f1861]) ).
fof(f1107,plain,
( ! [X0,X1] : ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f1871,plain,
spl0_177,
inference(avatar_split_clause,[],[f304,f1869]) ).
fof(f1869,plain,
( spl0_177
<=> ! [X0,X3,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f304,axiom,
! [X2,X3,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f1864,plain,
( spl0_176
| ~ spl0_16
| ~ spl0_128
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1859,f1855,f1376,f880,f1861]) ).
fof(f1855,plain,
( spl0_175
<=> 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_175])]) ).
fof(f1859,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_16
| ~ spl0_128
| ~ spl0_175 ),
inference(forward_demodulation,[],[f1857,f1430]) ).
fof(f1857,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_175 ),
inference(avatar_component_clause,[],[f1855]) ).
fof(f1858,plain,
spl0_175,
inference(avatar_split_clause,[],[f266,f1855]) ).
fof(f266,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(f1853,plain,
spl0_174,
inference(avatar_split_clause,[],[f261,f1851]) ).
fof(f1851,plain,
( spl0_174
<=> ! [X9,X0,X8] :
( c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f261,axiom,
! [X0,X8,X9] :
( c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) != X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f1849,plain,
spl0_173,
inference(avatar_split_clause,[],[f260,f1847]) ).
fof(f1847,plain,
( spl0_173
<=> ! [X9,X0,X8] :
( ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f260,axiom,
! [X0,X8,X9] :
( ~ c_lessequals(X9,X8,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f1845,plain,
spl0_172,
inference(avatar_split_clause,[],[f259,f1843]) ).
fof(f1843,plain,
( spl0_172
<=> ! [X9,X0,X8] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f259,axiom,
! [X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f1841,plain,
spl0_171,
inference(avatar_split_clause,[],[f200,f1839]) ).
fof(f1839,plain,
( spl0_171
<=> ! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f200,axiom,
! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
fof(f1837,plain,
spl0_170,
inference(avatar_split_clause,[],[f161,f1835]) ).
fof(f1835,plain,
( spl0_170
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f1833,plain,
spl0_169,
inference(avatar_split_clause,[],[f160,f1831]) ).
fof(f1831,plain,
( spl0_169
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f160,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f1826,plain,
spl0_168,
inference(avatar_split_clause,[],[f125,f1824]) ).
fof(f1824,plain,
( spl0_168
<=> ! [X24,X11,X0,X6,X70,X46] : hAPP(X6,hAPP(X11,X70)) = hAPP(c_Fun_Ocomp(X6,X11,X46,X24,X0),X70) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f125,axiom,
! [X70,X46,X11,X0,X6,X24] : hAPP(X6,hAPP(X11,X70)) = hAPP(c_Fun_Ocomp(X6,X11,X46,X24,X0),X70),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f1822,plain,
spl0_167,
inference(avatar_split_clause,[],[f59,f1820]) ).
fof(f1820,plain,
( spl0_167
<=> ! [X24,X47,X7,X0,X45,X46] : hAPP(c_COMBB(X7,X45,X24,X0,X46),X47) = hAPP(X7,hAPP(X45,X47)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f59,axiom,
! [X0,X46,X47,X7,X45,X24] : hAPP(c_COMBB(X7,X45,X24,X0,X46),X47) = hAPP(X7,hAPP(X45,X47)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
fof(f1818,plain,
spl0_166,
inference(avatar_split_clause,[],[f42,f1816]) ).
fof(f42,axiom,
! [X36,X34,X35,X32,X33] :
( ~ c_Natural_Oevalc(X32,X34,X36)
| ~ c_Natural_Oevalc(X33,X36,X35)
| c_Natural_Oevalc(c_Com_Ocom_OSemi(X32,X33),X34,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
fof(f1714,plain,
( ~ spl0_14
| spl0_165
| ~ spl0_86
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1589,f1411,f1173,f1712,f870]) ).
fof(f870,plain,
( spl0_14
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1712,plain,
( spl0_165
<=> ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1173,plain,
( spl0_86
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1411,plain,
( spl0_130
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1589,plain,
( ! [X0] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_86
| ~ spl0_130 ),
inference(superposition,[],[f1174,f1412]) ).
fof(f1412,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f1174,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f1642,plain,
spl0_164,
inference(avatar_split_clause,[],[f335,f1640]) ).
fof(f1640,plain,
( spl0_164
<=> ! [X0,X1,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X8,X0))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f335,axiom,
! [X0,X1,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X8,X0))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
fof(f1633,plain,
spl0_163,
inference(avatar_split_clause,[],[f301,f1631]) ).
fof(f1631,plain,
( spl0_163
<=> ! [X11,X0,X6,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X6,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f301,axiom,
! [X0,X11,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X6,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f1629,plain,
spl0_162,
inference(avatar_split_clause,[],[f300,f1627]) ).
fof(f1627,plain,
( spl0_162
<=> ! [X11,X0,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X11,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f300,axiom,
! [X0,X11,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X11,X1,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f1625,plain,
spl0_161,
inference(avatar_split_clause,[],[f299,f1623]) ).
fof(f1623,plain,
( spl0_161
<=> ! [X11,X0,X6,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f299,axiom,
! [X0,X11,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X6,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f1621,plain,
spl0_160,
inference(avatar_split_clause,[],[f298,f1619]) ).
fof(f1619,plain,
( spl0_160
<=> ! [X11,X0,X6,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X11,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f298,axiom,
! [X0,X11,X1,X6] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X11,X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X6,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f1617,plain,
spl0_159,
inference(avatar_split_clause,[],[f293,f1615]) ).
fof(f1615,plain,
( spl0_159
<=> ! [X38,X11,X23,X37] :
( X37 = X38
| hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X37,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f293,axiom,
! [X38,X11,X37,X23] :
( X37 = X38
| hBOOL(hAPP(X11,X37))
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
fof(f1613,plain,
spl0_158,
inference(avatar_split_clause,[],[f272,f1611]) ).
fof(f1611,plain,
( spl0_158
<=> ! [X0,X1,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X8,X0))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f272,axiom,
! [X0,X1,X8] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| ~ hBOOL(c_in(X1,X8,X0))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
fof(f1609,plain,
spl0_157,
inference(avatar_split_clause,[],[f252,f1607]) ).
fof(f1607,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f252,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f1605,plain,
spl0_156,
inference(avatar_split_clause,[],[f211,f1603]) ).
fof(f1603,plain,
( spl0_156
<=> ! [X0,X24,X31] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X31,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f211,axiom,
! [X31,X0,X24] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Oimage(X31,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
fof(f1601,plain,
spl0_155,
inference(avatar_split_clause,[],[f186,f1599]) ).
fof(f1599,plain,
( spl0_155
<=> ! [X9,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X9
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f186,axiom,
! [X0,X8,X9] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X9
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f1597,plain,
spl0_154,
inference(avatar_split_clause,[],[f185,f1595]) ).
fof(f1595,plain,
( spl0_154
<=> ! [X9,X0,X8] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X8
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f185,axiom,
! [X0,X8,X9] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X8
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f1587,plain,
spl0_153,
inference(avatar_split_clause,[],[f152,f1585]) ).
fof(f152,axiom,
! [X0,X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f1583,plain,
spl0_152,
inference(avatar_split_clause,[],[f133,f1581]) ).
fof(f1581,plain,
( spl0_152
<=> ! [X50,X51,X0,X49,X56,X54,X55,X52,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OSKIP,X0) = X49 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f133,axiom,
! [X50,X51,X0,X49,X56,X54,X55,X52,X53] : c_Com_Ocom_Ocom__case(X49,X50,X51,X52,X53,X54,X55,X56,c_Com_Ocom_OSKIP,X0) = X49,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).
fof(f1579,plain,
spl0_151,
inference(avatar_split_clause,[],[f131,f1577]) ).
fof(f1577,plain,
( spl0_151
<=> ! [X0,X8,X9,X1] :
( ~ hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f131,axiom,
! [X0,X1,X8,X9] :
( ~ hBOOL(hAPP(X8,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f1575,plain,
spl0_150,
inference(avatar_split_clause,[],[f130,f1573]) ).
fof(f1573,plain,
( spl0_150
<=> ! [X9,X0,X1,X8] :
( ~ hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f130,axiom,
! [X0,X1,X8,X9] :
( ~ hBOOL(hAPP(X9,X1))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f1571,plain,
spl0_149,
inference(avatar_split_clause,[],[f105,f1569]) ).
fof(f1569,plain,
( spl0_149
<=> ! [X24,X31,X23,X46] : hAPP(c_Fun_Ocomp(c_COMBK(X23,X24,X46),X31,X46,X24,t_a),v_x) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f105,axiom,
! [X31,X46,X24,X23] : hAPP(c_Fun_Ocomp(c_COMBK(X23,X24,X46),X31,X46,X24,t_a),v_x) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
fof(f1561,plain,
( spl0_148
| ~ spl0_12
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1244,f1209,f860,f1559]) ).
fof(f1559,plain,
( spl0_148
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f860,plain,
( spl0_12
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1209,plain,
( spl0_95
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1244,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_12
| ~ spl0_95 ),
inference(resolution,[],[f1210,f862]) ).
fof(f862,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f1210,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1209]) ).
fof(f1501,plain,
spl0_147,
inference(avatar_split_clause,[],[f583,f1499]) ).
fof(f1499,plain,
( spl0_147
<=> ! [X0,X1] : hBOOL(c_in(X1,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f583,plain,
! [X0,X1] : hBOOL(c_in(X1,hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0)),
inference(forward_demodulation,[],[f582,f91]) ).
fof(f582,plain,
! [X0,X1] : hBOOL(c_in(X1,c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X0)),
inference(forward_demodulation,[],[f481,f201]) ).
fof(f481,plain,
! [X0,X1] : hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0)),
inference(definition_unfolding,[],[f373,f149]) ).
fof(f373,axiom,
! [X0,X1] : hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
fof(f1497,plain,
spl0_146,
inference(avatar_split_clause,[],[f581,f1495]) ).
fof(f1495,plain,
( spl0_146
<=> ! [X0,X1] : c_The(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f581,plain,
! [X0,X1] : c_The(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X1,
inference(forward_demodulation,[],[f580,f91]) ).
fof(f580,plain,
! [X0,X1] : c_The(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X0) = X1,
inference(forward_demodulation,[],[f480,f201]) ).
fof(f480,plain,
! [X0,X1] : c_The(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X1,
inference(definition_unfolding,[],[f381,f149]) ).
fof(f381,axiom,
! [X0,X1] : c_The(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
fof(f1493,plain,
spl0_145,
inference(avatar_split_clause,[],[f579,f1491]) ).
fof(f1491,plain,
( spl0_145
<=> ! [X0,X1] : c_Set_Ocontents(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f579,plain,
! [X0,X1] : c_Set_Ocontents(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = X1,
inference(forward_demodulation,[],[f578,f91]) ).
fof(f578,plain,
! [X0,X1] : c_Set_Ocontents(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),X0) = X1,
inference(forward_demodulation,[],[f479,f201]) ).
fof(f479,plain,
! [X0,X1] : c_Set_Ocontents(c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),X0) = X1,
inference(definition_unfolding,[],[f387,f149]) ).
fof(f387,axiom,
! [X0,X1] : c_Set_Ocontents(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).
fof(f1489,plain,
spl0_144,
inference(avatar_split_clause,[],[f420,f1487]) ).
fof(f420,axiom,
! [X90,X0,X92,X74] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X92,X90,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X74,X92,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
fof(f1485,plain,
spl0_143,
inference(avatar_split_clause,[],[f285,f1483]) ).
fof(f1483,plain,
( spl0_143
<=> ! [X28,X20,X64,X27,X76,X29] :
( X27 = X76
| c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OLocal(X76,X20,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f285,axiom,
! [X28,X29,X76,X27,X20,X64] :
( X27 = X76
| c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OLocal(X76,X20,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
fof(f1481,plain,
spl0_142,
inference(avatar_split_clause,[],[f284,f1479]) ).
fof(f1479,plain,
( spl0_142
<=> ! [X20,X64,X29,X76,X27,X28] :
( X20 = X28
| c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OLocal(X76,X20,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f284,axiom,
! [X28,X29,X76,X27,X20,X64] :
( X20 = X28
| c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OLocal(X76,X20,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
fof(f1477,plain,
spl0_141,
inference(avatar_split_clause,[],[f283,f1475]) ).
fof(f1475,plain,
( spl0_141
<=> ! [X20,X64,X29,X76,X27,X28] :
( X29 = X64
| c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OLocal(X76,X20,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f283,axiom,
! [X28,X29,X76,X27,X64,X20] :
( X29 = X64
| c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OLocal(X76,X20,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
fof(f1473,plain,
spl0_140,
inference(avatar_split_clause,[],[f258,f1471]) ).
fof(f1471,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f258,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f1469,plain,
spl0_139,
inference(avatar_split_clause,[],[f257,f1467]) ).
fof(f1467,plain,
( spl0_139
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f257,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X2,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f1465,plain,
( spl0_138
| ~ spl0_35
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1414,f1372,f959,f1463]) ).
fof(f1463,plain,
( spl0_138
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f959,plain,
( spl0_35
<=> ! [X0,X8] : c_lessequals(X8,X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1414,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X0,X1)
| ~ spl0_35
| ~ spl0_127 ),
inference(resolution,[],[f1373,f960]) ).
fof(f960,plain,
( ! [X0,X8] : c_lessequals(X8,X8,tc_fun(X0,tc_bool))
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f1461,plain,
spl0_137,
inference(avatar_split_clause,[],[f256,f1459]) ).
fof(f1459,plain,
( spl0_137
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f256,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f1457,plain,
spl0_136,
inference(avatar_split_clause,[],[f111,f1455]) ).
fof(f1455,plain,
( spl0_136
<=> ! [X59,X60,X20,X21,X22,X28] :
( X20 = X28
| c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OCond(X28,X59,X60) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f111,axiom,
! [X21,X28,X59,X22,X60,X20] :
( X20 = X28
| c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OCond(X28,X59,X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
fof(f1453,plain,
spl0_135,
inference(avatar_split_clause,[],[f110,f1451]) ).
fof(f1451,plain,
( spl0_135
<=> ! [X28,X59,X60,X20,X22,X21] :
( X21 = X59
| c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OCond(X28,X59,X60) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f110,axiom,
! [X21,X28,X59,X22,X60,X20] :
( X21 = X59
| c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OCond(X28,X59,X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
fof(f1449,plain,
spl0_134,
inference(avatar_split_clause,[],[f109,f1447]) ).
fof(f1447,plain,
( spl0_134
<=> ! [X28,X59,X60,X20,X21,X22] :
( X22 = X60
| c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OCond(X28,X59,X60) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f109,axiom,
! [X21,X28,X59,X22,X60,X20] :
( X22 = X60
| c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OCond(X28,X59,X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
fof(f1445,plain,
spl0_133,
inference(avatar_split_clause,[],[f85,f1443]) ).
fof(f1443,plain,
( spl0_133
<=> ! [X58,X57,X20,X25,X28,X26] :
( X25 = X57
| c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCall(X57,X58,X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f85,axiom,
! [X58,X28,X57,X26,X25,X20] :
( X25 = X57
| c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCall(X57,X58,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
fof(f1441,plain,
spl0_132,
inference(avatar_split_clause,[],[f84,f1439]) ).
fof(f1439,plain,
( spl0_132
<=> ! [X57,X20,X25,X58,X28,X26] :
( X26 = X58
| c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCall(X57,X58,X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f84,axiom,
! [X58,X28,X57,X26,X25,X20] :
( X26 = X58
| c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCall(X57,X58,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
fof(f1437,plain,
spl0_131,
inference(avatar_split_clause,[],[f83,f1435]) ).
fof(f1435,plain,
( spl0_131
<=> ! [X57,X20,X25,X58,X28,X26] :
( X20 = X28
| c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCall(X57,X58,X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f83,axiom,
! [X28,X58,X57,X26,X25,X20] :
( X20 = X28
| c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCall(X57,X58,X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
fof(f1413,plain,
( spl0_130
| ~ spl0_12
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1242,f1205,f860,f1411]) ).
fof(f1205,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1242,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_12
| ~ spl0_94 ),
inference(resolution,[],[f1206,f862]) ).
fof(f1206,plain,
( ! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1205]) ).
fof(f1382,plain,
spl0_129,
inference(avatar_split_clause,[],[f370,f1380]) ).
fof(f370,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
fof(f1378,plain,
spl0_128,
inference(avatar_split_clause,[],[f369,f1376]) ).
fof(f369,axiom,
! [X24] :
( ~ class_Orderings_Obot(X24)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X24)),v_x) = c_Orderings_Obot__class_Obot(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f1374,plain,
spl0_127,
inference(avatar_split_clause,[],[f356,f1372]) ).
fof(f356,axiom,
! [X90,X0,X74] :
( c_Hoare__Mirabelle_Ohoare__derivs(X74,X90,X0)
| ~ c_lessequals(X90,X74,tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).
fof(f1370,plain,
spl0_126,
inference(avatar_split_clause,[],[f248,f1368]) ).
fof(f1368,plain,
( spl0_126
<=> ! [X38,X78,X23,X37] :
( X38 = X78
| ~ c_Natural_Oevalc(X23,X37,X38)
| ~ c_Natural_Oevalc(X23,X37,X78) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f248,axiom,
! [X38,X78,X37,X23] :
( X38 = X78
| ~ c_Natural_Oevalc(X23,X37,X38)
| ~ c_Natural_Oevalc(X23,X37,X78) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
fof(f1366,plain,
spl0_125,
inference(avatar_split_clause,[],[f241,f1364]) ).
fof(f1364,plain,
( spl0_125
<=> ! [X37,X40,X77,X23] :
( ~ c_Natural_Oevaln(X23,X37,X40,X77)
| c_Natural_Oevaln(X23,X37,c_Suc(X40),X77) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f241,axiom,
! [X40,X37,X77,X23] :
( ~ c_Natural_Oevaln(X23,X37,X40,X77)
| c_Natural_Oevaln(X23,X37,c_Suc(X40),X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
fof(f1362,plain,
spl0_124,
inference(avatar_split_clause,[],[f204,f1360]) ).
fof(f1360,plain,
( spl0_124
<=> ! [X0,X8] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f204,axiom,
! [X0,X8] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1358,plain,
spl0_123,
inference(avatar_split_clause,[],[f203,f1356]) ).
fof(f203,axiom,
! [X0,X8] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_HOL_Ominus__class_Ominus(X8,X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1354,plain,
spl0_122,
inference(avatar_split_clause,[],[f202,f1352]) ).
fof(f202,axiom,
! [X0,X9] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X9,tc_fun(X0,tc_bool)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f1350,plain,
( spl0_121
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1315,f1287,f1348]) ).
fof(f1348,plain,
( spl0_121
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1287,plain,
( spl0_108
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1315,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_108 ),
inference(factoring,[],[f1288]) ).
fof(f1288,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f1346,plain,
spl0_120,
inference(avatar_split_clause,[],[f201,f1344]) ).
fof(f1342,plain,
spl0_119,
inference(avatar_split_clause,[],[f154,f1340]) ).
fof(f1340,plain,
( spl0_119
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f154,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f1338,plain,
spl0_118,
inference(avatar_split_clause,[],[f153,f1336]) ).
fof(f153,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f1334,plain,
spl0_117,
inference(avatar_split_clause,[],[f75,f1332]) ).
fof(f1332,plain,
( spl0_117
<=> ! [X37,X40,X11,X23] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X37,X40,X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f75,axiom,
! [X40,X11,X37,X23] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevaln(c_Com_Ocom_OWhile(X11,X23),X37,X40,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).
fof(f1330,plain,
spl0_116,
inference(avatar_split_clause,[],[f21,f1328]) ).
fof(f21,axiom,
! [X0,X8,X9] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X9,tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f1326,plain,
spl0_115,
inference(avatar_split_clause,[],[f9,f1324]) ).
fof(f9,axiom,
! [X0,X8,X9] : c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f1322,plain,
spl0_114,
inference(avatar_split_clause,[],[f8,f1320]) ).
fof(f8,axiom,
! [X0,X8,X9] : c_lessequals(X9,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f1309,plain,
spl0_113,
inference(avatar_split_clause,[],[f635,f1307]) ).
fof(f1307,plain,
( spl0_113
<=> ! [X0,X1,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X7
| ~ hBOOL(hAPP(X7,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f635,plain,
! [X0,X1,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != X7
| ~ hBOOL(hAPP(X7,X1)) ),
inference(forward_demodulation,[],[f191,f91]) ).
fof(f191,axiom,
! [X0,X1,X7] :
( ~ hBOOL(hAPP(X7,X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Collect(X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
fof(f1305,plain,
( ~ spl0_11
| spl0_112
| ~ spl0_80
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f1223,f1161,f1149,f1303,f855]) ).
fof(f1303,plain,
( spl0_112
<=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1149,plain,
( spl0_80
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1161,plain,
( spl0_83
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1223,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_80
| ~ spl0_83 ),
inference(superposition,[],[f1162,f1150]) ).
fof(f1150,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1162,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f1301,plain,
spl0_111,
inference(avatar_split_clause,[],[f469,f1299]) ).
fof(f1299,plain,
( spl0_111
<=> ! [X4,X0,X63] :
( X4 = X63
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X4),X63)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f469,axiom,
! [X0,X4,X63] :
( X4 = X63
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X4),X63)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1297,plain,
spl0_110,
inference(avatar_split_clause,[],[f439,f1295]) ).
fof(f1295,plain,
( spl0_110
<=> ! [X26,X58] :
( X26 = X58
| hAPP(c_Com_Ocom_OBODY,X26) != hAPP(c_Com_Ocom_OBODY,X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f439,axiom,
! [X58,X26] :
( X26 = X58
| hAPP(c_Com_Ocom_OBODY,X26) != hAPP(c_Com_Ocom_OBODY,X58) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
fof(f1293,plain,
spl0_109,
inference(avatar_split_clause,[],[f360,f1291]) ).
fof(f1291,plain,
( spl0_109
<=> ! [X5] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X5))
| hAPP(c_Com_Obody,X5) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f360,axiom,
! [X5] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X5))
| hAPP(c_Com_Obody,X5) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
fof(f1289,plain,
spl0_108,
inference(avatar_split_clause,[],[f339,f1287]) ).
fof(f339,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1285,plain,
spl0_107,
inference(avatar_split_clause,[],[f199,f1283]) ).
fof(f1283,plain,
( spl0_107
<=> ! [X0,X1,X31] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f199,axiom,
! [X31,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X31,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
fof(f1281,plain,
spl0_106,
inference(avatar_split_clause,[],[f156,f1279]) ).
fof(f1279,plain,
( spl0_106
<=> ! [X29,X20,X64,X28] :
( X29 = X64
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X20,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f156,axiom,
! [X28,X29,X64,X20] :
( X29 = X64
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X20,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
fof(f1277,plain,
spl0_105,
inference(avatar_split_clause,[],[f155,f1275]) ).
fof(f1275,plain,
( spl0_105
<=> ! [X20,X64,X29,X28] :
( X20 = X28
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X20,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f155,axiom,
! [X28,X29,X20,X64] :
( X20 = X28
| c_Com_Ocom_OWhile(X28,X29) != c_Com_Ocom_OWhile(X20,X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
fof(f1273,plain,
spl0_104,
inference(avatar_split_clause,[],[f123,f1271]) ).
fof(f1271,plain,
( spl0_104
<=> ! [X6,X0,X44] :
( X6 = X44
| c_Option_Ooption_OSome(X44,X0) != c_Option_Ooption_OSome(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f123,axiom,
! [X0,X6,X44] :
( X6 = X44
| c_Option_Ooption_OSome(X44,X0) != c_Option_Ooption_OSome(X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
fof(f1269,plain,
spl0_103,
inference(avatar_split_clause,[],[f93,f1267]) ).
fof(f1267,plain,
( spl0_103
<=> ! [X59,X60,X21,X22] :
( X21 = X59
| c_Com_Ocom_OSemi(X59,X60) != c_Com_Ocom_OSemi(X21,X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f93,axiom,
! [X21,X59,X60,X22] :
( X21 = X59
| c_Com_Ocom_OSemi(X59,X60) != c_Com_Ocom_OSemi(X21,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
fof(f1265,plain,
spl0_102,
inference(avatar_split_clause,[],[f92,f1263]) ).
fof(f1263,plain,
( spl0_102
<=> ! [X22,X21,X60,X59] :
( X22 = X60
| c_Com_Ocom_OSemi(X59,X60) != c_Com_Ocom_OSemi(X21,X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f92,axiom,
! [X21,X59,X22,X60] :
( X22 = X60
| c_Com_Ocom_OSemi(X59,X60) != c_Com_Ocom_OSemi(X21,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
fof(f1261,plain,
spl0_101,
inference(avatar_split_clause,[],[f88,f1259]) ).
fof(f1259,plain,
( spl0_101
<=> ! [X37,X11,X23] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X37,X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f88,axiom,
! [X11,X37,X23] :
( hBOOL(hAPP(X11,X37))
| c_Natural_Oevalc(c_Com_Ocom_OWhile(X11,X23),X37,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
fof(f1257,plain,
( spl0_100
| ~ spl0_22
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1252,f1247,f907,f1254]) ).
fof(f1247,plain,
( spl0_99
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1252,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),t_a)
| ~ spl0_22
| ~ spl0_99 ),
inference(forward_demodulation,[],[f1251,f908]) ).
fof(f1251,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ spl0_99 ),
inference(forward_demodulation,[],[f1249,f201]) ).
fof(f1249,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f1250,plain,
spl0_99,
inference(avatar_split_clause,[],[f470,f1247]) ).
fof(f470,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),tc_Hoare__Mirabelle_Otriple(t_a),tc_bool),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a),
inference(definition_unfolding,[],[f440,f149]) ).
fof(f440,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1238,plain,
( ~ spl0_2
| spl0_98
| ~ spl0_79
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f1222,f1161,f1142,f1236,f810]) ).
fof(f1236,plain,
( spl0_98
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1142,plain,
( spl0_79
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1222,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_79
| ~ spl0_83 ),
inference(superposition,[],[f1162,f1143]) ).
fof(f1143,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1219,plain,
spl0_97,
inference(avatar_split_clause,[],[f333,f1217]) ).
fof(f1217,plain,
( spl0_97
<=> ! [X20,X29,X27,X25,X28,X26] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OLocal(X27,X28,X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f333,axiom,
! [X28,X29,X26,X27,X25,X20] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OLocal(X27,X28,X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
fof(f1215,plain,
spl0_96,
inference(avatar_split_clause,[],[f205,f1213]) ).
fof(f1213,plain,
( spl0_96
<=> ! [X0,X8] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f205,axiom,
! [X0,X8] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1211,plain,
spl0_95,
inference(avatar_split_clause,[],[f183,f1209]) ).
fof(f183,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1207,plain,
spl0_94,
inference(avatar_split_clause,[],[f182,f1205]) ).
fof(f182,axiom,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1203,plain,
spl0_93,
inference(avatar_split_clause,[],[f180,f1201]) ).
fof(f1201,plain,
( spl0_93
<=> ! [X38,X23,X1,X37] :
( c_Natural_Oevalc(X23,X37,X38)
| ~ c_Natural_Oevaln(X23,X37,X1,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f180,axiom,
! [X38,X1,X37,X23] :
( c_Natural_Oevalc(X23,X37,X38)
| ~ c_Natural_Oevaln(X23,X37,X1,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_1) ).
fof(f1199,plain,
spl0_92,
inference(avatar_split_clause,[],[f132,f1197]) ).
fof(f1197,plain,
( spl0_92
<=> ! [X32,X11,X33] :
( ~ c_Com_OWT(X32)
| ~ c_Com_OWT(X33)
| c_Com_OWT(c_Com_Ocom_OCond(X11,X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f132,axiom,
! [X11,X32,X33] :
( ~ c_Com_OWT(X32)
| ~ c_Com_OWT(X33)
| c_Com_OWT(c_Com_Ocom_OCond(X11,X32,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
fof(f1195,plain,
spl0_91,
inference(avatar_split_clause,[],[f102,f1193]) ).
fof(f1193,plain,
( spl0_91
<=> ! [X28,X20,X21,X29,X27,X22] : c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OLocal(X27,X28,X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f102,axiom,
! [X21,X28,X29,X27,X22,X20] : c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OLocal(X27,X28,X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
fof(f1191,plain,
spl0_90,
inference(avatar_split_clause,[],[f98,f1189]) ).
fof(f1189,plain,
( spl0_90
<=> ! [X38,X0,X40] :
( c_Hoare__Mirabelle_Otriple__valid(X40,X38,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X40),X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f98,axiom,
! [X40,X38,X0] :
( c_Hoare__Mirabelle_Otriple__valid(X40,X38,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(X40),X38,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
fof(f1187,plain,
spl0_89,
inference(avatar_split_clause,[],[f77,f1185]) ).
fof(f1185,plain,
( spl0_89
<=> ! [X59,X60,X20,X25,X28,X26] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCond(X28,X59,X60) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f77,axiom,
! [X28,X59,X26,X60,X25,X20] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OCond(X28,X59,X60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
fof(f1183,plain,
spl0_88,
inference(avatar_split_clause,[],[f61,f1181]) ).
fof(f1181,plain,
( spl0_88
<=> ! [X48,X1,X0] :
( ~ hBOOL(hAPP(X48,X1))
| hBOOL(c_in(X1,X48,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f61,axiom,
! [X48,X0,X1] :
( ~ hBOOL(hAPP(X48,X1))
| hBOOL(c_in(X1,X48,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1179,plain,
spl0_87,
inference(avatar_split_clause,[],[f60,f1177]) ).
fof(f1177,plain,
( spl0_87
<=> ! [X48,X1,X0] :
( hBOOL(hAPP(X48,X1))
| ~ hBOOL(c_in(X1,X48,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f60,axiom,
! [X48,X0,X1] :
( hBOOL(hAPP(X48,X1))
| ~ hBOOL(c_in(X1,X48,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1175,plain,
spl0_86,
inference(avatar_split_clause,[],[f17,f1173]) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1171,plain,
spl0_85,
inference(avatar_split_clause,[],[f16,f1169]) ).
fof(f1169,plain,
( spl0_85
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1167,plain,
spl0_84,
inference(avatar_split_clause,[],[f13,f1165]) ).
fof(f1165,plain,
( spl0_84
<=> ! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1163,plain,
spl0_83,
inference(avatar_split_clause,[],[f12,f1161]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1159,plain,
spl0_82,
inference(avatar_split_clause,[],[f6,f1157]) ).
fof(f1157,plain,
( spl0_82
<=> ! [X6,X4,X7] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X7))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X4,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f6,axiom,
! [X6,X7,X4] :
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X7))
| ~ c_Com_OWT(c_Com_Ocom_OCall(X4,X7,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
fof(f1155,plain,
spl0_81,
inference(avatar_split_clause,[],[f5,f1153]) ).
fof(f1153,plain,
( spl0_81
<=> ! [X6,X4,X5] :
( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X5))
| c_Com_OWT(c_Com_Ocom_OCall(X4,X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f5,axiom,
! [X6,X4,X5] :
( ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,X5))
| c_Com_OWT(c_Com_Ocom_OCall(X4,X5,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
fof(f1151,plain,
( spl0_80
| ~ spl0_11
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f1138,f1066,f855,f1149]) ).
fof(f1138,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_11
| ~ spl0_61 ),
inference(resolution,[],[f1067,f857]) ).
fof(f1144,plain,
( spl0_79
| ~ spl0_2
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f1137,f1066,f810,f1142]) ).
fof(f1137,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_2
| ~ spl0_61 ),
inference(resolution,[],[f1067,f812]) ).
fof(f1136,plain,
spl0_78,
inference(avatar_split_clause,[],[f430,f1134]) ).
fof(f430,axiom,
! [X0,X74] : c_Hoare__Mirabelle_Ohoare__derivs(X74,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
fof(f1132,plain,
spl0_77,
inference(avatar_split_clause,[],[f364,f1130]) ).
fof(f1130,plain,
( spl0_77
<=> ! [X0,X1] : hAPP(c_Option_Othe(X0),c_Option_Ooption_OSome(X1,X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f364,axiom,
! [X0,X1] : hAPP(c_Option_Othe(X0),c_Option_Ooption_OSome(X1,X0)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
fof(f1128,plain,
spl0_76,
inference(avatar_split_clause,[],[f346,f1126]) ).
fof(f1126,plain,
( spl0_76
<=> ! [X20,X26,X25,X58] : c_Com_Ocom_OCall(X25,X26,X20) != hAPP(c_Com_Ocom_OBODY,X58) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f346,axiom,
! [X58,X26,X25,X20] : c_Com_Ocom_OCall(X25,X26,X20) != hAPP(c_Com_Ocom_OBODY,X58),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).
fof(f1124,plain,
spl0_75,
inference(avatar_split_clause,[],[f340,f1122]) ).
fof(f1122,plain,
( spl0_75
<=> ! [X29,X27,X28,X26] : c_Com_Ocom_OLocal(X27,X28,X29) != hAPP(c_Com_Ocom_OBODY,X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f340,axiom,
! [X28,X29,X26,X27] : c_Com_Ocom_OLocal(X27,X28,X29) != hAPP(c_Com_Ocom_OBODY,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
fof(f1120,plain,
spl0_74,
inference(avatar_split_clause,[],[f325,f1118]) ).
fof(f1118,plain,
( spl0_74
<=> ! [X0,X1] : c_The(hAPP(c_fequal(X0),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f325,axiom,
! [X0,X1] : c_The(hAPP(c_fequal(X0),X1),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
fof(f1116,plain,
spl0_73,
inference(avatar_split_clause,[],[f286,f1114]) ).
fof(f1114,plain,
( spl0_73
<=> ! [X32,X33] :
( ~ c_Com_OWT(X32)
| ~ c_Com_OWT(X33)
| c_Com_OWT(c_Com_Ocom_OSemi(X32,X33)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f286,axiom,
! [X32,X33] :
( ~ c_Com_OWT(X32)
| ~ c_Com_OWT(X33)
| c_Com_OWT(c_Com_Ocom_OSemi(X32,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
fof(f1112,plain,
spl0_72,
inference(avatar_split_clause,[],[f239,f1110]) ).
fof(f1110,plain,
( spl0_72
<=> ! [X59,X60,X28,X26] : c_Com_Ocom_OCond(X28,X59,X60) != hAPP(c_Com_Ocom_OBODY,X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f239,axiom,
! [X28,X59,X26,X60] : c_Com_Ocom_OCond(X28,X59,X60) != hAPP(c_Com_Ocom_OBODY,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
fof(f1108,plain,
spl0_71,
inference(avatar_split_clause,[],[f192,f1106]) ).
fof(f192,axiom,
! [X0,X1] : ~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f1104,plain,
spl0_70,
inference(avatar_split_clause,[],[f171,f1102]) ).
fof(f1102,plain,
( spl0_70
<=> ! [X38,X37,X40] :
( X37 = X38
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X37,X40,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f171,axiom,
! [X40,X38,X37] :
( X37 = X38
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X37,X40,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
fof(f1100,plain,
spl0_69,
inference(avatar_split_clause,[],[f168,f1098]) ).
fof(f1098,plain,
( spl0_69
<=> ! [X59,X60,X20,X25,X26] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OSemi(X59,X60) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f168,axiom,
! [X59,X26,X60,X25,X20] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OSemi(X59,X60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
fof(f1096,plain,
spl0_68,
inference(avatar_split_clause,[],[f167,f1094]) ).
fof(f1094,plain,
( spl0_68
<=> ! [X59,X60,X20,X64,X28] : c_Com_Ocom_OCond(X28,X59,X60) != c_Com_Ocom_OWhile(X20,X64) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f167,axiom,
! [X28,X59,X60,X20,X64] : c_Com_Ocom_OCond(X28,X59,X60) != c_Com_Ocom_OWhile(X20,X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
fof(f1092,plain,
spl0_67,
inference(avatar_split_clause,[],[f148,f1090]) ).
fof(f1090,plain,
( spl0_67
<=> ! [X28,X21,X29,X27,X22] : c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OSemi(X21,X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f148,axiom,
! [X21,X28,X29,X27,X22] : c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OSemi(X21,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
fof(f1088,plain,
spl0_66,
inference(avatar_split_clause,[],[f135,f1086]) ).
fof(f1086,plain,
( spl0_66
<=> ! [X20,X64,X29,X27,X28] : c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OWhile(X20,X64) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f135,axiom,
! [X28,X29,X27,X20,X64] : c_Com_Ocom_OLocal(X27,X28,X29) != c_Com_Ocom_OWhile(X20,X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
fof(f1084,plain,
spl0_65,
inference(avatar_split_clause,[],[f126,f1082]) ).
fof(f1082,plain,
( spl0_65
<=> ! [X2,X1] :
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f126,axiom,
! [X2,X1] :
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
fof(f1080,plain,
spl0_64,
inference(avatar_split_clause,[],[f96,f1078]) ).
fof(f1078,plain,
( spl0_64
<=> ! [X59,X60,X20,X21,X22] : c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OSemi(X59,X60) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f96,axiom,
! [X21,X59,X22,X60,X20] : c_Com_Ocom_OCond(X20,X21,X22) != c_Com_Ocom_OSemi(X59,X60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
fof(f1076,plain,
spl0_63,
inference(avatar_split_clause,[],[f82,f1074]) ).
fof(f1074,plain,
( spl0_63
<=> ! [X0,X63] : c_Set_Oimage(c_COMBI(X0),X63,X0,X0) = X63 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f82,axiom,
! [X0,X63] : c_Set_Oimage(c_COMBI(X0),X63,X0,X0) = X63,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).
fof(f1072,plain,
spl0_62,
inference(avatar_split_clause,[],[f68,f1070]) ).
fof(f68,axiom,
! [X0,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X8,tc_fun(X0,tc_bool)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1068,plain,
spl0_61,
inference(avatar_split_clause,[],[f67,f1066]) ).
fof(f67,axiom,
! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1064,plain,
spl0_60,
inference(avatar_split_clause,[],[f56,f1062]) ).
fof(f1062,plain,
( spl0_60
<=> ! [X24,X0,X45,X7] : hAPP(c_COMBK(X7,X0,X24),X45) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f56,axiom,
! [X0,X7,X45,X24] : hAPP(c_COMBK(X7,X0,X24),X45) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f1060,plain,
spl0_59,
inference(avatar_split_clause,[],[f34,f1058]) ).
fof(f1058,plain,
( spl0_59
<=> ! [X20,X29,X25,X28,X26] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OWhile(X28,X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f34,axiom,
! [X28,X29,X26,X25,X20] : c_Com_Ocom_OCall(X25,X26,X20) != c_Com_Ocom_OWhile(X28,X29),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).
fof(f1054,plain,
spl0_58,
inference(avatar_split_clause,[],[f468,f1052]) ).
fof(f1052,plain,
( spl0_58
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f468,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1050,plain,
spl0_57,
inference(avatar_split_clause,[],[f429,f1048]) ).
fof(f1048,plain,
( spl0_57
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f429,axiom,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f1046,plain,
spl0_56,
inference(avatar_split_clause,[],[f344,f1044]) ).
fof(f1044,plain,
( spl0_56
<=> ! [X59,X60,X26] : c_Com_Ocom_OSemi(X59,X60) != hAPP(c_Com_Ocom_OBODY,X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f344,axiom,
! [X59,X26,X60] : c_Com_Ocom_OSemi(X59,X60) != hAPP(c_Com_Ocom_OBODY,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
fof(f1042,plain,
spl0_55,
inference(avatar_split_clause,[],[f341,f1040]) ).
fof(f1040,plain,
( spl0_55
<=> ! [X29,X28,X26] : c_Com_Ocom_OWhile(X28,X29) != hAPP(c_Com_Ocom_OBODY,X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f341,axiom,
! [X28,X29,X26] : c_Com_Ocom_OWhile(X28,X29) != hAPP(c_Com_Ocom_OBODY,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
fof(f1038,plain,
spl0_54,
inference(avatar_split_clause,[],[f337,f1036]) ).
fof(f1036,plain,
( spl0_54
<=> ! [X11,X39,X33] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X11,X33,X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f337,axiom,
! [X39,X11,X33] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X11,X33,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
fof(f1034,plain,
spl0_53,
inference(avatar_split_clause,[],[f336,f1032]) ).
fof(f1032,plain,
( spl0_53
<=> ! [X11,X39,X33] :
( c_Com_OWT(X39)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X11,X33,X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f336,axiom,
! [X39,X11,X33] :
( c_Com_OWT(X39)
| ~ c_Com_OWT(c_Com_Ocom_OCond(X11,X33,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
fof(f1030,plain,
spl0_52,
inference(avatar_split_clause,[],[f184,f1028]) ).
fof(f1028,plain,
( spl0_52
<=> ! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f184,axiom,
! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1026,plain,
spl0_51,
inference(avatar_split_clause,[],[f178,f1024]) ).
fof(f1024,plain,
( spl0_51
<=> ! [X38,X37] :
( X37 = X38
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,X37,X38) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f178,axiom,
! [X38,X37] :
( X37 = X38
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,X37,X38) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
fof(f1022,plain,
spl0_50,
inference(avatar_split_clause,[],[f163,f1020]) ).
fof(f1020,plain,
( spl0_50
<=> ! [X6,X23,X63] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X63,X6,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f163,axiom,
! [X6,X63,X23] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(X63,X6,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
fof(f1018,plain,
spl0_49,
inference(avatar_split_clause,[],[f162,f1016]) ).
fof(f1016,plain,
( spl0_49
<=> ! [X6,X23,X63] :
( ~ c_Com_OWT(X23)
| c_Com_OWT(c_Com_Ocom_OLocal(X63,X6,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f162,axiom,
! [X6,X63,X23] :
( ~ c_Com_OWT(X23)
| c_Com_OWT(c_Com_Ocom_OLocal(X63,X6,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
fof(f1014,plain,
spl0_48,
inference(avatar_split_clause,[],[f94,f1012]) ).
fof(f1012,plain,
( spl0_48
<=> ! [X20,X64,X60,X59] : c_Com_Ocom_OSemi(X59,X60) != c_Com_Ocom_OWhile(X20,X64) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f94,axiom,
! [X59,X60,X20,X64] : c_Com_Ocom_OSemi(X59,X60) != c_Com_Ocom_OWhile(X20,X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
fof(f1009,plain,
spl0_47,
inference(avatar_split_clause,[],[f450,f1007]) ).
fof(f1007,plain,
( spl0_47
<=> ! [X98,X99] :
( ~ class_HOL_Oord(X99)
| class_HOL_Oord(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f450,axiom,
! [X98,X99] :
( ~ class_HOL_Oord(X99)
| class_HOL_Oord(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f1005,plain,
spl0_46,
inference(avatar_split_clause,[],[f449,f1003]) ).
fof(f1003,plain,
( spl0_46
<=> ! [X98,X99] :
( ~ class_HOL_Ominus(X99)
| class_HOL_Ominus(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f449,axiom,
! [X98,X99] :
( ~ class_HOL_Ominus(X99)
| class_HOL_Ominus(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
fof(f1001,plain,
spl0_45,
inference(avatar_split_clause,[],[f448,f999]) ).
fof(f999,plain,
( spl0_45
<=> ! [X98,X99] :
( ~ class_Orderings_Obot(X99)
| class_Orderings_Obot(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f448,axiom,
! [X98,X99] :
( ~ class_Orderings_Obot(X99)
| class_Orderings_Obot(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f997,plain,
spl0_44,
inference(avatar_split_clause,[],[f447,f995]) ).
fof(f995,plain,
( spl0_44
<=> ! [X98,X99] :
( ~ class_Orderings_Oorder(X99)
| class_Orderings_Oorder(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f447,axiom,
! [X98,X99] :
( ~ class_Orderings_Oorder(X99)
| class_Orderings_Oorder(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f993,plain,
spl0_43,
inference(avatar_split_clause,[],[f446,f991]) ).
fof(f991,plain,
( spl0_43
<=> ! [X98,X99] :
( ~ class_Lattices_Olattice(X99)
| class_Lattices_Olattice(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f446,axiom,
! [X98,X99] :
( ~ class_Lattices_Olattice(X99)
| class_Lattices_Olattice(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f989,plain,
spl0_42,
inference(avatar_split_clause,[],[f445,f987]) ).
fof(f987,plain,
( spl0_42
<=> ! [X98,X99] :
( ~ class_Orderings_Opreorder(X99)
| class_Orderings_Opreorder(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f445,axiom,
! [X98,X99] :
( ~ class_Orderings_Opreorder(X99)
| class_Orderings_Opreorder(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f985,plain,
spl0_41,
inference(avatar_split_clause,[],[f444,f983]) ).
fof(f983,plain,
( spl0_41
<=> ! [X98,X99] :
( ~ class_Lattices_Obounded__lattice(X99)
| class_Lattices_Obounded__lattice(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f444,axiom,
! [X98,X99] :
( ~ class_Lattices_Obounded__lattice(X99)
| class_Lattices_Obounded__lattice(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f981,plain,
spl0_40,
inference(avatar_split_clause,[],[f443,f979]) ).
fof(f443,axiom,
! [X98,X99] :
( ~ class_Lattices_Olattice(X99)
| class_Lattices_Oupper__semilattice(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f977,plain,
spl0_39,
inference(avatar_split_clause,[],[f442,f975]) ).
fof(f975,plain,
( spl0_39
<=> ! [X98,X99] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X99)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X98,X99)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f442,axiom,
! [X98,X99] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X99)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X98,X99)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f973,plain,
spl0_38,
inference(avatar_split_clause,[],[f317,f971]) ).
fof(f971,plain,
( spl0_38
<=> ! [X20,X25,X26] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X25,X26,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f317,axiom,
! [X26,X25,X20] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X25,X26,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).
fof(f969,plain,
spl0_37,
inference(avatar_split_clause,[],[f315,f967]) ).
fof(f967,plain,
( spl0_37
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f315,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f965,plain,
spl0_36,
inference(avatar_split_clause,[],[f314,f963]) ).
fof(f963,plain,
( spl0_36
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f314,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f961,plain,
spl0_35,
inference(avatar_split_clause,[],[f311,f959]) ).
fof(f311,axiom,
! [X0,X8] : c_lessequals(X8,X8,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f957,plain,
spl0_34,
inference(avatar_split_clause,[],[f271,f955]) ).
fof(f955,plain,
( spl0_34
<=> ! [X39,X33] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X33,X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f271,axiom,
! [X39,X33] :
( c_Com_OWT(X33)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X33,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
fof(f953,plain,
spl0_33,
inference(avatar_split_clause,[],[f270,f951]) ).
fof(f951,plain,
( spl0_33
<=> ! [X39,X33] :
( c_Com_OWT(X39)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X33,X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f270,axiom,
! [X39,X33] :
( c_Com_OWT(X39)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(X33,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
fof(f949,plain,
spl0_32,
inference(avatar_split_clause,[],[f240,f947]) ).
fof(f947,plain,
( spl0_32
<=> ! [X20,X64,X76] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X76,X20,X64) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f240,axiom,
! [X76,X20,X64] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X76,X20,X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
fof(f945,plain,
spl0_31,
inference(avatar_split_clause,[],[f158,f943]) ).
fof(f943,plain,
( spl0_31
<=> ! [X11,X23] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X11,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f158,axiom,
! [X11,X23] :
( c_Com_OWT(X23)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(X11,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
fof(f941,plain,
spl0_30,
inference(avatar_split_clause,[],[f157,f939]) ).
fof(f939,plain,
( spl0_30
<=> ! [X11,X23] :
( ~ c_Com_OWT(X23)
| c_Com_OWT(c_Com_Ocom_OWhile(X11,X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f157,axiom,
! [X11,X23] :
( ~ c_Com_OWT(X23)
| c_Com_OWT(c_Com_Ocom_OWhile(X11,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_While_0) ).
fof(f937,plain,
spl0_29,
inference(avatar_split_clause,[],[f121,f935]) ).
fof(f935,plain,
( spl0_29
<=> ! [X0,X43] : c_Option_Ooption_ONone(X0) != c_Option_Ooption_OSome(X43,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f121,axiom,
! [X0,X43] : c_Option_Ooption_ONone(X0) != c_Option_Ooption_OSome(X43,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
fof(f933,plain,
spl0_28,
inference(avatar_split_clause,[],[f57,f931]) ).
fof(f931,plain,
( spl0_28
<=> ! [X0,X7] : hAPP(c_COMBI(X0),X7) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f57,axiom,
! [X0,X7] : hAPP(c_COMBI(X0),X7) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
fof(f929,plain,
spl0_27,
inference(avatar_split_clause,[],[f20,f927]) ).
fof(f927,plain,
( spl0_27
<=> ! [X22,X20,X21] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X20,X21,X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f20,axiom,
! [X21,X22,X20] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X20,X21,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
fof(f925,plain,
spl0_26,
inference(avatar_split_clause,[],[f348,f923]) ).
fof(f923,plain,
( spl0_26
<=> ! [X26] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f348,axiom,
! [X26] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
fof(f921,plain,
spl0_25,
inference(avatar_split_clause,[],[f338,f919]) ).
fof(f919,plain,
( spl0_25
<=> ! [X22,X21] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X21,X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f338,axiom,
! [X21,X22] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X21,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
fof(f917,plain,
spl0_24,
inference(avatar_split_clause,[],[f263,f915]) ).
fof(f915,plain,
( spl0_24
<=> ! [X65] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X65) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f263,axiom,
! [X65] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X65),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
fof(f913,plain,
spl0_23,
inference(avatar_split_clause,[],[f262,f911]) ).
fof(f911,plain,
( spl0_23
<=> ! [X37,X40] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X37,X40,X37) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f262,axiom,
! [X40,X37] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X37,X40,X37),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
fof(f909,plain,
spl0_22,
inference(avatar_split_clause,[],[f91,f907]) ).
fof(f905,plain,
spl0_21,
inference(avatar_split_clause,[],[f86,f903]) ).
fof(f903,plain,
( spl0_21
<=> ! [X20,X64] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X20,X64) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f86,axiom,
! [X20,X64] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X20,X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
fof(f901,plain,
spl0_20,
inference(avatar_split_clause,[],[f295,f899]) ).
fof(f899,plain,
( spl0_20
<=> ! [X40] : c_Suc(X40) != X40 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f295,axiom,
! [X40] : c_Suc(X40) != X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f897,plain,
spl0_19,
inference(avatar_split_clause,[],[f246,f895]) ).
fof(f246,axiom,
! [X37] : c_Natural_Oevalc(c_Com_Ocom_OSKIP,X37,X37),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
fof(f893,plain,
spl0_18,
inference(avatar_split_clause,[],[f467,f890]) ).
fof(f890,plain,
( spl0_18
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f467,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f888,plain,
spl0_17,
inference(avatar_split_clause,[],[f466,f885]) ).
fof(f885,plain,
( spl0_17
<=> class_HOL_Ominus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f466,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
fof(f883,plain,
spl0_16,
inference(avatar_split_clause,[],[f465,f880]) ).
fof(f465,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f878,plain,
spl0_15,
inference(avatar_split_clause,[],[f464,f875]) ).
fof(f875,plain,
( spl0_15
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f464,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f873,plain,
spl0_14,
inference(avatar_split_clause,[],[f463,f870]) ).
fof(f463,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f868,plain,
spl0_13,
inference(avatar_split_clause,[],[f462,f865]) ).
fof(f865,plain,
( spl0_13
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f462,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f863,plain,
spl0_12,
inference(avatar_split_clause,[],[f461,f860]) ).
fof(f461,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f858,plain,
spl0_11,
inference(avatar_split_clause,[],[f460,f855]) ).
fof(f460,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f853,plain,
spl0_10,
inference(avatar_split_clause,[],[f459,f850]) ).
fof(f459,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f848,plain,
spl0_9,
inference(avatar_split_clause,[],[f458,f845]) ).
fof(f845,plain,
( spl0_9
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f458,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f843,plain,
spl0_8,
inference(avatar_split_clause,[],[f457,f840]) ).
fof(f840,plain,
( spl0_8
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f457,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
fof(f838,plain,
spl0_7,
inference(avatar_split_clause,[],[f456,f835]) ).
fof(f456,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f833,plain,
spl0_6,
inference(avatar_split_clause,[],[f455,f830]) ).
fof(f830,plain,
( spl0_6
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f455,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f828,plain,
spl0_5,
inference(avatar_split_clause,[],[f454,f825]) ).
fof(f454,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f823,plain,
spl0_4,
inference(avatar_split_clause,[],[f453,f820]) ).
fof(f820,plain,
( spl0_4
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f453,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f818,plain,
spl0_3,
inference(avatar_split_clause,[],[f452,f815]) ).
fof(f815,plain,
( spl0_3
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f452,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f813,plain,
spl0_2,
inference(avatar_split_clause,[],[f451,f810]) ).
fof(f451,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f808,plain,
spl0_1,
inference(avatar_split_clause,[],[f46,f805]) ).
fof(f805,plain,
( spl0_1
<=> c_Com_OWT(c_Com_Ocom_OSKIP) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f46,axiom,
c_Com_OWT(c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV840-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 04:40:58 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (27639)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (27642)WARNING: value z3 for option sas not known
% 0.21/0.40 % (27643)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (27641)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (27645)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40 % (27644)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.40 % (27646)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.40 % (27640)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (27642)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)
% 1.50/0.60 % (27644)First to succeed.
% 1.62/0.61 TRYING [1]
% 1.62/0.62 % (27644)Refutation found. Thanks to Tanya!
% 1.62/0.62 % SZS status Unsatisfiable for theBenchmark
% 1.62/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.78/0.63 % (27644)------------------------------
% 1.78/0.63 % (27644)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.78/0.63 % (27644)Termination reason: Refutation
% 1.78/0.63
% 1.78/0.63 % (27644)Memory used [KB]: 4250
% 1.78/0.63 % (27644)Time elapsed: 0.217 s
% 1.78/0.63 % (27644)Instructions burned: 505 (million)
% 1.78/0.63 % (27644)------------------------------
% 1.78/0.63 % (27644)------------------------------
% 1.78/0.63 % (27639)Success in time 0.245 s
%------------------------------------------------------------------------------