TSTP Solution File: SWV689-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n024.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 : Sat Sep 2 13:57:38 EDT 2023
% Result : Unsatisfiable 0.28s 0.58s
% Output : Refutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 399
% Syntax : Number of formulae : 639 ( 271 unt; 0 def)
% Number of atoms : 1204 ( 164 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 957 ( 392 ~; 359 |; 0 &)
% ( 206 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 253 ( 251 usr; 207 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 665 (; 665 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2618,plain,
$false,
inference(avatar_sat_refutation,[],[f815,f820,f825,f830,f835,f840,f845,f850,f855,f860,f865,f870,f875,f880,f885,f890,f895,f900,f905,f910,f915,f920,f925,f930,f935,f940,f945,f950,f955,f960,f965,f969,f973,f978,f982,f986,f991,f995,f999,f1003,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1067,f1071,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1118,f1122,f1126,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1174,f1196,f1210,f1214,f1218,f1222,f1226,f1230,f1234,f1238,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1270,f1274,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1362,f1366,f1370,f1374,f1378,f1382,f1386,f1390,f1448,f1524,f1582,f1614,f1618,f1622,f1626,f1630,f1634,f1638,f1645,f1649,f1653,f1657,f1661,f1665,f1669,f1673,f1677,f1681,f1690,f1694,f1698,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1870,f2027,f2045,f2049,f2053,f2057,f2061,f2065,f2069,f2073,f2077,f2082,f2086,f2090,f2094,f2098,f2102,f2106,f2110,f2114,f2118,f2122,f2126,f2130,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2162,f2167,f2171,f2175,f2179,f2183,f2187,f2241,f2616,f2617]) ).
fof(f2617,plain,
( ~ spl0_37
| spl0_1
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2537,f2181,f812,f988]) ).
fof(f988,plain,
( spl0_37
<=> c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f812,plain,
( spl0_1
<=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f2181,plain,
( spl0_202
<=> ! [X9,X7,X4] :
( ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2537,plain,
( ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| spl0_1
| ~ spl0_202 ),
inference(resolution,[],[f2182,f814]) ).
fof(f814,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat)
| spl0_1 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f2182,plain,
( ! [X9,X7,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2181]) ).
fof(f2616,plain,
spl0_206,
inference(avatar_split_clause,[],[f30,f2614]) ).
fof(f2614,plain,
( spl0_206
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f30,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__of__nonneg_0) ).
fof(f2241,plain,
( spl0_204
| ~ spl0_205
| ~ spl0_166
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2220,f2047,f1867,f2238,f2234]) ).
fof(f2234,plain,
( spl0_204
<=> v_n = c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2238,plain,
( spl0_205
<=> c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1867,plain,
( spl0_166
<=> c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2047,plain,
( spl0_169
<=> ! [X4,X3] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f2220,plain,
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat)
| v_n = c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat)
| ~ spl0_166
| ~ spl0_169 ),
inference(resolution,[],[f2048,f1869]) ).
fof(f1869,plain,
( c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1867]) ).
fof(f2048,plain,
( ! [X3,X4] :
( ~ c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat)
| X3 = X4 )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f2047]) ).
fof(f2187,plain,
spl0_203,
inference(avatar_split_clause,[],[f758,f2185]) ).
fof(f2185,plain,
( spl0_203
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f758,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__neq__iff_0) ).
fof(f2183,plain,
spl0_202,
inference(avatar_split_clause,[],[f750,f2181]) ).
fof(f750,axiom,
! [X9,X7,X4] :
( ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__imp__diff__less_0) ).
fof(f2179,plain,
spl0_201,
inference(avatar_split_clause,[],[f697,f2177]) ).
fof(f2177,plain,
( spl0_201
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f697,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__Suc__Suc_0) ).
fof(f2175,plain,
spl0_200,
inference(avatar_split_clause,[],[f687,f2173]) ).
fof(f2173,plain,
( spl0_200
<=> ! [X9,X8,X7] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f687,axiom,
! [X8,X9,X7] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__lessD1_0) ).
fof(f2171,plain,
spl0_199,
inference(avatar_split_clause,[],[f686,f2169]) ).
fof(f2169,plain,
( spl0_199
<=> ! [X6,X5,X15] :
( ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f686,axiom,
! [X6,X15,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I2_J_0) ).
fof(f2167,plain,
( spl0_198
| ~ spl0_37
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1962,f1732,f988,f2164]) ).
fof(f2164,plain,
( spl0_198
<=> v_i = c_Divides_Odiv__class_Omod(v_i,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1732,plain,
( spl0_159
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1962,plain,
( v_i = c_Divides_Odiv__class_Omod(v_i,v_n,tc_nat)
| ~ spl0_37
| ~ spl0_159 ),
inference(resolution,[],[f1733,f990]) ).
fof(f990,plain,
( c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f988]) ).
fof(f1733,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1732]) ).
fof(f2162,plain,
spl0_197,
inference(avatar_split_clause,[],[f685,f2160]) ).
fof(f2160,plain,
( spl0_197
<=> ! [X6,X5,X15] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f685,axiom,
! [X6,X15,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I1_J_0) ).
fof(f2158,plain,
spl0_196,
inference(avatar_split_clause,[],[f675,f2156]) ).
fof(f2156,plain,
( spl0_196
<=> ! [X4,X3] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f675,axiom,
! [X3,X4] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__eq__less__or__eq_0) ).
fof(f2154,plain,
spl0_195,
inference(avatar_split_clause,[],[f587,f2152]) ).
fof(f2152,plain,
( spl0_195
<=> ! [X4,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f587,axiom,
! [X9,X4] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__reduce_0) ).
fof(f2150,plain,
spl0_194,
inference(avatar_split_clause,[],[f586,f2148]) ).
fof(f2148,plain,
( spl0_194
<=> ! [X4,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f586,axiom,
! [X9,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__reduce_1) ).
fof(f2146,plain,
spl0_193,
inference(avatar_split_clause,[],[f554,f2144]) ).
fof(f2144,plain,
( spl0_193
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X0),X1,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f554,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X0),X1,X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__diff__cancel_0) ).
fof(f2142,plain,
spl0_192,
inference(avatar_split_clause,[],[f545,f2140]) ).
fof(f2140,plain,
( spl0_192
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X0),X1,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f545,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X0),X1,X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__cancel_0) ).
fof(f2138,plain,
spl0_191,
inference(avatar_split_clause,[],[f544,f2136]) ).
fof(f2136,plain,
( spl0_191
<=> ! [X5,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f544,axiom,
! [X0,X5] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__ringb_Osubr0__iff_1) ).
fof(f2134,plain,
spl0_190,
inference(avatar_split_clause,[],[f472,f2132]) ).
fof(f2132,plain,
( spl0_190
<=> ! [X5,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f472,axiom,
! [X0,X5] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2130,plain,
spl0_189,
inference(avatar_split_clause,[],[f430,f2128]) ).
fof(f2128,plain,
( spl0_189
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f430,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2126,plain,
spl0_188,
inference(avatar_split_clause,[],[f427,f2124]) ).
fof(f2124,plain,
( spl0_188
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X14,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f427,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X14,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X14,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2122,plain,
( spl0_187
| ~ spl0_50
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1865,f1663,f1041,f2120]) ).
fof(f2120,plain,
( spl0_187
<=> ! [X18,X19] :
( c_lessequals(X18,X18,X19)
| ~ class_Orderings_Olinorder(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1041,plain,
( spl0_50
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1663,plain,
( spl0_143
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1865,plain,
( ! [X18,X19] :
( c_lessequals(X18,X18,X19)
| ~ class_Orderings_Olinorder(X19) )
| ~ spl0_50
| ~ spl0_143 ),
inference(duplicate_literal_removal,[],[f1858]) ).
fof(f1858,plain,
( ! [X18,X19] :
( c_lessequals(X18,X18,X19)
| ~ class_Orderings_Olinorder(X19)
| ~ class_Orderings_Olinorder(X19) )
| ~ spl0_50
| ~ spl0_143 ),
inference(resolution,[],[f1664,f1042]) ).
fof(f1042,plain,
( ! [X0,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1041]) ).
fof(f1664,plain,
( ! [X0,X6,X5] :
( c_HOL_Oord__class_Oless(X6,X5,X0)
| c_lessequals(X5,X6,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1663]) ).
fof(f2118,plain,
spl0_186,
inference(avatar_split_clause,[],[f419,f2116]) ).
fof(f2116,plain,
( spl0_186
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f419,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__Suc__right_0) ).
fof(f2114,plain,
spl0_185,
inference(avatar_split_clause,[],[f418,f2112]) ).
fof(f2112,plain,
( spl0_185
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f418,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__Suc_0) ).
fof(f2110,plain,
spl0_184,
inference(avatar_split_clause,[],[f417,f2108]) ).
fof(f2108,plain,
( spl0_184
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f417,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__idempotent_0) ).
fof(f2106,plain,
spl0_183,
inference(avatar_split_clause,[],[f410,f2104]) ).
fof(f2104,plain,
( spl0_183
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f410,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__is__0__eq_0) ).
fof(f2102,plain,
spl0_182,
inference(avatar_split_clause,[],[f409,f2100]) ).
fof(f2100,plain,
( spl0_182
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f409,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__is__0__eq_1) ).
fof(f2098,plain,
spl0_181,
inference(avatar_split_clause,[],[f379,f2096]) ).
fof(f2096,plain,
( spl0_181
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f379,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__0__left_0) ).
fof(f2094,plain,
spl0_180,
inference(avatar_split_clause,[],[f337,f2092]) ).
fof(f2092,plain,
( spl0_180
<=> ! [X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f337,axiom,
! [X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__1__iff__1_0) ).
fof(f2090,plain,
spl0_179,
inference(avatar_split_clause,[],[f307,f2088]) ).
fof(f2088,plain,
( spl0_179
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X6,X0) = c_Orderings_Oord__class_Omin(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f307,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X6,X0) = c_Orderings_Oord__class_Omin(X6,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__commute_0) ).
fof(f2086,plain,
spl0_178,
inference(avatar_split_clause,[],[f283,f2084]) ).
fof(f2084,plain,
( spl0_178
<=> ! [X3,X7,X8] :
( ~ c_lessequals(X8,X7,tc_nat)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f283,axiom,
! [X3,X8,X7] :
( ~ c_lessequals(X8,X7,tc_nat)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_trans__le__add1_0) ).
fof(f2082,plain,
spl0_177,
inference(avatar_split_clause,[],[f282,f2080]) ).
fof(f2080,plain,
( spl0_177
<=> ! [X4,X9,X3] :
( c_lessequals(X9,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f282,axiom,
! [X3,X9,X4] :
( c_lessequals(X9,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__leE_1) ).
fof(f2077,plain,
spl0_176,
inference(avatar_split_clause,[],[f281,f2075]) ).
fof(f2075,plain,
( spl0_176
<=> ! [X4,X9,X3] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f281,axiom,
! [X3,X9,X4] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__leE_0) ).
fof(f2073,plain,
spl0_175,
inference(avatar_split_clause,[],[f280,f2071]) ).
fof(f2071,plain,
( spl0_175
<=> ! [X6,X5,X15] :
( ~ c_lessequals(X5,X15,tc_nat)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f280,axiom,
! [X6,X15,X5] :
( ~ c_lessequals(X5,X15,tc_nat)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I4_J_0) ).
fof(f2069,plain,
spl0_174,
inference(avatar_split_clause,[],[f257,f2067]) ).
fof(f2067,plain,
( spl0_174
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Nat_Osemiring__1__class_Oof__nat(X4,X0) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f257,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Nat_Osemiring__1__class_Oof__nat(X4,X0) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__of__nat_0) ).
fof(f2065,plain,
spl0_173,
inference(avatar_split_clause,[],[f162,f2063]) ).
fof(f2063,plain,
( spl0_173
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,X1,X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f162,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,X1,X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2061,plain,
spl0_172,
inference(avatar_split_clause,[],[f160,f2059]) ).
fof(f2059,plain,
( spl0_172
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f160,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_double__eq__0__iff_1) ).
fof(f2057,plain,
spl0_171,
inference(avatar_split_clause,[],[f85,f2055]) ).
fof(f2055,plain,
( spl0_171
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f85,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__is__0_1) ).
fof(f2053,plain,
spl0_170,
inference(avatar_split_clause,[],[f84,f2051]) ).
fof(f2051,plain,
( spl0_170
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f84,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__is__0_0) ).
fof(f2049,plain,
spl0_169,
inference(avatar_split_clause,[],[f27,f2047]) ).
fof(f27,axiom,
! [X3,X4] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__antisym_0) ).
fof(f2045,plain,
spl0_168,
inference(avatar_split_clause,[],[f26,f2043]) ).
fof(f2043,plain,
( spl0_168
<=> ! [X6,X5] :
( X5 = X6
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f26,axiom,
! [X6,X5] :
( X5 = X6
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd_Oantisym_0) ).
fof(f2027,plain,
( ~ spl0_167
| ~ spl0_76
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1786,f1636,f1156,f2024]) ).
fof(f2024,plain,
( spl0_167
<=> c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1156,plain,
( spl0_76
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1636,plain,
( spl0_137
<=> ! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1786,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_76
| ~ spl0_137 ),
inference(superposition,[],[f1637,f1157]) ).
fof(f1157,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f1637,plain,
( ! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1636]) ).
fof(f1870,plain,
( ~ spl0_30
| spl0_166
| spl0_1
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1856,f1663,f812,f1867,f957]) ).
fof(f957,plain,
( spl0_30
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1856,plain,
( c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| spl0_1
| ~ spl0_143 ),
inference(resolution,[],[f1664,f814]) ).
fof(f1758,plain,
spl0_165,
inference(avatar_split_clause,[],[f743,f1756]) ).
fof(f1756,plain,
( spl0_165
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f743,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__asym_H_0) ).
fof(f1754,plain,
spl0_164,
inference(avatar_split_clause,[],[f742,f1752]) ).
fof(f1752,plain,
( spl0_164
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f742,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__iff__gr__or__eq_1) ).
fof(f1750,plain,
spl0_163,
inference(avatar_split_clause,[],[f741,f1748]) ).
fof(f1748,plain,
( spl0_163
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f741,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_xt1_I9_J_0) ).
fof(f1746,plain,
spl0_162,
inference(avatar_split_clause,[],[f740,f1744]) ).
fof(f1744,plain,
( spl0_162
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f740,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__difference__nat_2) ).
fof(f1742,plain,
spl0_161,
inference(avatar_split_clause,[],[f693,f1740]) ).
fof(f1740,plain,
( spl0_161
<=> ! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f693,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc__eq__0__disj_3) ).
fof(f1738,plain,
spl0_160,
inference(avatar_split_clause,[],[f692,f1736]) ).
fof(f1736,plain,
( spl0_160
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f692,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__less__eq_0) ).
fof(f1734,plain,
spl0_159,
inference(avatar_split_clause,[],[f684,f1732]) ).
fof(f684,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__if_0) ).
fof(f1730,plain,
( spl0_158
| ~ spl0_75
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1494,f1446,f1152,f1728]) ).
fof(f1728,plain,
( spl0_158
<=> ! [X1] : c_lessequals(X1,c_Suc(c_Suc(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1152,plain,
( spl0_75
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1446,plain,
( spl0_128
<=> ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_Suc(X10)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1494,plain,
( ! [X1] : c_lessequals(X1,c_Suc(c_Suc(X1)),tc_nat)
| ~ spl0_75
| ~ spl0_128 ),
inference(resolution,[],[f1447,f1153]) ).
fof(f1153,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1447,plain,
( ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_Suc(X10)),tc_nat)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f1726,plain,
spl0_157,
inference(avatar_split_clause,[],[f663,f1724]) ).
fof(f1724,plain,
( spl0_157
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f663,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__linear_0) ).
fof(f1722,plain,
spl0_156,
inference(avatar_split_clause,[],[f661,f1720]) ).
fof(f1720,plain,
( spl0_156
<=> ! [X4,X3] :
( c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f661,axiom,
! [X3,X4] :
( c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__le__mono_0) ).
fof(f1718,plain,
spl0_155,
inference(avatar_split_clause,[],[f660,f1716]) ).
fof(f1716,plain,
( spl0_155
<=> ! [X4,X3] :
( ~ c_lessequals(X4,X3,tc_nat)
| c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f660,axiom,
! [X3,X4] :
( ~ c_lessequals(X4,X3,tc_nat)
| c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__le__mono_1) ).
fof(f1714,plain,
spl0_154,
inference(avatar_split_clause,[],[f647,f1712]) ).
fof(f1712,plain,
( spl0_154
<=> ! [X5,X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X5,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f647,axiom,
! [X19,X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X5,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__eq__0__iff_1) ).
fof(f1710,plain,
spl0_153,
inference(avatar_split_clause,[],[f634,f1708]) ).
fof(f1708,plain,
( spl0_153
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f634,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_zero__less__abs__iff_0) ).
fof(f1706,plain,
spl0_152,
inference(avatar_split_clause,[],[f582,f1704]) ).
fof(f1704,plain,
( spl0_152
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f582,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__eq__0__iff_2) ).
fof(f1702,plain,
spl0_151,
inference(avatar_split_clause,[],[f581,f1700]) ).
fof(f1700,plain,
( spl0_151
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f581,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__eq__0__iff_1) ).
fof(f1698,plain,
spl0_150,
inference(avatar_split_clause,[],[f580,f1696]) ).
fof(f1696,plain,
( spl0_150
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f580,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__zero__right_0) ).
fof(f1694,plain,
spl0_149,
inference(avatar_split_clause,[],[f579,f1692]) ).
fof(f1692,plain,
( spl0_149
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f579,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__zero__left_0) ).
fof(f1690,plain,
spl0_148,
inference(avatar_split_clause,[],[f578,f1688]) ).
fof(f1688,plain,
( spl0_148
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f578,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Omul__0_0) ).
fof(f1681,plain,
spl0_147,
inference(avatar_split_clause,[],[f576,f1679]) ).
fof(f1679,plain,
( spl0_147
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f576,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult_Ozero__right_0) ).
fof(f1677,plain,
spl0_146,
inference(avatar_split_clause,[],[f572,f1675]) ).
fof(f1675,plain,
( spl0_146
<=> ! [X6,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f572,axiom,
! [X0,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__left_Ozero_0) ).
fof(f1673,plain,
spl0_145,
inference(avatar_split_clause,[],[f571,f1671]) ).
fof(f1671,plain,
( spl0_145
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f571,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1669,plain,
spl0_144,
inference(avatar_split_clause,[],[f518,f1667]) ).
fof(f1667,plain,
( spl0_144
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f518,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__not__le_1) ).
fof(f1665,plain,
spl0_143,
inference(avatar_split_clause,[],[f517,f1663]) ).
fof(f517,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__not__le_0) ).
fof(f1661,plain,
spl0_142,
inference(avatar_split_clause,[],[f511,f1659]) ).
fof(f1659,plain,
( spl0_142
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f511,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__le__not__le_1) ).
fof(f1657,plain,
spl0_141,
inference(avatar_split_clause,[],[f495,f1655]) ).
fof(f1655,plain,
( spl0_141
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f495,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__le__less_1) ).
fof(f1653,plain,
spl0_140,
inference(avatar_split_clause,[],[f494,f1651]) ).
fof(f1651,plain,
( spl0_140
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f494,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__imp__le_0) ).
fof(f1649,plain,
spl0_139,
inference(avatar_split_clause,[],[f374,f1647]) ).
fof(f1647,plain,
( spl0_139
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f374,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__le__zero__iff_1) ).
fof(f1645,plain,
spl0_138,
inference(avatar_split_clause,[],[f289,f1643]) ).
fof(f1643,plain,
( spl0_138
<=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f289,axiom,
! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__0_0) ).
fof(f1638,plain,
spl0_137,
inference(avatar_split_clause,[],[f285,f1636]) ).
fof(f285,axiom,
! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_odd__nat__equiv__def2_1) ).
fof(f1634,plain,
spl0_136,
inference(avatar_split_clause,[],[f266,f1632]) ).
fof(f1632,plain,
( spl0_136
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f266,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__square__less__zero_0) ).
fof(f1630,plain,
spl0_135,
inference(avatar_split_clause,[],[f235,f1628]) ).
fof(f1628,plain,
( spl0_135
<=> ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f235,axiom,
! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__cube_0) ).
fof(f1626,plain,
spl0_134,
inference(avatar_split_clause,[],[f203,f1624]) ).
fof(f1624,plain,
( spl0_134
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f203,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_zero__le__square_0) ).
fof(f1622,plain,
spl0_133,
inference(avatar_split_clause,[],[f150,f1620]) ).
fof(f1620,plain,
( spl0_133
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f150,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc0_0) ).
fof(f1618,plain,
spl0_132,
inference(avatar_split_clause,[],[f145,f1616]) ).
fof(f1616,plain,
( spl0_132
<=> ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f145,axiom,
! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__0_0) ).
fof(f1614,plain,
spl0_131,
inference(avatar_split_clause,[],[f96,f1612]) ).
fof(f1612,plain,
( spl0_131
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f96,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__eq__self__zero_0) ).
fof(f1582,plain,
( spl0_130
| ~ spl0_123
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1564,f1446,f1372,f1580]) ).
fof(f1580,plain,
( spl0_130
<=> ! [X5] : ~ c_HOL_Oord__class_Oless(c_Suc(X5),X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1372,plain,
( spl0_123
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1564,plain,
( ! [X5] : ~ c_HOL_Oord__class_Oless(c_Suc(X5),X5,tc_nat)
| ~ spl0_123
| ~ spl0_128 ),
inference(resolution,[],[f1373,f1447]) ).
fof(f1373,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1372]) ).
fof(f1524,plain,
( spl0_129
| ~ spl0_94
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1460,f1268,f1256,f1522]) ).
fof(f1522,plain,
( spl0_129
<=> ! [X12] : ~ c_lessequals(c_Suc(c_Suc(X12)),X12,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1256,plain,
( spl0_94
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1268,plain,
( spl0_97
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1460,plain,
( ! [X12] : ~ c_lessequals(c_Suc(c_Suc(X12)),X12,tc_nat)
| ~ spl0_94
| ~ spl0_97 ),
inference(resolution,[],[f1257,f1269]) ).
fof(f1269,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1257,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_Suc(X4),X3,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f1448,plain,
( spl0_128
| ~ spl0_85
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1409,f1268,f1220,f1446]) ).
fof(f1220,plain,
( spl0_85
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1409,plain,
( ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_Suc(X10)),tc_nat)
| ~ spl0_85
| ~ spl0_97 ),
inference(resolution,[],[f1221,f1269]) ).
fof(f1221,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_Suc(X4),X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1220]) ).
fof(f1390,plain,
spl0_127,
inference(avatar_split_clause,[],[f721,f1388]) ).
fof(f1388,plain,
( spl0_127
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f721,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__inverse2_0) ).
fof(f1386,plain,
spl0_126,
inference(avatar_split_clause,[],[f720,f1384]) ).
fof(f1384,plain,
( spl0_126
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f720,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__inverse_0) ).
fof(f1382,plain,
spl0_125,
inference(avatar_split_clause,[],[f678,f1380]) ).
fof(f1380,plain,
( spl0_125
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f678,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__SucI_0) ).
fof(f1378,plain,
spl0_124,
inference(avatar_split_clause,[],[f677,f1376]) ).
fof(f1376,plain,
( spl0_124
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f677,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__lessD_0) ).
fof(f1374,plain,
spl0_123,
inference(avatar_split_clause,[],[f672,f1372]) ).
fof(f672,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq_1) ).
fof(f1370,plain,
spl0_122,
inference(avatar_split_clause,[],[f671,f1368]) ).
fof(f1368,plain,
( spl0_122
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f671,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq_0) ).
fof(f1366,plain,
spl0_121,
inference(avatar_split_clause,[],[f659,f1364]) ).
fof(f1364,plain,
( spl0_121
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f659,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__ge__zero_0) ).
fof(f1362,plain,
spl0_120,
inference(avatar_split_clause,[],[f620,f1360]) ).
fof(f1360,plain,
( spl0_120
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f620,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__leD_0) ).
fof(f1358,plain,
spl0_119,
inference(avatar_split_clause,[],[f619,f1356]) ).
fof(f1356,plain,
( spl0_119
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_lessequals(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f619,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_lessequals(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__SucI_0) ).
fof(f1354,plain,
( spl0_118
| ~ spl0_30
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1175,f1116,f957,f1352]) ).
fof(f1352,plain,
( spl0_118
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1116,plain,
( spl0_66
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1175,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_30
| ~ spl0_66 ),
inference(resolution,[],[f1117,f959]) ).
fof(f959,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f1117,plain,
( ! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1350,plain,
spl0_117,
inference(avatar_split_clause,[],[f604,f1348]) ).
fof(f1348,plain,
( spl0_117
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f604,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__not__less__zero_0) ).
fof(f1346,plain,
spl0_116,
inference(avatar_split_clause,[],[f584,f1344]) ).
fof(f1344,plain,
( spl0_116
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f584,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__1_0) ).
fof(f1342,plain,
spl0_115,
inference(avatar_split_clause,[],[f561,f1340]) ).
fof(f1340,plain,
( spl0_115
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f561,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_gr0I_0) ).
fof(f1338,plain,
spl0_114,
inference(avatar_split_clause,[],[f543,f1336]) ).
fof(f1336,plain,
( spl0_114
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f543,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__self_0) ).
fof(f1334,plain,
spl0_113,
inference(avatar_split_clause,[],[f542,f1332]) ).
fof(f1332,plain,
( spl0_113
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f542,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__0__right_0) ).
fof(f1330,plain,
spl0_112,
inference(avatar_split_clause,[],[f540,f1328]) ).
fof(f1328,plain,
( spl0_112
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f540,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_eq__iff__diff__eq__0_0) ).
fof(f1326,plain,
spl0_111,
inference(avatar_split_clause,[],[f479,f1324]) ).
fof(f1324,plain,
( spl0_111
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f479,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1322,plain,
spl0_110,
inference(avatar_split_clause,[],[f478,f1320]) ).
fof(f1320,plain,
( spl0_110
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f478,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1318,plain,
spl0_109,
inference(avatar_split_clause,[],[f474,f1316]) ).
fof(f1316,plain,
( spl0_109
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f474,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_comm__monoid__add_Omult__1_0) ).
fof(f1314,plain,
spl0_108,
inference(avatar_split_clause,[],[f471,f1312]) ).
fof(f1312,plain,
( spl0_108
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f471,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1310,plain,
spl0_107,
inference(avatar_split_clause,[],[f470,f1308]) ).
fof(f1308,plain,
( spl0_107
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f470,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__0__left_0) ).
fof(f1306,plain,
spl0_106,
inference(avatar_split_clause,[],[f469,f1304]) ).
fof(f1304,plain,
( spl0_106
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f469,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1302,plain,
spl0_105,
inference(avatar_split_clause,[],[f468,f1300]) ).
fof(f1300,plain,
( spl0_105
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f468,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_of__nat__0__le__iff_0) ).
fof(f1298,plain,
spl0_104,
inference(avatar_split_clause,[],[f428,f1296]) ).
fof(f1296,plain,
( spl0_104
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f428,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__add__commute_0) ).
fof(f1294,plain,
spl0_103,
inference(avatar_split_clause,[],[f426,f1292]) ).
fof(f1292,plain,
( spl0_103
<=> ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f426,axiom,
! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__self_0) ).
fof(f1290,plain,
spl0_102,
inference(avatar_split_clause,[],[f425,f1288]) ).
fof(f1288,plain,
( spl0_102
<=> ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f425,axiom,
! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__by__0_0) ).
fof(f1286,plain,
spl0_101,
inference(avatar_split_clause,[],[f424,f1284]) ).
fof(f1284,plain,
( spl0_101
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f424,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__product__nat_1) ).
fof(f1282,plain,
spl0_100,
inference(avatar_split_clause,[],[f423,f1280]) ).
fof(f1280,plain,
( spl0_100
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f423,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__product__nat_2) ).
fof(f1278,plain,
spl0_99,
inference(avatar_split_clause,[],[f398,f1276]) ).
fof(f1276,plain,
( spl0_99
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f398,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc__eq__le_0) ).
fof(f1274,plain,
spl0_98,
inference(avatar_split_clause,[],[f397,f1272]) ).
fof(f1272,plain,
( spl0_98
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f397,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc__eq__le_1) ).
fof(f1270,plain,
( spl0_97
| ~ spl0_43
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1187,f1152,f1013,f1268]) ).
fof(f1013,plain,
( spl0_43
<=> ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1187,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_43
| ~ spl0_75 ),
inference(resolution,[],[f1153,f1014]) ).
fof(f1014,plain,
( ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f1266,plain,
spl0_96,
inference(avatar_split_clause,[],[f380,f1264]) ).
fof(f1264,plain,
( spl0_96
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f380,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_of__nat__0_0) ).
fof(f1262,plain,
spl0_95,
inference(avatar_split_clause,[],[f333,f1260]) ).
fof(f1260,plain,
( spl0_95
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f333,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_of__nat__less__0__iff_0) ).
fof(f1258,plain,
spl0_94,
inference(avatar_split_clause,[],[f319,f1256]) ).
fof(f319,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq__eq_1) ).
fof(f1254,plain,
spl0_93,
inference(avatar_split_clause,[],[f318,f1252]) ).
fof(f1252,plain,
( spl0_93
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f318,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq__eq_0) ).
fof(f1250,plain,
spl0_92,
inference(avatar_split_clause,[],[f164,f1248]) ).
fof(f1248,plain,
( spl0_92
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f164,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__eq__0_1) ).
fof(f1246,plain,
spl0_91,
inference(avatar_split_clause,[],[f161,f1244]) ).
fof(f1244,plain,
( spl0_91
<=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f161,axiom,
! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__mult__commute_0) ).
fof(f1242,plain,
spl0_90,
inference(avatar_split_clause,[],[f141,f1240]) ).
fof(f1240,plain,
( spl0_90
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f141,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvdI_0) ).
fof(f1238,plain,
spl0_89,
inference(avatar_split_clause,[],[f140,f1236]) ).
fof(f1236,plain,
( spl0_89
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f140,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__triv__left_0) ).
fof(f1234,plain,
spl0_88,
inference(avatar_split_clause,[],[f139,f1232]) ).
fof(f1232,plain,
( spl0_88
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__triv__right_0) ).
fof(f1230,plain,
spl0_87,
inference(avatar_split_clause,[],[f137,f1228]) ).
fof(f1228,plain,
( spl0_87
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f137,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__le1_0) ).
fof(f1226,plain,
spl0_86,
inference(avatar_split_clause,[],[f136,f1224]) ).
fof(f1224,plain,
( spl0_86
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f136,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X6,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__le2_0) ).
fof(f1222,plain,
spl0_85,
inference(avatar_split_clause,[],[f114,f1220]) ).
fof(f114,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__eq__Suc__le_1) ).
fof(f1218,plain,
spl0_84,
inference(avatar_split_clause,[],[f111,f1216]) ).
fof(f1216,plain,
( spl0_84
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_lessequals(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f111,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_lessequals(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__leI_0) ).
fof(f1214,plain,
spl0_83,
inference(avatar_split_clause,[],[f80,f1212]) ).
fof(f1212,plain,
( spl0_83
<=> ! [X17] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f80,axiom,
! [X17] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__nat__equiv__def2_1) ).
fof(f1210,plain,
spl0_82,
inference(avatar_split_clause,[],[f18,f1208]) ).
fof(f1208,plain,
( spl0_82
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f18,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__0__eq_0) ).
fof(f1196,plain,
( spl0_81
| ~ spl0_37
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1186,f1152,f988,f1193]) ).
fof(f1193,plain,
( spl0_81
<=> c_lessequals(v_i,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1186,plain,
( c_lessequals(v_i,v_n,tc_nat)
| ~ spl0_37
| ~ spl0_75 ),
inference(resolution,[],[f1153,f990]) ).
fof(f1174,plain,
spl0_80,
inference(avatar_split_clause,[],[f735,f1172]) ).
fof(f1172,plain,
( spl0_80
<=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f735,axiom,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__less__Suc_0) ).
fof(f1170,plain,
spl0_79,
inference(avatar_split_clause,[],[f713,f1168]) ).
fof(f1168,plain,
( spl0_79
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f713,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__0__eq__0_0) ).
fof(f1166,plain,
spl0_78,
inference(avatar_split_clause,[],[f666,f1164]) ).
fof(f1164,plain,
( spl0_78
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f666,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__le__linear_0) ).
fof(f1162,plain,
spl0_77,
inference(avatar_split_clause,[],[f575,f1160]) ).
fof(f1160,plain,
( spl0_77
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f575,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__is__0_1) ).
fof(f1158,plain,
spl0_76,
inference(avatar_split_clause,[],[f574,f1156]) ).
fof(f574,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__is__0_2) ).
fof(f1154,plain,
spl0_75,
inference(avatar_split_clause,[],[f562,f1152]) ).
fof(f562,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I5_J_0) ).
fof(f1150,plain,
spl0_74,
inference(avatar_split_clause,[],[f445,f1148]) ).
fof(f1148,plain,
( spl0_74
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f445,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__ge__self_0) ).
fof(f1146,plain,
spl0_73,
inference(avatar_split_clause,[],[f443,f1144]) ).
fof(f1144,plain,
( spl0_73
<=> ! [X29,X20] :
( X20 = X29
| c_Suc(X20) != c_Suc(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f443,axiom,
! [X29,X20] :
( X20 = X29
| c_Suc(X20) != c_Suc(X29) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat_Oinject_0) ).
fof(f1142,plain,
spl0_72,
inference(avatar_split_clause,[],[f320,f1140]) ).
fof(f1140,plain,
( spl0_72
<=> ! [X4] :
( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f320,axiom,
! [X4] :
( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_odd__pos_0) ).
fof(f1138,plain,
spl0_71,
inference(avatar_split_clause,[],[f186,f1136]) ).
fof(f1136,plain,
( spl0_71
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
| c_HOL_Otimes__class_Otimes(X5,X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f186,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
| c_HOL_Otimes__class_Otimes(X5,X5,X0) = X5 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__idem_0) ).
fof(f1134,plain,
spl0_70,
inference(avatar_split_clause,[],[f121,f1132]) ).
fof(f1132,plain,
( spl0_70
<=> ! [X5,X3] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f121,axiom,
! [X3,X5] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__iff__Suc__add_1) ).
fof(f1130,plain,
spl0_69,
inference(avatar_split_clause,[],[f120,f1128]) ).
fof(f1128,plain,
( spl0_69
<=> ! [X8,X3] : c_HOL_Oord__class_Oless(X8,c_Suc(c_HOL_Oplus__class_Oplus(X3,X8,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f120,axiom,
! [X3,X8] : c_HOL_Oord__class_Oless(X8,c_Suc(c_HOL_Oplus__class_Oplus(X3,X8,tc_nat)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__add__Suc2_0) ).
fof(f1126,plain,
spl0_68,
inference(avatar_split_clause,[],[f88,f1124]) ).
fof(f1124,plain,
( spl0_68
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f88,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__0R_0) ).
fof(f1122,plain,
spl0_67,
inference(avatar_split_clause,[],[f87,f1120]) ).
fof(f1120,plain,
( spl0_67
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f87,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__0L_0) ).
fof(f1118,plain,
spl0_66,
inference(avatar_split_clause,[],[f16,f1116]) ).
fof(f16,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__idem_0) ).
fof(f1103,plain,
spl0_65,
inference(avatar_split_clause,[],[f716,f1101]) ).
fof(f1101,plain,
( spl0_65
<=> ! [X4,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f716,axiom,
! [X3,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__le__self_0) ).
fof(f1099,plain,
spl0_64,
inference(avatar_split_clause,[],[f706,f1097]) ).
fof(f1097,plain,
( spl0_64
<=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f706,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_minus__nat_Odiff__0_0) ).
fof(f1095,plain,
spl0_63,
inference(avatar_split_clause,[],[f705,f1093]) ).
fof(f1093,plain,
( spl0_63
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f705,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__self__eq__0_0) ).
fof(f1091,plain,
spl0_62,
inference(avatar_split_clause,[],[f598,f1089]) ).
fof(f1089,plain,
( spl0_62
<=> ! [X4,X3] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f598,axiom,
! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__add1_0) ).
fof(f1087,plain,
spl0_61,
inference(avatar_split_clause,[],[f597,f1085]) ).
fof(f1085,plain,
( spl0_61
<=> ! [X4,X3] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f597,axiom,
! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__add2_0) ).
fof(f1083,plain,
spl0_60,
inference(avatar_split_clause,[],[f568,f1081]) ).
fof(f1081,plain,
( spl0_60
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f568,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__0__right_0) ).
fof(f1079,plain,
spl0_59,
inference(avatar_split_clause,[],[f559,f1077]) ).
fof(f1077,plain,
( spl0_59
<=> ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f559,axiom,
! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__add__less2_0) ).
fof(f1075,plain,
spl0_58,
inference(avatar_split_clause,[],[f558,f1073]) ).
fof(f1073,plain,
( spl0_58
<=> ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f558,axiom,
! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X8,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__add__less1_0) ).
fof(f1071,plain,
spl0_57,
inference(avatar_split_clause,[],[f477,f1069]) ).
fof(f1069,plain,
( spl0_57
<=> ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f477,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_plus__nat_Oadd__0_0) ).
fof(f1067,plain,
spl0_56,
inference(avatar_split_clause,[],[f475,f1065]) ).
fof(f1065,plain,
( spl0_56
<=> ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f475,axiom,
! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_natgb_Oadd__r0__iff_1) ).
fof(f1063,plain,
spl0_55,
inference(avatar_split_clause,[],[f338,f1061]) ).
fof(f1061,plain,
( spl0_55
<=> ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f338,axiom,
! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__square_0) ).
fof(f1059,plain,
spl0_54,
inference(avatar_split_clause,[],[f336,f1057]) ).
fof(f1057,plain,
( spl0_54
<=> ! [X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f336,axiom,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__Suc_1) ).
fof(f1055,plain,
spl0_53,
inference(avatar_split_clause,[],[f335,f1053]) ).
fof(f1053,plain,
( spl0_53
<=> ! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f335,axiom,
! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__Suc_0) ).
fof(f1051,plain,
spl0_52,
inference(avatar_split_clause,[],[f321,f1049]) ).
fof(f1049,plain,
( spl0_52
<=> ! [X4,X3] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f321,axiom,
! [X3,X4] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__less__eq__dividend_0) ).
fof(f1047,plain,
spl0_51,
inference(avatar_split_clause,[],[f749,f1045]) ).
fof(f1045,plain,
( spl0_51
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f749,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__le_1) ).
fof(f1043,plain,
spl0_50,
inference(avatar_split_clause,[],[f746,f1041]) ).
fof(f746,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__neq__iff_1) ).
fof(f1039,plain,
spl0_49,
inference(avatar_split_clause,[],[f745,f1037]) ).
fof(f1037,plain,
( spl0_49
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f745,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__irrefl_0) ).
fof(f1035,plain,
spl0_48,
inference(avatar_split_clause,[],[f637,f1033]) ).
fof(f1033,plain,
( spl0_48
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f637,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__eq__iff_0) ).
fof(f1031,plain,
spl0_47,
inference(avatar_split_clause,[],[f636,f1029]) ).
fof(f1029,plain,
( spl0_47
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f636,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__eq__refl_0) ).
fof(f1027,plain,
spl0_46,
inference(avatar_split_clause,[],[f305,f1025]) ).
fof(f1025,plain,
( spl0_46
<=> ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f305,axiom,
! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_gr0__conv__Suc_1) ).
fof(f1023,plain,
spl0_45,
inference(avatar_split_clause,[],[f277,f1021]) ).
fof(f1021,plain,
( spl0_45
<=> ! [X9] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f277,axiom,
! [X9] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__1__left_0) ).
fof(f1019,plain,
spl0_44,
inference(avatar_split_clause,[],[f35,f1017]) ).
fof(f1017,plain,
( spl0_44
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f35,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__refl_0) ).
fof(f1015,plain,
spl0_43,
inference(avatar_split_clause,[],[f681,f1013]) ).
fof(f681,axiom,
! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_lessI_0) ).
fof(f1011,plain,
spl0_42,
inference(avatar_split_clause,[],[f669,f1009]) ).
fof(f1009,plain,
( spl0_42
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f669,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less0_0) ).
fof(f1007,plain,
spl0_41,
inference(avatar_split_clause,[],[f623,f1005]) ).
fof(f1005,plain,
( spl0_41
<=> ! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f623,axiom,
! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__n__not__le__n_0) ).
fof(f1003,plain,
spl0_40,
inference(avatar_split_clause,[],[f567,f1001]) ).
fof(f1001,plain,
( spl0_40
<=> ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f567,axiom,
! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
fof(f999,plain,
spl0_39,
inference(avatar_split_clause,[],[f315,f997]) ).
fof(f997,plain,
( spl0_39
<=> ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f315,axiom,
! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le0_0) ).
fof(f995,plain,
spl0_38,
inference(avatar_split_clause,[],[f127,f993]) ).
fof(f993,plain,
( spl0_38
<=> ! [X20] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f127,axiom,
! [X20] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X20),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat_Osimps_I2_J_0) ).
fof(f991,plain,
spl0_37,
inference(avatar_split_clause,[],[f767,f988]) ).
fof(f767,axiom,
c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_CHAINED_0) ).
fof(f986,plain,
spl0_36,
inference(avatar_split_clause,[],[f747,f984]) ).
fof(f984,plain,
( spl0_36
<=> ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f747,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__less__le_1) ).
fof(f982,plain,
spl0_35,
inference(avatar_split_clause,[],[f638,f980]) ).
fof(f980,plain,
( spl0_35
<=> ! [X5] : c_lessequals(X5,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f638,axiom,
! [X5] : c_lessequals(X5,X5,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_eq__imp__le_0) ).
fof(f978,plain,
spl0_34,
inference(avatar_split_clause,[],[f454,f975]) ).
fof(f975,plain,
( spl0_34
<=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f454,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__zero__nat_0) ).
fof(f973,plain,
spl0_33,
inference(avatar_split_clause,[],[f185,f971]) ).
fof(f971,plain,
( spl0_33
<=> ! [X4] : c_Suc(X4) != X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f185,axiom,
! [X4] : c_Suc(X4) != X4,
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__n__not__n_0) ).
fof(f969,plain,
spl0_32,
inference(avatar_split_clause,[],[f34,f967]) ).
fof(f967,plain,
( spl0_32
<=> ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f34,axiom,
! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,X5,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd_Oeq__iff_0) ).
fof(f965,plain,
spl0_31,
inference(avatar_split_clause,[],[f798,f962]) ).
fof(f962,plain,
( spl0_31
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f798,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Orderings_Oorder) ).
fof(f960,plain,
spl0_30,
inference(avatar_split_clause,[],[f797,f957]) ).
fof(f797,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Orderings_Olinorder) ).
fof(f955,plain,
spl0_29,
inference(avatar_split_clause,[],[f796,f952]) ).
fof(f952,plain,
( spl0_29
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f796,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Orderings_Opreorder) ).
fof(f950,plain,
spl0_28,
inference(avatar_split_clause,[],[f795,f947]) ).
fof(f947,plain,
( spl0_28
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f795,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f945,plain,
spl0_27,
inference(avatar_split_clause,[],[f794,f942]) ).
fof(f942,plain,
( spl0_27
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f794,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f940,plain,
spl0_26,
inference(avatar_split_clause,[],[f793,f937]) ).
fof(f937,plain,
( spl0_26
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f793,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Divides_Osemiring__div) ).
fof(f935,plain,
spl0_25,
inference(avatar_split_clause,[],[f792,f932]) ).
fof(f932,plain,
( spl0_25
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f792,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f930,plain,
spl0_24,
inference(avatar_split_clause,[],[f791,f927]) ).
fof(f927,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f791,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f925,plain,
spl0_23,
inference(avatar_split_clause,[],[f790,f922]) ).
fof(f922,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f790,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f920,plain,
spl0_22,
inference(avatar_split_clause,[],[f789,f917]) ).
fof(f917,plain,
( spl0_22
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f789,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f915,plain,
spl0_21,
inference(avatar_split_clause,[],[f788,f912]) ).
fof(f912,plain,
( spl0_21
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f788,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f910,plain,
spl0_20,
inference(avatar_split_clause,[],[f787,f907]) ).
fof(f907,plain,
( spl0_20
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f787,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f905,plain,
spl0_19,
inference(avatar_split_clause,[],[f786,f902]) ).
fof(f902,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f786,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f900,plain,
spl0_18,
inference(avatar_split_clause,[],[f785,f897]) ).
fof(f897,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f785,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f895,plain,
spl0_17,
inference(avatar_split_clause,[],[f784,f892]) ).
fof(f892,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f784,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f890,plain,
spl0_16,
inference(avatar_split_clause,[],[f783,f887]) ).
fof(f887,plain,
( spl0_16
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f783,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f885,plain,
spl0_15,
inference(avatar_split_clause,[],[f782,f882]) ).
fof(f882,plain,
( spl0_15
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f782,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f880,plain,
spl0_14,
inference(avatar_split_clause,[],[f781,f877]) ).
fof(f877,plain,
( spl0_14
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f781,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f875,plain,
spl0_13,
inference(avatar_split_clause,[],[f780,f872]) ).
fof(f872,plain,
( spl0_13
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f780,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f870,plain,
spl0_12,
inference(avatar_split_clause,[],[f779,f867]) ).
fof(f867,plain,
( spl0_12
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f779,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f865,plain,
spl0_11,
inference(avatar_split_clause,[],[f778,f862]) ).
fof(f862,plain,
( spl0_11
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f778,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f860,plain,
spl0_10,
inference(avatar_split_clause,[],[f777,f857]) ).
fof(f857,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f777,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f855,plain,
spl0_9,
inference(avatar_split_clause,[],[f776,f852]) ).
fof(f852,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f776,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f850,plain,
spl0_8,
inference(avatar_split_clause,[],[f775,f847]) ).
fof(f847,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f775,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f845,plain,
spl0_7,
inference(avatar_split_clause,[],[f774,f842]) ).
fof(f842,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f774,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f840,plain,
spl0_6,
inference(avatar_split_clause,[],[f773,f837]) ).
fof(f837,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f773,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f835,plain,
spl0_5,
inference(avatar_split_clause,[],[f772,f832]) ).
fof(f832,plain,
( spl0_5
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f772,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f830,plain,
spl0_4,
inference(avatar_split_clause,[],[f771,f827]) ).
fof(f827,plain,
( spl0_4
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f771,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f825,plain,
spl0_3,
inference(avatar_split_clause,[],[f770,f822]) ).
fof(f822,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f770,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f820,plain,
spl0_2,
inference(avatar_split_clause,[],[f769,f817]) ).
fof(f817,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f769,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f815,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f768,f812]) ).
fof(f768,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19 % Problem : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% 0.19/0.20 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.21/0.41 % Computer : n024.cluster.edu
% 0.21/0.41 % Model : x86_64 x86_64
% 0.21/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.41 % Memory : 8042.1875MB
% 0.21/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.21/0.41 % CPULimit : 300
% 0.21/0.41 % WCLimit : 300
% 0.21/0.41 % DateTime : Wed Aug 30 17:43:07 EDT 2023
% 0.21/0.42 % CPUTime :
% 0.28/0.47 % (25329)Running in auto input_syntax mode. Trying TPTP
% 0.28/0.51 % (25331)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.28/0.51 % (25332)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.28/0.51 % (25333)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 Vampire---4 for (569ds/0Mi)
% 0.28/0.51 % (25334)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.28/0.51 % (25335)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 Vampire---4 for (531ds/0Mi)
% 0.28/0.51 % (25336)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 Vampire---4 for (522ds/0Mi)
% 0.28/0.51 % (25337)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 Vampire---4 for (497ds/0Mi)
% 0.28/0.57 % (25335)First to succeed.
% 0.28/0.58 % (25335)Refutation found. Thanks to Tanya!
% 0.28/0.58 % SZS status Unsatisfiable for Vampire---4
% 0.28/0.58 % SZS output start Proof for Vampire---4
% See solution above
% 0.28/0.59 % (25335)------------------------------
% 0.28/0.59 % (25335)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.59 % (25335)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.59 % (25335)Termination reason: Refutation
% 0.28/0.59
% 0.28/0.59 % (25335)Memory used [KB]: 7675
% 0.28/0.59 % (25335)Time elapsed: 0.071 s
% 0.28/0.59 % (25335)------------------------------
% 0.28/0.59 % (25335)------------------------------
% 0.28/0.59 % (25329)Success in time 0.159 s
% 0.28/0.59 % Vampire---4.8 exiting
%------------------------------------------------------------------------------