TSTP Solution File: SWV824-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV824-1 : 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:11:48 EDT 2024
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 410
% Syntax : Number of formulae : 658 ( 283 unt; 0 def)
% Number of atoms : 1265 ( 207 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1030 ( 423 ~; 396 |; 0 &)
% ( 211 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 246 ( 244 usr; 212 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 824 ( 824 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2746,plain,
$false,
inference(avatar_sat_refutation,[],[f717,f722,f727,f732,f737,f742,f747,f752,f757,f762,f767,f772,f777,f782,f787,f792,f797,f802,f807,f812,f817,f822,f827,f832,f837,f842,f847,f852,f857,f862,f866,f870,f874,f878,f882,f886,f890,f894,f898,f902,f906,f910,f914,f918,f922,f926,f930,f934,f938,f942,f946,f950,f954,f958,f962,f966,f970,f974,f978,f982,f986,f990,f994,f998,f1002,f1017,f1021,f1025,f1029,f1033,f1037,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1089,f1104,f1108,f1112,f1116,f1120,f1124,f1128,f1132,f1136,f1140,f1144,f1148,f1152,f1156,f1160,f1164,f1168,f1172,f1176,f1180,f1184,f1188,f1192,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1224,f1228,f1232,f1236,f1353,f1433,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1526,f1530,f1534,f1538,f1542,f1614,f1729,f1733,f1737,f1741,f1745,f1749,f1753,f1757,f1761,f1765,f1769,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1805,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1996,f2138,f2232,f2236,f2240,f2244,f2249,f2254,f2258,f2262,f2266,f2270,f2274,f2278,f2282,f2286,f2290,f2294,f2298,f2302,f2306,f2310,f2314,f2318,f2623,f2695,f2699,f2703,f2708,f2712,f2716,f2720,f2724,f2728,f2732,f2736,f2740,f2744,f2745]) ).
fof(f2745,plain,
( spl0_2
| ~ spl0_1
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2704,f2621,f714,f719]) ).
fof(f719,plain,
( spl0_2
<=> v_fun2(v_x,v_xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f714,plain,
( spl0_1
<=> v_fun1(v_x,v_xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f2621,plain,
( spl0_198
<=> ! [X0] :
( v_fun2(X0,v_xb)
| ~ v_fun1(X0,v_xa) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2704,plain,
( v_fun2(v_x,v_xb)
| ~ spl0_1
| ~ spl0_198 ),
inference(resolution,[],[f2622,f716]) ).
fof(f716,plain,
( v_fun1(v_x,v_xa)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f2622,plain,
( ! [X0] :
( ~ v_fun1(X0,v_xa)
| v_fun2(X0,v_xb) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2621]) ).
fof(f2744,plain,
spl0_211,
inference(avatar_split_clause,[],[f284,f2742]) ).
fof(f2742,plain,
( spl0_211
<=> ! [X4,X14,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X3,X2)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f284,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X14,X3,X2)
| c_HOL_Oord__class_Oless(X14,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
fof(f2740,plain,
spl0_210,
inference(avatar_split_clause,[],[f187,f2738]) ).
fof(f2738,plain,
( spl0_210
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f187,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
fof(f2736,plain,
spl0_209,
inference(avatar_split_clause,[],[f186,f2734]) ).
fof(f2734,plain,
( spl0_209
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f186,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
fof(f2732,plain,
spl0_208,
inference(avatar_split_clause,[],[f178,f2730]) ).
fof(f2730,plain,
( spl0_208
<=> ! [X4,X14,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X14,X3,X2)
| c_lessequals(X14,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f178,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X14,X3,X2)
| c_lessequals(X14,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
fof(f2728,plain,
spl0_207,
inference(avatar_split_clause,[],[f177,f2726]) ).
fof(f2726,plain,
( spl0_207
<=> ! [X4,X14,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X14,X4,X2)
| c_lessequals(X14,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f177,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X14,X4,X2)
| c_lessequals(X14,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
fof(f2724,plain,
spl0_206,
inference(avatar_split_clause,[],[f176,f2722]) ).
fof(f2722,plain,
( spl0_206
<=> ! [X4,X14,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X14,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X2),X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f176,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X14,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X2),X14,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
fof(f2720,plain,
spl0_205,
inference(avatar_split_clause,[],[f175,f2718]) ).
fof(f2718,plain,
( spl0_205
<=> ! [X2,X4,X3,X14] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X14,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X2),X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f175,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X14,X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X2),X14,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
fof(f2716,plain,
spl0_204,
inference(avatar_split_clause,[],[f138,f2714]) ).
fof(f2714,plain,
( spl0_204
<=> ! [X2,X5,X7,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X7,X3,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X7,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f138,axiom,
! [X2,X3,X7,X5] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X7,X3,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X7,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
fof(f2712,plain,
spl0_203,
inference(avatar_split_clause,[],[f137,f2710]) ).
fof(f2710,plain,
( spl0_203
<=> ! [X4,X14,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X14,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X14,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f137,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X14,X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X14,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
fof(f2708,plain,
spl0_202,
inference(avatar_split_clause,[],[f135,f2706]) ).
fof(f2706,plain,
( spl0_202
<=> ! [X4,X14,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f135,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
fof(f2703,plain,
spl0_201,
inference(avatar_split_clause,[],[f134,f2701]) ).
fof(f2701,plain,
( spl0_201
<=> ! [X4,X14,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X14,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f134,axiom,
! [X2,X3,X14,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X14,X2)
| ~ c_lessequals(X3,c_Orderings_Oord__class_Omin(X4,X14,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
fof(f2699,plain,
spl0_200,
inference(avatar_split_clause,[],[f11,f2697]) ).
fof(f2697,plain,
( spl0_200
<=> ! [X0,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f11,axiom,
! [X0,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
fof(f2695,plain,
spl0_199,
inference(avatar_split_clause,[],[f10,f2693]) ).
fof(f2693,plain,
( spl0_199
<=> ! [X0,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
| c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f10,axiom,
! [X0,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
| c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
fof(f2623,plain,
( spl0_198
| ~ spl0_3
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2412,f2292,f724,f2621]) ).
fof(f724,plain,
( spl0_3
<=> c_Natural_Oevaln(v_com,v_xa,v_n,v_xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f2292,plain,
( spl0_191
<=> ! [X2,X0,X1] :
( ~ c_Natural_Oevaln(v_com,X0,v_n,X1)
| v_fun2(X2,X1)
| ~ v_fun1(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2412,plain,
( ! [X0] :
( v_fun2(X0,v_xb)
| ~ v_fun1(X0,v_xa) )
| ~ spl0_3
| ~ spl0_191 ),
inference(resolution,[],[f2293,f726]) ).
fof(f726,plain,
( c_Natural_Oevaln(v_com,v_xa,v_n,v_xb)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f2293,plain,
( ! [X2,X0,X1] :
( ~ c_Natural_Oevaln(v_com,X0,v_n,X1)
| v_fun2(X2,X1)
| ~ v_fun1(X2,X0) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f2292]) ).
fof(f2318,plain,
spl0_197,
inference(avatar_split_clause,[],[f659,f2316]) ).
fof(f2316,plain,
( spl0_197
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(c_Suc(X0),c_Suc(X1),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f659,axiom,
! [X0,X1] : c_Orderings_Oord__class_Omin(c_Suc(X0),c_Suc(X1),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X0,X1,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
fof(f2314,plain,
spl0_196,
inference(avatar_split_clause,[],[f650,f2312]) ).
fof(f2312,plain,
( spl0_196
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(c_Suc(X0),c_Suc(X1),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f650,axiom,
! [X0,X1] : c_Orderings_Oord__class_Omax(c_Suc(X0),c_Suc(X1),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
fof(f2310,plain,
spl0_195,
inference(avatar_split_clause,[],[f639,f2308]) ).
fof(f2308,plain,
( spl0_195
<=> ! [X0,X1] :
( X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f639,axiom,
! [X0,X1] :
( X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
fof(f2306,plain,
spl0_194,
inference(avatar_split_clause,[],[f558,f2304]) ).
fof(f2304,plain,
( spl0_194
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f558,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2302,plain,
spl0_193,
inference(avatar_split_clause,[],[f557,f2300]) ).
fof(f2300,plain,
( spl0_193
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f557,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2298,plain,
spl0_192,
inference(avatar_split_clause,[],[f551,f2296]) ).
fof(f2296,plain,
( spl0_192
<=> ! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f551,axiom,
! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f2294,plain,
( spl0_191
| ~ spl0_31
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f2166,f1828,f864,f2292]) ).
fof(f864,plain,
( spl0_31
<=> ! [X36,X43,X51] :
( ~ v_fun1(X51,X36)
| v_fun2(X51,X43)
| ~ c_Natural_Oevaln(v_com,X36,c_Suc(v_n),X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1828,plain,
( spl0_170
<=> ! [X36,X6,X43,X1] :
( ~ c_Natural_Oevaln(X6,X36,X1,X43)
| c_Natural_Oevaln(X6,X36,c_Suc(X1),X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f2166,plain,
( ! [X2,X0,X1] :
( ~ c_Natural_Oevaln(v_com,X0,v_n,X1)
| v_fun2(X2,X1)
| ~ v_fun1(X2,X0) )
| ~ spl0_31
| ~ spl0_170 ),
inference(resolution,[],[f1829,f865]) ).
fof(f865,plain,
( ! [X51,X36,X43] :
( ~ c_Natural_Oevaln(v_com,X36,c_Suc(v_n),X43)
| v_fun2(X51,X43)
| ~ v_fun1(X51,X36) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f1829,plain,
( ! [X36,X1,X6,X43] :
( c_Natural_Oevaln(X6,X36,c_Suc(X1),X43)
| ~ c_Natural_Oevaln(X6,X36,X1,X43) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1828]) ).
fof(f2290,plain,
spl0_190,
inference(avatar_split_clause,[],[f548,f2288]) ).
fof(f2288,plain,
( spl0_190
<=> ! [X2,X5,X7] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,X2),X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f548,axiom,
! [X2,X7,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,X2),X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f2286,plain,
spl0_189,
inference(avatar_split_clause,[],[f547,f2284]) ).
fof(f2284,plain,
( spl0_189
<=> ! [X2,X5,X7] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X2),X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f547,axiom,
! [X2,X7,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X2),X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f2282,plain,
spl0_188,
inference(avatar_split_clause,[],[f537,f2280]) ).
fof(f2280,plain,
( spl0_188
<=> ! [X13,X9,X12] :
( ~ c_lessequals(X12,X13,tc_nat)
| ~ c_lessequals(X13,X9,tc_nat)
| c_lessequals(X12,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f537,axiom,
! [X9,X12,X13] :
( ~ c_lessequals(X12,X13,tc_nat)
| ~ c_lessequals(X13,X9,tc_nat)
| c_lessequals(X12,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2278,plain,
spl0_187,
inference(avatar_split_clause,[],[f426,f2276]) ).
fof(f2276,plain,
( spl0_187
<=> ! [X9,X0,X1] :
( X0 = X1
| c_HOL_Oplus__class_Oplus(X9,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X9,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f426,axiom,
! [X0,X1,X9] :
( X0 = X1
| c_HOL_Oplus__class_Oplus(X9,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X9,X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
fof(f2274,plain,
spl0_186,
inference(avatar_split_clause,[],[f425,f2272]) ).
fof(f2272,plain,
( spl0_186
<=> ! [X9,X0,X1] :
( X0 = X1
| c_HOL_Oplus__class_Oplus(X1,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f425,axiom,
! [X0,X1,X9] :
( X0 = X1
| c_HOL_Oplus__class_Oplus(X1,X9,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f2270,plain,
spl0_185,
inference(avatar_split_clause,[],[f336,f2268]) ).
fof(f2268,plain,
( spl0_185
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X0,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f336,axiom,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X0,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
fof(f2266,plain,
spl0_184,
inference(avatar_split_clause,[],[f235,f2264]) ).
fof(f2264,plain,
( spl0_184
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f235,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f2262,plain,
spl0_183,
inference(avatar_split_clause,[],[f232,f2260]) ).
fof(f2260,plain,
( spl0_183
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f232,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2258,plain,
spl0_182,
inference(avatar_split_clause,[],[f231,f2256]) ).
fof(f2256,plain,
( spl0_182
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f231,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2254,plain,
spl0_181,
inference(avatar_split_clause,[],[f230,f2252]) ).
fof(f2252,plain,
( spl0_181
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f230,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2249,plain,
spl0_180,
inference(avatar_split_clause,[],[f205,f2246]) ).
fof(f2246,plain,
( spl0_180
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f205,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
fof(f2244,plain,
spl0_179,
inference(avatar_split_clause,[],[f104,f2242]) ).
fof(f2242,plain,
( spl0_179
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f104,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X4,X3,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2240,plain,
spl0_178,
inference(avatar_split_clause,[],[f103,f2238]) ).
fof(f2238,plain,
( spl0_178
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f103,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2236,plain,
spl0_177,
inference(avatar_split_clause,[],[f102,f2234]) ).
fof(f2234,plain,
( spl0_177
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f102,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2232,plain,
spl0_176,
inference(avatar_split_clause,[],[f12,f2230]) ).
fof(f2230,plain,
( spl0_176
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f12,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
fof(f2138,plain,
( spl0_175
| ~ spl0_118
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2085,f1803,f1435,f2136]) ).
fof(f2136,plain,
( spl0_175
<=> ! [X0] :
( v_xb = X0
| ~ c_Natural_Oevalc(v_com,v_xa,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1435,plain,
( spl0_118
<=> c_Natural_Oevalc(v_com,v_xa,v_xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1803,plain,
( spl0_165
<=> ! [X37,X36,X6,X19] :
( X19 = X37
| ~ c_Natural_Oevalc(X6,X36,X37)
| ~ c_Natural_Oevalc(X6,X36,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2085,plain,
( ! [X0] :
( v_xb = X0
| ~ c_Natural_Oevalc(v_com,v_xa,X0) )
| ~ spl0_118
| ~ spl0_165 ),
inference(resolution,[],[f1804,f1437]) ).
fof(f1437,plain,
( c_Natural_Oevalc(v_com,v_xa,v_xb)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1435]) ).
fof(f1804,plain,
( ! [X36,X37,X6,X19] :
( ~ c_Natural_Oevalc(X6,X36,X37)
| X19 = X37
| ~ c_Natural_Oevalc(X6,X36,X19) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f1996,plain,
( spl0_174
| ~ spl0_87
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1379,f1214,f1122,f1994]) ).
fof(f1994,plain,
( spl0_174
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1122,plain,
( spl0_87
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1214,plain,
( spl0_110
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1379,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_87
| ~ spl0_110 ),
inference(resolution,[],[f1215,f1123]) ).
fof(f1123,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1215,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1214]) ).
fof(f1842,plain,
spl0_173,
inference(avatar_split_clause,[],[f649,f1840]) ).
fof(f1840,plain,
( spl0_173
<=> ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f649,axiom,
! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f1838,plain,
spl0_172,
inference(avatar_split_clause,[],[f648,f1836]) ).
fof(f1836,plain,
( spl0_172
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f648,axiom,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
fof(f1834,plain,
spl0_171,
inference(avatar_split_clause,[],[f640,f1832]) ).
fof(f1832,plain,
( spl0_171
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f640,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f1830,plain,
spl0_170,
inference(avatar_split_clause,[],[f636,f1828]) ).
fof(f636,axiom,
! [X36,X1,X6,X43] :
( ~ c_Natural_Oevaln(X6,X36,X1,X43)
| c_Natural_Oevaln(X6,X36,c_Suc(X1),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
fof(f1826,plain,
spl0_169,
inference(avatar_split_clause,[],[f582,f1824]) ).
fof(f1824,plain,
( spl0_169
<=> ! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f582,axiom,
! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
fof(f1822,plain,
spl0_168,
inference(avatar_split_clause,[],[f450,f1820]) ).
fof(f1820,plain,
( spl0_168
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f450,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,c_Orderings_Oord__class_Omin(X3,X4,X2),X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f1818,plain,
spl0_167,
inference(avatar_split_clause,[],[f446,f1816]) ).
fof(f1816,plain,
( spl0_167
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = c_Orderings_Oord__class_Omax(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f446,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X4,X2) = c_Orderings_Oord__class_Omax(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f1814,plain,
spl0_166,
inference(avatar_split_clause,[],[f344,f1812]) ).
fof(f1812,plain,
( spl0_166
<=> ! [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_166])]) ).
fof(f344,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f1805,plain,
spl0_165,
inference(avatar_split_clause,[],[f342,f1803]) ).
fof(f342,axiom,
! [X36,X37,X19,X6] :
( X19 = X37
| ~ c_Natural_Oevalc(X6,X36,X37)
| ~ c_Natural_Oevalc(X6,X36,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
fof(f1801,plain,
spl0_164,
inference(avatar_split_clause,[],[f340,f1799]) ).
fof(f1799,plain,
( spl0_164
<=> ! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f340,axiom,
! [X0,X1] :
( X0 = X1
| ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1797,plain,
spl0_163,
inference(avatar_split_clause,[],[f320,f1795]) ).
fof(f1795,plain,
( spl0_163
<=> ! [X13,X9,X1] :
( ~ c_HOL_Oord__class_Oless(X13,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X1,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f320,axiom,
! [X1,X9,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X1,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f1793,plain,
spl0_162,
inference(avatar_split_clause,[],[f288,f1791]) ).
fof(f1791,plain,
( spl0_162
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = c_Orderings_Oord__class_Omin(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f288,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X4,X2) = c_Orderings_Oord__class_Omin(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f1789,plain,
spl0_161,
inference(avatar_split_clause,[],[f259,f1787]) ).
fof(f1787,plain,
( spl0_161
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f259,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f1785,plain,
spl0_160,
inference(avatar_split_clause,[],[f226,f1783]) ).
fof(f1783,plain,
( spl0_160
<=> ! [X3,X4,X14] :
( ~ c_lessequals(X3,X14,tc_nat)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f226,axiom,
! [X3,X14,X4] :
( ~ c_lessequals(X3,X14,tc_nat)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
fof(f1781,plain,
spl0_159,
inference(avatar_split_clause,[],[f225,f1779]) ).
fof(f1779,plain,
( spl0_159
<=> ! [X9,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f225,axiom,
! [X0,X1,X9] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f1777,plain,
spl0_158,
inference(avatar_split_clause,[],[f224,f1775]) ).
fof(f1775,plain,
( spl0_158
<=> ! [X9,X0,X1] :
( c_lessequals(X9,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f224,axiom,
! [X0,X1,X9] :
( c_lessequals(X9,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f1773,plain,
spl0_157,
inference(avatar_split_clause,[],[f223,f1771]) ).
fof(f1771,plain,
( spl0_157
<=> ! [X13,X0,X12] :
( ~ c_lessequals(X12,X13,tc_nat)
| c_lessequals(X12,c_HOL_Oplus__class_Oplus(X13,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f223,axiom,
! [X0,X12,X13] :
( ~ c_lessequals(X12,X13,tc_nat)
| c_lessequals(X12,c_HOL_Oplus__class_Oplus(X13,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
fof(f1769,plain,
spl0_156,
inference(avatar_split_clause,[],[f147,f1767]) ).
fof(f1767,plain,
( spl0_156
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f147,axiom,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1765,plain,
( spl0_155
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1663,f1516,f1763]) ).
fof(f1763,plain,
( spl0_155
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1516,plain,
( spl0_138
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_lessequals(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1663,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_138 ),
inference(factoring,[],[f1517]) ).
fof(f1517,plain,
( ! [X2,X3,X4] :
( c_lessequals(X4,X3,X2)
| c_lessequals(X3,X4,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1516]) ).
fof(f1761,plain,
spl0_154,
inference(avatar_split_clause,[],[f146,f1759]) ).
fof(f1759,plain,
( spl0_154
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f146,axiom,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1757,plain,
spl0_153,
inference(avatar_split_clause,[],[f91,f1755]) ).
fof(f1755,plain,
( spl0_153
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X3,X4,X2) = c_HOL_Otimes__class_Otimes(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f91,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Otimes__class_Otimes(X3,X4,X2) = c_HOL_Otimes__class_Otimes(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f1753,plain,
spl0_152,
inference(avatar_split_clause,[],[f63,f1751]) ).
fof(f1751,plain,
( spl0_152
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f63,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f1749,plain,
spl0_151,
inference(avatar_split_clause,[],[f62,f1747]) ).
fof(f1747,plain,
( spl0_151
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f62,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f1745,plain,
spl0_150,
inference(avatar_split_clause,[],[f24,f1743]) ).
fof(f1743,plain,
( spl0_150
<=> ! [X13,X9,X12] :
( c_HOL_Oord__class_Oless(X12,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f24,axiom,
! [X9,X12,X13] :
( c_HOL_Oord__class_Oless(X12,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f1741,plain,
spl0_149,
inference(avatar_split_clause,[],[f23,f1739]) ).
fof(f1739,plain,
( spl0_149
<=> ! [X13,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X13,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f23,axiom,
! [X0,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X13,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
fof(f1737,plain,
spl0_148,
inference(avatar_split_clause,[],[f22,f1735]) ).
fof(f1735,plain,
( spl0_148
<=> ! [X13,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X0,X13,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f22,axiom,
! [X0,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| c_HOL_Oord__class_Oless(X12,c_HOL_Oplus__class_Oplus(X0,X13,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f1733,plain,
spl0_147,
inference(avatar_split_clause,[],[f9,f1731]) ).
fof(f1731,plain,
( spl0_147
<=> ! [X2,X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X3,X4,X2) = c_HOL_Oplus__class_Oplus(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f9,axiom,
! [X2,X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X3,X4,X2) = c_HOL_Oplus__class_Oplus(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f1729,plain,
spl0_146,
inference(avatar_split_clause,[],[f6,f1727]) ).
fof(f1727,plain,
( spl0_146
<=> ! [X2,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,X7,X2) = c_HOL_Oplus__class_Oplus(X7,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f6,axiom,
! [X2,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,X7,X2) = c_HOL_Oplus__class_Oplus(X7,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1614,plain,
( spl0_145
| ~ spl0_41
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1371,f1210,f904,f1612]) ).
fof(f1612,plain,
( spl0_145
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f904,plain,
( spl0_41
<=> ! [X1] : ~ c_lessequals(c_Suc(X1),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1210,plain,
( spl0_109
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1371,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_41
| ~ spl0_109 ),
inference(resolution,[],[f1211,f905]) ).
fof(f905,plain,
( ! [X1] : ~ c_lessequals(c_Suc(X1),X1,tc_nat)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f904]) ).
fof(f1211,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1210]) ).
fof(f1542,plain,
spl0_144,
inference(avatar_split_clause,[],[f667,f1540]) ).
fof(f1540,plain,
( spl0_144
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f667,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f1538,plain,
spl0_143,
inference(avatar_split_clause,[],[f666,f1536]) ).
fof(f1536,plain,
( spl0_143
<=> ! [X1,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f666,axiom,
! [X3,X1] :
( ~ c_HOL_Oord__class_Oless(X3,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
fof(f1534,plain,
spl0_142,
inference(avatar_split_clause,[],[f619,f1532]) ).
fof(f1532,plain,
( spl0_142
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f619,axiom,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f1530,plain,
spl0_141,
inference(avatar_split_clause,[],[f618,f1528]) ).
fof(f1528,plain,
( spl0_141
<=> ! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f618,axiom,
! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f1526,plain,
spl0_140,
inference(avatar_split_clause,[],[f616,f1524]) ).
fof(f1524,plain,
( spl0_140
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f616,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1522,plain,
( spl0_139
| ~ spl0_32
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1355,f1198,f868,f1520]) ).
fof(f1520,plain,
( spl0_139
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f868,plain,
( spl0_32
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1198,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1355,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_32
| ~ spl0_106 ),
inference(resolution,[],[f1199,f869]) ).
fof(f869,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f868]) ).
fof(f1199,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1198]) ).
fof(f1518,plain,
spl0_138,
inference(avatar_split_clause,[],[f615,f1516]) ).
fof(f615,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X4,X2)
| c_lessequals(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1514,plain,
spl0_137,
inference(avatar_split_clause,[],[f613,f1512]) ).
fof(f1512,plain,
( spl0_137
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f613,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1510,plain,
spl0_136,
inference(avatar_split_clause,[],[f612,f1508]) ).
fof(f1508,plain,
( spl0_136
<=> ! [X2,X5,X7] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X5,X2)
| ~ c_HOL_Oord__class_Oless(X5,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f612,axiom,
! [X2,X7,X5] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X7,X5,X2)
| ~ c_HOL_Oord__class_Oless(X5,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1506,plain,
spl0_135,
inference(avatar_split_clause,[],[f549,f1504]) ).
fof(f1504,plain,
( spl0_135
<=> ! [X11,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X3,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f549,axiom,
! [X3,X11] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X11,X3,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
fof(f1502,plain,
spl0_134,
inference(avatar_split_clause,[],[f481,f1500]) ).
fof(f1500,plain,
( spl0_134
<=> ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f481,axiom,
! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).
fof(f1498,plain,
spl0_133,
inference(avatar_split_clause,[],[f360,f1496]) ).
fof(f1496,plain,
( spl0_133
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f360,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1494,plain,
spl0_132,
inference(avatar_split_clause,[],[f359,f1492]) ).
fof(f1492,plain,
( spl0_132
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f359,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2)
| c_lessequals(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1490,plain,
spl0_131,
inference(avatar_split_clause,[],[f321,f1488]) ).
fof(f1488,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f321,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f1486,plain,
spl0_130,
inference(avatar_split_clause,[],[f254,f1484]) ).
fof(f1484,plain,
( spl0_130
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f254,axiom,
! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f1482,plain,
spl0_129,
inference(avatar_split_clause,[],[f243,f1480]) ).
fof(f1480,plain,
( spl0_129
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f243,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1478,plain,
spl0_128,
inference(avatar_split_clause,[],[f241,f1476]) ).
fof(f1476,plain,
( spl0_128
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f241,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X4,X2)
| ~ c_HOL_Oord__class_Oless(X4,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1474,plain,
spl0_127,
inference(avatar_split_clause,[],[f240,f1472]) ).
fof(f1472,plain,
( spl0_127
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f240,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,X3,X2)
| c_HOL_Oord__class_Oless(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f1470,plain,
spl0_126,
inference(avatar_split_clause,[],[f214,f1468]) ).
fof(f1468,plain,
( spl0_126
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f214,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1466,plain,
spl0_125,
inference(avatar_split_clause,[],[f213,f1464]) ).
fof(f1464,plain,
( spl0_125
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f213,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1462,plain,
spl0_124,
inference(avatar_split_clause,[],[f210,f1460]) ).
fof(f1460,plain,
( spl0_124
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f210,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1458,plain,
spl0_123,
inference(avatar_split_clause,[],[f209,f1456]) ).
fof(f1456,plain,
( spl0_123
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f209,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1454,plain,
spl0_122,
inference(avatar_split_clause,[],[f76,f1452]) ).
fof(f1452,plain,
( spl0_122
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f76,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1450,plain,
spl0_121,
inference(avatar_split_clause,[],[f70,f1448]) ).
fof(f1448,plain,
( spl0_121
<=> ! [X2,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f70,axiom,
! [X2,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X2),X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1446,plain,
spl0_120,
inference(avatar_split_clause,[],[f36,f1444]) ).
fof(f1444,plain,
( spl0_120
<=> ! [X18,X16,X17,X15] :
( X16 = X18
| c_Com_Ocom_OSemi(X15,X16) != c_Com_Ocom_OSemi(X17,X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f36,axiom,
! [X18,X16,X17,X15] :
( X16 = X18
| c_Com_Ocom_OSemi(X15,X16) != c_Com_Ocom_OSemi(X17,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
fof(f1442,plain,
spl0_119,
inference(avatar_split_clause,[],[f35,f1440]) ).
fof(f1440,plain,
( spl0_119
<=> ! [X18,X17,X16,X15] :
( X15 = X17
| c_Com_Ocom_OSemi(X15,X16) != c_Com_Ocom_OSemi(X17,X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f35,axiom,
! [X18,X16,X17,X15] :
( X15 = X17
| c_Com_Ocom_OSemi(X15,X16) != c_Com_Ocom_OSemi(X17,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
fof(f1438,plain,
( spl0_118
| ~ spl0_3
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f1428,f1234,f724,f1435]) ).
fof(f1234,plain,
( spl0_115
<=> ! [X37,X36,X6,X3] :
( c_Natural_Oevalc(X6,X36,X37)
| ~ c_Natural_Oevaln(X6,X36,X3,X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1428,plain,
( c_Natural_Oevalc(v_com,v_xa,v_xb)
| ~ spl0_3
| ~ spl0_115 ),
inference(resolution,[],[f1235,f726]) ).
fof(f1235,plain,
( ! [X3,X36,X37,X6] :
( ~ c_Natural_Oevaln(X6,X36,X3,X37)
| c_Natural_Oevalc(X6,X36,X37) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1234]) ).
fof(f1433,plain,
spl0_117,
inference(avatar_split_clause,[],[f15,f1431]) ).
fof(f1431,plain,
( spl0_117
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f15,axiom,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f1353,plain,
( spl0_116
| ~ spl0_85
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1264,f1122,f1114,f1351]) ).
fof(f1351,plain,
( spl0_116
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1114,plain,
( spl0_85
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1264,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_85
| ~ spl0_87 ),
inference(resolution,[],[f1115,f1123]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f1236,plain,
spl0_115,
inference(avatar_split_clause,[],[f670,f1234]) ).
fof(f670,axiom,
! [X3,X36,X37,X6] :
( c_Natural_Oevalc(X6,X36,X37)
| ~ c_Natural_Oevaln(X6,X36,X3,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_1) ).
fof(f1232,plain,
spl0_114,
inference(avatar_split_clause,[],[f664,f1230]) ).
fof(f1230,plain,
( spl0_114
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f664,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1228,plain,
spl0_113,
inference(avatar_split_clause,[],[f663,f1226]) ).
fof(f1226,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f663,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1224,plain,
spl0_112,
inference(avatar_split_clause,[],[f656,f1222]) ).
fof(f1222,plain,
( spl0_112
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f656,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X1),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1220,plain,
spl0_111,
inference(avatar_split_clause,[],[f655,f1218]) ).
fof(f1218,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f655,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1216,plain,
spl0_110,
inference(avatar_split_clause,[],[f629,f1214]) ).
fof(f629,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1212,plain,
spl0_109,
inference(avatar_split_clause,[],[f628,f1210]) ).
fof(f628,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1208,plain,
( spl0_108
| ~ spl0_29
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1085,f1051,f854,f1206]) ).
fof(f1206,plain,
( spl0_108
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f854,plain,
( spl0_29
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1051,plain,
( spl0_75
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1085,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_29
| ~ spl0_75 ),
inference(resolution,[],[f1052,f856]) ).
fof(f856,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f1052,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X3,X2) = X3 )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f1204,plain,
spl0_107,
inference(avatar_split_clause,[],[f622,f1202]) ).
fof(f1202,plain,
( spl0_107
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f622,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1200,plain,
spl0_106,
inference(avatar_split_clause,[],[f621,f1198]) ).
fof(f621,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1196,plain,
spl0_105,
inference(avatar_split_clause,[],[f509,f1194]) ).
fof(f1194,plain,
( spl0_105
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f509,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1192,plain,
spl0_104,
inference(avatar_split_clause,[],[f508,f1190]) ).
fof(f1190,plain,
( spl0_104
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f508,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f1188,plain,
spl0_103,
inference(avatar_split_clause,[],[f500,f1186]) ).
fof(f1186,plain,
( spl0_103
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f500,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1184,plain,
spl0_102,
inference(avatar_split_clause,[],[f499,f1182]) ).
fof(f1182,plain,
( spl0_102
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f499,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1180,plain,
spl0_101,
inference(avatar_split_clause,[],[f498,f1178]) ).
fof(f1178,plain,
( spl0_101
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f498,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1176,plain,
spl0_100,
inference(avatar_split_clause,[],[f497,f1174]) ).
fof(f1174,plain,
( spl0_100
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f497,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1172,plain,
spl0_99,
inference(avatar_split_clause,[],[f496,f1170]) ).
fof(f1170,plain,
( spl0_99
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f496,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1168,plain,
spl0_98,
inference(avatar_split_clause,[],[f491,f1166]) ).
fof(f1166,plain,
( spl0_98
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f491,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1164,plain,
spl0_97,
inference(avatar_split_clause,[],[f384,f1162]) ).
fof(f1162,plain,
( spl0_97
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f384,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1160,plain,
spl0_96,
inference(avatar_split_clause,[],[f331,f1158]) ).
fof(f1158,plain,
( spl0_96
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f331,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1156,plain,
spl0_95,
inference(avatar_split_clause,[],[f319,f1154]) ).
fof(f1154,plain,
( spl0_95
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f319,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1152,plain,
spl0_94,
inference(avatar_split_clause,[],[f92,f1150]) ).
fof(f1150,plain,
( spl0_94
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f92,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1148,plain,
spl0_93,
inference(avatar_split_clause,[],[f89,f1146]) ).
fof(f1146,plain,
( spl0_93
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f89,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1144,plain,
spl0_92,
inference(avatar_split_clause,[],[f88,f1142]) ).
fof(f1142,plain,
( spl0_92
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f88,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1140,plain,
spl0_91,
inference(avatar_split_clause,[],[f57,f1138]) ).
fof(f1138,plain,
( spl0_91
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f57,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1136,plain,
spl0_90,
inference(avatar_split_clause,[],[f56,f1134]) ).
fof(f1134,plain,
( spl0_90
<=> ! [X2,X4,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f56,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X4,X2),X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1132,plain,
spl0_89,
inference(avatar_split_clause,[],[f38,f1130]) ).
fof(f1130,plain,
( spl0_89
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f38,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1128,plain,
spl0_88,
inference(avatar_split_clause,[],[f37,f1126]) ).
fof(f1126,plain,
( spl0_88
<=> ! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f37,axiom,
! [X2,X3,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X3,X4,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1124,plain,
( spl0_87
| ~ spl0_42
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1090,f1055,f908,f1122]) ).
fof(f908,plain,
( spl0_42
<=> ! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1055,plain,
( spl0_76
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1090,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_42
| ~ spl0_76 ),
inference(resolution,[],[f1056,f909]) ).
fof(f909,plain,
( ! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f1056,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1120,plain,
spl0_86,
inference(avatar_split_clause,[],[f30,f1118]) ).
fof(f1118,plain,
( spl0_86
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f30,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
fof(f1116,plain,
spl0_85,
inference(avatar_split_clause,[],[f29,f1114]) ).
fof(f29,axiom,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
fof(f1112,plain,
spl0_84,
inference(avatar_split_clause,[],[f7,f1110]) ).
fof(f1110,plain,
( spl0_84
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f7,axiom,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f1108,plain,
spl0_83,
inference(avatar_split_clause,[],[f4,f1106]) ).
fof(f1106,plain,
( spl0_83
<=> ! [X2,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X5,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f4,axiom,
! [X2,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X5,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1104,plain,
spl0_82,
inference(avatar_split_clause,[],[f3,f1102]) ).
fof(f1102,plain,
( spl0_82
<=> ! [X2,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f3,axiom,
! [X2,X5] :
( ~ class_Divides_Osemiring__div(X2)
| c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1089,plain,
( spl0_81
| ~ spl0_29
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f1084,f1047,f854,f1087]) ).
fof(f1087,plain,
( spl0_81
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1047,plain,
( spl0_74
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1084,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_29
| ~ spl0_74 ),
inference(resolution,[],[f1048,f856]) ).
fof(f1048,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X3,X2) = X3 )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f1073,plain,
spl0_80,
inference(avatar_split_clause,[],[f665,f1071]) ).
fof(f1071,plain,
( spl0_80
<=> ! [X36,X37,X1] :
( X36 = X37
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X36,X1,X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f665,axiom,
! [X36,X1,X37] :
( X36 = X37
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X36,X1,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
fof(f1069,plain,
spl0_79,
inference(avatar_split_clause,[],[f643,f1067]) ).
fof(f1067,plain,
( spl0_79
<=> ! [X4,X3] :
( X3 = X4
| c_Suc(X3) != c_Suc(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f643,axiom,
! [X3,X4] :
( X3 = X4
| c_Suc(X3) != c_Suc(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
fof(f1065,plain,
spl0_78,
inference(avatar_split_clause,[],[f614,f1063]) ).
fof(f1063,plain,
( spl0_78
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f614,axiom,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1061,plain,
spl0_77,
inference(avatar_split_clause,[],[f445,f1059]) ).
fof(f1059,plain,
( spl0_77
<=> ! [X20,X41] :
( X20 = X41
| c_Com_Ocom_OBODY(X20) != c_Com_Ocom_OBODY(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f445,axiom,
! [X41,X20] :
( X20 = X41
| c_Com_Ocom_OBODY(X20) != c_Com_Ocom_OBODY(X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
fof(f1057,plain,
spl0_76,
inference(avatar_split_clause,[],[f358,f1055]) ).
fof(f358,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
fof(f1053,plain,
spl0_75,
inference(avatar_split_clause,[],[f354,f1051]) ).
fof(f354,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omax(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1049,plain,
spl0_74,
inference(avatar_split_clause,[],[f330,f1047]) ).
fof(f330,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Oord__class_Omin(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1045,plain,
spl0_73,
inference(avatar_split_clause,[],[f277,f1043]) ).
fof(f1043,plain,
( spl0_73
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f277,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1041,plain,
spl0_72,
inference(avatar_split_clause,[],[f216,f1039]) ).
fof(f1039,plain,
( spl0_72
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f216,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f1037,plain,
spl0_71,
inference(avatar_split_clause,[],[f215,f1035]) ).
fof(f1035,plain,
( spl0_71
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f215,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f1033,plain,
spl0_70,
inference(avatar_split_clause,[],[f143,f1031]) ).
fof(f1031,plain,
( spl0_70
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f143,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0R_0) ).
fof(f1029,plain,
spl0_69,
inference(avatar_split_clause,[],[f142,f1027]) ).
fof(f1027,plain,
( spl0_69
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f142,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0L_0) ).
fof(f1025,plain,
spl0_68,
inference(avatar_split_clause,[],[f97,f1023]) ).
fof(f1023,plain,
( spl0_68
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f97,axiom,
! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1021,plain,
spl0_67,
inference(avatar_split_clause,[],[f46,f1019]) ).
fof(f1019,plain,
( spl0_67
<=> ! [X0,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f46,axiom,
! [X0,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X0,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
fof(f1017,plain,
spl0_66,
inference(avatar_split_clause,[],[f45,f1015]) ).
fof(f1015,plain,
( spl0_66
<=> ! [X0,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X0,X12,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f45,axiom,
! [X0,X12] : c_HOL_Oord__class_Oless(X12,c_Suc(c_HOL_Oplus__class_Oplus(X0,X12,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1002,plain,
spl0_65,
inference(avatar_split_clause,[],[f513,f1000]) ).
fof(f1000,plain,
( spl0_65
<=> ! [X36,X37] :
( X36 = X37
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,X36,X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f513,axiom,
! [X36,X37] :
( X36 = X37
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,X36,X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
fof(f998,plain,
spl0_64,
inference(avatar_split_clause,[],[f493,f996]) ).
fof(f996,plain,
( spl0_64
<=> ! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f493,axiom,
! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f994,plain,
spl0_63,
inference(avatar_split_clause,[],[f492,f992]) ).
fof(f992,plain,
( spl0_63
<=> ! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f492,axiom,
! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
fof(f990,plain,
spl0_62,
inference(avatar_split_clause,[],[f451,f988]) ).
fof(f988,plain,
( spl0_62
<=> ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f451,axiom,
! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).
fof(f986,plain,
spl0_61,
inference(avatar_split_clause,[],[f449,f984]) ).
fof(f984,plain,
( spl0_61
<=> ! [X1] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f449,axiom,
! [X1] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
fof(f982,plain,
spl0_60,
inference(avatar_split_clause,[],[f448,f980]) ).
fof(f980,plain,
( spl0_60
<=> ! [X1] : c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f448,axiom,
! [X1] : c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
fof(f978,plain,
spl0_59,
inference(avatar_split_clause,[],[f431,f976]) ).
fof(f976,plain,
( spl0_59
<=> ! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f431,axiom,
! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
fof(f974,plain,
spl0_58,
inference(avatar_split_clause,[],[f406,f972]) ).
fof(f972,plain,
( spl0_58
<=> ! [X13,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),X12,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f406,axiom,
! [X12,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),X12,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f970,plain,
spl0_57,
inference(avatar_split_clause,[],[f405,f968]) ).
fof(f968,plain,
( spl0_57
<=> ! [X13,X12] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X12,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f405,axiom,
! [X12,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),X12,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f966,plain,
spl0_56,
inference(avatar_split_clause,[],[f334,f964]) ).
fof(f964,plain,
( spl0_56
<=> ! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f334,axiom,
! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f962,plain,
spl0_55,
inference(avatar_split_clause,[],[f333,f960]) ).
fof(f960,plain,
( spl0_55
<=> ! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f333,axiom,
! [X0,X1] : c_lessequals(X1,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
fof(f958,plain,
spl0_54,
inference(avatar_split_clause,[],[f291,f956]) ).
fof(f956,plain,
( spl0_54
<=> ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f291,axiom,
! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f954,plain,
spl0_53,
inference(avatar_split_clause,[],[f126,f952]) ).
fof(f952,plain,
( spl0_53
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f126,axiom,
! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f950,plain,
spl0_52,
inference(avatar_split_clause,[],[f125,f948]) ).
fof(f948,plain,
( spl0_52
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f125,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f946,plain,
spl0_51,
inference(avatar_split_clause,[],[f540,f944]) ).
fof(f944,plain,
( spl0_51
<=> ! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f540,axiom,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f942,plain,
spl0_50,
inference(avatar_split_clause,[],[f539,f940]) ).
fof(f940,plain,
( spl0_50
<=> ! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f539,axiom,
! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f938,plain,
spl0_49,
inference(avatar_split_clause,[],[f328,f936]) ).
fof(f936,plain,
( spl0_49
<=> ! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f328,axiom,
! [X2,X3] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f934,plain,
spl0_48,
inference(avatar_split_clause,[],[f327,f932]) ).
fof(f932,plain,
( spl0_48
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f327,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f930,plain,
spl0_47,
inference(avatar_split_clause,[],[f326,f928]) ).
fof(f928,plain,
( spl0_47
<=> ! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f326,axiom,
! [X2,X3] :
( ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X3,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f926,plain,
spl0_46,
inference(avatar_split_clause,[],[f280,f924]) ).
fof(f924,plain,
( spl0_46
<=> ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f280,axiom,
! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
fof(f922,plain,
spl0_45,
inference(avatar_split_clause,[],[f85,f920]) ).
fof(f920,plain,
( spl0_45
<=> ! [X20,X16,X15] : c_Com_Ocom_OSemi(X15,X16) != c_Com_Ocom_OBODY(X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f85,axiom,
! [X16,X15,X20] : c_Com_Ocom_OSemi(X15,X16) != c_Com_Ocom_OBODY(X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
fof(f918,plain,
spl0_44,
inference(avatar_split_clause,[],[f635,f916]) ).
fof(f916,plain,
( spl0_44
<=> ! [X36,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X36,X1,X36) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f635,axiom,
! [X36,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X36,X1,X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
fof(f914,plain,
spl0_43,
inference(avatar_split_clause,[],[f634,f912]) ).
fof(f912,plain,
( spl0_43
<=> ! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X42) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f634,axiom,
! [X42] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X42),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
fof(f910,plain,
spl0_42,
inference(avatar_split_clause,[],[f631,f908]) ).
fof(f631,axiom,
! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f906,plain,
spl0_41,
inference(avatar_split_clause,[],[f627,f904]) ).
fof(f627,axiom,
! [X1] : ~ c_lessequals(c_Suc(X1),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f902,plain,
spl0_40,
inference(avatar_split_clause,[],[f507,f900]) ).
fof(f900,plain,
( spl0_40
<=> ! [X2,X3] : c_Fun_Oid(X3,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f507,axiom,
! [X2,X3] : c_Fun_Oid(X3,X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
fof(f898,plain,
spl0_39,
inference(avatar_split_clause,[],[f385,f896]) ).
fof(f896,plain,
( spl0_39
<=> ! [X18,X17] : c_Com_Ocom_OSemi(X17,X18) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f385,axiom,
! [X18,X17] : c_Com_Ocom_OSemi(X17,X18) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
fof(f894,plain,
spl0_38,
inference(avatar_split_clause,[],[f310,f892]) ).
fof(f892,plain,
( spl0_38
<=> ! [X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f310,axiom,
! [X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f890,plain,
spl0_37,
inference(avatar_split_clause,[],[f117,f888]) ).
fof(f888,plain,
( spl0_37
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f117,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f886,plain,
spl0_36,
inference(avatar_split_clause,[],[f626,f884]) ).
fof(f884,plain,
( spl0_36
<=> ! [X1] : c_Suc(X1) != X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f626,axiom,
! [X1] : c_Suc(X1) != X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f882,plain,
spl0_35,
inference(avatar_split_clause,[],[f536,f880]) ).
fof(f880,plain,
( spl0_35
<=> ! [X1] : c_lessequals(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f536,axiom,
! [X1] : c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f878,plain,
spl0_34,
inference(avatar_split_clause,[],[f478,f876]) ).
fof(f876,plain,
( spl0_34
<=> ! [X20] : c_Com_Ocom_OBODY(X20) != c_Com_Ocom_OSKIP ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f478,axiom,
! [X20] : c_Com_Ocom_OBODY(X20) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
fof(f874,plain,
spl0_33,
inference(avatar_split_clause,[],[f337,f872]) ).
fof(f872,plain,
( spl0_33
<=> ! [X36] : c_Natural_Oevalc(c_Com_Ocom_OSKIP,X36,X36) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f337,axiom,
! [X36] : c_Natural_Oevalc(c_Com_Ocom_OSKIP,X36,X36),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
fof(f870,plain,
spl0_32,
inference(avatar_split_clause,[],[f325,f868]) ).
fof(f325,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f866,plain,
spl0_31,
inference(avatar_split_clause,[],[f674,f864]) ).
fof(f674,axiom,
! [X51,X36,X43] :
( ~ v_fun1(X51,X36)
| v_fun2(X51,X43)
| ~ c_Natural_Oevaln(v_com,X36,c_Suc(v_n),X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f862,plain,
spl0_30,
inference(avatar_split_clause,[],[f701,f859]) ).
fof(f859,plain,
( spl0_30
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f701,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f857,plain,
spl0_29,
inference(avatar_split_clause,[],[f700,f854]) ).
fof(f700,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f852,plain,
spl0_28,
inference(avatar_split_clause,[],[f699,f849]) ).
fof(f849,plain,
( spl0_28
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f699,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f847,plain,
spl0_27,
inference(avatar_split_clause,[],[f698,f844]) ).
fof(f844,plain,
( spl0_27
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f698,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f842,plain,
spl0_26,
inference(avatar_split_clause,[],[f697,f839]) ).
fof(f839,plain,
( spl0_26
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f697,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f837,plain,
spl0_25,
inference(avatar_split_clause,[],[f696,f834]) ).
fof(f834,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f696,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f832,plain,
spl0_24,
inference(avatar_split_clause,[],[f695,f829]) ).
fof(f829,plain,
( spl0_24
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f695,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f827,plain,
spl0_23,
inference(avatar_split_clause,[],[f694,f824]) ).
fof(f824,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f694,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f822,plain,
spl0_22,
inference(avatar_split_clause,[],[f693,f819]) ).
fof(f819,plain,
( spl0_22
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f693,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f817,plain,
spl0_21,
inference(avatar_split_clause,[],[f692,f814]) ).
fof(f814,plain,
( spl0_21
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f692,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f812,plain,
spl0_20,
inference(avatar_split_clause,[],[f691,f809]) ).
fof(f809,plain,
( spl0_20
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f691,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f807,plain,
spl0_19,
inference(avatar_split_clause,[],[f690,f804]) ).
fof(f804,plain,
( spl0_19
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f690,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f802,plain,
spl0_18,
inference(avatar_split_clause,[],[f689,f799]) ).
fof(f799,plain,
( spl0_18
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f689,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f797,plain,
spl0_17,
inference(avatar_split_clause,[],[f688,f794]) ).
fof(f794,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f688,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f792,plain,
spl0_16,
inference(avatar_split_clause,[],[f687,f789]) ).
fof(f789,plain,
( spl0_16
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f687,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f787,plain,
spl0_15,
inference(avatar_split_clause,[],[f686,f784]) ).
fof(f784,plain,
( spl0_15
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f686,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f782,plain,
spl0_14,
inference(avatar_split_clause,[],[f685,f779]) ).
fof(f779,plain,
( spl0_14
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f685,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f777,plain,
spl0_13,
inference(avatar_split_clause,[],[f684,f774]) ).
fof(f774,plain,
( spl0_13
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f684,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f772,plain,
spl0_12,
inference(avatar_split_clause,[],[f683,f769]) ).
fof(f769,plain,
( spl0_12
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f683,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f767,plain,
spl0_11,
inference(avatar_split_clause,[],[f682,f764]) ).
fof(f764,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f682,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f762,plain,
spl0_10,
inference(avatar_split_clause,[],[f681,f759]) ).
fof(f759,plain,
( spl0_10
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f681,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f757,plain,
spl0_9,
inference(avatar_split_clause,[],[f680,f754]) ).
fof(f754,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f680,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f752,plain,
spl0_8,
inference(avatar_split_clause,[],[f679,f749]) ).
fof(f749,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f679,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f747,plain,
spl0_7,
inference(avatar_split_clause,[],[f678,f744]) ).
fof(f744,plain,
( spl0_7
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f678,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f742,plain,
spl0_6,
inference(avatar_split_clause,[],[f677,f739]) ).
fof(f739,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f677,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f737,plain,
spl0_5,
inference(avatar_split_clause,[],[f676,f734]) ).
fof(f734,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f676,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f732,plain,
spl0_4,
inference(avatar_split_clause,[],[f675,f729]) ).
fof(f729,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f675,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f727,plain,
spl0_3,
inference(avatar_split_clause,[],[f672,f724]) ).
fof(f672,axiom,
c_Natural_Oevaln(v_com,v_xa,v_n,v_xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f722,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f673,f719]) ).
fof(f673,axiom,
~ v_fun2(v_x,v_xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f717,plain,
spl0_1,
inference(avatar_split_clause,[],[f671,f714]) ).
fof(f671,axiom,
v_fun1(v_x,v_xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV824-1 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 3 21:02:53 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (29883)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (29886)WARNING: value z3 for option sas not known
% 0.22/0.42 % (29888)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.42 % (29885)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.42 % (29887)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.42 % (29890)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.42 % (29889)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.42 % (29886)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.42 % (29884)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.49 % (29888)First to succeed.
% 0.22/0.49 TRYING [1]
% 0.22/0.49 % (29888)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29883"
% 0.22/0.50 % (29888)Refutation found. Thanks to Tanya!
% 0.22/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.50 % (29888)------------------------------
% 0.22/0.50 % (29888)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.50 % (29888)Termination reason: Refutation
% 0.22/0.50
% 0.22/0.50 % (29888)Memory used [KB]: 2176
% 0.22/0.50 % (29888)Time elapsed: 0.076 s
% 0.22/0.50 % (29888)Instructions burned: 122 (million)
% 0.22/0.50 % (29883)Success in time 0.126 s
%------------------------------------------------------------------------------