TSTP Solution File: SWV898-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV898-1 : 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 : n023.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 17:07:26 EDT 2024
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 344
% Syntax : Number of formulae : 550 ( 240 unt; 0 def)
% Number of atoms : 1014 ( 151 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 761 ( 297 ~; 287 |; 0 &)
% ( 177 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 208 ( 206 usr; 180 prp; 0-5 aty)
% Number of functors : 36 ( 36 usr; 9 con; 0-5 aty)
% Number of variables : 712 ( 712 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1568,plain,
$false,
inference(avatar_sat_refutation,[],[f651,f656,f661,f666,f671,f676,f681,f686,f691,f696,f701,f706,f711,f716,f721,f726,f731,f736,f741,f746,f751,f756,f761,f766,f770,f774,f778,f782,f786,f790,f794,f798,f802,f806,f810,f814,f819,f823,f827,f831,f835,f839,f843,f847,f851,f855,f859,f863,f867,f871,f875,f879,f884,f891,f897,f904,f908,f913,f917,f921,f925,f929,f933,f937,f941,f945,f950,f954,f958,f962,f966,f970,f974,f978,f982,f986,f990,f994,f998,f1002,f1006,f1023,f1028,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1088,f1092,f1096,f1100,f1104,f1108,f1112,f1116,f1120,f1124,f1128,f1132,f1136,f1172,f1176,f1180,f1184,f1188,f1196,f1200,f1204,f1208,f1212,f1234,f1238,f1242,f1246,f1250,f1255,f1259,f1263,f1267,f1271,f1275,f1279,f1283,f1287,f1291,f1295,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1342,f1346,f1350,f1354,f1358,f1362,f1366,f1370,f1396,f1480,f1485,f1489,f1493,f1497,f1501,f1505,f1509,f1513,f1517,f1521,f1525,f1530,f1534,f1538,f1542,f1546,f1550,f1554,f1558,f1562,f1566,f1567]) ).
fof(f1567,plain,
( ~ spl0_37
| ~ spl0_120
| spl0_155 ),
inference(avatar_split_clause,[],[f1432,f1393,f1210,f816]) ).
fof(f816,plain,
( spl0_37
<=> c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1210,plain,
( spl0_120
<=> ! [X22,X2,X21,X12] :
( ~ c_Finite__Set_Ofinite(X22,X2)
| c_Finite__Set_Ofinite(c_Set_Oimage(X21,X22,X2,X12),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1393,plain,
( spl0_155
<=> c_Finite__Set_Ofinite(c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1432,plain,
( ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| ~ spl0_120
| spl0_155 ),
inference(resolution,[],[f1395,f1211]) ).
fof(f1211,plain,
( ! [X2,X21,X22,X12] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X21,X22,X2,X12),X12)
| ~ c_Finite__Set_Ofinite(X22,X2) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1210]) ).
fof(f1395,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom))
| spl0_155 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f1566,plain,
spl0_177,
inference(avatar_split_clause,[],[f456,f1564]) ).
fof(f1564,plain,
( spl0_177
<=> ! [X6,X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OatMost(X6,X2) != c_SetInterval_Oord__class_OatMost(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f456,axiom,
! [X2,X6,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OatMost(X6,X2) != c_SetInterval_Oord__class_OatMost(X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__eq__iff_0) ).
fof(f1562,plain,
spl0_176,
inference(avatar_split_clause,[],[f419,f1560]) ).
fof(f1560,plain,
( spl0_176
<=> ! [X46,X29,X27,X2] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X46,X29,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X27,X46,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X27,X29,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f419,axiom,
! [X2,X46,X29,X27] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X46,X29,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X27,X46,X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X27,X29,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
fof(f1558,plain,
spl0_175,
inference(avatar_split_clause,[],[f408,f1556]) ).
fof(f1556,plain,
( spl0_175
<=> ! [X6,X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OatLeast(X6,X2) != c_SetInterval_Oord__class_OatLeast(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f408,axiom,
! [X2,X6,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OatLeast(X6,X2) != c_SetInterval_Oord__class_OatLeast(X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__eq__iff_0) ).
fof(f1554,plain,
spl0_174,
inference(avatar_split_clause,[],[f393,f1552]) ).
fof(f1552,plain,
( spl0_174
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oboolean__algebra(X2)
| X6 = X7
| c_HOL_Ouminus__class_Ouminus(X6,X2) != c_HOL_Ouminus__class_Ouminus(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f393,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oboolean__algebra(X2)
| X6 = X7
| c_HOL_Ouminus__class_Ouminus(X6,X2) != c_HOL_Ouminus__class_Ouminus(X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
fof(f1550,plain,
spl0_173,
inference(avatar_split_clause,[],[f306,f1548]) ).
fof(f1548,plain,
( spl0_173
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f306,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f1546,plain,
spl0_172,
inference(avatar_split_clause,[],[f305,f1544]) ).
fof(f1544,plain,
( spl0_172
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f305,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) != X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f1542,plain,
spl0_171,
inference(avatar_split_clause,[],[f304,f1540]) ).
fof(f1540,plain,
( spl0_171
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f304,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f1538,plain,
spl0_170,
inference(avatar_split_clause,[],[f300,f1536]) ).
fof(f1536,plain,
( spl0_170
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f300,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X7,X6,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f1534,plain,
spl0_169,
inference(avatar_split_clause,[],[f299,f1532]) ).
fof(f1532,plain,
( spl0_169
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f299,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) != X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f1530,plain,
spl0_168,
inference(avatar_split_clause,[],[f298,f1528]) ).
fof(f1528,plain,
( spl0_168
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f298,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_lessequals(X6,X7,X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f1525,plain,
spl0_167,
inference(avatar_split_clause,[],[f272,f1523]) ).
fof(f1523,plain,
( spl0_167
<=> ! [X38,X2,X8] :
( ~ class_HOL_Oord(X2)
| ~ c_lessequals(X38,X8,X2)
| c_in(X38,c_SetInterval_Oord__class_OatMost(X8,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f272,axiom,
! [X2,X38,X8] :
( ~ class_HOL_Oord(X2)
| ~ c_lessequals(X38,X8,X2)
| c_in(X38,c_SetInterval_Oord__class_OatMost(X8,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__iff_1) ).
fof(f1521,plain,
spl0_166,
inference(avatar_split_clause,[],[f271,f1519]) ).
fof(f1519,plain,
( spl0_166
<=> ! [X38,X2,X8] :
( ~ class_HOL_Oord(X2)
| c_lessequals(X38,X8,X2)
| ~ c_in(X38,c_SetInterval_Oord__class_OatMost(X8,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f271,axiom,
! [X2,X38,X8] :
( ~ class_HOL_Oord(X2)
| c_lessequals(X38,X8,X2)
| ~ c_in(X38,c_SetInterval_Oord__class_OatMost(X8,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__iff_0) ).
fof(f1517,plain,
spl0_165,
inference(avatar_split_clause,[],[f219,f1515]) ).
fof(f1515,plain,
( spl0_165
<=> ! [X38,X2,X8] :
( ~ class_HOL_Oord(X2)
| ~ c_lessequals(X8,X38,X2)
| c_in(X38,c_SetInterval_Oord__class_OatLeast(X8,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f219,axiom,
! [X2,X38,X8] :
( ~ class_HOL_Oord(X2)
| ~ c_lessequals(X8,X38,X2)
| c_in(X38,c_SetInterval_Oord__class_OatLeast(X8,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).
fof(f1513,plain,
spl0_164,
inference(avatar_split_clause,[],[f218,f1511]) ).
fof(f1511,plain,
( spl0_164
<=> ! [X38,X2,X8] :
( ~ class_HOL_Oord(X2)
| c_lessequals(X8,X38,X2)
| ~ c_in(X38,c_SetInterval_Oord__class_OatLeast(X8,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f218,axiom,
! [X2,X38,X8] :
( ~ class_HOL_Oord(X2)
| c_lessequals(X8,X38,X2)
| ~ c_in(X38,c_SetInterval_Oord__class_OatLeast(X8,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).
fof(f1509,plain,
spl0_163,
inference(avatar_split_clause,[],[f203,f1507]) ).
fof(f1507,plain,
( spl0_163
<=> ! [X6,X2,X0] : c_Set_Oinsert(X6,X0,X2) = c_Set_Oinsert(X6,c_Set_Oinsert(X6,X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f203,axiom,
! [X2,X0,X6] : c_Set_Oinsert(X6,X0,X2) = c_Set_Oinsert(X6,c_Set_Oinsert(X6,X0,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f1505,plain,
spl0_162,
inference(avatar_split_clause,[],[f202,f1503]) ).
fof(f1503,plain,
( spl0_162
<=> ! [X6,X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OgreaterThan(X6,X2) != c_SetInterval_Oord__class_OgreaterThan(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f202,axiom,
! [X2,X6,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OgreaterThan(X6,X2) != c_SetInterval_Oord__class_OgreaterThan(X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThan__eq__iff_0) ).
fof(f1501,plain,
spl0_161,
inference(avatar_split_clause,[],[f189,f1499]) ).
fof(f1499,plain,
( spl0_161
<=> ! [X11,X2,X12] :
( ~ c_Fun_Obij(X11,X2,X12)
| c_Fun_Oinj__on(X11,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f189,axiom,
! [X2,X11,X12] :
( ~ c_Fun_Obij(X11,X2,X12)
| c_Fun_Oinj__on(X11,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__def_0) ).
fof(f1497,plain,
spl0_160,
inference(avatar_split_clause,[],[f75,f1495]) ).
fof(f1495,plain,
( spl0_160
<=> ! [X2,X0,X14] :
( c_in(X14,X0,X2)
| c_in(X14,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f75,axiom,
! [X2,X0,X14] :
( c_in(X14,X0,X2)
| c_in(X14,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
fof(f1493,plain,
spl0_159,
inference(avatar_split_clause,[],[f74,f1491]) ).
fof(f1491,plain,
( spl0_159
<=> ! [X2,X0,X14] :
( ~ c_in(X14,X0,X2)
| ~ c_in(X14,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f74,axiom,
! [X2,X0,X14] :
( ~ c_in(X14,X0,X2)
| ~ c_in(X14,c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
fof(f1489,plain,
spl0_158,
inference(avatar_split_clause,[],[f50,f1487]) ).
fof(f1487,plain,
( spl0_158
<=> ! [X2] : c_Fun_Oid(X2) = c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),c_Fun_Oid(X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f50,axiom,
! [X2] : c_Fun_Oid(X2) = c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),c_Fun_Oid(X2),X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__id_0) ).
fof(f1485,plain,
( ~ spl0_157
| ~ spl0_30
| spl0_155 ),
inference(avatar_split_clause,[],[f1433,f1393,f788,f1482]) ).
fof(f1482,plain,
( spl0_157
<=> class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(tc_Com_Ocom)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f788,plain,
( spl0_30
<=> ! [X2,X0] :
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1433,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(tc_Com_Ocom))
| ~ spl0_30
| spl0_155 ),
inference(resolution,[],[f1395,f789]) ).
fof(f789,plain,
( ! [X2,X0] :
( c_Finite__Set_Ofinite(X0,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f1480,plain,
spl0_156,
inference(avatar_split_clause,[],[f8,f1478]) ).
fof(f1478,plain,
( spl0_156
<=> ! [X6,X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OlessThan(X6,X2) != c_SetInterval_Oord__class_OlessThan(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f8,axiom,
! [X2,X6,X7] :
( ~ class_Orderings_Olinorder(X2)
| X6 = X7
| c_SetInterval_Oord__class_OlessThan(X6,X2) != c_SetInterval_Oord__class_OlessThan(X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
fof(f1396,plain,
( ~ spl0_155
| ~ spl0_120
| spl0_126 ),
inference(avatar_split_clause,[],[f1296,f1252,f1210,f1393]) ).
fof(f1252,plain,
( spl0_126
<=> c_Finite__Set_Ofinite(c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1296,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom))
| ~ spl0_120
| spl0_126 ),
inference(resolution,[],[f1254,f1211]) ).
fof(f1254,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom)
| spl0_126 ),
inference(avatar_component_clause,[],[f1252]) ).
fof(f1370,plain,
spl0_154,
inference(avatar_split_clause,[],[f522,f1368]) ).
fof(f1368,plain,
( spl0_154
<=> ! [X29,X2,X27] :
( c_Hoare__Mirabelle_Ohoare__derivs(X27,X29,X2)
| ~ c_lessequals(X29,X27,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f522,axiom,
! [X2,X29,X27] :
( c_Hoare__Mirabelle_Ohoare__derivs(X27,X29,X2)
| ~ c_lessequals(X29,X27,tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).
fof(f1366,plain,
spl0_153,
inference(avatar_split_clause,[],[f450,f1364]) ).
fof(f1364,plain,
( spl0_153
<=> ! [X4,X0,X5,X2] :
( ~ c_in(X4,X0,X2)
| c_in(X4,c_Set_Oinsert(X5,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f450,axiom,
! [X2,X0,X4,X5] :
( ~ c_in(X4,X0,X2)
| c_in(X4,c_Set_Oinsert(X5,X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
fof(f1362,plain,
spl0_152,
inference(avatar_split_clause,[],[f399,f1360]) ).
fof(f1360,plain,
( spl0_152
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f399,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f1358,plain,
spl0_151,
inference(avatar_split_clause,[],[f397,f1356]) ).
fof(f1356,plain,
( spl0_151
<=> ! [X44,X20,X14,X28] :
( X20 = X28
| ~ c_Natural_Oevalc(X14,X44,X28)
| ~ c_Natural_Oevalc(X14,X44,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f397,axiom,
! [X28,X44,X14,X20] :
( X20 = X28
| ~ c_Natural_Oevalc(X14,X44,X28)
| ~ c_Natural_Oevalc(X14,X44,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
fof(f1354,plain,
spl0_150,
inference(avatar_split_clause,[],[f389,f1352]) ).
fof(f1352,plain,
( spl0_150
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f389,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f1350,plain,
spl0_149,
inference(avatar_split_clause,[],[f376,f1348]) ).
fof(f1348,plain,
( spl0_149
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f376,axiom,
! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
fof(f1346,plain,
spl0_148,
inference(avatar_split_clause,[],[f374,f1344]) ).
fof(f1344,plain,
( spl0_148
<=> ! [X2,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f374,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f1342,plain,
( ~ spl0_147
| ~ spl0_30
| spl0_126 ),
inference(avatar_split_clause,[],[f1297,f1252,f788,f1339]) ).
fof(f1339,plain,
( spl0_147
<=> class_Finite__Set_Ofinite_Ofinite(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1297,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(tc_Com_Ocom)
| ~ spl0_30
| spl0_126 ),
inference(resolution,[],[f1254,f789]) ).
fof(f1337,plain,
spl0_146,
inference(avatar_split_clause,[],[f373,f1335]) ).
fof(f1335,plain,
( spl0_146
<=> ! [X2,X0,X1] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f373,axiom,
! [X2,X0,X1] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f1333,plain,
spl0_145,
inference(avatar_split_clause,[],[f355,f1331]) ).
fof(f1331,plain,
( spl0_145
<=> ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f355,axiom,
! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f1329,plain,
spl0_144,
inference(avatar_split_clause,[],[f354,f1327]) ).
fof(f1327,plain,
( spl0_144
<=> ! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f354,axiom,
! [X2,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f1325,plain,
spl0_143,
inference(avatar_split_clause,[],[f338,f1323]) ).
fof(f1323,plain,
( spl0_143
<=> ! [X22,X2,X27] :
( ~ c_Finite__Set_Ofinite(X22,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X22,X27,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f338,axiom,
! [X2,X27,X22] :
( ~ c_Finite__Set_Ofinite(X22,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X22,X27,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f1321,plain,
spl0_142,
inference(avatar_split_clause,[],[f337,f1319]) ).
fof(f1319,plain,
( spl0_142
<=> ! [X22,X2,X27] :
( ~ c_Finite__Set_Ofinite(X27,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X22,X27,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f337,axiom,
! [X2,X27,X22] :
( ~ c_Finite__Set_Ofinite(X27,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X22,X27,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f1317,plain,
spl0_141,
inference(avatar_split_clause,[],[f336,f1315]) ).
fof(f1315,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f336,axiom,
! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
fof(f1313,plain,
spl0_140,
inference(avatar_split_clause,[],[f328,f1311]) ).
fof(f1311,plain,
( spl0_140
<=> ! [X22,X2,X27] :
( c_Finite__Set_Ofinite(X22,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X22,X27,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f328,axiom,
! [X2,X27,X22] :
( c_Finite__Set_Ofinite(X22,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X22,X27,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
fof(f1309,plain,
spl0_139,
inference(avatar_split_clause,[],[f327,f1307]) ).
fof(f1307,plain,
( spl0_139
<=> ! [X22,X2,X27] :
( c_Finite__Set_Ofinite(X27,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X22,X27,tc_fun(X2,tc_bool)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f327,axiom,
! [X2,X27,X22] :
( c_Finite__Set_Ofinite(X27,X2)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X22,X27,tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
fof(f1305,plain,
spl0_138,
inference(avatar_split_clause,[],[f282,f1303]) ).
fof(f1303,plain,
( spl0_138
<=> ! [X2,X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f282,axiom,
! [X2,X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f1301,plain,
spl0_137,
inference(avatar_split_clause,[],[f281,f1299]) ).
fof(f1299,plain,
( spl0_137
<=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f281,axiom,
! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f1295,plain,
spl0_136,
inference(avatar_split_clause,[],[f259,f1293]) ).
fof(f1293,plain,
( spl0_136
<=> ! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f259,axiom,
! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f1291,plain,
spl0_135,
inference(avatar_split_clause,[],[f258,f1289]) ).
fof(f1289,plain,
( spl0_135
<=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f258,axiom,
! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f1287,plain,
spl0_134,
inference(avatar_split_clause,[],[f233,f1285]) ).
fof(f1285,plain,
( spl0_134
<=> ! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f233,axiom,
! [X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X0,X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
fof(f1283,plain,
spl0_133,
inference(avatar_split_clause,[],[f232,f1281]) ).
fof(f1281,plain,
( spl0_133
<=> ! [X2,X0] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f232,axiom,
! [X2,X0] : c_HOL_Ominus__class_Ominus(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
fof(f1279,plain,
spl0_132,
inference(avatar_split_clause,[],[f172,f1277]) ).
fof(f1277,plain,
( spl0_132
<=> ! [X2,X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f172,axiom,
! [X2,X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
fof(f1275,plain,
spl0_131,
inference(avatar_split_clause,[],[f171,f1273]) ).
fof(f1273,plain,
( spl0_131
<=> ! [X11,X0,X12,X2,X1] :
( c_Fun_Oinj__on(X11,X0,X2,X12)
| ~ c_Fun_Obij__betw(X11,X0,X1,X2,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f171,axiom,
! [X2,X0,X11,X1,X12] :
( c_Fun_Oinj__on(X11,X0,X2,X12)
| ~ c_Fun_Obij__betw(X11,X0,X1,X2,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
fof(f1271,plain,
spl0_130,
inference(avatar_split_clause,[],[f132,f1269]) ).
fof(f1269,plain,
( spl0_130
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f132,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f1267,plain,
spl0_129,
inference(avatar_split_clause,[],[f131,f1265]) ).
fof(f1265,plain,
( spl0_129
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f131,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f1263,plain,
spl0_128,
inference(avatar_split_clause,[],[f100,f1261]) ).
fof(f1261,plain,
( spl0_128
<=> ! [X6,X2,X0,X7] :
( ~ hBOOL(hAPP(X0,X6))
| hBOOL(hAPP(c_Set_Oinsert(X7,X0,X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f100,axiom,
! [X2,X0,X6,X7] :
( ~ hBOOL(hAPP(X0,X6))
| hBOOL(hAPP(c_Set_Oinsert(X7,X0,X2),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1259,plain,
spl0_127,
inference(avatar_split_clause,[],[f88,f1257]) ).
fof(f1257,plain,
( spl0_127
<=> ! [X6,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_HOL_Ouminus__class_Ouminus(X6,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f88,axiom,
! [X2,X6] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_HOL_Ouminus__class_Ouminus(X6,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
fof(f1255,plain,
( ~ spl0_126
| spl0_54
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1228,f1210,f888,f1252]) ).
fof(f888,plain,
( spl0_54
<=> c_Finite__Set_Ofinite(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1228,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom)
| spl0_54
| ~ spl0_120 ),
inference(resolution,[],[f1211,f890]) ).
fof(f890,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))
| spl0_54 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f1250,plain,
spl0_125,
inference(avatar_split_clause,[],[f87,f1248]) ).
fof(f1248,plain,
( spl0_125
<=> ! [X6,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X6,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f87,axiom,
! [X2,X6] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X6,X2),X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
fof(f1246,plain,
spl0_124,
inference(avatar_split_clause,[],[f77,f1244]) ).
fof(f1244,plain,
( spl0_124
<=> ! [X6,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X6,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f77,axiom,
! [X2,X6] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X6,X2),X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
fof(f1242,plain,
spl0_123,
inference(avatar_split_clause,[],[f76,f1240]) ).
fof(f1240,plain,
( spl0_123
<=> ! [X6,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ouminus__class_Ouminus(X6,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f76,axiom,
! [X2,X6] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_HOL_Ouminus__class_Ouminus(X6,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
fof(f1238,plain,
spl0_122,
inference(avatar_split_clause,[],[f11,f1236]) ).
fof(f1236,plain,
( spl0_122
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f11,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f1234,plain,
spl0_121,
inference(avatar_split_clause,[],[f10,f1232]) ).
fof(f1232,plain,
( spl0_121
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f10,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f1212,plain,
spl0_120,
inference(avatar_split_clause,[],[f572,f1210]) ).
fof(f572,axiom,
! [X2,X21,X22,X12] :
( ~ c_Finite__Set_Ofinite(X22,X2)
| c_Finite__Set_Ofinite(c_Set_Oimage(X21,X22,X2,X12),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f1208,plain,
spl0_119,
inference(avatar_split_clause,[],[f557,f1206]) ).
fof(f1206,plain,
( spl0_119
<=> ! [X6,X2,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X6,X7,X2)
| c_lessequals(X7,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f557,axiom,
! [X2,X6,X7] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X6,X7,X2)
| c_lessequals(X7,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1204,plain,
( spl0_118
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f515,f653,f1202]) ).
fof(f1202,plain,
( spl0_118
<=> ! [X5,X33] :
( c_Com_OWT(X5)
| hAPP(c_Com_Obody,X33) != c_Option_Ooption_OSome(X5,tc_Com_Ocom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f653,plain,
( spl0_2
<=> c_Com_OWT__bodies ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f515,axiom,
! [X5,X33] :
( ~ c_Com_OWT__bodies
| c_Com_OWT(X5)
| hAPP(c_Com_Obody,X33) != c_Option_Ooption_OSome(X5,tc_Com_Ocom) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
fof(f1200,plain,
spl0_117,
inference(avatar_split_clause,[],[f231,f1198]) ).
fof(f1198,plain,
( spl0_117
<=> ! [X41,X2,X4] :
( X4 = X41
| c_Option_Ooption_OSome(X4,X2) != c_Option_Ooption_OSome(X41,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f231,axiom,
! [X2,X41,X4] :
( X4 = X41
| c_Option_Ooption_OSome(X4,X2) != c_Option_Ooption_OSome(X41,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
fof(f1196,plain,
spl0_116,
inference(avatar_split_clause,[],[f214,f1194]) ).
fof(f1194,plain,
( spl0_116
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f214,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f1188,plain,
spl0_115,
inference(avatar_split_clause,[],[f213,f1186]) ).
fof(f1186,plain,
( spl0_115
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f213,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f1184,plain,
spl0_114,
inference(avatar_split_clause,[],[f191,f1182]) ).
fof(f1182,plain,
( spl0_114
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f191,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X2),X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f1180,plain,
spl0_113,
inference(avatar_split_clause,[],[f190,f1178]) ).
fof(f1178,plain,
( spl0_113
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f190,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Orderings_Otop__class_Otop(X2) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f1176,plain,
spl0_112,
inference(avatar_split_clause,[],[f137,f1174]) ).
fof(f1174,plain,
( spl0_112
<=> ! [X2,X0,X4] :
( ~ c_in(X4,X0,X2)
| c_Set_Oinsert(X4,X0,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f137,axiom,
! [X2,X0,X4] :
( ~ c_in(X4,X0,X2)
| c_Set_Oinsert(X4,X0,X2) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f1172,plain,
spl0_111,
inference(avatar_split_clause,[],[f133,f1170]) ).
fof(f1170,plain,
( spl0_111
<=> ! [X32,X31] :
( X31 = X32
| hAPP(c_Com_Ocom_OBODY,X31) != hAPP(c_Com_Ocom_OBODY,X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f133,axiom,
! [X31,X32] :
( X31 = X32
| hAPP(c_Com_Ocom_OBODY,X31) != hAPP(c_Com_Ocom_OBODY,X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
fof(f1136,plain,
( spl0_110
| ~ spl0_14
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1018,f984,f713,f1134]) ).
fof(f1134,plain,
( spl0_110
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f713,plain,
( spl0_14
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f984,plain,
( spl0_76
<=> ! [X6,X2] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1018,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_14
| ~ spl0_76 ),
inference(resolution,[],[f985,f715]) ).
fof(f715,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f985,plain,
( ! [X2,X6] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X2) = X6 )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1132,plain,
spl0_109,
inference(avatar_split_clause,[],[f547,f1130]) ).
fof(f1130,plain,
( spl0_109
<=> ! [X2,X12,X19] : c_Finite__Set_Ofinite(c_Map_Odom(c_Map_Omap__of(X19,X2,X12),X2,X12),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f547,axiom,
! [X2,X19,X12] : c_Finite__Set_Ofinite(c_Map_Odom(c_Map_Omap__of(X19,X2,X12),X2,X12),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__map__of_0) ).
fof(f1128,plain,
spl0_108,
inference(avatar_split_clause,[],[f432,f1126]) ).
fof(f1126,plain,
( spl0_108
<=> ! [X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Otop__class_Otop(X2) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f432,axiom,
! [X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Otop__class_Otop(X2) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
fof(f1124,plain,
spl0_107,
inference(avatar_split_clause,[],[f413,f1122]) ).
fof(f1122,plain,
( spl0_107
<=> ! [X2,X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X4,X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f413,axiom,
! [X2,X0,X4] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Set_Oinsert(X4,X0,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f1120,plain,
spl0_106,
inference(avatar_split_clause,[],[f364,f1118]) ).
fof(f1118,plain,
( spl0_106
<=> ! [X2,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f364,axiom,
! [X2,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1116,plain,
spl0_105,
inference(avatar_split_clause,[],[f363,f1114]) ).
fof(f1114,plain,
( spl0_105
<=> ! [X2,X1,X4] : c_lessequals(X1,c_Set_Oinsert(X4,X1,X2),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f363,axiom,
! [X2,X1,X4] : c_lessequals(X1,c_Set_Oinsert(X4,X1,X2),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1112,plain,
spl0_104,
inference(avatar_split_clause,[],[f351,f1110]) ).
fof(f1110,plain,
( spl0_104
<=> ! [X2,X0] : c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f351,axiom,
! [X2,X0] : c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f1108,plain,
spl0_103,
inference(avatar_split_clause,[],[f333,f1106]) ).
fof(f1106,plain,
( spl0_103
<=> ! [X2,X0,X4] :
( c_Finite__Set_Ofinite(X0,X2)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X4,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f333,axiom,
! [X2,X0,X4] :
( c_Finite__Set_Ofinite(X0,X2)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X4,X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f1104,plain,
spl0_102,
inference(avatar_split_clause,[],[f332,f1102]) ).
fof(f1102,plain,
( spl0_102
<=> ! [X2,X0,X4] :
( ~ c_Finite__Set_Ofinite(X0,X2)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X4,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f332,axiom,
! [X2,X0,X4] :
( ~ c_Finite__Set_Ofinite(X0,X2)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X4,X0,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f1100,plain,
spl0_101,
inference(avatar_split_clause,[],[f313,f1098]) ).
fof(f1098,plain,
( spl0_101
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f313,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f1096,plain,
spl0_100,
inference(avatar_split_clause,[],[f312,f1094]) ).
fof(f1094,plain,
( spl0_100
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f312,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f1092,plain,
( spl0_99
| ~ spl0_4
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1017,f984,f663,f1090]) ).
fof(f1090,plain,
( spl0_99
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f663,plain,
( spl0_4
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1017,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
| ~ spl0_4
| ~ spl0_76 ),
inference(resolution,[],[f985,f665]) ).
fof(f665,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f1088,plain,
spl0_98,
inference(avatar_split_clause,[],[f309,f1086]) ).
fof(f1086,plain,
( spl0_98
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f309,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1084,plain,
spl0_97,
inference(avatar_split_clause,[],[f308,f1082]) ).
fof(f1082,plain,
( spl0_97
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f308,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1080,plain,
spl0_96,
inference(avatar_split_clause,[],[f297,f1078]) ).
fof(f1078,plain,
( spl0_96
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f297,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f1076,plain,
spl0_95,
inference(avatar_split_clause,[],[f296,f1074]) ).
fof(f1074,plain,
( spl0_95
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f296,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f1072,plain,
spl0_94,
inference(avatar_split_clause,[],[f292,f1070]) ).
fof(f1070,plain,
( spl0_94
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f292,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f1068,plain,
spl0_93,
inference(avatar_split_clause,[],[f291,f1066]) ).
fof(f1066,plain,
( spl0_93
<=> ! [X6,X2,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f291,axiom,
! [X2,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X2),X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f1064,plain,
spl0_92,
inference(avatar_split_clause,[],[f280,f1062]) ).
fof(f1062,plain,
( spl0_92
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X2),X6,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f280,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X2),X6,X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1060,plain,
spl0_91,
inference(avatar_split_clause,[],[f279,f1058]) ).
fof(f1058,plain,
( spl0_91
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f279,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(X2),X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1056,plain,
spl0_90,
inference(avatar_split_clause,[],[f276,f1054]) ).
fof(f1054,plain,
( spl0_90
<=> ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f276,axiom,
! [X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f1052,plain,
spl0_89,
inference(avatar_split_clause,[],[f269,f1050]) ).
fof(f1050,plain,
( spl0_89
<=> ! [X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Obot__class_Obot(X2) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f269,axiom,
! [X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_Orderings_Obot__class_Obot(X2) = c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
fof(f1048,plain,
( spl0_88
| ~ spl0_13
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1014,f960,f708,f1046]) ).
fof(f1046,plain,
( spl0_88
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f708,plain,
( spl0_13
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f960,plain,
( spl0_70
<=> ! [X6,X2] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1014,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_13
| ~ spl0_70 ),
inference(resolution,[],[f961,f710]) ).
fof(f710,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f961,plain,
( ! [X2,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X2) = X6 )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f1044,plain,
spl0_87,
inference(avatar_split_clause,[],[f257,f1042]) ).
fof(f1042,plain,
( spl0_87
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X6,X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f257,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X6,X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1040,plain,
spl0_86,
inference(avatar_split_clause,[],[f256,f1038]) ).
fof(f1038,plain,
( spl0_86
<=> ! [X6,X2] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f256,axiom,
! [X2,X6] :
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(X2),X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1036,plain,
spl0_85,
inference(avatar_split_clause,[],[f174,f1034]) ).
fof(f1034,plain,
( spl0_85
<=> ! [X6,X2] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X2),X2) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f174,axiom,
! [X2,X6] :
( ~ class_Lattices_Oboolean__algebra(X2)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X2),X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
fof(f1032,plain,
spl0_84,
inference(avatar_split_clause,[],[f55,f1030]) ).
fof(f1030,plain,
( spl0_84
<=> ! [X2,X11,X12] : c_Fun_Ocomp(X11,c_Fun_Oid(X2),X2,X12,X2) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f55,axiom,
! [X2,X11,X12] : c_Fun_Ocomp(X11,c_Fun_Oid(X2),X2,X12,X2) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__id_0) ).
fof(f1028,plain,
spl0_83,
inference(avatar_split_clause,[],[f54,f1026]) ).
fof(f1026,plain,
( spl0_83
<=> ! [X2,X12,X23] : c_Fun_Ocomp(c_Fun_Oid(X12),X23,X12,X12,X2) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f54,axiom,
! [X2,X12,X23] : c_Fun_Ocomp(c_Fun_Oid(X12),X23,X12,X12,X2) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__o_0) ).
fof(f1023,plain,
( spl0_82
| ~ spl0_3
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1013,f960,f658,f1021]) ).
fof(f1021,plain,
( spl0_82
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f658,plain,
( spl0_3
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1013,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_3
| ~ spl0_70 ),
inference(resolution,[],[f961,f660]) ).
fof(f660,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f1006,plain,
spl0_81,
inference(avatar_split_clause,[],[f593,f1004]) ).
fof(f1004,plain,
( spl0_81
<=> ! [X61,X60] :
( ~ class_Finite__Set_Ofinite_Ofinite(X60)
| ~ class_Finite__Set_Ofinite_Ofinite(X61)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f593,axiom,
! [X60,X61] :
( ~ class_Finite__Set_Ofinite_Ofinite(X60)
| ~ class_Finite__Set_Ofinite_Ofinite(X61)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f1002,plain,
spl0_80,
inference(avatar_split_clause,[],[f514,f1000]) ).
fof(f1000,plain,
( spl0_80
<=> ! [X6,X2] : hAPP(c_Option_Othe(X2),c_Option_Ooption_OSome(X6,X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f514,axiom,
! [X2,X6] : hAPP(c_Option_Othe(X2),c_Option_Ooption_OSome(X6,X2)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
fof(f998,plain,
spl0_79,
inference(avatar_split_clause,[],[f504,f996]) ).
fof(f996,plain,
( spl0_79
<=> ! [X2,X42] : c_Set_Oimage(c_Fun_Oid(X2),X42,X2,X2) = X42 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f504,axiom,
! [X2,X42] : c_Set_Oimage(c_Fun_Oid(X2),X42,X2,X2) = X42,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__id_0) ).
fof(f994,plain,
spl0_78,
inference(avatar_split_clause,[],[f502,f992]) ).
fof(f992,plain,
( spl0_78
<=> ! [X2,X42] : c_Set_Oimage(c_COMBI(X2),X42,X2,X2) = X42 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f502,axiom,
! [X2,X42] : c_Set_Oimage(c_COMBI(X2),X42,X2,X2) = X42,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).
fof(f990,plain,
spl0_77,
inference(avatar_split_clause,[],[f445,f988]) ).
fof(f988,plain,
( spl0_77
<=> ! [X2,X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f445,axiom,
! [X2,X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X2,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f986,plain,
spl0_76,
inference(avatar_split_clause,[],[f444,f984]) ).
fof(f444,axiom,
! [X2,X6] :
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X6,X6,X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f982,plain,
spl0_75,
inference(avatar_split_clause,[],[f277,f980]) ).
fof(f980,plain,
( spl0_75
<=> ! [X11,X2,X12] :
( ~ c_Fun_Obij(X11,X2,X12)
| c_Fun_Osurj(X11,X2,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f277,axiom,
! [X2,X11,X12] :
( ~ c_Fun_Obij(X11,X2,X12)
| c_Fun_Osurj(X11,X2,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__def_1) ).
fof(f978,plain,
spl0_74,
inference(avatar_split_clause,[],[f268,f976]) ).
fof(f976,plain,
( spl0_74
<=> ! [X2,X27] : c_Hoare__Mirabelle_Ohoare__derivs(X27,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f268,axiom,
! [X2,X27] : c_Hoare__Mirabelle_Ohoare__derivs(X27,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
fof(f974,plain,
spl0_73,
inference(avatar_split_clause,[],[f246,f972]) ).
fof(f972,plain,
( spl0_73
<=> ! [X2,X42] : c_Set_Ovimage(c_COMBI(X2),X42,X2,X2) = X42 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f246,axiom,
! [X2,X42] : c_Set_Ovimage(c_COMBI(X2),X42,X2,X2) = X42,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
fof(f970,plain,
spl0_72,
inference(avatar_split_clause,[],[f119,f968]) ).
fof(f968,plain,
( spl0_72
<=> ! [X2,X0] : c_Set_Ovimage(c_Fun_Oid(X2),X0,X2,X2) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f119,axiom,
! [X2,X0] : c_Set_Ovimage(c_Fun_Oid(X2),X0,X2,X2) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__id_0) ).
fof(f966,plain,
spl0_71,
inference(avatar_split_clause,[],[f52,f964]) ).
fof(f964,plain,
( spl0_71
<=> ! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X2,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f52,axiom,
! [X2,X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X2,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f962,plain,
spl0_70,
inference(avatar_split_clause,[],[f51,f960]) ).
fof(f51,axiom,
! [X2,X6] :
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X6,X2) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f958,plain,
spl0_69,
inference(avatar_split_clause,[],[f40,f956]) ).
fof(f956,plain,
( spl0_69
<=> ! [X6,X18,X2] :
( ~ hBOOL(hAPP(X18,X6))
| c_in(X6,X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f40,axiom,
! [X2,X18,X6] :
( ~ hBOOL(hAPP(X18,X6))
| c_in(X6,X18,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f954,plain,
spl0_68,
inference(avatar_split_clause,[],[f39,f952]) ).
fof(f952,plain,
( spl0_68
<=> ! [X6,X2,X18] :
( ~ c_in(X6,X18,X2)
| hBOOL(hAPP(X18,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f39,axiom,
! [X2,X18,X6] :
( ~ c_in(X6,X18,X2)
| hBOOL(hAPP(X18,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f950,plain,
spl0_67,
inference(avatar_split_clause,[],[f27,f948]) ).
fof(f948,plain,
( spl0_67
<=> ! [X11,X2,X12] : c_Fun_Oinj__on(X11,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f27,axiom,
! [X2,X11,X12] : c_Fun_Oinj__on(X11,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
fof(f945,plain,
spl0_66,
inference(avatar_split_clause,[],[f626,f943]) ).
fof(f943,plain,
( spl0_66
<=> ! [X2,X26,X42] :
( X26 = X42
| ~ c_fequal(X26,X42,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f626,axiom,
! [X2,X26,X42] :
( X26 = X42
| ~ c_fequal(X26,X42,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f941,plain,
spl0_65,
inference(avatar_split_clause,[],[f430,f939]) ).
fof(f939,plain,
( spl0_65
<=> ! [X6,X2,X0] : hBOOL(hAPP(c_Set_Oinsert(X6,X0,X2),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f430,axiom,
! [X2,X0,X6] : hBOOL(hAPP(c_Set_Oinsert(X6,X0,X2),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f937,plain,
spl0_64,
inference(avatar_split_clause,[],[f418,f935]) ).
fof(f935,plain,
( spl0_64
<=> ! [X6,X2] : ~ c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f418,axiom,
! [X2,X6] : ~ c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
fof(f933,plain,
spl0_63,
inference(avatar_split_clause,[],[f390,f931]) ).
fof(f931,plain,
( spl0_63
<=> ! [X6,X2] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f390,axiom,
! [X2,X6] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f929,plain,
spl0_62,
inference(avatar_split_clause,[],[f301,f927]) ).
fof(f927,plain,
( spl0_62
<=> ! [X6,X2] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f301,axiom,
! [X2,X6] :
( ~ class_Orderings_Obot(X2)
| c_lessequals(c_Orderings_Obot__class_Obot(X2),X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f925,plain,
spl0_61,
inference(avatar_split_clause,[],[f290,f923]) ).
fof(f923,plain,
( spl0_61
<=> ! [X6,X2] :
( ~ class_Orderings_Otop(X2)
| c_lessequals(X6,c_Orderings_Otop__class_Otop(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f290,axiom,
! [X2,X6] :
( ~ class_Orderings_Otop(X2)
| c_lessequals(X6,c_Orderings_Otop__class_Otop(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f921,plain,
spl0_60,
inference(avatar_split_clause,[],[f273,f919]) ).
fof(f919,plain,
( spl0_60
<=> ! [X6,X2] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f273,axiom,
! [X2,X6] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f917,plain,
spl0_59,
inference(avatar_split_clause,[],[f230,f915]) ).
fof(f915,plain,
( spl0_59
<=> ! [X6,X2] : c_in(X6,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f230,axiom,
! [X2,X6] : c_in(X6,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f913,plain,
( ~ spl0_58
| ~ spl0_30
| spl0_54 ),
inference(avatar_split_clause,[],[f892,f888,f788,f910]) ).
fof(f910,plain,
( spl0_58
<=> class_Finite__Set_Ofinite_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f892,plain,
( ~ class_Finite__Set_Ofinite_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))
| ~ spl0_30
| spl0_54 ),
inference(resolution,[],[f890,f789]) ).
fof(f908,plain,
spl0_57,
inference(avatar_split_clause,[],[f46,f906]) ).
fof(f906,plain,
( spl0_57
<=> ! [X6,X2,X1] : c_in(X6,c_Set_Oinsert(X6,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f46,axiom,
! [X2,X1,X6] : c_in(X6,c_Set_Oinsert(X6,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f904,plain,
( spl0_56
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f899,f894,f901]) ).
fof(f901,plain,
( spl0_56
<=> c_lessequals(v_F,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f894,plain,
( spl0_55
<=> c_lessequals(v_F,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f899,plain,
( c_lessequals(v_F,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ spl0_55 ),
inference(forward_demodulation,[],[f898,f571]) ).
fof(f571,axiom,
! [X2,X0,X11,X24,X12,X23] : c_Set_Oimage(X11,c_Set_Oimage(X23,X0,X24,X12),X12,X2) = c_Set_Oimage(c_COMBB(X11,X23,X12,X2,X24),X0,X24,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
fof(f898,plain,
( c_lessequals(v_F,c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ spl0_55 ),
inference(forward_demodulation,[],[f896,f571]) ).
fof(f896,plain,
( c_lessequals(v_F,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f897,plain,
spl0_55,
inference(avatar_split_clause,[],[f585,f894]) ).
fof(f585,axiom,
c_lessequals(v_F,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f891,plain,
( ~ spl0_54
| spl0_53 ),
inference(avatar_split_clause,[],[f886,f881,f888]) ).
fof(f881,plain,
( spl0_53
<=> c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f886,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Option_Othe(tc_Com_Ocom),c_Set_Oimage(c_Com_Obody,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Option_Ooption(tc_Com_Ocom)),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))
| spl0_53 ),
inference(forward_demodulation,[],[f885,f571]) ).
fof(f885,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))
| spl0_53 ),
inference(forward_demodulation,[],[f883,f571]) ).
fof(f883,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))
| spl0_53 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f884,plain,
~ spl0_53,
inference(avatar_split_clause,[],[f586,f881]) ).
fof(f586,axiom,
~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f879,plain,
spl0_52,
inference(avatar_split_clause,[],[f599,f877]) ).
fof(f877,plain,
( spl0_52
<=> ! [X61,X60] :
( ~ class_HOL_Oord(X61)
| class_HOL_Oord(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f599,axiom,
! [X60,X61] :
( ~ class_HOL_Oord(X61)
| class_HOL_Oord(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f875,plain,
spl0_51,
inference(avatar_split_clause,[],[f598,f873]) ).
fof(f873,plain,
( spl0_51
<=> ! [X61,X60] :
( ~ class_Orderings_Obot(X61)
| class_Orderings_Obot(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f598,axiom,
! [X60,X61] :
( ~ class_Orderings_Obot(X61)
| class_Orderings_Obot(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f871,plain,
spl0_50,
inference(avatar_split_clause,[],[f597,f869]) ).
fof(f869,plain,
( spl0_50
<=> ! [X61,X60] :
( ~ class_Orderings_Otop(X61)
| class_Orderings_Otop(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f597,axiom,
! [X60,X61] :
( ~ class_Orderings_Otop(X61)
| class_Orderings_Otop(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f867,plain,
spl0_49,
inference(avatar_split_clause,[],[f596,f865]) ).
fof(f865,plain,
( spl0_49
<=> ! [X61,X60] :
( ~ class_Orderings_Oorder(X61)
| class_Orderings_Oorder(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f596,axiom,
! [X60,X61] :
( ~ class_Orderings_Oorder(X61)
| class_Orderings_Oorder(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f863,plain,
spl0_48,
inference(avatar_split_clause,[],[f595,f861]) ).
fof(f861,plain,
( spl0_48
<=> ! [X61,X60] :
( ~ class_Lattices_Olattice(X61)
| class_Lattices_Olattice(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f595,axiom,
! [X60,X61] :
( ~ class_Lattices_Olattice(X61)
| class_Lattices_Olattice(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f859,plain,
spl0_47,
inference(avatar_split_clause,[],[f594,f857]) ).
fof(f857,plain,
( spl0_47
<=> ! [X61,X60] :
( ~ class_Orderings_Opreorder(X61)
| class_Orderings_Opreorder(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f594,axiom,
! [X60,X61] :
( ~ class_Orderings_Opreorder(X61)
| class_Orderings_Opreorder(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f855,plain,
spl0_46,
inference(avatar_split_clause,[],[f592,f853]) ).
fof(f853,plain,
( spl0_46
<=> ! [X61,X60] :
( ~ class_Lattices_Oboolean__algebra(X61)
| class_Lattices_Oboolean__algebra(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f592,axiom,
! [X60,X61] :
( ~ class_Lattices_Oboolean__algebra(X61)
| class_Lattices_Oboolean__algebra(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f851,plain,
spl0_45,
inference(avatar_split_clause,[],[f591,f849]) ).
fof(f849,plain,
( spl0_45
<=> ! [X61,X60] :
( ~ class_Lattices_Obounded__lattice(X61)
| class_Lattices_Obounded__lattice(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f591,axiom,
! [X60,X61] :
( ~ class_Lattices_Obounded__lattice(X61)
| class_Lattices_Obounded__lattice(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f847,plain,
spl0_44,
inference(avatar_split_clause,[],[f590,f845]) ).
fof(f845,plain,
( spl0_44
<=> ! [X61,X60] :
( ~ class_Lattices_Odistrib__lattice(X61)
| class_Lattices_Odistrib__lattice(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f590,axiom,
! [X60,X61] :
( ~ class_Lattices_Odistrib__lattice(X61)
| class_Lattices_Odistrib__lattice(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f843,plain,
spl0_43,
inference(avatar_split_clause,[],[f589,f841]) ).
fof(f841,plain,
( spl0_43
<=> ! [X61,X60] :
( ~ class_Lattices_Olattice(X61)
| class_Lattices_Olower__semilattice(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f589,axiom,
! [X60,X61] :
( ~ class_Lattices_Olattice(X61)
| class_Lattices_Olower__semilattice(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f839,plain,
spl0_42,
inference(avatar_split_clause,[],[f588,f837]) ).
fof(f837,plain,
( spl0_42
<=> ! [X61,X60] :
( ~ class_Lattices_Olattice(X61)
| class_Lattices_Oupper__semilattice(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f588,axiom,
! [X60,X61] :
( ~ class_Lattices_Olattice(X61)
| class_Lattices_Oupper__semilattice(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f835,plain,
spl0_41,
inference(avatar_split_clause,[],[f587,f833]) ).
fof(f833,plain,
( spl0_41
<=> ! [X61,X60] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X61)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f587,axiom,
! [X60,X61] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X61)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X60,X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f831,plain,
spl0_40,
inference(avatar_split_clause,[],[f567,f829]) ).
fof(f829,plain,
( spl0_40
<=> ! [X2,X0] : c_lessequals(X0,X0,tc_fun(X2,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f567,axiom,
! [X2,X0] : c_lessequals(X0,X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f827,plain,
spl0_39,
inference(avatar_split_clause,[],[f564,f825]) ).
fof(f825,plain,
( spl0_39
<=> ! [X6,X2] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X6,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f564,axiom,
! [X2,X6] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X6,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f823,plain,
spl0_38,
inference(avatar_split_clause,[],[f563,f821]) ).
fof(f821,plain,
( spl0_38
<=> ! [X6,X2] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X6,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f563,axiom,
! [X2,X6] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X6,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f819,plain,
spl0_37,
inference(avatar_split_clause,[],[f556,f816]) ).
fof(f556,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).
fof(f814,plain,
spl0_36,
inference(avatar_split_clause,[],[f331,f812]) ).
fof(f812,plain,
( spl0_36
<=> ! [X2] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f331,axiom,
! [X2] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f810,plain,
spl0_35,
inference(avatar_split_clause,[],[f198,f808]) ).
fof(f808,plain,
( spl0_35
<=> ! [X2,X0] : c_Fun_Oinj__on(c_COMBI(X2),X0,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f198,axiom,
! [X2,X0] : c_Fun_Oinj__on(c_COMBI(X2),X0,X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
fof(f806,plain,
spl0_34,
inference(avatar_split_clause,[],[f168,f804]) ).
fof(f804,plain,
( spl0_34
<=> ! [X6,X2] : hAPP(c_Fun_Oid(X2),X6) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f168,axiom,
! [X2,X6] : hAPP(c_Fun_Oid(X2),X6) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
fof(f802,plain,
spl0_33,
inference(avatar_split_clause,[],[f44,f800]) ).
fof(f800,plain,
( spl0_33
<=> ! [X2,X0] : c_Fun_Oinj__on(c_Fun_Oid(X2),X0,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f44,axiom,
! [X2,X0] : c_Fun_Oinj__on(c_Fun_Oid(X2),X0,X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
fof(f798,plain,
spl0_32,
inference(avatar_split_clause,[],[f38,f796]) ).
fof(f796,plain,
( spl0_32
<=> ! [X2,X17] : hAPP(c_COMBI(X2),X17) = X17 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f38,axiom,
! [X2,X17] : hAPP(c_COMBI(X2),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
fof(f794,plain,
spl0_31,
inference(avatar_split_clause,[],[f622,f792]) ).
fof(f792,plain,
( spl0_31
<=> ! [X61] :
( ~ class_Finite__Set_Ofinite_Ofinite(X61)
| class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f622,axiom,
! [X61] :
( ~ class_Finite__Set_Ofinite_Ofinite(X61)
| class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
fof(f790,plain,
spl0_30,
inference(avatar_split_clause,[],[f581,f788]) ).
fof(f581,axiom,
! [X2,X0] :
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f786,plain,
( spl0_29
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f516,f648,f784]) ).
fof(f784,plain,
( spl0_29
<=> ! [X28] : v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X28) != X28 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f648,plain,
( spl0_1
<=> c_Hoare__Mirabelle_Ostate__not__singleton ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f516,axiom,
! [X28] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(X28) != X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__stateE_0) ).
fof(f782,plain,
spl0_28,
inference(avatar_split_clause,[],[f204,f780]) ).
fof(f780,plain,
( spl0_28
<=> ! [X11,X2,X12] : c_Map_Omap__le(X11,X11,X2,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f204,axiom,
! [X2,X11,X12] : c_Map_Omap__le(X11,X11,X2,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).
fof(f778,plain,
spl0_27,
inference(avatar_split_clause,[],[f144,f776]) ).
fof(f776,plain,
( spl0_27
<=> ! [X2] : c_Fun_Osurj(c_Fun_Oid(X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f144,axiom,
! [X2] : c_Fun_Osurj(c_Fun_Oid(X2),X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__id_0) ).
fof(f774,plain,
spl0_26,
inference(avatar_split_clause,[],[f84,f772]) ).
fof(f772,plain,
( spl0_26
<=> ! [X2] : c_Fun_Obij(c_Fun_Oid(X2),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f84,axiom,
! [X2] : c_Fun_Obij(c_Fun_Oid(X2),X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__id_0) ).
fof(f770,plain,
spl0_25,
inference(avatar_split_clause,[],[f625,f768]) ).
fof(f768,plain,
( spl0_25
<=> ! [X6,X2] : c_fequal(X6,X6,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f625,axiom,
! [X2,X6] : c_fequal(X6,X6,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f766,plain,
spl0_24,
inference(avatar_split_clause,[],[f621,f763]) ).
fof(f763,plain,
( spl0_24
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f621,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f761,plain,
spl0_23,
inference(avatar_split_clause,[],[f620,f758]) ).
fof(f758,plain,
( spl0_23
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f620,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f756,plain,
spl0_22,
inference(avatar_split_clause,[],[f619,f753]) ).
fof(f753,plain,
( spl0_22
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f619,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f751,plain,
spl0_21,
inference(avatar_split_clause,[],[f618,f748]) ).
fof(f748,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f618,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f746,plain,
spl0_20,
inference(avatar_split_clause,[],[f617,f743]) ).
fof(f743,plain,
( spl0_20
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f617,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f741,plain,
spl0_19,
inference(avatar_split_clause,[],[f616,f738]) ).
fof(f738,plain,
( spl0_19
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f616,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f736,plain,
spl0_18,
inference(avatar_split_clause,[],[f615,f733]) ).
fof(f733,plain,
( spl0_18
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f615,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f731,plain,
spl0_17,
inference(avatar_split_clause,[],[f614,f728]) ).
fof(f728,plain,
( spl0_17
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f614,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(f726,plain,
spl0_16,
inference(avatar_split_clause,[],[f613,f723]) ).
fof(f723,plain,
( spl0_16
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f613,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f721,plain,
spl0_15,
inference(avatar_split_clause,[],[f612,f718]) ).
fof(f718,plain,
( spl0_15
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f612,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f716,plain,
spl0_14,
inference(avatar_split_clause,[],[f611,f713]) ).
fof(f611,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f711,plain,
spl0_13,
inference(avatar_split_clause,[],[f610,f708]) ).
fof(f610,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f706,plain,
spl0_12,
inference(avatar_split_clause,[],[f609,f703]) ).
fof(f703,plain,
( spl0_12
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f609,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f701,plain,
spl0_11,
inference(avatar_split_clause,[],[f608,f698]) ).
fof(f698,plain,
( spl0_11
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f608,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f696,plain,
spl0_10,
inference(avatar_split_clause,[],[f607,f693]) ).
fof(f693,plain,
( spl0_10
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f607,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f691,plain,
spl0_9,
inference(avatar_split_clause,[],[f606,f688]) ).
fof(f688,plain,
( spl0_9
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f606,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f686,plain,
spl0_8,
inference(avatar_split_clause,[],[f605,f683]) ).
fof(f683,plain,
( spl0_8
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f605,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f681,plain,
spl0_7,
inference(avatar_split_clause,[],[f604,f678]) ).
fof(f678,plain,
( spl0_7
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f604,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f676,plain,
spl0_6,
inference(avatar_split_clause,[],[f603,f673]) ).
fof(f673,plain,
( spl0_6
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f603,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f671,plain,
spl0_5,
inference(avatar_split_clause,[],[f602,f668]) ).
fof(f668,plain,
( spl0_5
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f602,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f666,plain,
spl0_4,
inference(avatar_split_clause,[],[f601,f663]) ).
fof(f601,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f661,plain,
spl0_3,
inference(avatar_split_clause,[],[f600,f658]) ).
fof(f600,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f656,plain,
spl0_2,
inference(avatar_split_clause,[],[f584,f653]) ).
fof(f584,axiom,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f651,plain,
spl0_1,
inference(avatar_split_clause,[],[f583,f648]) ).
fof(f583,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV898-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.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 : Tue Apr 30 05:02:25 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (15830)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.40 % (15832)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (15833)WARNING: value z3 for option sas not known
% 0.14/0.40 % (15831)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (15834)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (15833)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)
% 0.14/0.40 % (15835)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)
% 0.14/0.40 % (15836)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)
% 0.14/0.40 % (15837)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.44 % (15835)First to succeed.
% 0.20/0.45 % (15835)Refutation found. Thanks to Tanya!
% 0.20/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.46 % (15835)------------------------------
% 0.20/0.46 % (15835)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.46 % (15835)Termination reason: Refutation
% 0.20/0.46
% 0.20/0.46 % (15835)Memory used [KB]: 1874
% 0.20/0.46 % (15835)Time elapsed: 0.052 s
% 0.20/0.46 % (15835)Instructions burned: 86 (million)
% 0.20/0.46 % (15835)------------------------------
% 0.20/0.46 % (15835)------------------------------
% 0.20/0.46 % (15830)Success in time 0.087 s
%------------------------------------------------------------------------------