TSTP Solution File: LCL760-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL760-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:53:00 EDT 2024
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 459
% Syntax : Number of formulae : 779 ( 332 unt; 0 def)
% Number of atoms : 1485 ( 312 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1200 ( 494 ~; 469 |; 0 &)
% ( 237 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 276 ( 274 usr; 238 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 11 con; 0-5 aty)
% Number of variables : 918 ( 918 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2848,plain,
$false,
inference(avatar_sat_refutation,[],[f849,f854,f859,f864,f869,f874,f879,f884,f889,f894,f899,f904,f909,f914,f919,f924,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f979,f984,f989,f994,f999,f1003,f1008,f1014,f1018,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1050,f1054,f1058,f1062,f1066,f1070,f1074,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1107,f1111,f1115,f1120,f1124,f1128,f1132,f1136,f1140,f1144,f1148,f1152,f1156,f1160,f1164,f1170,f1174,f1178,f1182,f1186,f1190,f1194,f1198,f1202,f1206,f1210,f1214,f1218,f1222,f1226,f1230,f1234,f1238,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1270,f1274,f1278,f1283,f1287,f1328,f1341,f1366,f1370,f1374,f1378,f1382,f1386,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1423,f1427,f1431,f1435,f1439,f1443,f1447,f1479,f1493,f1497,f1501,f1505,f1509,f1513,f1517,f1521,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1629,f1655,f1659,f1663,f1667,f1671,f1675,f1680,f1685,f1689,f1693,f1697,f1701,f1705,f1709,f1761,f1765,f1769,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1830,f1834,f1839,f1843,f1847,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f2171,f2175,f2179,f2183,f2187,f2191,f2195,f2199,f2203,f2207,f2211,f2215,f2219,f2223,f2227,f2231,f2235,f2239,f2243,f2247,f2251,f2255,f2259,f2263,f2267,f2271,f2275,f2279,f2283,f2287,f2291,f2295,f2299,f2303,f2307,f2311,f2315,f2319,f2323,f2327,f2331,f2335,f2383,f2712,f2810,f2816,f2820,f2825,f2844]) ).
fof(f2844,plain,
( spl0_235
| ~ spl0_237 ),
inference(avatar_contradiction_clause,[],[f2826]) ).
fof(f2826,plain,
( $false
| spl0_235
| ~ spl0_237 ),
inference(resolution,[],[f2824,f2815]) ).
fof(f2815,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| spl0_235 ),
inference(avatar_component_clause,[],[f2813]) ).
fof(f2813,plain,
( spl0_235
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2824,plain,
( ! [X10,X9] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2823]) ).
fof(f2823,plain,
( spl0_237
<=> ! [X9,X10] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2825,plain,
( spl0_237
| ~ spl0_219
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2821,f2818,f2285,f2823]) ).
fof(f2285,plain,
( spl0_219
<=> ! [X8,X7] : c_Lambda_Osubstn(X7,X8,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X8),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2818,plain,
( spl0_236
<=> ! [X9,X10] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2821,plain,
( ! [X10,X9] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ spl0_219
| ~ spl0_236 ),
inference(forward_demodulation,[],[f2819,f2286]) ).
fof(f2286,plain,
( ! [X8,X7] : c_Lambda_Osubstn(X7,X8,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X8),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2285]) ).
fof(f2819,plain,
( ! [X10,X9] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2818]) ).
fof(f2820,plain,
spl0_236,
inference(avatar_split_clause,[],[f653,f2818]) ).
fof(f653,plain,
! [X10,X9] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(definition_unfolding,[],[f612,f61,f61]) ).
fof(f61,axiom,
! [X0] : c_Suc(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f612,axiom,
! [X10,X9] : hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(X10))),c_Suc(X9))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(X10),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),X9,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2816,plain,
( ~ spl0_235
| ~ spl0_219
| spl0_234 ),
inference(avatar_split_clause,[],[f2811,f2807,f2285,f2813]) ).
fof(f2807,plain,
( spl0_234
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2811,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ spl0_219
| spl0_234 ),
inference(forward_demodulation,[],[f2809,f2286]) ).
fof(f2809,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| spl0_234 ),
inference(avatar_component_clause,[],[f2807]) ).
fof(f2810,plain,
~ spl0_234,
inference(avatar_split_clause,[],[f652,f2807]) ).
fof(f652,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(definition_unfolding,[],[f615,f61,f61]) ).
fof(f615,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f2712,plain,
( spl0_233
| ~ spl0_32
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2643,f2285,f1001,f2710]) ).
fof(f2710,plain,
( spl0_233
<=> ! [X0] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubstn(v_s,c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1001,plain,
( spl0_32
<=> ! [X9,X10] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f2643,plain,
( ! [X0] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubstn(v_s,c_Lambda_OdB_OVar(X0),c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ spl0_32
| ~ spl0_219 ),
inference(superposition,[],[f1002,f2286]) ).
fof(f1002,plain,
( ! [X10,X9] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9)))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f2383,plain,
( spl0_232
| ~ spl0_47
| ~ spl0_91
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1757,f1703,f1244,f1064,f2381]) ).
fof(f2381,plain,
( spl0_232
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1064,plain,
( spl0_47
<=> ! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X42)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1244,plain,
( spl0_91
<=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1703,plain,
( spl0_158
<=> ! [X22] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X22)),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1757,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
| ~ spl0_47
| ~ spl0_91
| ~ spl0_158 ),
inference(forward_demodulation,[],[f1747,f1245]) ).
fof(f1245,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f1747,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))
| ~ spl0_47
| ~ spl0_158 ),
inference(superposition,[],[f1704,f1065]) ).
fof(f1065,plain,
( ! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X42))
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1704,plain,
( ! [X22] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X22)),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1703]) ).
fof(f2335,plain,
spl0_231,
inference(avatar_split_clause,[],[f782,f2333]) ).
fof(f2333,plain,
( spl0_231
<=> ! [X22] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X22),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X22,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f782,plain,
! [X22] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X22),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X22,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f781,f356]) ).
fof(f356,axiom,
! [X14] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Ozero__class_Ozero(tc_nat)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
fof(f781,plain,
! [X22] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X22),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X22,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f684,f105]) ).
fof(f105,axiom,
! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f684,plain,
! [X22] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X22),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X22,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f129,f61]) ).
fof(f129,axiom,
! [X22] : c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(X22),tc_Lambda_OdB) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X22,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).
fof(f2331,plain,
spl0_230,
inference(avatar_split_clause,[],[f714,f2329]) ).
fof(f2329,plain,
( spl0_230
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f714,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f379,f61]) ).
fof(f379,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f2327,plain,
spl0_229,
inference(avatar_split_clause,[],[f711,f2325]) ).
fof(f2325,plain,
( spl0_229
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X0)),c_HOL_Oone__class_Oone(tc_nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f711,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X0)),c_HOL_Oone__class_Oone(tc_nat)) = X0 ),
inference(definition_unfolding,[],[f552,f61]) ).
fof(f552,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not0__implies__Suc_0) ).
fof(f2323,plain,
spl0_228,
inference(avatar_split_clause,[],[f710,f2321]) ).
fof(f2321,plain,
( spl0_228
<=> ! [X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X15)),c_HOL_Oone__class_Oone(tc_nat)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f710,plain,
! [X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X15)),c_HOL_Oone__class_Oone(tc_nat)) = X15 ),
inference(definition_unfolding,[],[f525,f61]) ).
fof(f525,axiom,
! [X15] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X15
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(X15)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oexhaust_0) ).
fof(f2319,plain,
spl0_227,
inference(avatar_split_clause,[],[f709,f2317]) ).
fof(f2317,plain,
( spl0_227
<=> ! [X26] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X26
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X26)),c_HOL_Oone__class_Oone(tc_nat)) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f709,plain,
! [X26] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X26
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X26)),c_HOL_Oone__class_Oone(tc_nat)) = X26 ),
inference(definition_unfolding,[],[f546,f61]) ).
fof(f546,axiom,
! [X26] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X26
| c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(X26)) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Onchotomy_0) ).
fof(f2315,plain,
spl0_226,
inference(avatar_split_clause,[],[f704,f2313]) ).
fof(f2313,plain,
( spl0_226
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f704,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f378,f61]) ).
fof(f378,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f2311,plain,
( spl0_225
| ~ spl0_94
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1755,f1703,f1256,f2309]) ).
fof(f2309,plain,
( spl0_225
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1256,plain,
( spl0_94
<=> ! [X9,X10] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1755,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_Lambda_OdB_OdB__size(X0),tc_nat)
| ~ spl0_94
| ~ spl0_158 ),
inference(superposition,[],[f1257,f1704]) ).
fof(f1257,plain,
( ! [X10,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9),X10,tc_nat)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f2307,plain,
spl0_224,
inference(avatar_split_clause,[],[f608,f2305]) ).
fof(f2305,plain,
( spl0_224
<=> ! [X62,X48,X60,X31,X61,X2] : hAPP(c_COMBC(X31,X60,X48,X61,X2),X62) = hAPP(hAPP(X31,X62),X60) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f608,axiom,
! [X31,X2,X48,X62,X60,X61] : hAPP(c_COMBC(X31,X60,X48,X61,X2),X62) = hAPP(hAPP(X31,X62),X60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f2303,plain,
spl0_223,
inference(avatar_split_clause,[],[f600,f2301]) ).
fof(f2301,plain,
( spl0_223
<=> ! [X59,X43,X44,X58] :
( X44 = X59
| hAPP(hAPP(c_Lambda_OdB_OApp,X43),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f600,axiom,
! [X58,X59,X44,X43] :
( X44 = X59
| hAPP(hAPP(c_Lambda_OdB_OApp,X43),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f2299,plain,
spl0_222,
inference(avatar_split_clause,[],[f599,f2297]) ).
fof(f2297,plain,
( spl0_222
<=> ! [X59,X58,X44,X43] :
( X43 = X58
| hAPP(hAPP(c_Lambda_OdB_OApp,X43),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f599,axiom,
! [X58,X59,X44,X43] :
( X43 = X58
| hAPP(hAPP(c_Lambda_OdB_OApp,X43),X44) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f2295,plain,
spl0_221,
inference(avatar_split_clause,[],[f587,f2293]) ).
fof(f2293,plain,
( spl0_221
<=> ! [X0,X56] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X56,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X56,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f587,axiom,
! [X0,X56] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X56,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X56,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
fof(f2291,plain,
spl0_220,
inference(avatar_split_clause,[],[f586,f2289]) ).
fof(f2289,plain,
( spl0_220
<=> ! [X0,X7,X8,X49] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X49,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f586,axiom,
! [X0,X49,X8,X7] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X49,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f2287,plain,
spl0_219,
inference(avatar_split_clause,[],[f567,f2285]) ).
fof(f567,axiom,
! [X8,X7] : c_Lambda_Osubstn(X7,X8,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,X7),X8),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
fof(f2283,plain,
spl0_218,
inference(avatar_split_clause,[],[f450,f2281]) ).
fof(f2281,plain,
( spl0_218
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Power_Opower__class_Opower(X14,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f450,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_Power_Opower__class_Opower(X14,X0,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_0) ).
fof(f2279,plain,
spl0_217,
inference(avatar_split_clause,[],[f390,f2277]) ).
fof(f2277,plain,
( spl0_217
<=> ! [X12,X7,X8] :
( ~ c_Lambda_Obeta(X8,X7)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X8),X12),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f390,axiom,
! [X8,X7,X12] :
( ~ c_Lambda_Obeta(X8,X7)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X8),X12),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
fof(f2275,plain,
spl0_216,
inference(avatar_split_clause,[],[f389,f2273]) ).
fof(f2273,plain,
( spl0_216
<=> ! [X12,X7,X8] :
( ~ c_Lambda_Obeta(X8,X7)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X12),X8),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f389,axiom,
! [X8,X7,X12] :
( ~ c_Lambda_Obeta(X8,X7)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X12),X8),hAPP(hAPP(c_Lambda_OdB_OApp,X12),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
fof(f2271,plain,
spl0_215,
inference(avatar_split_clause,[],[f355,f2269]) ).
fof(f2269,plain,
( spl0_215
<=> ! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__List__Xupt__Xinduct__1(X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f355,axiom,
! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__List__Xupt__Xinduct__1(X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
fof(f2267,plain,
( spl0_214
| ~ spl0_95
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1754,f1703,f1260,f2265]) ).
fof(f2265,plain,
( spl0_214
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1260,plain,
( spl0_95
<=> ! [X9,X10] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1754,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_95
| ~ spl0_158 ),
inference(superposition,[],[f1261,f1704]) ).
fof(f1261,plain,
( ! [X10,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10),X10,tc_nat)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1260]) ).
fof(f2263,plain,
spl0_213,
inference(avatar_split_clause,[],[f352,f2261]) ).
fof(f2261,plain,
( spl0_213
<=> ! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinduct__1(X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f352,axiom,
! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinduct__1(X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
fof(f2259,plain,
spl0_212,
inference(avatar_split_clause,[],[f350,f2257]) ).
fof(f2257,plain,
( spl0_212
<=> ! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinducts__1(X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f350,axiom,
! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__Nat__Xnat__Xinducts__1(X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_0) ).
fof(f2255,plain,
spl0_211,
inference(avatar_split_clause,[],[f349,f2253]) ).
fof(f2253,plain,
( spl0_211
<=> ! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__List__Xreplicate__Xinduct__1(X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f349,axiom,
! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__List__Xreplicate__Xinduct__1(X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_0) ).
fof(f2251,plain,
spl0_210,
inference(avatar_split_clause,[],[f338,f2249]) ).
fof(f2249,plain,
( spl0_210
<=> ! [X0,X31] :
( hBOOL(hAPP(X31,X0))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f338,axiom,
! [X31,X0] :
( hBOOL(hAPP(X31,X0))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_0) ).
fof(f2247,plain,
spl0_209,
inference(avatar_split_clause,[],[f332,f2245]) ).
fof(f2245,plain,
( spl0_209
<=> ! [X6,X31] :
( ~ hBOOL(hAPP(X31,X6))
| ~ hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X31)))
| hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f332,axiom,
! [X31,X6] :
( ~ hBOOL(hAPP(X31,X6))
| ~ hBOOL(hAPP(X31,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X31)))
| hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct_1) ).
fof(f2243,plain,
spl0_208,
inference(avatar_split_clause,[],[f331,f2241]) ).
fof(f2241,plain,
( spl0_208
<=> ! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__List__Xlexn__Xinduct__1(X31))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f331,axiom,
! [X31,X42] :
( hBOOL(hAPP(X31,X42))
| ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,v_sko__List__Xlexn__Xinduct__1(X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lexn_Oinduct_0) ).
fof(f2239,plain,
spl0_207,
inference(avatar_split_clause,[],[f309,f2237]) ).
fof(f2237,plain,
( spl0_207
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f309,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f2235,plain,
spl0_206,
inference(avatar_split_clause,[],[f308,f2233]) ).
fof(f2233,plain,
( spl0_206
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f308,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f2231,plain,
spl0_205,
inference(avatar_split_clause,[],[f299,f2229]) ).
fof(f2229,plain,
( spl0_205
<=> ! [X6,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,tc_nat),c_HOL_Otimes__class_Otimes(X0,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f299,axiom,
! [X0,X1,X6] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,tc_nat),c_HOL_Otimes__class_Otimes(X0,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
fof(f2227,plain,
spl0_204,
inference(avatar_split_clause,[],[f298,f2225]) ).
fof(f2225,plain,
( spl0_204
<=> ! [X6,X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,tc_nat),c_HOL_Otimes__class_Otimes(X6,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f298,axiom,
! [X0,X1,X6] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,tc_nat),c_HOL_Otimes__class_Otimes(X6,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
fof(f2223,plain,
( spl0_203
| ~ spl0_124
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1749,f1703,f1445,f2221]) ).
fof(f2221,plain,
( spl0_203
<=> ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1445,plain,
( spl0_124
<=> ! [X14] : c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1749,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Lambda_OdB_OdB__size(X0),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
| ~ spl0_124
| ~ spl0_158 ),
inference(superposition,[],[f1446,f1704]) ).
fof(f1446,plain,
( ! [X14] : c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f2219,plain,
spl0_202,
inference(avatar_split_clause,[],[f292,f2217]) ).
fof(f2217,plain,
( spl0_202
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f292,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f2215,plain,
spl0_201,
inference(avatar_split_clause,[],[f291,f2213]) ).
fof(f2213,plain,
( spl0_201
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f291,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_Nat_Osemiring__1__class_Oof__nat(X0,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f2211,plain,
spl0_200,
inference(avatar_split_clause,[],[f285,f2209]) ).
fof(f2209,plain,
( spl0_200
<=> ! [X3,X4,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f285,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
fof(f2207,plain,
spl0_199,
inference(avatar_split_clause,[],[f249,f2205]) ).
fof(f2205,plain,
( spl0_199
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f249,axiom,
! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
fof(f2203,plain,
spl0_198,
inference(avatar_split_clause,[],[f171,f2201]) ).
fof(f2201,plain,
( spl0_198
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_HOL_Oone__class_Oone(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f171,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Oone__class_Oone(X2)),c_HOL_Oone__class_Oone(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f2199,plain,
spl0_197,
inference(avatar_split_clause,[],[f140,f2197]) ).
fof(f2197,plain,
( spl0_197
<=> ! [X27,X8,X10] :
( ~ c_Lambda_Obeta(X27,X8)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X27),X10),hAPP(hAPP(c_Lambda_Olift,X8),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f140,axiom,
! [X10,X8,X27] :
( ~ c_Lambda_Obeta(X27,X8)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,X27),X10),hAPP(hAPP(c_Lambda_Olift,X8),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
fof(f2195,plain,
spl0_196,
inference(avatar_split_clause,[],[f82,f2193]) ).
fof(f2193,plain,
( spl0_196
<=> ! [X6,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X6,X1,tc_nat),c_HOL_Otimes__class_Otimes(X6,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f82,axiom,
! [X0,X1,X6] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X6,X1,tc_nat),c_HOL_Otimes__class_Otimes(X6,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
fof(f2191,plain,
spl0_195,
inference(avatar_split_clause,[],[f79,f2189]) ).
fof(f2189,plain,
( spl0_195
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f79,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).
fof(f2187,plain,
spl0_194,
inference(avatar_split_clause,[],[f78,f2185]) ).
fof(f2185,plain,
( spl0_194
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f78,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).
fof(f2183,plain,
spl0_193,
inference(avatar_split_clause,[],[f63,f2181]) ).
fof(f2181,plain,
( spl0_193
<=> ! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X3,X4,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X4,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f63,axiom,
! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X3,X4,X2) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X4,X2),X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f2179,plain,
( spl0_192
| ~ spl0_144
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1748,f1703,f1563,f2177]) ).
fof(f2177,plain,
( spl0_192
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1563,plain,
( spl0_144
<=> ! [X14] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1748,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)),tc_nat)
| ~ spl0_144
| ~ spl0_158 ),
inference(superposition,[],[f1564,f1704]) ).
fof(f1564,plain,
( ! [X14] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f2175,plain,
spl0_191,
inference(avatar_split_clause,[],[f43,f2173]) ).
fof(f2173,plain,
( spl0_191
<=> ! [X15,X13,X14,X2] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X15,X2)
| ~ c_HOL_Oord__class_Oless(X15,X13,X2)
| c_HOL_Oord__class_Oless(X14,X13,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f43,axiom,
! [X2,X14,X15,X13] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X15,X2)
| ~ c_HOL_Oord__class_Oless(X15,X13,X2)
| c_HOL_Oord__class_Oless(X14,X13,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f2171,plain,
spl0_190,
inference(avatar_split_clause,[],[f42,f2169]) ).
fof(f2169,plain,
( spl0_190
<=> ! [X15,X13,X14,X2] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X15,X14,X2)
| ~ c_HOL_Oord__class_Oless(X13,X15,X2)
| c_HOL_Oord__class_Oless(X13,X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f42,axiom,
! [X2,X14,X15,X13] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X15,X14,X2)
| ~ c_HOL_Oord__class_Oless(X13,X15,X2)
| c_HOL_Oord__class_Oless(X13,X14,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f1879,plain,
spl0_189,
inference(avatar_split_clause,[],[f601,f1877]) ).
fof(f1877,plain,
( spl0_189
<=> ! [X1,X8,X49] :
( c_Lambda_OdB_OVar(X1) = X8
| c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f601,axiom,
! [X49,X1,X8] :
( c_Lambda_OdB_OVar(X1) = X8
| c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
fof(f1875,plain,
spl0_188,
inference(avatar_split_clause,[],[f585,f1873]) ).
fof(f1873,plain,
( spl0_188
<=> ! [X1,X8,X49] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X49
| c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f585,axiom,
! [X49,X1,X8] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X49
| c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
fof(f1871,plain,
spl0_187,
inference(avatar_split_clause,[],[f572,f1869]) ).
fof(f1869,plain,
( spl0_187
<=> ! [X27,X8,X49] :
( c_Lambda_OdB_OAbs(X27) = X8
| c_Lambda_OdB_OAbs(X27) != c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f572,axiom,
! [X49,X8,X27] :
( c_Lambda_OdB_OAbs(X27) = X8
| c_Lambda_OdB_OAbs(X27) != c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
fof(f1867,plain,
spl0_186,
inference(avatar_split_clause,[],[f429,f1865]) ).
fof(f1865,plain,
( spl0_186
<=> ! [X3,X4,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f429,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X5,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
fof(f1863,plain,
spl0_185,
inference(avatar_split_clause,[],[f428,f1861]) ).
fof(f1861,plain,
( spl0_185
<=> ! [X3,X4,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f428,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X5,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
fof(f1859,plain,
spl0_184,
inference(avatar_split_clause,[],[f427,f1857]) ).
fof(f1857,plain,
( spl0_184
<=> ! [X3,X4,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f427,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X5,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
fof(f1855,plain,
spl0_183,
inference(avatar_split_clause,[],[f426,f1853]) ).
fof(f1853,plain,
( spl0_183
<=> ! [X2,X5,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X4,X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f426,axiom,
! [X2,X3,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X5,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X4,X2),X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
fof(f1851,plain,
spl0_182,
inference(avatar_split_clause,[],[f403,f1849]) ).
fof(f1849,plain,
( spl0_182
<=> ! [X6,X7,X8] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X7),X6)),X8),X6) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f403,axiom,
! [X8,X6,X7] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X7),X6)),X8),X6) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f1847,plain,
spl0_181,
inference(avatar_split_clause,[],[f398,f1845]) ).
fof(f1845,plain,
( spl0_181
<=> ! [X27,X8,X49] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X49
| c_Lambda_OdB_OAbs(X27) != c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f398,axiom,
! [X49,X8,X27] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X49
| c_Lambda_OdB_OAbs(X27) != c_List_Ofoldl(c_Lambda_OdB_OApp,X8,X49,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
fof(f1843,plain,
spl0_180,
inference(avatar_split_clause,[],[f343,f1841]) ).
fof(f1841,plain,
( spl0_180
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f343,axiom,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1839,plain,
spl0_179,
inference(avatar_split_clause,[],[f342,f1837]) ).
fof(f1837,plain,
( spl0_179
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f342,axiom,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1834,plain,
spl0_178,
inference(avatar_split_clause,[],[f336,f1832]) ).
fof(f1832,plain,
( spl0_178
<=> ! [X0,X31] :
( hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f336,axiom,
! [X31,X0] :
( hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_0) ).
fof(f1830,plain,
( spl0_177
| ~ spl0_99
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1751,f1703,f1276,f1828]) ).
fof(f1828,plain,
( spl0_177
<=> ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1276,plain,
( spl0_99
<=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1751,plain,
( ! [X0] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) != c_Lambda_OdB_OdB__size(X0)
| ~ spl0_99
| ~ spl0_158 ),
inference(superposition,[],[f1277,f1704]) ).
fof(f1277,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) != X0
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1825,plain,
spl0_176,
inference(avatar_split_clause,[],[f335,f1823]) ).
fof(f1823,plain,
( spl0_176
<=> ! [X0,X31] :
( ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f335,axiom,
! [X31,X0] :
( ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X31,c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_5) ).
fof(f1821,plain,
spl0_175,
inference(avatar_split_clause,[],[f282,f1819]) ).
fof(f1819,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f282,axiom,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).
fof(f1817,plain,
spl0_174,
inference(avatar_split_clause,[],[f281,f1815]) ).
fof(f1815,plain,
( spl0_174
<=> ! [X2,X14,X15] :
( ~ class_Orderings_Olinorder(X2)
| X14 = X15
| c_HOL_Oord__class_Oless(X15,X14,X2)
| c_HOL_Oord__class_Oless(X14,X15,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f281,axiom,
! [X2,X14,X15] :
( ~ class_Orderings_Olinorder(X2)
| X14 = X15
| c_HOL_Oord__class_Oless(X15,X14,X2)
| c_HOL_Oord__class_Oless(X14,X15,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f1813,plain,
spl0_173,
inference(avatar_split_clause,[],[f258,f1811]) ).
fof(f1811,plain,
( spl0_173
<=> ! [X6,X0] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f258,axiom,
! [X0,X6] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).
fof(f1809,plain,
spl0_172,
inference(avatar_split_clause,[],[f257,f1807]) ).
fof(f1807,plain,
( spl0_172
<=> ! [X6,X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X6,X0,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f257,axiom,
! [X0,X6] :
( c_Ring__and__Field_Odvd__class_Odvd(X6,X0,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).
fof(f1805,plain,
spl0_171,
inference(avatar_split_clause,[],[f231,f1803]) ).
fof(f1803,plain,
( spl0_171
<=> ! [X0,X14] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X14,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f231,axiom,
! [X0,X14] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X14,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_1) ).
fof(f1801,plain,
spl0_170,
inference(avatar_split_clause,[],[f139,f1799]) ).
fof(f1799,plain,
( spl0_170
<=> ! [X6,X10] :
( ~ c_HOL_Oord__class_Oless(X10,X6,tc_nat)
| c_Lambda_OdB_OVar(X10) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X10)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f139,axiom,
! [X10,X6] :
( ~ c_HOL_Oord__class_Oless(X10,X6,tc_nat)
| c_Lambda_OdB_OVar(X10) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X10)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f1797,plain,
spl0_169,
inference(avatar_split_clause,[],[f105,f1795]) ).
fof(f1795,plain,
( spl0_169
<=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1793,plain,
spl0_168,
inference(avatar_split_clause,[],[f93,f1791]) ).
fof(f1791,plain,
( spl0_168
<=> ! [X6,X9,X10] :
( c_HOL_Oord__class_Oless(X10,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f93,axiom,
! [X10,X6,X9] :
( c_HOL_Oord__class_Oless(X10,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f1789,plain,
spl0_167,
inference(avatar_split_clause,[],[f92,f1787]) ).
fof(f1787,plain,
( spl0_167
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f92,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
fof(f1785,plain,
( spl0_166
| ~ spl0_123
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1750,f1703,f1441,f1783]) ).
fof(f1783,plain,
( spl0_166
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1441,plain,
( spl0_123
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1750,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X0))
| ~ spl0_123
| ~ spl0_158 ),
inference(superposition,[],[f1442,f1704]) ).
fof(f1442,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f1781,plain,
spl0_165,
inference(avatar_split_clause,[],[f91,f1779]) ).
fof(f1779,plain,
( spl0_165
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f91,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X13),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f1777,plain,
spl0_164,
inference(avatar_split_clause,[],[f65,f1775]) ).
fof(f1775,plain,
( spl0_164
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = X3
| c_HOL_Oone__class_Oone(X2) = c_Divides_Odiv__class_Odiv(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f65,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = X3
| c_HOL_Oone__class_Oone(X2) = c_Divides_Odiv__class_Odiv(X3,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f1773,plain,
spl0_163,
inference(avatar_split_clause,[],[f5,f1771]) ).
fof(f1771,plain,
( spl0_163
<=> ! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| c_HOL_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f5,axiom,
! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| c_HOL_Ozero__class_Ozero(X2) != c_Divides_Odiv__class_Omod(X4,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
fof(f1769,plain,
spl0_162,
inference(avatar_split_clause,[],[f4,f1767]) ).
fof(f1767,plain,
( spl0_162
<=> ! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f4,axiom,
! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X4,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
fof(f1765,plain,
spl0_161,
inference(avatar_split_clause,[],[f2,f1763]) ).
fof(f1763,plain,
( spl0_161
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
fof(f1761,plain,
spl0_160,
inference(avatar_split_clause,[],[f1,f1759]) ).
fof(f1759,plain,
( spl0_160
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
fof(f1709,plain,
spl0_159,
inference(avatar_split_clause,[],[f784,f1707]) ).
fof(f1707,plain,
( spl0_159
<=> ! [X7,X8] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),c_Lambda_Osubstn(X8,X7,c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f784,plain,
! [X8,X7] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),c_Lambda_Osubstn(X8,X7,c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f518,f567]) ).
fof(f518,axiom,
! [X8,X7] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X8)),X7),hAPP(hAPP(hAPP(c_Lambda_Osubst,X8),X7),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f1705,plain,
spl0_158,
inference(avatar_split_clause,[],[f777,f1703]) ).
fof(f777,plain,
! [X22] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X22)),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f776,f356]) ).
fof(f776,plain,
! [X22] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f682,f671]) ).
fof(f671,plain,
! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),
inference(definition_unfolding,[],[f62,f61]) ).
fof(f62,axiom,
! [X0] : c_Suc(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
fof(f682,plain,
! [X22] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f489,f61]) ).
fof(f489,axiom,
! [X22] : c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(X22)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).
fof(f1701,plain,
spl0_157,
inference(avatar_split_clause,[],[f513,f1699]) ).
fof(f1699,plain,
( spl0_157
<=> ! [X7,X10] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X7),X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f513,axiom,
! [X10,X7] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X7))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X7),X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f1697,plain,
spl0_156,
inference(avatar_split_clause,[],[f466,f1695]) ).
fof(f1695,plain,
( spl0_156
<=> ! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f466,axiom,
! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X2),X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f1693,plain,
spl0_155,
inference(avatar_split_clause,[],[f465,f1691]) ).
fof(f1691,plain,
( spl0_155
<=> ! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f465,axiom,
! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X2),X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f1689,plain,
spl0_154,
inference(avatar_split_clause,[],[f392,f1687]) ).
fof(f1687,plain,
( spl0_154
<=> ! [X48,X47,X46,X2] :
( c_List_Olist_ONil(X48) = X47
| c_List_Olist_ONil(X2) != c_List_Omap(X46,X47,X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f392,axiom,
! [X2,X48,X46,X47] :
( c_List_Olist_ONil(X48) = X47
| c_List_Olist_ONil(X2) != c_List_Omap(X46,X47,X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
fof(f1685,plain,
spl0_153,
inference(avatar_split_clause,[],[f347,f1683]) ).
fof(f1683,plain,
( spl0_153
<=> ! [X3,X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X3) != X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f347,axiom,
! [X3,X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X3) != X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
fof(f1680,plain,
spl0_152,
inference(avatar_split_clause,[],[f328,f1678]) ).
fof(f1678,plain,
( spl0_152
<=> ! [X0,X31] :
( hBOOL(hAPP(X31,X0))
| ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f328,axiom,
! [X31,X0] :
( hBOOL(hAPP(X31,X0))
| ~ hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).
fof(f1675,plain,
spl0_151,
inference(avatar_split_clause,[],[f327,f1673]) ).
fof(f1673,plain,
( spl0_151
<=> ! [X0,X31] :
( ~ hBOOL(hAPP(X31,X0))
| hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f327,axiom,
! [X31,X0] :
( ~ hBOOL(hAPP(X31,X0))
| hBOOL(hAPP(X31,c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).
fof(f1671,plain,
spl0_150,
inference(avatar_split_clause,[],[f303,f1669]) ).
fof(f1669,plain,
( spl0_150
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Oone__class_Oone(X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f303,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Oone__class_Oone(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f1667,plain,
spl0_149,
inference(avatar_split_clause,[],[f289,f1665]) ).
fof(f1665,plain,
( spl0_149
<=> ! [X13,X14,X15] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X13,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f289,axiom,
! [X14,X15,X13] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X13,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
fof(f1663,plain,
spl0_148,
inference(avatar_split_clause,[],[f110,f1661]) ).
fof(f1661,plain,
( spl0_148
<=> ! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X3,X4,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f110,axiom,
! [X2,X3,X4] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X3,X4,X2),X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f1659,plain,
spl0_147,
inference(avatar_split_clause,[],[f109,f1657]) ).
fof(f1657,plain,
( spl0_147
<=> ! [X2,X0,X1] :
( ~ class_Nat_Osemiring__char__0(X2)
| X0 = X1
| c_Nat_Osemiring__1__class_Oof__nat(X1,X2) != c_Nat_Osemiring__1__class_Oof__nat(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f109,axiom,
! [X2,X0,X1] :
( ~ class_Nat_Osemiring__char__0(X2)
| X0 = X1
| c_Nat_Osemiring__1__class_Oof__nat(X1,X2) != c_Nat_Osemiring__1__class_Oof__nat(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f1655,plain,
spl0_146,
inference(avatar_split_clause,[],[f25,f1653]) ).
fof(f1653,plain,
( spl0_146
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X0,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f25,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X0,tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f1629,plain,
( spl0_145
| ~ spl0_19
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1358,f1272,f936,f1626]) ).
fof(f1626,plain,
( spl0_145
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f936,plain,
( spl0_19
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1272,plain,
( spl0_98
<=> ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1358,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_19
| ~ spl0_98 ),
inference(resolution,[],[f1273,f938]) ).
fof(f938,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f936]) ).
fof(f1273,plain,
( ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1272]) ).
fof(f1565,plain,
spl0_144,
inference(avatar_split_clause,[],[f664,f1563]) ).
fof(f664,plain,
! [X14] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f558,f61]) ).
fof(f558,axiom,
! [X14] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X14),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f1561,plain,
( spl0_143
| ~ spl0_25
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1342,f1232,f966,f1559]) ).
fof(f1559,plain,
( spl0_143
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f966,plain,
( spl0_25
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1232,plain,
( spl0_88
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1342,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_25
| ~ spl0_88 ),
inference(resolution,[],[f1233,f968]) ).
fof(f968,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f966]) ).
fof(f1233,plain,
( ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f1557,plain,
spl0_142,
inference(avatar_split_clause,[],[f511,f1555]) ).
fof(f1555,plain,
( spl0_142
<=> ! [X42,X19,X20,X21,X2] : hAPP(X19,X42) = c_Lambda_OdB_OdB__case(X19,X20,X21,c_Lambda_OdB_OVar(X42),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f511,axiom,
! [X2,X21,X19,X42,X20] : hAPP(X19,X42) = c_Lambda_OdB_OdB__case(X19,X20,X21,c_Lambda_OdB_OVar(X42),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
fof(f1553,plain,
spl0_141,
inference(avatar_split_clause,[],[f491,f1551]) ).
fof(f1551,plain,
( spl0_141
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X0
| c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f491,axiom,
! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X0
| c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
fof(f1549,plain,
spl0_140,
inference(avatar_split_clause,[],[f490,f1547]) ).
fof(f1547,plain,
( spl0_140
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X1
| c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f490,axiom,
! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X1
| c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
fof(f1545,plain,
spl0_139,
inference(avatar_split_clause,[],[f460,f1543]) ).
fof(f1543,plain,
( spl0_139
<=> ! [X54,X11,X30,X7] :
( ~ c_Lambda_Obeta(X7,X54)
| ~ c_Type_Otyping(X11,X7,X30)
| c_Type_Otyping(X11,X54,X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f460,axiom,
! [X11,X54,X7,X30] :
( ~ c_Lambda_Obeta(X7,X54)
| ~ c_Type_Otyping(X11,X7,X30)
| c_Type_Otyping(X11,X54,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f1541,plain,
spl0_138,
inference(avatar_split_clause,[],[f325,f1539]) ).
fof(f1539,plain,
( spl0_138
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f325,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1537,plain,
spl0_137,
inference(avatar_split_clause,[],[f324,f1535]) ).
fof(f1535,plain,
( spl0_137
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f324,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1533,plain,
spl0_136,
inference(avatar_split_clause,[],[f323,f1531]) ).
fof(f1531,plain,
( spl0_136
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f323,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1529,plain,
spl0_135,
inference(avatar_split_clause,[],[f322,f1527]) ).
fof(f1527,plain,
( spl0_135
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f322,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1525,plain,
spl0_134,
inference(avatar_split_clause,[],[f321,f1523]) ).
fof(f1523,plain,
( spl0_134
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f321,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),c_HOL_Ozero__class_Ozero(X2)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1521,plain,
spl0_133,
inference(avatar_split_clause,[],[f319,f1519]) ).
fof(f1519,plain,
( spl0_133
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f319,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),c_HOL_Ozero__class_Ozero(X2)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1517,plain,
( spl0_132
| ~ spl0_25
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1337,f1228,f966,f1515]) ).
fof(f1515,plain,
( spl0_132
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1228,plain,
( spl0_87
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1337,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_25
| ~ spl0_87 ),
inference(resolution,[],[f1229,f968]) ).
fof(f1229,plain,
( ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,X3,X2) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f1513,plain,
spl0_131,
inference(avatar_split_clause,[],[f317,f1511]) ).
fof(f1511,plain,
( spl0_131
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f317,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f1509,plain,
spl0_130,
inference(avatar_split_clause,[],[f273,f1507]) ).
fof(f1507,plain,
( spl0_130
<=> ! [X0,X1] :
( X0 = X1
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f273,axiom,
! [X0,X1] :
( X0 = X1
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f1505,plain,
spl0_129,
inference(avatar_split_clause,[],[f269,f1503]) ).
fof(f1503,plain,
( spl0_129
<=> ! [X14,X15] :
( X14 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f269,axiom,
! [X14,X15] :
( X14 = X15
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X15,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X15,X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
fof(f1501,plain,
spl0_128,
inference(avatar_split_clause,[],[f125,f1499]) ).
fof(f1499,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X1,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).
fof(f1497,plain,
spl0_127,
inference(avatar_split_clause,[],[f60,f1495]) ).
fof(f1495,plain,
( spl0_127
<=> ! [X2,X19,X20,X21,X22] : c_Lambda_OdB_OdB__case(X19,X20,X21,c_Lambda_OdB_OAbs(X22),X2) = hAPP(X21,X22) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f60,axiom,
! [X2,X21,X19,X22,X20] : c_Lambda_OdB_OdB__case(X19,X20,X21,c_Lambda_OdB_OAbs(X22),X2) = hAPP(X21,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
fof(f1493,plain,
spl0_126,
inference(avatar_split_clause,[],[f46,f1491]) ).
fof(f1491,plain,
( spl0_126
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X3,X4,X2) = c_HOL_Otimes__class_Otimes(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f46,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X3,X4,X2) = c_HOL_Otimes__class_Otimes(X4,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f1479,plain,
( spl0_125
| ~ spl0_11
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f1334,f1216,f896,f1477]) ).
fof(f1477,plain,
( spl0_125
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f896,plain,
( spl0_11
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1216,plain,
( spl0_84
<=> ! [X2,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X14,c_HOL_Oone__class_Oone(tc_nat),X2) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1334,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_11
| ~ spl0_84 ),
inference(resolution,[],[f1217,f898]) ).
fof(f898,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f1217,plain,
( ! [X2,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X14,c_HOL_Oone__class_Oone(tc_nat),X2) = X14 )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f1447,plain,
spl0_124,
inference(avatar_split_clause,[],[f660,f1445]) ).
fof(f660,plain,
! [X14] : c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f367,f61]) ).
fof(f367,axiom,
! [X14] : c_HOL_Oord__class_Oless(X14,c_Suc(X14),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f1443,plain,
spl0_123,
inference(avatar_split_clause,[],[f656,f1441]) ).
fof(f656,plain,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Oone__class_Oone(tc_nat)),
inference(definition_unfolding,[],[f597,f61]) ).
fof(f597,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
fof(f1439,plain,
spl0_122,
inference(avatar_split_clause,[],[f594,f1437]) ).
fof(f1437,plain,
( spl0_122
<=> ! [X6,X12] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X6)),X12),X6) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f594,axiom,
! [X6,X12] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X6)),X12),X6) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f1435,plain,
spl0_121,
inference(avatar_split_clause,[],[f509,f1433]) ).
fof(f1433,plain,
( spl0_121
<=> ! [X2,X14,X15] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X15,X2)
| ~ c_HOL_Oord__class_Oless(X15,X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f509,axiom,
! [X2,X14,X15] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X15,X2)
| ~ c_HOL_Oord__class_Oless(X15,X14,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1431,plain,
spl0_120,
inference(avatar_split_clause,[],[f506,f1429]) ).
fof(f1429,plain,
( spl0_120
<=> ! [X2,X14,X15] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X15,X14,X2)
| ~ c_HOL_Oord__class_Oless(X14,X15,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f506,axiom,
! [X2,X14,X15] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X15,X14,X2)
| ~ c_HOL_Oord__class_Oless(X14,X15,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1427,plain,
spl0_119,
inference(avatar_split_clause,[],[f505,f1425]) ).
fof(f1425,plain,
( spl0_119
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f505,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1423,plain,
spl0_118,
inference(avatar_split_clause,[],[f467,f1421]) ).
fof(f1421,plain,
( spl0_118
<=> ! [X16,X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f467,axiom,
! [X16,X14] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X16,X14,tc_nat),X16,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
fof(f1419,plain,
spl0_117,
inference(avatar_split_clause,[],[f414,f1417]) ).
fof(f1417,plain,
( spl0_117
<=> ! [X2,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X14,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f414,axiom,
! [X2,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X14,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f1415,plain,
spl0_116,
inference(avatar_split_clause,[],[f413,f1413]) ).
fof(f1413,plain,
( spl0_116
<=> ! [X2,X3] :
( ~ class_Power_Opower(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f413,axiom,
! [X2,X3] :
( ~ class_Power_Opower(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f1411,plain,
spl0_115,
inference(avatar_split_clause,[],[f410,f1409]) ).
fof(f1409,plain,
( spl0_115
<=> ! [X11,X30,X10] :
( ~ c_Type_Otyping(X11,c_Lambda_OdB_OVar(X10),X30)
| hAPP(X11,X10) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f410,axiom,
! [X10,X11,X30] :
( ~ c_Type_Otyping(X11,c_Lambda_OdB_OVar(X10),X30)
| hAPP(X11,X10) = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f1407,plain,
spl0_114,
inference(avatar_split_clause,[],[f314,f1405]) ).
fof(f1405,plain,
( spl0_114
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f314,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1403,plain,
spl0_113,
inference(avatar_split_clause,[],[f259,f1401]) ).
fof(f1401,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f259,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f1399,plain,
spl0_112,
inference(avatar_split_clause,[],[f256,f1397]) ).
fof(f1397,plain,
( spl0_112
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f256,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,c_HOL_Oone__class_Oone(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f1395,plain,
spl0_111,
inference(avatar_split_clause,[],[f209,f1393]) ).
fof(f1393,plain,
( spl0_111
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f209,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f1391,plain,
( ~ spl0_110
| ~ spl0_91
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1359,f1276,f1244,f1388]) ).
fof(f1388,plain,
( spl0_110
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1359,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| ~ spl0_91
| ~ spl0_99 ),
inference(superposition,[],[f1277,f1245]) ).
fof(f1386,plain,
spl0_109,
inference(avatar_split_clause,[],[f208,f1384]) ).
fof(f1384,plain,
( spl0_109
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f208,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Odiv(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f1382,plain,
spl0_108,
inference(avatar_split_clause,[],[f202,f1380]) ).
fof(f1380,plain,
( spl0_108
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f202,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1378,plain,
spl0_107,
inference(avatar_split_clause,[],[f201,f1376]) ).
fof(f1376,plain,
( spl0_107
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f201,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1374,plain,
spl0_106,
inference(avatar_split_clause,[],[f198,f1372]) ).
fof(f1372,plain,
( spl0_106
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f198,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1370,plain,
spl0_105,
inference(avatar_split_clause,[],[f197,f1368]) ).
fof(f1368,plain,
( spl0_105
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f197,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1366,plain,
spl0_104,
inference(avatar_split_clause,[],[f26,f1364]) ).
fof(f1364,plain,
( spl0_104
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f26,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X2),X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1341,plain,
( ~ spl0_27
| spl0_103
| ~ spl0_64
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1319,f1184,f1134,f1339,f976]) ).
fof(f976,plain,
( spl0_27
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1339,plain,
( spl0_103
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1134,plain,
( spl0_64
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1184,plain,
( spl0_76
<=> ! [X6,X2,X4] :
( ~ class_Ring__and__Field_Odvd(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X4,X6,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1319,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_64
| ~ spl0_76 ),
inference(superposition,[],[f1185,f1135]) ).
fof(f1135,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f1185,plain,
( ! [X2,X6,X4] :
( c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X4,X6,X2),X2)
| ~ class_Ring__and__Field_Odvd(X2) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1184]) ).
fof(f1328,plain,
( spl0_102
| ~ spl0_19
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f1288,f1168,f936,f1325]) ).
fof(f1325,plain,
( spl0_102
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1168,plain,
( spl0_72
<=> ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1288,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_19
| ~ spl0_72 ),
inference(resolution,[],[f1169,f938]) ).
fof(f1169,plain,
( ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f1287,plain,
spl0_101,
inference(avatar_split_clause,[],[f791,f1285]) ).
fof(f1285,plain,
( spl0_101
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f791,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
inference(forward_demodulation,[],[f790,f356]) ).
fof(f790,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
inference(forward_demodulation,[],[f712,f105]) ).
fof(f712,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f550,f61]) ).
fof(f550,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1283,plain,
spl0_100,
inference(avatar_split_clause,[],[f780,f1280]) ).
fof(f1280,plain,
( spl0_100
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f780,plain,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(forward_demodulation,[],[f779,f340]) ).
fof(f340,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f779,plain,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(forward_demodulation,[],[f417,f340]) ).
fof(f417,axiom,
! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).
fof(f1278,plain,
spl0_99,
inference(avatar_split_clause,[],[f654,f1276]) ).
fof(f654,plain,
! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) != X0,
inference(definition_unfolding,[],[f595,f61]) ).
fof(f595,axiom,
! [X0] : c_Suc(X0) != X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f1274,plain,
spl0_98,
inference(avatar_split_clause,[],[f523,f1272]) ).
fof(f523,axiom,
! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1270,plain,
spl0_97,
inference(avatar_split_clause,[],[f514,f1268]) ).
fof(f1268,plain,
( spl0_97
<=> ! [X27] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f514,axiom,
! [X27] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X27))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X27))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f1266,plain,
spl0_96,
inference(avatar_split_clause,[],[f468,f1264]) ).
fof(f1264,plain,
( spl0_96
<=> ! [X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f468,axiom,
! [X1] :
( c_HOL_Oone__class_Oone(tc_nat) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
fof(f1262,plain,
spl0_95,
inference(avatar_split_clause,[],[f441,f1260]) ).
fof(f441,axiom,
! [X10,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1258,plain,
spl0_94,
inference(avatar_split_clause,[],[f440,f1256]) ).
fof(f440,axiom,
! [X10,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1254,plain,
spl0_93,
inference(avatar_split_clause,[],[f400,f1252]) ).
fof(f1252,plain,
( spl0_93
<=> ! [X2,X48,X3,X46] : c_List_Ofoldl(X46,X3,c_List_Olist_ONil(X48),X2,X48) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f400,axiom,
! [X2,X3,X48,X46] : c_List_Ofoldl(X46,X3,c_List_Olist_ONil(X48),X2,X48) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
fof(f1250,plain,
spl0_92,
inference(avatar_split_clause,[],[f395,f1248]) ).
fof(f1248,plain,
( spl0_92
<=> ! [X2,X48,X46] : c_List_Olist_ONil(X2) = c_List_Omap(X46,c_List_Olist_ONil(X48),X48,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f395,axiom,
! [X2,X48,X46] : c_List_Olist_ONil(X2) = c_List_Omap(X46,c_List_Olist_ONil(X48),X48,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
fof(f1246,plain,
spl0_91,
inference(avatar_split_clause,[],[f357,f1244]) ).
fof(f357,axiom,
! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f1242,plain,
spl0_90,
inference(avatar_split_clause,[],[f356,f1240]) ).
fof(f1240,plain,
( spl0_90
<=> ! [X14] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Ozero__class_Ozero(tc_nat)) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1238,plain,
spl0_89,
inference(avatar_split_clause,[],[f337,f1236]) ).
fof(f1236,plain,
( spl0_89
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f337,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1234,plain,
spl0_88,
inference(avatar_split_clause,[],[f313,f1232]) ).
fof(f313,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X2),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1230,plain,
spl0_87,
inference(avatar_split_clause,[],[f312,f1228]) ).
fof(f312,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X3,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1226,plain,
spl0_86,
inference(avatar_split_clause,[],[f236,f1224]) ).
fof(f1224,plain,
( spl0_86
<=> ! [X2,X11,X30,X14] : hAPP(c_Type_Oshift(X11,X14,X30,X2),X14) = X30 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f236,axiom,
! [X2,X11,X14,X30] : hAPP(c_Type_Oshift(X11,X14,X30,X2),X14) = X30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f1222,plain,
spl0_85,
inference(avatar_split_clause,[],[f219,f1220]) ).
fof(f1220,plain,
( spl0_85
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_Power_Opower__class_Opower(X3,c_HOL_Oone__class_Oone(tc_nat),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f219,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_Power_Opower__class_Opower(X3,c_HOL_Oone__class_Oone(tc_nat),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
fof(f1218,plain,
spl0_84,
inference(avatar_split_clause,[],[f218,f1216]) ).
fof(f218,axiom,
! [X2,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X14,c_HOL_Oone__class_Oone(tc_nat),X2) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1214,plain,
spl0_83,
inference(avatar_split_clause,[],[f186,f1212]) ).
fof(f1212,plain,
( spl0_83
<=> ! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f186,axiom,
! [X2,X3] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Odiv(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f1210,plain,
spl0_82,
inference(avatar_split_clause,[],[f130,f1208]) ).
fof(f1208,plain,
( spl0_82
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f130,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1206,plain,
spl0_81,
inference(avatar_split_clause,[],[f73,f1204]) ).
fof(f1204,plain,
( spl0_81
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f73,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f1202,plain,
spl0_80,
inference(avatar_split_clause,[],[f72,f1200]) ).
fof(f1200,plain,
( spl0_80
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f72,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f1198,plain,
spl0_79,
inference(avatar_split_clause,[],[f71,f1196]) ).
fof(f1196,plain,
( spl0_79
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f71,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f1194,plain,
spl0_78,
inference(avatar_split_clause,[],[f70,f1192]) ).
fof(f1192,plain,
( spl0_78
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f70,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oone__class_Oone(X2),X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f1190,plain,
spl0_77,
inference(avatar_split_clause,[],[f69,f1188]) ).
fof(f1188,plain,
( spl0_77
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f69,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X2),X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(f1186,plain,
spl0_76,
inference(avatar_split_clause,[],[f68,f1184]) ).
fof(f68,axiom,
! [X2,X6,X4] :
( ~ class_Ring__and__Field_Odvd(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X4,X6,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f1182,plain,
spl0_75,
inference(avatar_split_clause,[],[f67,f1180]) ).
fof(f1180,plain,
( spl0_75
<=> ! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f67,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f1178,plain,
spl0_74,
inference(avatar_split_clause,[],[f66,f1176]) ).
fof(f1176,plain,
( spl0_74
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f66,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f1174,plain,
spl0_73,
inference(avatar_split_clause,[],[f47,f1172]) ).
fof(f1172,plain,
( spl0_73
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f47,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1170,plain,
spl0_72,
inference(avatar_split_clause,[],[f19,f1168]) ).
fof(f19,axiom,
! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
fof(f1164,plain,
spl0_71,
inference(avatar_split_clause,[],[f764,f1162]) ).
fof(f1162,plain,
( spl0_71
<=> ! [X1] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f764,plain,
! [X1] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat),
inference(forward_demodulation,[],[f763,f356]) ).
fof(f763,plain,
! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
inference(forward_demodulation,[],[f672,f671]) ).
fof(f672,plain,
! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat),
inference(definition_unfolding,[],[f562,f61,f61]) ).
fof(f562,axiom,
! [X1] : c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_2) ).
fof(f1160,plain,
spl0_70,
inference(avatar_split_clause,[],[f760,f1158]) ).
fof(f1158,plain,
( spl0_70
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f760,plain,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(forward_demodulation,[],[f669,f662]) ).
fof(f662,plain,
c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
inference(definition_unfolding,[],[f539,f61]) ).
fof(f539,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
fof(f669,plain,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f533,f61]) ).
fof(f533,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1156,plain,
spl0_69,
inference(avatar_split_clause,[],[f602,f1154]) ).
fof(f1154,plain,
( spl0_69
<=> ! [X42,X59,X58] : c_Lambda_OdB_OVar(X42) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X59) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f602,axiom,
! [X58,X59,X42] : c_Lambda_OdB_OVar(X42) != hAPP(hAPP(c_Lambda_OdB_OApp,X58),X59),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f1152,plain,
spl0_68,
inference(avatar_split_clause,[],[f591,f1150]) ).
fof(f1150,plain,
( spl0_68
<=> ! [X57,X42] :
( X42 = X57
| c_Lambda_OdB_OVar(X42) != c_Lambda_OdB_OVar(X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f591,axiom,
! [X57,X42] :
( X42 = X57
| c_Lambda_OdB_OVar(X42) != c_Lambda_OdB_OVar(X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f1148,plain,
spl0_67,
inference(avatar_split_clause,[],[f412,f1146]) ).
fof(f1146,plain,
( spl0_67
<=> ! [X18] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f412,axiom,
! [X18] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X18,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__if_0) ).
fof(f1144,plain,
spl0_66,
inference(avatar_split_clause,[],[f383,f1142]) ).
fof(f1142,plain,
( spl0_66
<=> ! [X34,X44,X43] : c_Lambda_OdB_OAbs(X34) != hAPP(hAPP(c_Lambda_OdB_OApp,X43),X44) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f383,axiom,
! [X44,X34,X43] : c_Lambda_OdB_OAbs(X34) != hAPP(hAPP(c_Lambda_OdB_OApp,X43),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f1140,plain,
spl0_65,
inference(avatar_split_clause,[],[f340,f1138]) ).
fof(f1138,plain,
( spl0_65
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1136,plain,
spl0_64,
inference(avatar_split_clause,[],[f339,f1134]) ).
fof(f339,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f1132,plain,
spl0_63,
inference(avatar_split_clause,[],[f296,f1130]) ).
fof(f1130,plain,
( spl0_63
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f296,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1128,plain,
spl0_62,
inference(avatar_split_clause,[],[f239,f1126]) ).
fof(f1126,plain,
( spl0_62
<=> ! [X22,X34] :
( X22 = X34
| c_Lambda_OdB_OAbs(X22) != c_Lambda_OdB_OAbs(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f239,axiom,
! [X34,X22] :
( X22 = X34
| c_Lambda_OdB_OAbs(X22) != c_Lambda_OdB_OAbs(X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f1124,plain,
spl0_61,
inference(avatar_split_clause,[],[f238,f1122]) ).
fof(f1122,plain,
( spl0_61
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f238,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1120,plain,
spl0_60,
inference(avatar_split_clause,[],[f184,f1118]) ).
fof(f1118,plain,
( spl0_60
<=> ! [X7,X8] :
( ~ c_Lambda_Obeta(X8,X7)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X8),c_Lambda_OdB_OAbs(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f184,axiom,
! [X8,X7] :
( ~ c_Lambda_Obeta(X8,X7)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X8),c_Lambda_OdB_OAbs(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f1115,plain,
spl0_59,
inference(avatar_split_clause,[],[f759,f1113]) ).
fof(f1113,plain,
( spl0_59
<=> ! [X1] : c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f759,plain,
! [X1] : c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
inference(forward_demodulation,[],[f667,f662]) ).
fof(f667,plain,
! [X1] : c_Divides_Odiv__class_Odiv(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) = X1,
inference(definition_unfolding,[],[f565,f61]) ).
fof(f565,axiom,
! [X1] : c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).
fof(f1111,plain,
spl0_58,
inference(avatar_split_clause,[],[f651,f1109]) ).
fof(f1109,plain,
( spl0_58
<=> ! [X66,X65,X2] :
( X65 = X66
| ~ c_fequal(X65,X66,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f651,axiom,
! [X2,X65,X66] :
( X65 = X66
| ~ c_fequal(X65,X66,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1107,plain,
spl0_57,
inference(avatar_split_clause,[],[f568,f1105]) ).
fof(f1105,plain,
( spl0_57
<=> ! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X42),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f568,axiom,
! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(X42),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
fof(f1103,plain,
spl0_56,
inference(avatar_split_clause,[],[f512,f1101]) ).
fof(f1101,plain,
( spl0_56
<=> ! [X55,X14] : c_Type_Otyping(X55,c_Lambda_OdB_OVar(X14),hAPP(X55,X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f512,axiom,
! [X55,X14] : c_Type_Otyping(X55,c_Lambda_OdB_OVar(X14),hAPP(X55,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f1099,plain,
spl0_55,
inference(avatar_split_clause,[],[f310,f1097]) ).
fof(f1097,plain,
( spl0_55
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f310,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
fof(f1095,plain,
spl0_54,
inference(avatar_split_clause,[],[f204,f1093]) ).
fof(f1093,plain,
( spl0_54
<=> ! [X2] :
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f204,axiom,
! [X2] :
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1091,plain,
spl0_53,
inference(avatar_split_clause,[],[f203,f1089]) ).
fof(f1089,plain,
( spl0_53
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f203,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1087,plain,
spl0_52,
inference(avatar_split_clause,[],[f75,f1085]) ).
fof(f1085,plain,
( spl0_52
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f75,axiom,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
fof(f1083,plain,
spl0_51,
inference(avatar_split_clause,[],[f74,f1081]) ).
fof(f1081,plain,
( spl0_51
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f74,axiom,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
fof(f1079,plain,
spl0_50,
inference(avatar_split_clause,[],[f762,f1076]) ).
fof(f1076,plain,
( spl0_50
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f762,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(forward_demodulation,[],[f183,f412]) ).
fof(f183,axiom,
! [X14] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_2) ).
fof(f1074,plain,
spl0_49,
inference(avatar_split_clause,[],[f617,f1072]) ).
fof(f1072,plain,
( spl0_49
<=> ! [X64,X63] :
( ~ class_Orderings_Oorder(X64)
| class_Orderings_Oorder(tc_fun(X63,X64)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f617,axiom,
! [X63,X64] :
( ~ class_Orderings_Oorder(X64)
| class_Orderings_Oorder(tc_fun(X63,X64)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1070,plain,
spl0_48,
inference(avatar_split_clause,[],[f616,f1068]) ).
fof(f1068,plain,
( spl0_48
<=> ! [X64,X63] :
( ~ class_Orderings_Opreorder(X64)
| class_Orderings_Opreorder(tc_fun(X63,X64)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f616,axiom,
! [X63,X64] :
( ~ class_Orderings_Opreorder(X64)
| class_Orderings_Opreorder(tc_fun(X63,X64)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1066,plain,
spl0_47,
inference(avatar_split_clause,[],[f569,f1064]) ).
fof(f569,axiom,
! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
fof(f1062,plain,
spl0_46,
inference(avatar_split_clause,[],[f286,f1060]) ).
fof(f1060,plain,
( spl0_46
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f286,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1058,plain,
spl0_45,
inference(avatar_split_clause,[],[f264,f1056]) ).
fof(f1056,plain,
( spl0_45
<=> ! [X2,X14] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f264,axiom,
! [X2,X14] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X14,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1054,plain,
spl0_44,
inference(avatar_split_clause,[],[f263,f1052]) ).
fof(f1052,plain,
( spl0_44
<=> ! [X2,X14] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f263,axiom,
! [X2,X14] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X14,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1050,plain,
spl0_43,
inference(avatar_split_clause,[],[f262,f1048]) ).
fof(f1048,plain,
( spl0_43
<=> ! [X2,X14] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f262,axiom,
! [X2,X14] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X14,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1046,plain,
spl0_42,
inference(avatar_split_clause,[],[f758,f1044]) ).
fof(f1044,plain,
( spl0_42
<=> ! [X6] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f758,plain,
! [X6] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X6,tc_nat),
inference(forward_demodulation,[],[f663,f662]) ).
fof(f663,plain,
! [X6] : c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X6,tc_nat),
inference(definition_unfolding,[],[f553,f61]) ).
fof(f553,axiom,
! [X6] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).
fof(f1042,plain,
spl0_41,
inference(avatar_split_clause,[],[f405,f1040]) ).
fof(f1040,plain,
( spl0_41
<=> ! [X34,X42] : c_Lambda_OdB_OAbs(X34) != c_Lambda_OdB_OVar(X42) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f405,axiom,
! [X34,X42] : c_Lambda_OdB_OAbs(X34) != c_Lambda_OdB_OVar(X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f1038,plain,
spl0_40,
inference(avatar_split_clause,[],[f353,f1036]) ).
fof(f1036,plain,
( spl0_40
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f353,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f1034,plain,
spl0_39,
inference(avatar_split_clause,[],[f77,f1032]) ).
fof(f1032,plain,
( spl0_39
<=> ! [X2,X23] : c_List_Olistsp(X23,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f77,axiom,
! [X2,X23] : c_List_Olistsp(X23,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
fof(f1030,plain,
spl0_38,
inference(avatar_split_clause,[],[f650,f1028]) ).
fof(f1028,plain,
( spl0_38
<=> ! [X2,X14] : c_fequal(X14,X14,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f650,axiom,
! [X2,X14] : c_fequal(X14,X14,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1026,plain,
spl0_37,
inference(avatar_split_clause,[],[f408,f1024]) ).
fof(f1024,plain,
( spl0_37
<=> ! [X7,X10] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X10),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f408,axiom,
! [X10,X7] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X10),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f1022,plain,
spl0_36,
inference(avatar_split_clause,[],[f287,f1020]) ).
fof(f1020,plain,
( spl0_36
<=> ! [X14] : c_Ring__and__Field_Odvd__class_Odvd(X14,X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f287,axiom,
! [X14] : c_Ring__and__Field_Odvd__class_Odvd(X14,X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
fof(f1018,plain,
spl0_35,
inference(avatar_split_clause,[],[f260,f1016]) ).
fof(f1016,plain,
( spl0_35
<=> ! [X14] : ~ c_HOL_Oord__class_Oless(X14,X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f260,axiom,
! [X14] : ~ c_HOL_Oord__class_Oless(X14,X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1014,plain,
( spl0_34
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1009,f1005,f1011]) ).
fof(f1011,plain,
( spl0_34
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_ra,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1005,plain,
( spl0_33
<=> hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1009,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_ra,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1007,f567]) ).
fof(f1007,plain,
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f1008,plain,
spl0_33,
inference(avatar_split_clause,[],[f611,f1005]) ).
fof(f611,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1003,plain,
spl0_32,
inference(avatar_split_clause,[],[f614,f1001]) ).
fof(f614,axiom,
! [X10,X9] : hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(X10)),X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f999,plain,
spl0_31,
inference(avatar_split_clause,[],[f647,f996]) ).
fof(f996,plain,
( spl0_31
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f647,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f994,plain,
spl0_30,
inference(avatar_split_clause,[],[f646,f991]) ).
fof(f991,plain,
( spl0_30
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f646,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f989,plain,
spl0_29,
inference(avatar_split_clause,[],[f645,f986]) ).
fof(f986,plain,
( spl0_29
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f645,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f984,plain,
spl0_28,
inference(avatar_split_clause,[],[f644,f981]) ).
fof(f981,plain,
( spl0_28
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f644,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f979,plain,
spl0_27,
inference(avatar_split_clause,[],[f643,f976]) ).
fof(f643,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f974,plain,
spl0_26,
inference(avatar_split_clause,[],[f642,f971]) ).
fof(f971,plain,
( spl0_26
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f642,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f969,plain,
spl0_25,
inference(avatar_split_clause,[],[f641,f966]) ).
fof(f641,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f964,plain,
spl0_24,
inference(avatar_split_clause,[],[f640,f961]) ).
fof(f961,plain,
( spl0_24
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f640,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f959,plain,
spl0_23,
inference(avatar_split_clause,[],[f639,f956]) ).
fof(f956,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f639,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f954,plain,
spl0_22,
inference(avatar_split_clause,[],[f638,f951]) ).
fof(f951,plain,
( spl0_22
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f638,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f949,plain,
spl0_21,
inference(avatar_split_clause,[],[f637,f946]) ).
fof(f946,plain,
( spl0_21
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f637,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f944,plain,
spl0_20,
inference(avatar_split_clause,[],[f636,f941]) ).
fof(f941,plain,
( spl0_20
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f636,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f939,plain,
spl0_19,
inference(avatar_split_clause,[],[f635,f936]) ).
fof(f635,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f934,plain,
spl0_18,
inference(avatar_split_clause,[],[f634,f931]) ).
fof(f931,plain,
( spl0_18
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f634,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(f929,plain,
spl0_17,
inference(avatar_split_clause,[],[f633,f926]) ).
fof(f926,plain,
( spl0_17
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f633,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f924,plain,
spl0_16,
inference(avatar_split_clause,[],[f632,f921]) ).
fof(f921,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f632,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f919,plain,
spl0_15,
inference(avatar_split_clause,[],[f631,f916]) ).
fof(f916,plain,
( spl0_15
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f631,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f914,plain,
spl0_14,
inference(avatar_split_clause,[],[f630,f911]) ).
fof(f911,plain,
( spl0_14
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f630,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f909,plain,
spl0_13,
inference(avatar_split_clause,[],[f629,f906]) ).
fof(f906,plain,
( spl0_13
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f629,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f904,plain,
spl0_12,
inference(avatar_split_clause,[],[f628,f901]) ).
fof(f901,plain,
( spl0_12
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f628,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f899,plain,
spl0_11,
inference(avatar_split_clause,[],[f627,f896]) ).
fof(f627,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f894,plain,
spl0_10,
inference(avatar_split_clause,[],[f626,f891]) ).
fof(f891,plain,
( spl0_10
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f626,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f889,plain,
spl0_9,
inference(avatar_split_clause,[],[f625,f886]) ).
fof(f886,plain,
( spl0_9
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f625,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f884,plain,
spl0_8,
inference(avatar_split_clause,[],[f624,f881]) ).
fof(f881,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f624,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f879,plain,
spl0_7,
inference(avatar_split_clause,[],[f623,f876]) ).
fof(f876,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f623,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f874,plain,
spl0_6,
inference(avatar_split_clause,[],[f622,f871]) ).
fof(f871,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f622,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f869,plain,
spl0_5,
inference(avatar_split_clause,[],[f621,f866]) ).
fof(f866,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f621,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f864,plain,
spl0_4,
inference(avatar_split_clause,[],[f620,f861]) ).
fof(f861,plain,
( spl0_4
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f620,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f859,plain,
spl0_3,
inference(avatar_split_clause,[],[f619,f856]) ).
fof(f856,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f619,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f854,plain,
spl0_2,
inference(avatar_split_clause,[],[f618,f851]) ).
fof(f851,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f618,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f849,plain,
spl0_1,
inference(avatar_split_clause,[],[f613,f846]) ).
fof(f846,plain,
( spl0_1
<=> hBOOL(hAPP(c_InductTermi_OIT,v_s)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f613,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL760-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 13:09:31 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (19208)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.41 % (19211)WARNING: value z3 for option sas not known
% 0.22/0.41 % (19209)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.41 % (19211)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.41 % (19210)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.41 % (19212)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.41 % (19213)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.41 % (19214)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.41 % (19215)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.49 % (19213)First to succeed.
% 0.22/0.50 % (19213)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19208"
% 0.22/0.50 % (19213)Refutation found. Thanks to Tanya!
% 0.22/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.51 % (19213)------------------------------
% 0.22/0.51 % (19213)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.51 % (19213)Termination reason: Refutation
% 0.22/0.51
% 0.22/0.51 % (19213)Memory used [KB]: 2376
% 0.22/0.51 % (19213)Time elapsed: 0.091 s
% 0.22/0.51 % (19213)Instructions burned: 142 (million)
% 0.22/0.51 % (19208)Success in time 0.142 s
%------------------------------------------------------------------------------