TSTP Solution File: SWV844-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV844-1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:11:56 EDT 2024
% Result : Unsatisfiable 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 316
% Syntax : Number of formulae : 495 ( 236 unt; 0 def)
% Number of atoms : 861 ( 106 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 604 ( 238 ~; 205 |; 0 &)
% ( 161 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 199 ( 197 usr; 162 prp; 0-6 aty)
% Number of functors : 44 ( 44 usr; 15 con; 0-5 aty)
% Number of variables : 533 ( 533 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1835,plain,
$false,
inference(avatar_sat_refutation,[],[f1059,f1064,f1069,f1074,f1079,f1084,f1089,f1094,f1099,f1104,f1109,f1114,f1119,f1124,f1129,f1134,f1139,f1144,f1149,f1154,f1159,f1164,f1169,f1174,f1179,f1184,f1189,f1194,f1199,f1204,f1209,f1214,f1219,f1224,f1229,f1234,f1239,f1244,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1342,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1387,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1420,f1424,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1497,f1508,f1512,f1516,f1520,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1589,f1616,f1625,f1629,f1633,f1637,f1642,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1696,f1700,f1705,f1709,f1713,f1717,f1721,f1725,f1729,f1733,f1737,f1741,f1750,f1754,f1779,f1783,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1829,f1833,f1834]) ).
fof(f1834,plain,
( spl0_63
| ~ spl0_62
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1785,f1781,f1339,f1344]) ).
fof(f1344,plain,
( spl0_63
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1339,plain,
( spl0_62
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1781,plain,
( spl0_149
<=> ! [X65] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X65)),hAPP(v_c0,X65)),hAPP(v_Q_H,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X65)),hAPP(v_c0,X65)),hAPP(v_Q,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1785,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ spl0_62
| ~ spl0_149 ),
inference(resolution,[],[f1782,f1341]) ).
fof(f1341,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f1782,plain,
( ! [X65] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X65)),hAPP(v_c0,X65)),hAPP(v_Q_H,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X65)),hAPP(v_c0,X65)),hAPP(v_Q,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1781]) ).
fof(f1833,plain,
spl0_161,
inference(avatar_split_clause,[],[f716,f1831]) ).
fof(f1831,plain,
( spl0_161
<=> ! [X0,X14,X15] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X14),X15),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f716,axiom,
! [X0,X14,X15] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X14),X15),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
fof(f1829,plain,
spl0_160,
inference(avatar_split_clause,[],[f711,f1827]) ).
fof(f1827,plain,
( spl0_160
<=> ! [X0,X44,X42] :
( c_Finite__Set_Ofinite(X42,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f711,axiom,
! [X0,X44,X42] :
( c_Finite__Set_Ofinite(X42,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
fof(f1825,plain,
spl0_159,
inference(avatar_split_clause,[],[f710,f1823]) ).
fof(f1823,plain,
( spl0_159
<=> ! [X0,X44,X42] :
( c_Finite__Set_Ofinite(X44,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f710,axiom,
! [X0,X44,X42] :
( c_Finite__Set_Ofinite(X44,X0)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
fof(f1821,plain,
spl0_158,
inference(avatar_split_clause,[],[f564,f1819]) ).
fof(f1819,plain,
( spl0_158
<=> ! [X17,X13,X0,X3,X28] :
( X3 = X17
| ~ c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3,X0,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f564,axiom,
! [X3,X28,X0,X17,X13] :
( X3 = X17
| ~ c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3,X0,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
fof(f1817,plain,
spl0_157,
inference(avatar_split_clause,[],[f562,f1815]) ).
fof(f1815,plain,
( spl0_157
<=> ! [X13,X0,X17,X28] : hAPP(hAPP(c_Finite__Set_Ofold(X28,X13,X0),X17),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))) = X17 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f562,axiom,
! [X28,X0,X17,X13] : hAPP(hAPP(c_Finite__Set_Ofold(X28,X13,X0),X17),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).
fof(f1813,plain,
spl0_156,
inference(avatar_split_clause,[],[f558,f1811]) ).
fof(f1811,plain,
( spl0_156
<=> ! [X0,X44,X42] :
( ~ c_Finite__Set_Ofinite(X42,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f558,axiom,
! [X0,X44,X42] :
( ~ c_Finite__Set_Ofinite(X42,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f1809,plain,
spl0_155,
inference(avatar_split_clause,[],[f557,f1807]) ).
fof(f1807,plain,
( spl0_155
<=> ! [X0,X44,X42] :
( ~ c_Finite__Set_Ofinite(X44,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f557,axiom,
! [X0,X44,X42] :
( ~ c_Finite__Set_Ofinite(X44,X0)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f1805,plain,
spl0_154,
inference(avatar_split_clause,[],[f523,f1803]) ).
fof(f1803,plain,
( spl0_154
<=> ! [X0,X14] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X14)) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f523,axiom,
! [X0,X14] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X14)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
fof(f1801,plain,
spl0_153,
inference(avatar_split_clause,[],[f516,f1799]) ).
fof(f1799,plain,
( spl0_153
<=> ! [X3,X13,X0,X5,X28] :
( hAPP(X28,X3) = X5
| c_Fun_Ofun__upd(X28,X3,X5,X0,X13) != X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f516,axiom,
! [X28,X3,X0,X5,X13] :
( hAPP(X28,X3) = X5
| c_Fun_Ofun__upd(X28,X3,X5,X0,X13) != X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
fof(f1797,plain,
spl0_152,
inference(avatar_split_clause,[],[f174,f1795]) ).
fof(f1795,plain,
( spl0_152
<=> ! [X18,X21] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),c_Suc(X18))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f174,axiom,
! [X21,X18] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),c_Suc(X18))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1793,plain,
spl0_151,
inference(avatar_split_clause,[],[f54,f1791]) ).
fof(f1791,plain,
( spl0_151
<=> ! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f54,axiom,
! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f1789,plain,
spl0_150,
inference(avatar_split_clause,[],[f53,f1787]) ).
fof(f1787,plain,
( spl0_150
<=> ! [X0,X15] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X15) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f53,axiom,
! [X0,X15] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X15) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f1783,plain,
spl0_149,
inference(avatar_split_clause,[],[f984,f1781]) ).
fof(f984,axiom,
! [X65] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X65)),hAPP(v_c0,X65)),hAPP(v_Q_H,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X65)),hAPP(v_c0,X65)),hAPP(v_Q,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1779,plain,
spl0_148,
inference(avatar_split_clause,[],[f982,f1776]) ).
fof(f1776,plain,
( spl0_148
<=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f982,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1754,plain,
spl0_147,
inference(avatar_split_clause,[],[f950,f1752]) ).
fof(f1752,plain,
( spl0_147
<=> ! [X3,X0,X14] : c_Set_Oinsert(X3,X14,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X14,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f950,axiom,
! [X3,X0,X14] : c_Set_Oinsert(X3,X14,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X14,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f1750,plain,
( spl0_145
| ~ spl0_146
| ~ spl0_26
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f1486,f1418,f1181,f1747,f1743]) ).
fof(f1743,plain,
( spl0_145
<=> c_Orderings_Oord__class_Omax(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1747,plain,
( spl0_146
<=> class_Orderings_Olinorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1181,plain,
( spl0_26
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1418,plain,
( spl0_81
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Oord__class_Omax(X0) = c_Lattices_Oupper__semilattice__class_Osup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1486,plain,
( ~ class_Orderings_Olinorder(tc_bool)
| c_Orderings_Oord__class_Omax(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(tc_bool)
| ~ spl0_26
| ~ spl0_81 ),
inference(resolution,[],[f1419,f1183]) ).
fof(f1183,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f1419,plain,
( ! [X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X0) = c_Lattices_Oupper__semilattice__class_Osup(X0) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f1741,plain,
spl0_144,
inference(avatar_split_clause,[],[f928,f1739]) ).
fof(f1739,plain,
( spl0_144
<=> ! [X44,X57,X0,X56] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,X56,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,X57,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f928,axiom,
! [X0,X56,X57,X44] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,X56,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,X57,X0)
| c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
fof(f1737,plain,
spl0_143,
inference(avatar_split_clause,[],[f920,f1735]) ).
fof(f1735,plain,
( spl0_143
<=> ! [X44,X0,X56,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Set_Oinsert(X45,X56,tc_Hoare__Mirabelle_Otriple(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f920,axiom,
! [X0,X56,X44,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Set_Oinsert(X45,X56,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
fof(f1733,plain,
spl0_142,
inference(avatar_split_clause,[],[f845,f1731]) ).
fof(f1731,plain,
( spl0_142
<=> ! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f845,axiom,
! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f1729,plain,
spl0_141,
inference(avatar_split_clause,[],[f807,f1727]) ).
fof(f1727,plain,
( spl0_141
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f807,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f1725,plain,
spl0_140,
inference(avatar_split_clause,[],[f806,f1723]) ).
fof(f1723,plain,
( spl0_140
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Otop__class_Otop(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f806,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Otop__class_Otop(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f1721,plain,
spl0_139,
inference(avatar_split_clause,[],[f745,f1719]) ).
fof(f1719,plain,
( spl0_139
<=> ! [X0,X1,X15] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X15),c_Set_Oinsert(X1,X15,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f745,axiom,
! [X0,X1,X15] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X15),c_Set_Oinsert(X1,X15,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1717,plain,
spl0_138,
inference(avatar_split_clause,[],[f734,f1715]) ).
fof(f1715,plain,
( spl0_138
<=> ! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f734,axiom,
! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1713,plain,
spl0_137,
inference(avatar_split_clause,[],[f563,f1711]) ).
fof(f1711,plain,
( spl0_137
<=> ! [X0,X14] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X14),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f563,axiom,
! [X0,X14] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X14),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
fof(f1709,plain,
spl0_136,
inference(avatar_split_clause,[],[f560,f1707]) ).
fof(f1707,plain,
( spl0_136
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f560,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1705,plain,
spl0_135,
inference(avatar_split_clause,[],[f559,f1703]) ).
fof(f1703,plain,
( spl0_135
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f559,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1700,plain,
spl0_134,
inference(avatar_split_clause,[],[f347,f1698]) ).
fof(f1698,plain,
( spl0_134
<=> ! [X18,X21] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),X18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f347,axiom,
! [X21,X18] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1696,plain,
spl0_133,
inference(avatar_split_clause,[],[f131,f1694]) ).
fof(f1694,plain,
( spl0_133
<=> ! [X4,X0,X6,X3,X7] :
( ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0)
| hAPP(hAPP(X4,X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f131,axiom,
! [X3,X0,X6,X7,X4] :
( ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0)
| hAPP(hAPP(X4,X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__idem_0) ).
fof(f1670,plain,
spl0_132,
inference(avatar_split_clause,[],[f972,f1668]) ).
fof(f1668,plain,
( spl0_132
<=> ! [X0,X1,X14] :
( ~ hBOOL(c_in(X1,X14,X0))
| c_Set_Oinsert(X1,X14,X0) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f972,axiom,
! [X0,X1,X14] :
( ~ hBOOL(c_in(X1,X14,X0))
| c_Set_Oinsert(X1,X14,X0) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f1666,plain,
spl0_131,
inference(avatar_split_clause,[],[f969,f1664]) ).
fof(f1664,plain,
( spl0_131
<=> ! [X5,X0,X3,X14] :
( ~ hBOOL(hAPP(X14,X3))
| hBOOL(hAPP(c_Set_Oinsert(X5,X14,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f969,axiom,
! [X3,X0,X14,X5] :
( ~ hBOOL(hAPP(X14,X3))
| hBOOL(hAPP(c_Set_Oinsert(X5,X14,X0),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1662,plain,
spl0_130,
inference(avatar_split_clause,[],[f953,f1660]) ).
fof(f1660,plain,
( spl0_130
<=> ! [X13] :
( ~ class_Orderings_Obot(X13)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X13)),v_x) = c_Orderings_Obot__class_Obot(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f953,axiom,
! [X13] :
( ~ class_Orderings_Obot(X13)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X13)),v_x) = c_Orderings_Obot__class_Obot(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
fof(f1658,plain,
spl0_129,
inference(avatar_split_clause,[],[f848,f1656]) ).
fof(f1656,plain,
( spl0_129
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f848,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
fof(f1654,plain,
spl0_128,
inference(avatar_split_clause,[],[f826,f1652]) ).
fof(f1652,plain,
( spl0_128
<=> ! [X13] :
( ~ class_Orderings_Otop(X13)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X13)),v_x) = c_Orderings_Otop__class_Otop(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f826,axiom,
! [X13] :
( ~ class_Orderings_Otop(X13)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X13)),v_x) = c_Orderings_Otop__class_Otop(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
fof(f1650,plain,
spl0_127,
inference(avatar_split_clause,[],[f824,f1648]) ).
fof(f1648,plain,
( spl0_127
<=> ! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f824,axiom,
! [X0] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
fof(f1646,plain,
spl0_126,
inference(avatar_split_clause,[],[f718,f1644]) ).
fof(f1644,plain,
( spl0_126
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Obot__class_Obot(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f718,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Obot__class_Obot(X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1642,plain,
( ~ spl0_125
| ~ spl0_73
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1620,f1579,f1385,f1639]) ).
fof(f1639,plain,
( spl0_125
<=> class_Orderings_Otop(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1385,plain,
( spl0_73
<=> ! [X21] : ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X21)),X21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1579,plain,
( spl0_117
<=> ! [X0,X3] :
( ~ class_Orderings_Otop(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1620,plain,
( ~ class_Orderings_Otop(tc_nat)
| ~ spl0_73
| ~ spl0_117 ),
inference(resolution,[],[f1580,f1386]) ).
fof(f1386,plain,
( ! [X21] : ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X21)),X21))
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f1580,plain,
( ! [X3,X0] :
( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0)))
| ~ class_Orderings_Otop(X0) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1579]) ).
fof(f1637,plain,
spl0_124,
inference(avatar_split_clause,[],[f717,f1635]) ).
fof(f1635,plain,
( spl0_124
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f717,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1633,plain,
spl0_123,
inference(avatar_split_clause,[],[f525,f1631]) ).
fof(f1631,plain,
( spl0_123
<=> ! [X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f525,axiom,
! [X3,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
fof(f1629,plain,
spl0_122,
inference(avatar_split_clause,[],[f52,f1627]) ).
fof(f1627,plain,
( spl0_122
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f52,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1625,plain,
spl0_121,
inference(avatar_split_clause,[],[f51,f1623]) ).
fof(f1623,plain,
( spl0_121
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f51,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1616,plain,
( ~ spl0_13
| spl0_120
| ~ spl0_45
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1597,f1494,f1271,f1613,f1116]) ).
fof(f1116,plain,
( spl0_13
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1613,plain,
( spl0_120
<=> c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1271,plain,
( spl0_45
<=> ! [X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1494,plain,
( spl0_98
<=> c_Orderings_Oord__class_Omax(tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1597,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_45
| ~ spl0_98 ),
inference(superposition,[],[f1272,f1496]) ).
fof(f1496,plain,
( c_Orderings_Oord__class_Omax(tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(tc_nat)
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1494]) ).
fof(f1272,plain,
( ! [X0] :
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1271]) ).
fof(f1589,plain,
spl0_119,
inference(avatar_split_clause,[],[f1042,f1587]) ).
fof(f1587,plain,
( spl0_119
<=> ! [X69,X0,X68] :
( X68 = X69
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X68),X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1042,axiom,
! [X0,X68,X69] :
( X68 = X69
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X68),X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1585,plain,
spl0_118,
inference(avatar_split_clause,[],[f942,f1583]) ).
fof(f1583,plain,
( spl0_118
<=> ! [X13,X48,X0,X42] :
( ~ c_Finite__Set_Ofinite(X42,X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(X48,X42,X0,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f942,axiom,
! [X48,X0,X42,X13] :
( ~ c_Finite__Set_Ofinite(X42,X0)
| c_Finite__Set_Ofinite(c_Set_Oimage(X48,X42,X0,X13),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f1581,plain,
spl0_117,
inference(avatar_split_clause,[],[f846,f1579]) ).
fof(f846,axiom,
! [X3,X0] :
( ~ class_Orderings_Otop(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f1577,plain,
spl0_116,
inference(avatar_split_clause,[],[f804,f1575]) ).
fof(f1575,plain,
( spl0_116
<=> ! [X51,X50,X49,X52] :
( X49 = X51
| c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f804,axiom,
! [X50,X51,X49,X52] :
( X49 = X51
| c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
fof(f1573,plain,
spl0_115,
inference(avatar_split_clause,[],[f803,f1571]) ).
fof(f1571,plain,
( spl0_115
<=> ! [X52,X50,X51,X49] :
( X50 = X52
| c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f803,axiom,
! [X50,X51,X49,X52] :
( X50 = X52
| c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
fof(f1569,plain,
spl0_114,
inference(avatar_split_clause,[],[f794,f1567]) ).
fof(f1567,plain,
( spl0_114
<=> ! [X0,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X14) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f794,axiom,
! [X0,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1565,plain,
spl0_113,
inference(avatar_split_clause,[],[f793,f1563]) ).
fof(f1563,plain,
( spl0_113
<=> ! [X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f793,axiom,
! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1561,plain,
spl0_112,
inference(avatar_split_clause,[],[f719,f1559]) ).
fof(f1559,plain,
( spl0_112
<=> ! [X0,X3] :
( ~ class_Orderings_Obot(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f719,axiom,
! [X3,X0] :
( ~ class_Orderings_Obot(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1557,plain,
spl0_111,
inference(avatar_split_clause,[],[f568,f1555]) ).
fof(f1555,plain,
( spl0_111
<=> ! [X13,X0,X17,X28] : c_Nitpick_Ofold__graph_H(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f568,axiom,
! [X28,X0,X17,X13] : c_Nitpick_Ofold__graph_H(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
fof(f1553,plain,
spl0_110,
inference(avatar_split_clause,[],[f567,f1551]) ).
fof(f1551,plain,
( spl0_110
<=> ! [X13,X0,X17,X28] : c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f567,axiom,
! [X28,X0,X17,X13] : c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
fof(f1549,plain,
spl0_109,
inference(avatar_split_clause,[],[f556,f1547]) ).
fof(f1547,plain,
( spl0_109
<=> ! [X17,X13,X0,X14,X3,X28] :
( c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofold__graph(X28,X17,X14,X3,X0,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f556,axiom,
! [X28,X3,X0,X14,X17,X13] :
( c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofold__graph(X28,X17,X14,X3,X0,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
fof(f1545,plain,
spl0_108,
inference(avatar_split_clause,[],[f466,f1543]) ).
fof(f1543,plain,
( spl0_108
<=> ! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f466,axiom,
! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
fof(f1541,plain,
spl0_107,
inference(avatar_split_clause,[],[f465,f1539]) ).
fof(f1539,plain,
( spl0_107
<=> ! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f465,axiom,
! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
fof(f1537,plain,
spl0_106,
inference(avatar_split_clause,[],[f253,f1535]) ).
fof(f1535,plain,
( spl0_106
<=> ! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),X14) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f253,axiom,
! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f1533,plain,
spl0_105,
inference(avatar_split_clause,[],[f252,f1531]) ).
fof(f1531,plain,
( spl0_105
<=> ! [X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f252,axiom,
! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1529,plain,
spl0_104,
inference(avatar_split_clause,[],[f211,f1527]) ).
fof(f1527,plain,
( spl0_104
<=> ! [X28,X34,X0,X5,X3] : hAPP(c_Fun_Ofun__upd(X28,X3,X5,X0,X34),X3) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f211,axiom,
! [X28,X3,X0,X34,X5] : hAPP(c_Fun_Ofun__upd(X28,X3,X5,X0,X34),X3) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
fof(f1525,plain,
( ~ spl0_103
| spl0_2
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1500,f1478,f1061,f1522]) ).
fof(f1522,plain,
( spl0_103
<=> hBOOL(hAPP(v_F,v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1061,plain,
( spl0_2
<=> hBOOL(c_in(v_x,v_F,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1478,plain,
( spl0_96
<=> ! [X64,X0,X3] :
( ~ hBOOL(hAPP(X64,X3))
| hBOOL(c_in(X3,X64,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1500,plain,
( ~ hBOOL(hAPP(v_F,v_x))
| spl0_2
| ~ spl0_96 ),
inference(resolution,[],[f1479,f1063]) ).
fof(f1063,plain,
( ~ hBOOL(c_in(v_x,v_F,t_a))
| spl0_2 ),
inference(avatar_component_clause,[],[f1061]) ).
fof(f1479,plain,
( ! [X3,X0,X64] :
( hBOOL(c_in(X3,X64,X0))
| ~ hBOOL(hAPP(X64,X3)) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f1520,plain,
spl0_102,
inference(avatar_split_clause,[],[f210,f1518]) ).
fof(f1518,plain,
( spl0_102
<=> ! [X13,X0,X3,X28] : c_Fun_Ofun__upd(X28,X3,hAPP(X28,X3),X0,X13) = X28 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f210,axiom,
! [X28,X3,X0,X13] : c_Fun_Ofun__upd(X28,X3,hAPP(X28,X3),X0,X13) = X28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
fof(f1516,plain,
spl0_101,
inference(avatar_split_clause,[],[f83,f1514]) ).
fof(f1514,plain,
( spl0_101
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f83,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1512,plain,
spl0_100,
inference(avatar_split_clause,[],[f73,f1510]) ).
fof(f1510,plain,
( spl0_100
<=> ! [X0,X3,X31] :
( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X31,X0)
| hAPP(hAPP(X31,X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f73,axiom,
! [X31,X3,X0] :
( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X31,X0)
| hAPP(hAPP(X31,X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__idem_0) ).
fof(f1508,plain,
spl0_99,
inference(avatar_split_clause,[],[f66,f1506]) ).
fof(f1506,plain,
( spl0_99
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f66,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1497,plain,
( spl0_98
| ~ spl0_19
| ~ spl0_13
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f1485,f1418,f1116,f1146,f1494]) ).
fof(f1146,plain,
( spl0_19
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1485,plain,
( ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Oord__class_Omax(tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(tc_nat)
| ~ spl0_13
| ~ spl0_81 ),
inference(resolution,[],[f1419,f1118]) ).
fof(f1118,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1484,plain,
spl0_97,
inference(avatar_split_clause,[],[f960,f1482]) ).
fof(f1482,plain,
( spl0_97
<=> ! [X64,X0,X3] :
( hBOOL(hAPP(X64,X3))
| ~ hBOOL(c_in(X3,X64,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f960,axiom,
! [X3,X0,X64] :
( hBOOL(hAPP(X64,X3))
| ~ hBOOL(c_in(X3,X64,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f1480,plain,
spl0_96,
inference(avatar_split_clause,[],[f959,f1478]) ).
fof(f959,axiom,
! [X3,X0,X64] :
( ~ hBOOL(hAPP(X64,X3))
| hBOOL(c_in(X3,X64,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f1476,plain,
spl0_95,
inference(avatar_split_clause,[],[f951,f1474]) ).
fof(f1474,plain,
( spl0_95
<=> ! [X0,X1,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X14,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f951,axiom,
! [X0,X1,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X14,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f1472,plain,
spl0_94,
inference(avatar_split_clause,[],[f948,f1470]) ).
fof(f1470,plain,
( spl0_94
<=> ! [X0,X1,X14] :
( c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f948,axiom,
! [X0,X1,X14] :
( c_Finite__Set_Ofinite(X14,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f1468,plain,
spl0_93,
inference(avatar_split_clause,[],[f947,f1466]) ).
fof(f1466,plain,
( spl0_93
<=> ! [X0,X1,X14] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f947,axiom,
! [X0,X1,X14] :
( ~ c_Finite__Set_Ofinite(X14,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f1464,plain,
spl0_92,
inference(avatar_split_clause,[],[f865,f1462]) ).
fof(f1462,plain,
( spl0_92
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f865,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1460,plain,
spl0_91,
inference(avatar_split_clause,[],[f864,f1458]) ).
fof(f1458,plain,
( spl0_91
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f864,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1456,plain,
spl0_90,
inference(avatar_split_clause,[],[f859,f1454]) ).
fof(f1454,plain,
( spl0_90
<=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f859,axiom,
! [X3,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
fof(f1452,plain,
spl0_89,
inference(avatar_split_clause,[],[f728,f1450]) ).
fof(f1450,plain,
( spl0_89
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f728,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f1448,plain,
spl0_88,
inference(avatar_split_clause,[],[f496,f1446]) ).
fof(f1446,plain,
( spl0_88
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f496,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).
fof(f1444,plain,
spl0_87,
inference(avatar_split_clause,[],[f495,f1442]) ).
fof(f1442,plain,
( spl0_87
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f495,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).
fof(f1440,plain,
spl0_86,
inference(avatar_split_clause,[],[f196,f1438]) ).
fof(f1438,plain,
( spl0_86
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Oord__class_Omin(X0) = c_Lattices_Olower__semilattice__class_Oinf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f196,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Orderings_Oord__class_Omin(X0) = c_Lattices_Olower__semilattice__class_Oinf(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).
fof(f1436,plain,
spl0_85,
inference(avatar_split_clause,[],[f64,f1434]) ).
fof(f1434,plain,
( spl0_85
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f64,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1432,plain,
spl0_84,
inference(avatar_split_clause,[],[f63,f1430]) ).
fof(f1430,plain,
( spl0_84
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f63,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1428,plain,
spl0_83,
inference(avatar_split_clause,[],[f62,f1426]) ).
fof(f1426,plain,
( spl0_83
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f62,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1424,plain,
spl0_82,
inference(avatar_split_clause,[],[f58,f1422]) ).
fof(f1422,plain,
( spl0_82
<=> ! [X0,X3] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f58,axiom,
! [X3,X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
fof(f1420,plain,
spl0_81,
inference(avatar_split_clause,[],[f32,f1418]) ).
fof(f32,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Orderings_Oord__class_Omax(X0) = c_Lattices_Oupper__semilattice__class_Osup(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__max_0) ).
fof(f1415,plain,
spl0_80,
inference(avatar_split_clause,[],[f992,f1413]) ).
fof(f1413,plain,
( spl0_80
<=> ! [X66,X67] :
( ~ class_Finite__Set_Ofinite_Ofinite(X66)
| ~ class_Finite__Set_Ofinite_Ofinite(X67)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f992,axiom,
! [X66,X67] :
( ~ class_Finite__Set_Ofinite_Ofinite(X66)
| ~ class_Finite__Set_Ofinite_Ofinite(X67)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f1411,plain,
spl0_79,
inference(avatar_split_clause,[],[f956,f1409]) ).
fof(f1409,plain,
( spl0_79
<=> ! [X0,X1,X15] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X15,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f956,axiom,
! [X0,X1,X15] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X15,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
fof(f1407,plain,
spl0_78,
inference(avatar_split_clause,[],[f945,f1405]) ).
fof(f1405,plain,
( spl0_78
<=> ! [X0,X44] : c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f945,axiom,
! [X0,X44] : c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
fof(f1403,plain,
spl0_77,
inference(avatar_split_clause,[],[f931,f1401]) ).
fof(f1401,plain,
( spl0_77
<=> ! [X0,X11] : ~ hBOOL(c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f931,axiom,
! [X0,X11] : ~ hBOOL(c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f1399,plain,
spl0_76,
inference(avatar_split_clause,[],[f792,f1397]) ).
fof(f1397,plain,
( spl0_76
<=> ! [X40,X13,X0,X32] : hAPP(c_COMBK(X32,X0,X13),X40) = X32 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f792,axiom,
! [X40,X0,X32,X13] : hAPP(c_COMBK(X32,X0,X13),X40) = X32,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f1395,plain,
spl0_75,
inference(avatar_split_clause,[],[f735,f1393]) ).
fof(f1393,plain,
( spl0_75
<=> ! [X13,X0,X28] : c_Fun_Oinj__on(X28,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f735,axiom,
! [X28,X0,X13] : c_Fun_Oinj__on(X28,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f1391,plain,
spl0_74,
inference(avatar_split_clause,[],[f690,f1389]) ).
fof(f1389,plain,
( spl0_74
<=> ! [X0,X3] : hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f690,axiom,
! [X3,X0] : hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f1387,plain,
spl0_73,
inference(avatar_split_clause,[],[f244,f1385]) ).
fof(f244,axiom,
! [X21] : ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X21)),X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1383,plain,
spl0_72,
inference(avatar_split_clause,[],[f213,f1381]) ).
fof(f1381,plain,
( spl0_72
<=> ! [X6,X4,X0,X7] :
( c_OrderedGroup_Oab__semigroup__idem__mult(X4,X0)
| ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f213,axiom,
! [X0,X6,X7,X4] :
( c_OrderedGroup_Oab__semigroup__idem__mult(X4,X0)
| ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).
fof(f1379,plain,
spl0_71,
inference(avatar_split_clause,[],[f198,f1377]) ).
fof(f1377,plain,
( spl0_71
<=> ! [X3] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),c_Suc(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f198,axiom,
! [X3] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),c_Suc(X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f1375,plain,
spl0_70,
inference(avatar_split_clause,[],[f8,f1373]) ).
fof(f1373,plain,
( spl0_70
<=> ! [X9,X8] :
( X8 = X9
| c_Suc(X8) != c_Suc(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f8,axiom,
! [X8,X9] :
( X8 = X9
| c_Suc(X8) != c_Suc(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f1371,plain,
spl0_69,
inference(avatar_split_clause,[],[f1041,f1369]) ).
fof(f1369,plain,
( spl0_69
<=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1041,axiom,
! [X3,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1367,plain,
spl0_68,
inference(avatar_split_clause,[],[f944,f1365]) ).
fof(f1365,plain,
( spl0_68
<=> ! [X0,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f944,axiom,
! [X3,X0] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f1363,plain,
spl0_67,
inference(avatar_split_clause,[],[f926,f1361]) ).
fof(f1361,plain,
( spl0_67
<=> ! [X0,X3,X14] : hBOOL(hAPP(c_Set_Oinsert(X3,X14,X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f926,axiom,
! [X3,X0,X14] : hBOOL(hAPP(c_Set_Oinsert(X3,X14,X0),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f1359,plain,
spl0_66,
inference(avatar_split_clause,[],[f825,f1357]) ).
fof(f1357,plain,
( spl0_66
<=> ! [X0,X3] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f825,axiom,
! [X3,X0] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f1355,plain,
spl0_65,
inference(avatar_split_clause,[],[f266,f1353]) ).
fof(f1353,plain,
( spl0_65
<=> ! [X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f266,axiom,
! [X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f1351,plain,
spl0_64,
inference(avatar_split_clause,[],[f59,f1349]) ).
fof(f1349,plain,
( spl0_64
<=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f59,axiom,
! [X3] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1347,plain,
~ spl0_63,
inference(avatar_split_clause,[],[f983,f1344]) ).
fof(f983,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1342,plain,
spl0_62,
inference(avatar_split_clause,[],[f981,f1339]) ).
fof(f981,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1337,plain,
spl0_61,
inference(avatar_split_clause,[],[f1000,f1335]) ).
fof(f1335,plain,
( spl0_61
<=> ! [X66,X67] :
( ~ class_HOL_Oord(X67)
| class_HOL_Oord(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1000,axiom,
! [X66,X67] :
( ~ class_HOL_Oord(X67)
| class_HOL_Oord(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f1333,plain,
spl0_60,
inference(avatar_split_clause,[],[f999,f1331]) ).
fof(f1331,plain,
( spl0_60
<=> ! [X66,X67] :
( ~ class_HOL_Ominus(X67)
| class_HOL_Ominus(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f999,axiom,
! [X66,X67] :
( ~ class_HOL_Ominus(X67)
| class_HOL_Ominus(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
fof(f1329,plain,
spl0_59,
inference(avatar_split_clause,[],[f998,f1327]) ).
fof(f1327,plain,
( spl0_59
<=> ! [X66,X67] :
( ~ class_HOL_Ouminus(X67)
| class_HOL_Ouminus(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f998,axiom,
! [X66,X67] :
( ~ class_HOL_Ouminus(X67)
| class_HOL_Ouminus(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
fof(f1325,plain,
spl0_58,
inference(avatar_split_clause,[],[f997,f1323]) ).
fof(f1323,plain,
( spl0_58
<=> ! [X66,X67] :
( ~ class_Orderings_Obot(X67)
| class_Orderings_Obot(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f997,axiom,
! [X66,X67] :
( ~ class_Orderings_Obot(X67)
| class_Orderings_Obot(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1321,plain,
spl0_57,
inference(avatar_split_clause,[],[f996,f1319]) ).
fof(f1319,plain,
( spl0_57
<=> ! [X66,X67] :
( ~ class_Orderings_Otop(X67)
| class_Orderings_Otop(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f996,axiom,
! [X66,X67] :
( ~ class_Orderings_Otop(X67)
| class_Orderings_Otop(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f1317,plain,
spl0_56,
inference(avatar_split_clause,[],[f995,f1315]) ).
fof(f1315,plain,
( spl0_56
<=> ! [X66,X67] :
( ~ class_Orderings_Oorder(X67)
| class_Orderings_Oorder(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f995,axiom,
! [X66,X67] :
( ~ class_Orderings_Oorder(X67)
| class_Orderings_Oorder(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1313,plain,
spl0_55,
inference(avatar_split_clause,[],[f994,f1311]) ).
fof(f1311,plain,
( spl0_55
<=> ! [X66,X67] :
( ~ class_Lattices_Olattice(X67)
| class_Lattices_Olattice(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f994,axiom,
! [X66,X67] :
( ~ class_Lattices_Olattice(X67)
| class_Lattices_Olattice(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f1309,plain,
spl0_54,
inference(avatar_split_clause,[],[f993,f1307]) ).
fof(f1307,plain,
( spl0_54
<=> ! [X66,X67] :
( ~ class_Orderings_Opreorder(X67)
| class_Orderings_Opreorder(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f993,axiom,
! [X66,X67] :
( ~ class_Orderings_Opreorder(X67)
| class_Orderings_Opreorder(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1305,plain,
spl0_53,
inference(avatar_split_clause,[],[f991,f1303]) ).
fof(f1303,plain,
( spl0_53
<=> ! [X66,X67] :
( ~ class_Lattices_Oboolean__algebra(X67)
| class_Lattices_Oboolean__algebra(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f991,axiom,
! [X66,X67] :
( ~ class_Lattices_Oboolean__algebra(X67)
| class_Lattices_Oboolean__algebra(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f1301,plain,
spl0_52,
inference(avatar_split_clause,[],[f990,f1299]) ).
fof(f1299,plain,
( spl0_52
<=> ! [X66,X67] :
( ~ class_Lattices_Obounded__lattice(X67)
| class_Lattices_Obounded__lattice(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f990,axiom,
! [X66,X67] :
( ~ class_Lattices_Obounded__lattice(X67)
| class_Lattices_Obounded__lattice(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f1297,plain,
spl0_51,
inference(avatar_split_clause,[],[f989,f1295]) ).
fof(f1295,plain,
( spl0_51
<=> ! [X66,X67] :
( ~ class_Lattices_Odistrib__lattice(X67)
| class_Lattices_Odistrib__lattice(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f989,axiom,
! [X66,X67] :
( ~ class_Lattices_Odistrib__lattice(X67)
| class_Lattices_Odistrib__lattice(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f1293,plain,
spl0_50,
inference(avatar_split_clause,[],[f988,f1291]) ).
fof(f1291,plain,
( spl0_50
<=> ! [X66,X67] :
( ~ class_Lattices_Olattice(X67)
| class_Lattices_Olower__semilattice(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f988,axiom,
! [X66,X67] :
( ~ class_Lattices_Olattice(X67)
| class_Lattices_Olower__semilattice(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f1289,plain,
spl0_49,
inference(avatar_split_clause,[],[f987,f1287]) ).
fof(f1287,plain,
( spl0_49
<=> ! [X66,X67] :
( ~ class_Lattices_Olattice(X67)
| class_Lattices_Oupper__semilattice(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f987,axiom,
! [X66,X67] :
( ~ class_Lattices_Olattice(X67)
| class_Lattices_Oupper__semilattice(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f1285,plain,
spl0_48,
inference(avatar_split_clause,[],[f986,f1283]) ).
fof(f1283,plain,
( spl0_48
<=> ! [X66,X67] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X67)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f986,axiom,
! [X66,X67] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X67)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f1281,plain,
spl0_47,
inference(avatar_split_clause,[],[f946,f1279]) ).
fof(f1279,plain,
( spl0_47
<=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f946,axiom,
! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f1277,plain,
spl0_46,
inference(avatar_split_clause,[],[f276,f1275]) ).
fof(f1275,plain,
( spl0_46
<=> ! [X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f276,axiom,
! [X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__inf_0) ).
fof(f1273,plain,
spl0_45,
inference(avatar_split_clause,[],[f164,f1271]) ).
fof(f164,axiom,
! [X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__sup_0) ).
fof(f1269,plain,
spl0_44,
inference(avatar_split_clause,[],[f102,f1267]) ).
fof(f1267,plain,
( spl0_44
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f102,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__min_0) ).
fof(f1265,plain,
spl0_43,
inference(avatar_split_clause,[],[f15,f1263]) ).
fof(f1263,plain,
( spl0_43
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f15,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__max_0) ).
fof(f1261,plain,
spl0_42,
inference(avatar_split_clause,[],[f974,f1259]) ).
fof(f1259,plain,
( spl0_42
<=> ! [X0,X14] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f974,axiom,
! [X0,X14] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f1257,plain,
spl0_41,
inference(avatar_split_clause,[],[f877,f1255]) ).
fof(f1255,plain,
( spl0_41
<=> ! [X52,X51] : c_Com_Ocom_OSemi(X51,X52) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f877,axiom,
! [X51,X52] : c_Com_Ocom_OSemi(X51,X52) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
fof(f1253,plain,
spl0_40,
inference(avatar_split_clause,[],[f251,f1251]) ).
fof(f1251,plain,
( spl0_40
<=> ! [X21] : c_Suc(X21) != X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f251,axiom,
! [X21] : c_Suc(X21) != X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f1249,plain,
spl0_39,
inference(avatar_split_clause,[],[f1037,f1246]) ).
fof(f1246,plain,
( spl0_39
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1037,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f1244,plain,
spl0_38,
inference(avatar_split_clause,[],[f1036,f1241]) ).
fof(f1241,plain,
( spl0_38
<=> class_HOL_Ominus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1036,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
fof(f1239,plain,
spl0_37,
inference(avatar_split_clause,[],[f1035,f1236]) ).
fof(f1236,plain,
( spl0_37
<=> class_HOL_Ouminus(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1035,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
fof(f1234,plain,
spl0_36,
inference(avatar_split_clause,[],[f1034,f1231]) ).
fof(f1231,plain,
( spl0_36
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1034,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f1229,plain,
spl0_35,
inference(avatar_split_clause,[],[f1033,f1226]) ).
fof(f1226,plain,
( spl0_35
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1033,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f1224,plain,
spl0_34,
inference(avatar_split_clause,[],[f1032,f1221]) ).
fof(f1221,plain,
( spl0_34
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1032,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f1219,plain,
spl0_33,
inference(avatar_split_clause,[],[f1031,f1216]) ).
fof(f1216,plain,
( spl0_33
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1031,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f1214,plain,
spl0_32,
inference(avatar_split_clause,[],[f1030,f1211]) ).
fof(f1211,plain,
( spl0_32
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1030,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f1209,plain,
spl0_31,
inference(avatar_split_clause,[],[f1029,f1206]) ).
fof(f1206,plain,
( spl0_31
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1029,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f1204,plain,
spl0_30,
inference(avatar_split_clause,[],[f1028,f1201]) ).
fof(f1201,plain,
( spl0_30
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1028,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(f1199,plain,
spl0_29,
inference(avatar_split_clause,[],[f1027,f1196]) ).
fof(f1196,plain,
( spl0_29
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1027,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1194,plain,
spl0_28,
inference(avatar_split_clause,[],[f1026,f1191]) ).
fof(f1191,plain,
( spl0_28
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1026,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1189,plain,
spl0_27,
inference(avatar_split_clause,[],[f1025,f1186]) ).
fof(f1186,plain,
( spl0_27
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1025,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1184,plain,
spl0_26,
inference(avatar_split_clause,[],[f1024,f1181]) ).
fof(f1024,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1179,plain,
spl0_25,
inference(avatar_split_clause,[],[f1023,f1176]) ).
fof(f1176,plain,
( spl0_25
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1023,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f1174,plain,
spl0_24,
inference(avatar_split_clause,[],[f1022,f1171]) ).
fof(f1171,plain,
( spl0_24
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1022,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f1169,plain,
spl0_23,
inference(avatar_split_clause,[],[f1021,f1166]) ).
fof(f1166,plain,
( spl0_23
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1021,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
fof(f1164,plain,
spl0_22,
inference(avatar_split_clause,[],[f1020,f1161]) ).
fof(f1161,plain,
( spl0_22
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1020,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1159,plain,
spl0_21,
inference(avatar_split_clause,[],[f1019,f1156]) ).
fof(f1156,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1019,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1154,plain,
spl0_20,
inference(avatar_split_clause,[],[f1018,f1151]) ).
fof(f1151,plain,
( spl0_20
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1018,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f1149,plain,
spl0_19,
inference(avatar_split_clause,[],[f1017,f1146]) ).
fof(f1017,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1144,plain,
spl0_18,
inference(avatar_split_clause,[],[f1016,f1141]) ).
fof(f1141,plain,
( spl0_18
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1016,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1139,plain,
spl0_17,
inference(avatar_split_clause,[],[f1015,f1136]) ).
fof(f1136,plain,
( spl0_17
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1015,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1134,plain,
spl0_16,
inference(avatar_split_clause,[],[f1014,f1131]) ).
fof(f1131,plain,
( spl0_16
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1014,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1129,plain,
spl0_15,
inference(avatar_split_clause,[],[f1013,f1126]) ).
fof(f1126,plain,
( spl0_15
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1013,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1124,plain,
spl0_14,
inference(avatar_split_clause,[],[f1012,f1121]) ).
fof(f1121,plain,
( spl0_14
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1012,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1119,plain,
spl0_13,
inference(avatar_split_clause,[],[f1011,f1116]) ).
fof(f1011,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1114,plain,
spl0_12,
inference(avatar_split_clause,[],[f1010,f1111]) ).
fof(f1111,plain,
( spl0_12
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1010,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1109,plain,
spl0_11,
inference(avatar_split_clause,[],[f1009,f1106]) ).
fof(f1106,plain,
( spl0_11
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1009,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1104,plain,
spl0_10,
inference(avatar_split_clause,[],[f1008,f1101]) ).
fof(f1101,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1008,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1099,plain,
spl0_9,
inference(avatar_split_clause,[],[f1007,f1096]) ).
fof(f1096,plain,
( spl0_9
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1007,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1094,plain,
spl0_8,
inference(avatar_split_clause,[],[f1006,f1091]) ).
fof(f1091,plain,
( spl0_8
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1006,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1089,plain,
spl0_7,
inference(avatar_split_clause,[],[f1005,f1086]) ).
fof(f1086,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1005,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1084,plain,
spl0_6,
inference(avatar_split_clause,[],[f1004,f1081]) ).
fof(f1081,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1004,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1079,plain,
spl0_5,
inference(avatar_split_clause,[],[f1003,f1076]) ).
fof(f1076,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1003,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1074,plain,
spl0_4,
inference(avatar_split_clause,[],[f1002,f1071]) ).
fof(f1071,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1002,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1069,plain,
spl0_3,
inference(avatar_split_clause,[],[f1001,f1066]) ).
fof(f1066,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1001,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1064,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f980,f1061]) ).
fof(f980,axiom,
~ hBOOL(c_in(v_x,v_F,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1059,plain,
spl0_1,
inference(avatar_split_clause,[],[f979,f1056]) ).
fof(f1056,plain,
( spl0_1
<=> c_Finite__Set_Ofinite(v_F,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f979,axiom,
c_Finite__Set_Ofinite(v_F,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV844-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 21:06:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (1903)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1907)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.44 % (1906)WARNING: value z3 for option sas not known
% 0.21/0.44 % (1904)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.44 % (1906)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.44 % (1905)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.44 % (1908)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)
% 0.21/0.44 % (1910)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)
% 0.21/0.44 % (1909)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)
% 0.21/0.51 % (1908)First to succeed.
% 0.21/0.51 % (1908)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1903"
% 0.21/0.51 % (1908)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (1908)------------------------------
% 0.21/0.52 % (1908)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.52 % (1908)Termination reason: Refutation
% 0.21/0.52
% 0.21/0.52 % (1908)Memory used [KB]: 2301
% 0.21/0.52 % (1908)Time elapsed: 0.075 s
% 0.21/0.52 % (1908)Instructions burned: 131 (million)
% 0.21/0.52 % (1903)Success in time 0.161 s
%------------------------------------------------------------------------------