TSTP Solution File: SWV690-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV690-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:10:17 EDT 2024
% Result : Unsatisfiable 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 378
% Syntax : Number of formulae : 605 ( 264 unt; 0 def)
% Number of atoms : 1133 ( 146 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 883 ( 355 ~; 333 |; 0 &)
% ( 195 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 231 ( 229 usr; 196 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 622 ( 622 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2531,plain,
$false,
inference(avatar_sat_refutation,[],[f816,f821,f826,f831,f836,f841,f846,f851,f856,f861,f866,f871,f876,f881,f886,f891,f896,f901,f906,f911,f916,f921,f926,f931,f936,f941,f946,f951,f956,f961,f966,f971,f975,f979,f984,f988,f992,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1033,f1037,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1097,f1101,f1105,f1109,f1113,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1171,f1175,f1179,f1183,f1217,f1221,f1225,f1229,f1234,f1238,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1270,f1274,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1319,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1407,f1501,f1570,f1590,f1594,f1598,f1602,f1606,f1610,f1614,f1618,f1625,f1629,f1633,f1637,f1641,f1645,f1649,f1653,f1657,f1661,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1704,f1826,f1967,f1971,f1975,f1979,f1983,f1987,f1992,f1996,f2000,f2004,f2008,f2012,f2016,f2020,f2024,f2028,f2032,f2037,f2041,f2045,f2049,f2053,f2057,f2061,f2065,f2069,f2073,f2078,f2082,f2308,f2485,f2489,f2493,f2497,f2501,f2505,f2509,f2513,f2517,f2521,f2525,f2529,f2530]) ).
fof(f2530,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2410,f2071,f818,f813]) ).
fof(f813,plain,
( spl0_1
<=> c_HOL_Oord__class_Oless(v_k,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f818,plain,
( spl0_2
<=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_k,v_i,tc_nat),v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2071,plain,
( spl0_179
<=> ! [X9,X7,X4] :
( ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f2410,plain,
( ~ c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| spl0_2
| ~ spl0_179 ),
inference(resolution,[],[f2072,f820]) ).
fof(f820,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_k,v_i,tc_nat),v_n,tc_nat)
| spl0_2 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f2072,plain,
( ! [X9,X7,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f2071]) ).
fof(f2529,plain,
spl0_195,
inference(avatar_split_clause,[],[f391,f2527]) ).
fof(f2527,plain,
( spl0_195
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X6,X0)
| c_Orderings_Oord__class_Omin(X5,X6,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f391,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X6,X0)
| c_Orderings_Oord__class_Omin(X5,X6,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2525,plain,
spl0_194,
inference(avatar_split_clause,[],[f390,f2523]) ).
fof(f2523,plain,
( spl0_194
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f390,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f2521,plain,
spl0_193,
inference(avatar_split_clause,[],[f339,f2519]) ).
fof(f2519,plain,
( spl0_193
<=> ! [X4,X3] : c_Orderings_Oord__class_Omin(c_Suc(X3),c_Suc(X4),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X3,X4,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f339,axiom,
! [X3,X4] : c_Orderings_Oord__class_Omin(c_Suc(X3),c_Suc(X4),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X3,X4,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
fof(f2517,plain,
spl0_192,
inference(avatar_split_clause,[],[f262,f2515]) ).
fof(f2515,plain,
( spl0_192
<=> ! [X6,X5,X15] :
( X6 = X15
| c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f262,axiom,
! [X6,X15,X5] :
( X6 = X15
| c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
fof(f2513,plain,
spl0_191,
inference(avatar_split_clause,[],[f260,f2511]) ).
fof(f2511,plain,
( spl0_191
<=> ! [X4,X9,X3] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X3,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f260,axiom,
! [X3,X9,X4] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X3,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f2509,plain,
spl0_190,
inference(avatar_split_clause,[],[f248,f2507]) ).
fof(f2507,plain,
( spl0_190
<=> ! [X4,X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f248,axiom,
! [X3,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__add_2) ).
fof(f2505,plain,
spl0_189,
inference(avatar_split_clause,[],[f246,f2503]) ).
fof(f2503,plain,
( spl0_189
<=> ! [X4,X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f246,axiom,
! [X3,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_0) ).
fof(f2501,plain,
spl0_188,
inference(avatar_split_clause,[],[f244,f2499]) ).
fof(f2499,plain,
( spl0_188
<=> ! [X4,X3] :
( c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f244,axiom,
! [X3,X4] :
( c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_2) ).
fof(f2497,plain,
spl0_187,
inference(avatar_split_clause,[],[f243,f2495]) ).
fof(f2495,plain,
( spl0_187
<=> ! [X4,X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f243,axiom,
! [X3,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_3) ).
fof(f2493,plain,
spl0_186,
inference(avatar_split_clause,[],[f98,f2491]) ).
fof(f2491,plain,
( spl0_186
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f98,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
fof(f2489,plain,
spl0_185,
inference(avatar_split_clause,[],[f97,f2487]) ).
fof(f2487,plain,
( spl0_185
<=> ! [X4,X0,X3] :
( ~ class_Nat_Osemiring__char__0(X0)
| X3 = X4
| c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f97,axiom,
! [X3,X0,X4] :
( ~ class_Nat_Osemiring__char__0(X0)
| X3 = X4
| c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f2485,plain,
spl0_184,
inference(avatar_split_clause,[],[f32,f2483]) ).
fof(f2483,plain,
( spl0_184
<=> ! [X6,X5,X15] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f32,axiom,
! [X6,X15,X5] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X15,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X5,X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
fof(f2308,plain,
( spl0_182
| ~ spl0_183
| ~ spl0_86
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2113,f1969,f1231,f2305,f2301]) ).
fof(f2301,plain,
( spl0_182
<=> v_n = v_k ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2305,plain,
( spl0_183
<=> c_lessequals(v_n,v_k,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1231,plain,
( spl0_86
<=> c_lessequals(v_k,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1969,plain,
( spl0_154
<=> ! [X4,X3] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2113,plain,
( ~ c_lessequals(v_n,v_k,tc_nat)
| v_n = v_k
| ~ spl0_86
| ~ spl0_154 ),
inference(resolution,[],[f1970,f1233]) ).
fof(f1233,plain,
( c_lessequals(v_k,v_n,tc_nat)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1231]) ).
fof(f1970,plain,
( ! [X3,X4] :
( ~ c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat)
| X3 = X4 )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1969]) ).
fof(f2082,plain,
spl0_181,
inference(avatar_split_clause,[],[f758,f2080]) ).
fof(f2080,plain,
( spl0_181
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f758,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f2078,plain,
( ~ spl0_31
| spl0_180
| spl0_2
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1790,f1627,f818,f2075,f963]) ).
fof(f963,plain,
( spl0_31
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2075,plain,
( spl0_180
<=> c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_k,v_i,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1627,plain,
( spl0_134
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1790,plain,
( c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_k,v_i,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| spl0_2
| ~ spl0_134 ),
inference(resolution,[],[f1628,f820]) ).
fof(f1628,plain,
( ! [X0,X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X6,X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1627]) ).
fof(f2073,plain,
spl0_179,
inference(avatar_split_clause,[],[f750,f2071]) ).
fof(f750,axiom,
! [X9,X7,X4] :
( ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f2069,plain,
spl0_178,
inference(avatar_split_clause,[],[f697,f2067]) ).
fof(f2067,plain,
( spl0_178
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f697,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f2065,plain,
spl0_177,
inference(avatar_split_clause,[],[f687,f2063]) ).
fof(f2063,plain,
( spl0_177
<=> ! [X9,X8,X7] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f687,axiom,
! [X8,X9,X7] :
( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f2061,plain,
spl0_176,
inference(avatar_split_clause,[],[f686,f2059]) ).
fof(f2059,plain,
( spl0_176
<=> ! [X6,X5,X15] :
( ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f686,axiom,
! [X6,X15,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
fof(f2057,plain,
spl0_175,
inference(avatar_split_clause,[],[f685,f2055]) ).
fof(f2055,plain,
( spl0_175
<=> ! [X6,X5,X15] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f685,axiom,
! [X6,X15,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f2053,plain,
spl0_174,
inference(avatar_split_clause,[],[f674,f2051]) ).
fof(f2051,plain,
( spl0_174
<=> ! [X4,X3] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f674,axiom,
! [X3,X4] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
fof(f2049,plain,
spl0_173,
inference(avatar_split_clause,[],[f588,f2047]) ).
fof(f2047,plain,
( spl0_173
<=> ! [X4,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f588,axiom,
! [X9,X4] :
( c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).
fof(f2045,plain,
spl0_172,
inference(avatar_split_clause,[],[f587,f2043]) ).
fof(f2043,plain,
( spl0_172
<=> ! [X4,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f587,axiom,
! [X9,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).
fof(f2041,plain,
spl0_171,
inference(avatar_split_clause,[],[f431,f2039]) ).
fof(f2039,plain,
( spl0_171
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f431,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2037,plain,
spl0_170,
inference(avatar_split_clause,[],[f428,f2035]) ).
fof(f2035,plain,
( spl0_170
<=> ! [X0,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X14,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f428,axiom,
! [X0,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X14,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2032,plain,
spl0_169,
inference(avatar_split_clause,[],[f420,f2030]) ).
fof(f2030,plain,
( spl0_169
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f420,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f2028,plain,
spl0_168,
inference(avatar_split_clause,[],[f419,f2026]) ).
fof(f2026,plain,
( spl0_168
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f419,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
fof(f2024,plain,
spl0_167,
inference(avatar_split_clause,[],[f411,f2022]) ).
fof(f2022,plain,
( spl0_167
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f411,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f2020,plain,
spl0_166,
inference(avatar_split_clause,[],[f410,f2018]) ).
fof(f2018,plain,
( spl0_166
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f410,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f2016,plain,
spl0_165,
inference(avatar_split_clause,[],[f380,f2014]) ).
fof(f2014,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f380,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f2012,plain,
spl0_164,
inference(avatar_split_clause,[],[f337,f2010]) ).
fof(f2010,plain,
( spl0_164
<=> ! [X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f337,axiom,
! [X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).
fof(f2008,plain,
spl0_163,
inference(avatar_split_clause,[],[f307,f2006]) ).
fof(f2006,plain,
( spl0_163
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X6,X0) = c_Orderings_Oord__class_Omin(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f307,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X6,X0) = c_Orderings_Oord__class_Omin(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f2004,plain,
spl0_162,
inference(avatar_split_clause,[],[f284,f2002]) ).
fof(f2002,plain,
( spl0_162
<=> ! [X3,X7,X8] :
( ~ c_lessequals(X8,X7,tc_nat)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X3,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f284,axiom,
! [X3,X8,X7] :
( ~ c_lessequals(X8,X7,tc_nat)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X3,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
fof(f2000,plain,
spl0_161,
inference(avatar_split_clause,[],[f283,f1998]) ).
fof(f1998,plain,
( spl0_161
<=> ! [X3,X7,X8] :
( ~ c_lessequals(X8,X7,tc_nat)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f283,axiom,
! [X3,X8,X7] :
( ~ c_lessequals(X8,X7,tc_nat)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
fof(f1996,plain,
spl0_160,
inference(avatar_split_clause,[],[f282,f1994]) ).
fof(f1994,plain,
( spl0_160
<=> ! [X4,X9,X3] :
( c_lessequals(X9,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f282,axiom,
! [X3,X9,X4] :
( c_lessequals(X9,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f1992,plain,
( spl0_159
| ~ spl0_1
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1873,f1669,f813,f1989]) ).
fof(f1989,plain,
( spl0_159
<=> v_k = c_Divides_Odiv__class_Omod(v_k,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1669,plain,
( spl0_144
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1873,plain,
( v_k = c_Divides_Odiv__class_Omod(v_k,v_n,tc_nat)
| ~ spl0_1
| ~ spl0_144 ),
inference(resolution,[],[f1670,f815]) ).
fof(f815,plain,
( c_HOL_Oord__class_Oless(v_k,v_n,tc_nat)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f1670,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f1987,plain,
spl0_158,
inference(avatar_split_clause,[],[f281,f1985]) ).
fof(f1985,plain,
( spl0_158
<=> ! [X4,X9,X3] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f281,axiom,
! [X3,X9,X4] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f1983,plain,
spl0_157,
inference(avatar_split_clause,[],[f158,f1981]) ).
fof(f1981,plain,
( spl0_157
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f158,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f1979,plain,
spl0_156,
inference(avatar_split_clause,[],[f85,f1977]) ).
fof(f1977,plain,
( spl0_156
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f85,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1975,plain,
spl0_155,
inference(avatar_split_clause,[],[f84,f1973]) ).
fof(f1973,plain,
( spl0_155
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f84,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1971,plain,
spl0_154,
inference(avatar_split_clause,[],[f28,f1969]) ).
fof(f28,axiom,
! [X3,X4] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1967,plain,
spl0_153,
inference(avatar_split_clause,[],[f27,f1965]) ).
fof(f1965,plain,
( spl0_153
<=> ! [X6,X5] :
( X5 = X6
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f27,axiom,
! [X6,X5] :
( X5 = X6
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
fof(f1826,plain,
( ~ spl0_152
| ~ spl0_30
| ~ spl0_86
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1777,f1623,f1231,f958,f1823]) ).
fof(f1823,plain,
( spl0_152
<=> c_HOL_Oord__class_Oless(v_n,v_k,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f958,plain,
( spl0_30
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1623,plain,
( spl0_133
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1777,plain,
( ~ class_Orderings_Opreorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(v_n,v_k,tc_nat)
| ~ spl0_86
| ~ spl0_133 ),
inference(resolution,[],[f1624,f1233]) ).
fof(f1624,plain,
( ! [X0,X6,X5] :
( ~ c_lessequals(X6,X5,X0)
| ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1623]) ).
fof(f1704,plain,
( spl0_151
| ~ spl0_94
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1455,f1405,f1264,f1702]) ).
fof(f1702,plain,
( spl0_151
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1264,plain,
( spl0_94
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1405,plain,
( spl0_122
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1455,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_94
| ~ spl0_122 ),
inference(resolution,[],[f1406,f1265]) ).
fof(f1265,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_Suc(X4),X3,tc_nat)
| ~ c_lessequals(X3,X4,tc_nat) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f1406,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1405]) ).
fof(f1695,plain,
spl0_150,
inference(avatar_split_clause,[],[f744,f1693]) ).
fof(f1693,plain,
( spl0_150
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f744,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1691,plain,
spl0_149,
inference(avatar_split_clause,[],[f742,f1689]) ).
fof(f1689,plain,
( spl0_149
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f742,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1687,plain,
spl0_148,
inference(avatar_split_clause,[],[f741,f1685]) ).
fof(f1685,plain,
( spl0_148
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f741,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1683,plain,
spl0_147,
inference(avatar_split_clause,[],[f740,f1681]) ).
fof(f1681,plain,
( spl0_147
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f740,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_2) ).
fof(f1679,plain,
spl0_146,
inference(avatar_split_clause,[],[f692,f1677]) ).
fof(f1677,plain,
( spl0_146
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f692,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f1675,plain,
spl0_145,
inference(avatar_split_clause,[],[f691,f1673]) ).
fof(f1673,plain,
( spl0_145
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f691,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
fof(f1671,plain,
spl0_144,
inference(avatar_split_clause,[],[f684,f1669]) ).
fof(f684,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f1667,plain,
spl0_143,
inference(avatar_split_clause,[],[f664,f1665]) ).
fof(f1665,plain,
( spl0_143
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f664,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1661,plain,
spl0_142,
inference(avatar_split_clause,[],[f662,f1659]) ).
fof(f1659,plain,
( spl0_142
<=> ! [X4,X3] :
( c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f662,axiom,
! [X3,X4] :
( c_lessequals(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f1657,plain,
spl0_141,
inference(avatar_split_clause,[],[f661,f1655]) ).
fof(f1655,plain,
( spl0_141
<=> ! [X4,X3] :
( ~ c_lessequals(X4,X3,tc_nat)
| c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f661,axiom,
! [X3,X4] :
( ~ c_lessequals(X4,X3,tc_nat)
| c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f1653,plain,
spl0_140,
inference(avatar_split_clause,[],[f648,f1651]) ).
fof(f1651,plain,
( spl0_140
<=> ! [X5,X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X5,tc_nat),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f648,axiom,
! [X19,X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X5,tc_nat),X19,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
fof(f1649,plain,
spl0_139,
inference(avatar_split_clause,[],[f581,f1647]) ).
fof(f1647,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f581,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1645,plain,
spl0_138,
inference(avatar_split_clause,[],[f580,f1643]) ).
fof(f1643,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f580,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1641,plain,
spl0_137,
inference(avatar_split_clause,[],[f579,f1639]) ).
fof(f1639,plain,
( spl0_137
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f579,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f1637,plain,
spl0_136,
inference(avatar_split_clause,[],[f572,f1635]) ).
fof(f1635,plain,
( spl0_136
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f572,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1633,plain,
spl0_135,
inference(avatar_split_clause,[],[f518,f1631]) ).
fof(f1631,plain,
( spl0_135
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f518,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1629,plain,
spl0_134,
inference(avatar_split_clause,[],[f512,f1627]) ).
fof(f512,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1625,plain,
spl0_133,
inference(avatar_split_clause,[],[f511,f1623]) ).
fof(f511,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1618,plain,
spl0_132,
inference(avatar_split_clause,[],[f495,f1616]) ).
fof(f1616,plain,
( spl0_132
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f495,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1614,plain,
spl0_131,
inference(avatar_split_clause,[],[f494,f1612]) ).
fof(f1612,plain,
( spl0_131
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f494,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1610,plain,
spl0_130,
inference(avatar_split_clause,[],[f289,f1608]) ).
fof(f1608,plain,
( spl0_130
<=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f289,axiom,
! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f1606,plain,
spl0_129,
inference(avatar_split_clause,[],[f285,f1604]) ).
fof(f1604,plain,
( spl0_129
<=> ! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f285,axiom,
! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def2_1) ).
fof(f1602,plain,
spl0_128,
inference(avatar_split_clause,[],[f236,f1600]) ).
fof(f1600,plain,
( spl0_128
<=> ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f236,axiom,
! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).
fof(f1598,plain,
spl0_127,
inference(avatar_split_clause,[],[f150,f1596]) ).
fof(f1596,plain,
( spl0_127
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f150,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1594,plain,
spl0_126,
inference(avatar_split_clause,[],[f145,f1592]) ).
fof(f1592,plain,
( spl0_126
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f145,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1590,plain,
spl0_125,
inference(avatar_split_clause,[],[f95,f1588]) ).
fof(f1588,plain,
( spl0_125
<=> ! [X5,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f95,axiom,
! [X1,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
fof(f1570,plain,
( spl0_124
| ~ spl0_37
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1557,f1365,f990,f1568]) ).
fof(f1568,plain,
( spl0_124
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f990,plain,
( spl0_37
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1365,plain,
( spl0_119
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1557,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_37
| ~ spl0_119 ),
inference(resolution,[],[f1366,f991]) ).
fof(f991,plain,
( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f990]) ).
fof(f1366,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f1501,plain,
( spl0_123
| ~ spl0_31
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f1184,f1128,f963,f1499]) ).
fof(f1499,plain,
( spl0_123
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1128,plain,
( spl0_68
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1184,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_31
| ~ spl0_68 ),
inference(resolution,[],[f1129,f965]) ).
fof(f965,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f963]) ).
fof(f1129,plain,
( ! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f1407,plain,
( spl0_122
| ~ spl0_44
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1199,f1156,f1019,f1405]) ).
fof(f1019,plain,
( spl0_44
<=> ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1156,plain,
( spl0_75
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1199,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_44
| ~ spl0_75 ),
inference(resolution,[],[f1157,f1020]) ).
fof(f1020,plain,
( ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1157,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f1375,plain,
spl0_121,
inference(avatar_split_clause,[],[f721,f1373]) ).
fof(f1373,plain,
( spl0_121
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f721,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f1371,plain,
spl0_120,
inference(avatar_split_clause,[],[f720,f1369]) ).
fof(f1369,plain,
( spl0_120
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f720,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1367,plain,
spl0_119,
inference(avatar_split_clause,[],[f678,f1365]) ).
fof(f678,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1363,plain,
spl0_118,
inference(avatar_split_clause,[],[f677,f1361]) ).
fof(f1361,plain,
( spl0_118
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f677,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1359,plain,
spl0_117,
inference(avatar_split_clause,[],[f672,f1357]) ).
fof(f1357,plain,
( spl0_117
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f672,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1355,plain,
spl0_116,
inference(avatar_split_clause,[],[f671,f1353]) ).
fof(f1353,plain,
( spl0_116
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f671,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1351,plain,
spl0_115,
inference(avatar_split_clause,[],[f621,f1349]) ).
fof(f1349,plain,
( spl0_115
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f621,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1347,plain,
spl0_114,
inference(avatar_split_clause,[],[f620,f1345]) ).
fof(f1345,plain,
( spl0_114
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_lessequals(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f620,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_lessequals(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1343,plain,
spl0_113,
inference(avatar_split_clause,[],[f585,f1341]) ).
fof(f1341,plain,
( spl0_113
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f585,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1339,plain,
spl0_112,
inference(avatar_split_clause,[],[f561,f1337]) ).
fof(f1337,plain,
( spl0_112
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f561,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1335,plain,
spl0_111,
inference(avatar_split_clause,[],[f479,f1333]) ).
fof(f1333,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f479,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1331,plain,
spl0_110,
inference(avatar_split_clause,[],[f478,f1329]) ).
fof(f1329,plain,
( spl0_110
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f478,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1327,plain,
spl0_109,
inference(avatar_split_clause,[],[f474,f1325]) ).
fof(f1325,plain,
( spl0_109
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f474,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1323,plain,
spl0_108,
inference(avatar_split_clause,[],[f471,f1321]) ).
fof(f1321,plain,
( spl0_108
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f471,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1319,plain,
( spl0_107
| ~ spl0_38
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1197,f1156,f994,f1316]) ).
fof(f1316,plain,
( spl0_107
<=> c_lessequals(v_i,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f994,plain,
( spl0_38
<=> c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1197,plain,
( c_lessequals(v_i,v_n,tc_nat)
| ~ spl0_38
| ~ spl0_75 ),
inference(resolution,[],[f1157,f996]) ).
fof(f996,plain,
( c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f994]) ).
fof(f1314,plain,
spl0_106,
inference(avatar_split_clause,[],[f470,f1312]) ).
fof(f1312,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f470,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1310,plain,
spl0_105,
inference(avatar_split_clause,[],[f469,f1308]) ).
fof(f1308,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f469,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1306,plain,
spl0_104,
inference(avatar_split_clause,[],[f429,f1304]) ).
fof(f1304,plain,
( spl0_104
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f429,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f1302,plain,
spl0_103,
inference(avatar_split_clause,[],[f427,f1300]) ).
fof(f1300,plain,
( spl0_103
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f427,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1298,plain,
spl0_102,
inference(avatar_split_clause,[],[f426,f1296]) ).
fof(f1296,plain,
( spl0_102
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f426,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1294,plain,
spl0_101,
inference(avatar_split_clause,[],[f425,f1292]) ).
fof(f1292,plain,
( spl0_101
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f425,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
fof(f1290,plain,
spl0_100,
inference(avatar_split_clause,[],[f424,f1288]) ).
fof(f1288,plain,
( spl0_100
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f424,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
fof(f1286,plain,
spl0_99,
inference(avatar_split_clause,[],[f399,f1284]) ).
fof(f1284,plain,
( spl0_99
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f399,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1282,plain,
spl0_98,
inference(avatar_split_clause,[],[f398,f1280]) ).
fof(f1280,plain,
( spl0_98
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f398,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1278,plain,
spl0_97,
inference(avatar_split_clause,[],[f381,f1276]) ).
fof(f1276,plain,
( spl0_97
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f381,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1274,plain,
spl0_96,
inference(avatar_split_clause,[],[f367,f1272]) ).
fof(f1272,plain,
( spl0_96
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f367,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
fof(f1270,plain,
spl0_95,
inference(avatar_split_clause,[],[f333,f1268]) ).
fof(f1268,plain,
( spl0_95
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f333,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1266,plain,
spl0_94,
inference(avatar_split_clause,[],[f319,f1264]) ).
fof(f319,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1262,plain,
spl0_93,
inference(avatar_split_clause,[],[f318,f1260]) ).
fof(f1260,plain,
( spl0_93
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f318,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1258,plain,
spl0_92,
inference(avatar_split_clause,[],[f161,f1256]) ).
fof(f1256,plain,
( spl0_92
<=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f161,axiom,
! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1254,plain,
spl0_91,
inference(avatar_split_clause,[],[f141,f1252]) ).
fof(f1252,plain,
( spl0_91
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f141,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f1250,plain,
spl0_90,
inference(avatar_split_clause,[],[f140,f1248]) ).
fof(f1248,plain,
( spl0_90
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f140,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f1246,plain,
spl0_89,
inference(avatar_split_clause,[],[f139,f1244]) ).
fof(f1244,plain,
( spl0_89
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f1242,plain,
spl0_88,
inference(avatar_split_clause,[],[f137,f1240]) ).
fof(f1240,plain,
( spl0_88
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f137,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1238,plain,
spl0_87,
inference(avatar_split_clause,[],[f136,f1236]) ).
fof(f1236,plain,
( spl0_87
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f136,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1234,plain,
( spl0_86
| ~ spl0_1
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1198,f1156,f813,f1231]) ).
fof(f1198,plain,
( c_lessequals(v_k,v_n,tc_nat)
| ~ spl0_1
| ~ spl0_75 ),
inference(resolution,[],[f1157,f815]) ).
fof(f1229,plain,
spl0_85,
inference(avatar_split_clause,[],[f114,f1227]) ).
fof(f1227,plain,
( spl0_85
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f114,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
fof(f1225,plain,
spl0_84,
inference(avatar_split_clause,[],[f111,f1223]) ).
fof(f1223,plain,
( spl0_84
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_lessequals(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f111,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_lessequals(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
fof(f1221,plain,
spl0_83,
inference(avatar_split_clause,[],[f80,f1219]) ).
fof(f1219,plain,
( spl0_83
<=> ! [X17] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f80,axiom,
! [X17] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def2_1) ).
fof(f1217,plain,
spl0_82,
inference(avatar_split_clause,[],[f19,f1215]) ).
fof(f1215,plain,
( spl0_82
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f19,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1183,plain,
spl0_81,
inference(avatar_split_clause,[],[f735,f1181]) ).
fof(f1181,plain,
( spl0_81
<=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f735,axiom,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1179,plain,
spl0_80,
inference(avatar_split_clause,[],[f713,f1177]) ).
fof(f1177,plain,
( spl0_80
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f713,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1175,plain,
spl0_79,
inference(avatar_split_clause,[],[f667,f1173]) ).
fof(f1173,plain,
( spl0_79
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f667,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_nat)
| c_lessequals(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1171,plain,
( spl0_78
| ~ spl0_64
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1125,f1111,f1099,f1168]) ).
fof(f1168,plain,
( spl0_78
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1099,plain,
( spl0_64
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1111,plain,
( spl0_67
<=> ! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,X9,tc_nat),v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1125,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat)
| ~ spl0_64
| ~ spl0_67 ),
inference(superposition,[],[f1112,f1100]) ).
fof(f1100,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1112,plain,
( ! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,X9,tc_nat),v_n,tc_nat)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1166,plain,
spl0_77,
inference(avatar_split_clause,[],[f576,f1164]) ).
fof(f1164,plain,
( spl0_77
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f576,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f1162,plain,
spl0_76,
inference(avatar_split_clause,[],[f575,f1160]) ).
fof(f1160,plain,
( spl0_76
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f575,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f1158,plain,
spl0_75,
inference(avatar_split_clause,[],[f562,f1156]) ).
fof(f562,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
fof(f1154,plain,
spl0_74,
inference(avatar_split_clause,[],[f444,f1152]) ).
fof(f1152,plain,
( spl0_74
<=> ! [X29,X20] :
( X20 = X29
| c_Suc(X20) != c_Suc(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f444,axiom,
! [X29,X20] :
( X20 = X29
| c_Suc(X20) != c_Suc(X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f1150,plain,
spl0_73,
inference(avatar_split_clause,[],[f320,f1148]) ).
fof(f1148,plain,
( spl0_73
<=> ! [X4] :
( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f320,axiom,
! [X4] :
( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__pos_0) ).
fof(f1146,plain,
spl0_72,
inference(avatar_split_clause,[],[f121,f1144]) ).
fof(f1144,plain,
( spl0_72
<=> ! [X5,X3] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f121,axiom,
! [X3,X5] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f1142,plain,
spl0_71,
inference(avatar_split_clause,[],[f120,f1140]) ).
fof(f1140,plain,
( spl0_71
<=> ! [X8,X3] : c_HOL_Oord__class_Oless(X8,c_Suc(c_HOL_Oplus__class_Oplus(X3,X8,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f120,axiom,
! [X3,X8] : c_HOL_Oord__class_Oless(X8,c_Suc(c_HOL_Oplus__class_Oplus(X3,X8,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1138,plain,
spl0_70,
inference(avatar_split_clause,[],[f88,f1136]) ).
fof(f1136,plain,
( spl0_70
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f88,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0R_0) ).
fof(f1134,plain,
spl0_69,
inference(avatar_split_clause,[],[f87,f1132]) ).
fof(f1132,plain,
( spl0_69
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f87,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0L_0) ).
fof(f1130,plain,
spl0_68,
inference(avatar_split_clause,[],[f17,f1128]) ).
fof(f17,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1113,plain,
spl0_67,
inference(avatar_split_clause,[],[f761,f1111]) ).
fof(f761,axiom,
! [X9] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,X9,tc_nat),v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_i__diff_0) ).
fof(f1109,plain,
spl0_66,
inference(avatar_split_clause,[],[f716,f1107]) ).
fof(f1107,plain,
( spl0_66
<=> ! [X4,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f716,axiom,
! [X3,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1105,plain,
spl0_65,
inference(avatar_split_clause,[],[f706,f1103]) ).
fof(f1103,plain,
( spl0_65
<=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f706,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1101,plain,
spl0_64,
inference(avatar_split_clause,[],[f705,f1099]) ).
fof(f705,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1097,plain,
spl0_63,
inference(avatar_split_clause,[],[f598,f1095]) ).
fof(f1095,plain,
( spl0_63
<=> ! [X4,X3] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f598,axiom,
! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f1093,plain,
spl0_62,
inference(avatar_split_clause,[],[f597,f1091]) ).
fof(f1091,plain,
( spl0_62
<=> ! [X5,X3] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X3,X5,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f597,axiom,
! [X3,X5] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X3,X5,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
fof(f1089,plain,
spl0_61,
inference(avatar_split_clause,[],[f569,f1087]) ).
fof(f1087,plain,
( spl0_61
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f569,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1085,plain,
spl0_60,
inference(avatar_split_clause,[],[f559,f1083]) ).
fof(f1083,plain,
( spl0_60
<=> ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f559,axiom,
! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1081,plain,
spl0_59,
inference(avatar_split_clause,[],[f558,f1079]) ).
fof(f1079,plain,
( spl0_59
<=> ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f558,axiom,
! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X8,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1077,plain,
spl0_58,
inference(avatar_split_clause,[],[f477,f1075]) ).
fof(f1075,plain,
( spl0_58
<=> ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f477,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f1073,plain,
spl0_57,
inference(avatar_split_clause,[],[f476,f1071]) ).
fof(f1071,plain,
( spl0_57
<=> ! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f476,axiom,
! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f1069,plain,
spl0_56,
inference(avatar_split_clause,[],[f338,f1067]) ).
fof(f1067,plain,
( spl0_56
<=> ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f338,axiom,
! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).
fof(f1065,plain,
spl0_55,
inference(avatar_split_clause,[],[f336,f1063]) ).
fof(f1063,plain,
( spl0_55
<=> ! [X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f336,axiom,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_1) ).
fof(f1061,plain,
spl0_54,
inference(avatar_split_clause,[],[f335,f1059]) ).
fof(f1059,plain,
( spl0_54
<=> ! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f335,axiom,
! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_0) ).
fof(f1057,plain,
spl0_53,
inference(avatar_split_clause,[],[f321,f1055]) ).
fof(f1055,plain,
( spl0_53
<=> ! [X4,X3] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f321,axiom,
! [X3,X4] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
fof(f1053,plain,
spl0_52,
inference(avatar_split_clause,[],[f749,f1051]) ).
fof(f1051,plain,
( spl0_52
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f749,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1049,plain,
spl0_51,
inference(avatar_split_clause,[],[f746,f1047]) ).
fof(f1047,plain,
( spl0_51
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f746,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1045,plain,
spl0_50,
inference(avatar_split_clause,[],[f745,f1043]) ).
fof(f1043,plain,
( spl0_50
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f745,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1041,plain,
spl0_49,
inference(avatar_split_clause,[],[f638,f1039]) ).
fof(f1039,plain,
( spl0_49
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f638,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1037,plain,
spl0_48,
inference(avatar_split_clause,[],[f637,f1035]) ).
fof(f1035,plain,
( spl0_48
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f637,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1033,plain,
spl0_47,
inference(avatar_split_clause,[],[f305,f1031]) ).
fof(f1031,plain,
( spl0_47
<=> ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f305,axiom,
! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f1029,plain,
spl0_46,
inference(avatar_split_clause,[],[f277,f1027]) ).
fof(f1027,plain,
( spl0_46
<=> ! [X9] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f277,axiom,
! [X9] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).
fof(f1025,plain,
spl0_45,
inference(avatar_split_clause,[],[f36,f1023]) ).
fof(f1023,plain,
( spl0_45
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f36,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1021,plain,
spl0_44,
inference(avatar_split_clause,[],[f682,f1019]) ).
fof(f682,axiom,
! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f1017,plain,
spl0_43,
inference(avatar_split_clause,[],[f669,f1015]) ).
fof(f1015,plain,
( spl0_43
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f669,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f1013,plain,
spl0_42,
inference(avatar_split_clause,[],[f624,f1011]) ).
fof(f1011,plain,
( spl0_42
<=> ! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f624,axiom,
! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1009,plain,
spl0_41,
inference(avatar_split_clause,[],[f568,f1007]) ).
fof(f1007,plain,
( spl0_41
<=> ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f568,axiom,
! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
fof(f1005,plain,
spl0_40,
inference(avatar_split_clause,[],[f315,f1003]) ).
fof(f1003,plain,
( spl0_40
<=> ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f315,axiom,
! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1001,plain,
spl0_39,
inference(avatar_split_clause,[],[f127,f999]) ).
fof(f999,plain,
( spl0_39
<=> ! [X20] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f127,axiom,
! [X20] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f997,plain,
spl0_38,
inference(avatar_split_clause,[],[f762,f994]) ).
fof(f762,axiom,
c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_0) ).
fof(f992,plain,
spl0_37,
inference(avatar_split_clause,[],[f748,f990]) ).
fof(f748,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f988,plain,
spl0_36,
inference(avatar_split_clause,[],[f641,f986]) ).
fof(f986,plain,
( spl0_36
<=> ! [X4] : c_lessequals(X4,X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f641,axiom,
! [X4] : c_lessequals(X4,X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f984,plain,
spl0_35,
inference(avatar_split_clause,[],[f455,f981]) ).
fof(f981,plain,
( spl0_35
<=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f455,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
fof(f979,plain,
spl0_34,
inference(avatar_split_clause,[],[f185,f977]) ).
fof(f977,plain,
( spl0_34
<=> ! [X4] : c_Suc(X4) != X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f185,axiom,
! [X4] : c_Suc(X4) != X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f975,plain,
spl0_33,
inference(avatar_split_clause,[],[f35,f973]) ).
fof(f973,plain,
( spl0_33
<=> ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f35,axiom,
! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
fof(f971,plain,
spl0_32,
inference(avatar_split_clause,[],[f799,f968]) ).
fof(f968,plain,
( spl0_32
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f799,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f966,plain,
spl0_31,
inference(avatar_split_clause,[],[f798,f963]) ).
fof(f798,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f961,plain,
spl0_30,
inference(avatar_split_clause,[],[f797,f958]) ).
fof(f797,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f956,plain,
spl0_29,
inference(avatar_split_clause,[],[f796,f953]) ).
fof(f953,plain,
( spl0_29
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f796,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f951,plain,
spl0_28,
inference(avatar_split_clause,[],[f795,f948]) ).
fof(f948,plain,
( spl0_28
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f795,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f946,plain,
spl0_27,
inference(avatar_split_clause,[],[f794,f943]) ).
fof(f943,plain,
( spl0_27
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f794,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f941,plain,
spl0_26,
inference(avatar_split_clause,[],[f793,f938]) ).
fof(f938,plain,
( spl0_26
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f793,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f936,plain,
spl0_25,
inference(avatar_split_clause,[],[f792,f933]) ).
fof(f933,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f792,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f931,plain,
spl0_24,
inference(avatar_split_clause,[],[f791,f928]) ).
fof(f928,plain,
( spl0_24
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f791,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f926,plain,
spl0_23,
inference(avatar_split_clause,[],[f790,f923]) ).
fof(f923,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f790,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f921,plain,
spl0_22,
inference(avatar_split_clause,[],[f789,f918]) ).
fof(f918,plain,
( spl0_22
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f789,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f916,plain,
spl0_21,
inference(avatar_split_clause,[],[f788,f913]) ).
fof(f913,plain,
( spl0_21
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f788,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f911,plain,
spl0_20,
inference(avatar_split_clause,[],[f787,f908]) ).
fof(f908,plain,
( spl0_20
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f787,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f906,plain,
spl0_19,
inference(avatar_split_clause,[],[f786,f903]) ).
fof(f903,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f786,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f901,plain,
spl0_18,
inference(avatar_split_clause,[],[f785,f898]) ).
fof(f898,plain,
( spl0_18
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f785,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f896,plain,
spl0_17,
inference(avatar_split_clause,[],[f784,f893]) ).
fof(f893,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f784,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f891,plain,
spl0_16,
inference(avatar_split_clause,[],[f783,f888]) ).
fof(f888,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f783,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(f886,plain,
spl0_15,
inference(avatar_split_clause,[],[f782,f883]) ).
fof(f883,plain,
( spl0_15
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f782,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f881,plain,
spl0_14,
inference(avatar_split_clause,[],[f781,f878]) ).
fof(f878,plain,
( spl0_14
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f781,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(f876,plain,
spl0_13,
inference(avatar_split_clause,[],[f780,f873]) ).
fof(f873,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f780,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f871,plain,
spl0_12,
inference(avatar_split_clause,[],[f779,f868]) ).
fof(f868,plain,
( spl0_12
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f779,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f866,plain,
spl0_11,
inference(avatar_split_clause,[],[f778,f863]) ).
fof(f863,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f778,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f861,plain,
spl0_10,
inference(avatar_split_clause,[],[f777,f858]) ).
fof(f858,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f777,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f856,plain,
spl0_9,
inference(avatar_split_clause,[],[f776,f853]) ).
fof(f853,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f776,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f851,plain,
spl0_8,
inference(avatar_split_clause,[],[f775,f848]) ).
fof(f848,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f775,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f846,plain,
spl0_7,
inference(avatar_split_clause,[],[f774,f843]) ).
fof(f843,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f774,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(f841,plain,
spl0_6,
inference(avatar_split_clause,[],[f773,f838]) ).
fof(f838,plain,
( spl0_6
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f773,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f836,plain,
spl0_5,
inference(avatar_split_clause,[],[f772,f833]) ).
fof(f833,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f772,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(f831,plain,
spl0_4,
inference(avatar_split_clause,[],[f771,f828]) ).
fof(f828,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f771,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(f826,plain,
spl0_3,
inference(avatar_split_clause,[],[f770,f823]) ).
fof(f823,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f770,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(f821,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f769,f818]) ).
fof(f769,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_k,v_i,tc_nat),v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f816,plain,
spl0_1,
inference(avatar_split_clause,[],[f768,f813]) ).
fof(f768,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV690-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 21:12:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (18208)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.40 % (18221)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.40 % (18222)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.41 % (18223)WARNING: value z3 for option sas not known
% 0.20/0.41 % (18224)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.41 % (18226)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)
% 0.20/0.41 % (18223)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)
% 0.20/0.41 % (18225)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)
% 0.20/0.41 % (18227)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.50 % (18225)First to succeed.
% 0.20/0.51 % (18225)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18208"
% 0.20/0.51 % (18225)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (18225)------------------------------
% 0.20/0.51 % (18225)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.51 % (18225)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (18225)Memory used [KB]: 2177
% 0.20/0.51 % (18225)Time elapsed: 0.095 s
% 0.20/0.51 % (18225)Instructions burned: 100 (million)
% 0.20/0.51 % (18208)Success in time 0.159 s
%------------------------------------------------------------------------------