TSTP Solution File: LCL851-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL851-1 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:55:32 EDT 2024
% Result : Unsatisfiable 1.34s 0.57s
% Output : Refutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 670
% Syntax : Number of formulae : 1176 ( 471 unt; 0 def)
% Number of atoms : 2354 ( 398 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 2022 ( 844 ~; 830 |; 0 &)
% ( 348 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 392 ( 390 usr; 349 prp; 0-3 aty)
% Number of functors : 52 ( 52 usr; 8 con; 0-5 aty)
% Number of variables : 1632 (1632 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5464,plain,
$false,
inference(avatar_sat_refutation,[],[f1178,f1183,f1188,f1193,f1198,f1203,f1208,f1213,f1218,f1223,f1228,f1233,f1238,f1243,f1248,f1253,f1258,f1263,f1268,f1273,f1278,f1283,f1288,f1293,f1298,f1303,f1308,f1313,f1318,f1323,f1328,f1333,f1338,f1343,f1348,f1353,f1358,f1362,f1367,f1373,f1377,f1381,f1385,f1389,f1394,f1398,f1402,f1406,f1410,f1414,f1418,f1423,f1429,f1433,f1437,f1441,f1445,f1449,f1453,f1457,f1461,f1465,f1469,f1473,f1477,f1482,f1486,f1490,f1494,f1499,f1503,f1507,f1511,f1515,f1519,f1523,f1527,f1531,f1535,f1539,f1543,f1547,f1551,f1555,f1559,f1563,f1567,f1571,f1578,f1582,f1586,f1590,f1594,f1598,f1602,f1606,f1610,f1614,f1618,f1622,f1626,f1630,f1634,f1638,f1642,f1646,f1650,f1654,f1665,f1681,f1687,f1691,f1695,f1699,f1703,f1707,f1711,f1715,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1763,f1767,f1771,f1775,f1779,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1816,f1820,f1824,f1828,f1835,f1971,f2000,f2004,f2008,f2012,f2016,f2020,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2143,f2147,f2151,f2155,f2159,f2163,f2167,f2248,f2352,f2440,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2480,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2516,f2526,f2530,f2534,f2538,f2542,f2546,f2695,f2797,f2801,f2805,f2809,f2813,f2817,f2821,f2825,f2829,f2833,f2837,f2841,f2845,f2849,f2853,f2857,f2861,f2865,f2869,f2873,f2877,f2881,f2886,f2890,f2895,f2899,f2904,f2908,f2912,f2917,f2921,f2925,f2934,f3245,f3319,f3323,f3327,f3331,f3338,f3342,f3346,f3350,f3354,f3358,f3362,f3366,f3370,f3374,f3383,f3387,f3391,f3395,f3399,f3403,f3407,f3411,f3415,f3419,f3429,f3433,f3437,f3441,f3445,f3449,f3453,f3457,f3461,f3465,f3472,f3476,f3480,f3484,f3488,f3493,f3497,f3501,f3505,f3510,f3516,f3721,f3950,f4306,f4522,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4614,f4618,f4622,f4644,f4648,f4652,f4656,f4660,f4664,f4668,f4672,f4676,f4680,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4750,f4754,f4758,f4762,f4766,f5256,f5463]) ).
fof(f5463,plain,
( ~ spl0_45
| spl0_40
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f5460,f4704,f1370,f1391]) ).
fof(f1391,plain,
( spl0_45
<=> c_Type_Otyping(v_ea____,v_ta____,v_Ta____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1370,plain,
( spl0_40
<=> c_Type_Otyping(c_Type_Oshift(v_ea____,c_Orderings_Obot__class_Obot(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_Orderings_Obot__class_Obot(tc_nat)),v_Ta____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f4704,plain,
( spl0_332
<=> ! [X11,X0,X64,X23,X19] :
( ~ c_Type_Otyping(X11,X19,X23)
| c_Type_Otyping(c_Type_Oshift(X11,X0,X64,tc_Type_Otype),c_Lambda_Olift(X19,X0),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f5460,plain,
( ~ c_Type_Otyping(v_ea____,v_ta____,v_Ta____)
| spl0_40
| ~ spl0_332 ),
inference(resolution,[],[f4705,f1372]) ).
fof(f1372,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_Orderings_Obot__class_Obot(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_Orderings_Obot__class_Obot(tc_nat)),v_Ta____)
| spl0_40 ),
inference(avatar_component_clause,[],[f1370]) ).
fof(f4705,plain,
( ! [X0,X11,X19,X23,X64] :
( c_Type_Otyping(c_Type_Oshift(X11,X0,X64,tc_Type_Otype),c_Lambda_Olift(X19,X0),X23)
| ~ c_Type_Otyping(X11,X19,X23) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f4704]) ).
fof(f5256,plain,
( spl0_348
| ~ spl0_122
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f5006,f4604,f1729,f5254]) ).
fof(f5254,plain,
( spl0_348
<=> ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f1729,plain,
( spl0_122
<=> ! [X1,X10] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f4604,plain,
( spl0_313
<=> ! [X1,X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat)),X1) = c_Orderings_Oord__class_Omax(X10,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f5006,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_122
| ~ spl0_313 ),
inference(superposition,[],[f1730,f4605]) ).
fof(f4605,plain,
( ! [X10,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat)),X1) = c_Orderings_Oord__class_Omax(X10,X1,tc_nat)
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f4604]) ).
fof(f1730,plain,
( ! [X10,X1] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10),tc_nat)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1729]) ).
fof(f4766,plain,
spl0_347,
inference(avatar_split_clause,[],[f1127,f4764]) ).
fof(f4764,plain,
( spl0_347
<=> ! [X9,X10] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X10))
| hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f1127,plain,
! [X10,X9] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X10))
| hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X9))) ),
inference(forward_demodulation,[],[f826,f855]) ).
fof(f855,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__nat__def_0) ).
fof(f826,axiom,
! [X10,X9] :
( hBOOL(hAPP(X9,X10))
| ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_0) ).
fof(f4762,plain,
spl0_346,
inference(avatar_split_clause,[],[f1126,f4760]) ).
fof(f4760,plain,
( spl0_346
<=> ! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__Nat__Xnat__Xinduct__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f1126,plain,
! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__Nat__Xnat__Xinduct__1(X9))) ),
inference(forward_demodulation,[],[f852,f855]) ).
fof(f852,axiom,
! [X9,X15] :
( hBOOL(hAPP(X9,X15))
| ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X9,v_sko__Nat__Xnat__Xinduct__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
fof(f4758,plain,
spl0_345,
inference(avatar_split_clause,[],[f1125,f4756]) ).
fof(f4756,plain,
( spl0_345
<=> ! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__List__Xupt__Xinduct__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f1125,plain,
! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__List__Xupt__Xinduct__1(X9))) ),
inference(forward_demodulation,[],[f856,f855]) ).
fof(f856,axiom,
! [X9,X15] :
( hBOOL(hAPP(X9,X15))
| ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X9,v_sko__List__Xupt__Xinduct__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
fof(f4754,plain,
spl0_344,
inference(avatar_split_clause,[],[f1124,f4752]) ).
fof(f4752,plain,
( spl0_344
<=> ! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__List__Xreplicate__Xinduct__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f1124,plain,
! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__List__Xreplicate__Xinduct__1(X9))) ),
inference(forward_demodulation,[],[f843,f855]) ).
fof(f843,axiom,
! [X9,X15] :
( hBOOL(hAPP(X9,X15))
| ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X9,v_sko__List__Xreplicate__Xinduct__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_0) ).
fof(f4750,plain,
spl0_343,
inference(avatar_split_clause,[],[f1123,f4748]) ).
fof(f4748,plain,
( spl0_343
<=> ! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__Nat__Xnat__Xinducts__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f1123,plain,
! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__Nat__Xnat__Xinducts__1(X9))) ),
inference(forward_demodulation,[],[f847,f855]) ).
fof(f847,axiom,
! [X9,X15] :
( hBOOL(hAPP(X9,X15))
| ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X9,v_sko__Nat__Xnat__Xinducts__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_0) ).
fof(f4746,plain,
spl0_342,
inference(avatar_split_clause,[],[f1122,f4744]) ).
fof(f4744,plain,
( spl0_342
<=> ! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__List__Xlexn__Xinduct__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f1122,plain,
! [X9,X15] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X15))
| hBOOL(hAPP(X9,v_sko__List__Xlexn__Xinduct__1(X9))) ),
inference(forward_demodulation,[],[f812,f855]) ).
fof(f812,axiom,
! [X9,X15] :
( hBOOL(hAPP(X9,X15))
| ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X9,v_sko__List__Xlexn__Xinduct__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lexn_Oinduct_0) ).
fof(f4742,plain,
spl0_341,
inference(avatar_split_clause,[],[f1121,f4740]) ).
fof(f4740,plain,
( spl0_341
<=> ! [X9,X10] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X10))
| ~ hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f1121,plain,
! [X10,X9] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,X10))
| ~ hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X9))) ),
inference(forward_demodulation,[],[f859,f855]) ).
fof(f859,axiom,
! [X10,X9] :
( hBOOL(hAPP(X9,X10))
| ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_infinite__descent0_1) ).
fof(f4738,plain,
spl0_340,
inference(avatar_split_clause,[],[f1084,f4736]) ).
fof(f4736,plain,
( spl0_340
<=> ! [X9,X3] :
( hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ hBOOL(hAPP(X9,X3))
| ~ hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f1084,plain,
! [X3,X9] :
( hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ hBOOL(hAPP(X9,X3))
| ~ hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X9))) ),
inference(forward_demodulation,[],[f813,f855]) ).
fof(f813,axiom,
! [X3,X9] :
( ~ hBOOL(hAPP(X9,X3))
| ~ hBOOL(hAPP(X9,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(X9)))
| hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct_1) ).
fof(f4734,plain,
spl0_339,
inference(avatar_split_clause,[],[f1075,f4732]) ).
fof(f4732,plain,
( spl0_339
<=> ! [X5,X10] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f1075,plain,
! [X10,X5] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
inference(forward_demodulation,[],[f536,f855]) ).
fof(f536,axiom,
! [X10,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f4730,plain,
( spl0_338
| ~ spl0_137
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2555,f2350,f1789,f4728]) ).
fof(f4728,plain,
( spl0_338
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f1789,plain,
( spl0_137
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f2350,plain,
( spl0_192
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f2555,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_137
| ~ spl0_192 ),
inference(resolution,[],[f2351,f1790]) ).
fof(f1790,plain,
( ! [X10,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X10),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1789]) ).
fof(f2351,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2350]) ).
fof(f4726,plain,
spl0_337,
inference(avatar_split_clause,[],[f1074,f4724]) ).
fof(f4724,plain,
( spl0_337
<=> ! [X5,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f1074,plain,
! [X10,X5] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
inference(forward_demodulation,[],[f535,f855]) ).
fof(f535,axiom,
! [X10,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f4722,plain,
spl0_336,
inference(avatar_split_clause,[],[f1042,f4720]) ).
fof(f4720,plain,
( spl0_336
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),X10,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f1042,plain,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),X10,tc_nat) = X1 ),
inference(forward_demodulation,[],[f35,f855]) ).
fof(f35,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),X10,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).
fof(f4718,plain,
spl0_335,
inference(avatar_split_clause,[],[f1041,f4716]) ).
fof(f4716,plain,
( spl0_335
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X1,tc_nat),X10,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f1041,plain,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X1,tc_nat),X10,tc_nat) = X1 ),
inference(forward_demodulation,[],[f34,f855]) ).
fof(f34,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X10,X1,tc_nat),X10,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).
fof(f4714,plain,
spl0_334,
inference(avatar_split_clause,[],[f1040,f4712]) ).
fof(f4712,plain,
( spl0_334
<=> ! [X10] :
( c_Suc(c_HOL_Ominus__class_Ominus(X10,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat)) = X10
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f1040,plain,
! [X10] :
( c_Suc(c_HOL_Ominus__class_Ominus(X10,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat)) = X10
| ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f1039,f855]) ).
fof(f1039,plain,
! [X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X10,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X10 ),
inference(forward_demodulation,[],[f743,f855]) ).
fof(f743,axiom,
! [X10] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X10,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
fof(f4710,plain,
spl0_333,
inference(avatar_split_clause,[],[f1023,f4708]) ).
fof(f4708,plain,
( spl0_333
<=> ! [X2,X16] :
( c_Orderings_Obot__class_Obot(tc_nat) = X16
| c_Nitpick_Onat__gcd(X2,X16) = c_Nitpick_Onat__gcd(X16,c_Divides_Odiv__class_Omod(X2,X16,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f1023,plain,
! [X2,X16] :
( c_Orderings_Obot__class_Obot(tc_nat) = X16
| c_Nitpick_Onat__gcd(X2,X16) = c_Nitpick_Onat__gcd(X16,c_Divides_Odiv__class_Omod(X2,X16,tc_nat)) ),
inference(forward_demodulation,[],[f655,f855]) ).
fof(f655,axiom,
! [X2,X16] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X16
| c_Nitpick_Onat__gcd(X2,X16) = c_Nitpick_Onat__gcd(X16,c_Divides_Odiv__class_Omod(X2,X16,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__gcd_Osimps_1) ).
fof(f4706,plain,
spl0_332,
inference(avatar_split_clause,[],[f901,f4704]) ).
fof(f901,axiom,
! [X0,X11,X19,X23,X64] :
( ~ c_Type_Otyping(X11,X19,X23)
| c_Type_Otyping(c_Type_Oshift(X11,X0,X64,tc_Type_Otype),c_Lambda_Olift(X19,X0),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
fof(f4702,plain,
spl0_331,
inference(avatar_split_clause,[],[f878,f4700]) ).
fof(f4700,plain,
( spl0_331
<=> ! [X61,X23,X9,X2] :
( hBOOL(hAPP(X9,X61))
| hBOOL(hAPP(X9,X23))
| c_Type_Osko__Type__Xtype__induct__1__1(X9) != c_Type_Otype_OFun(X61,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f878,axiom,
! [X2,X9,X61,X23] :
( hBOOL(hAPP(X9,X61))
| hBOOL(hAPP(X9,X23))
| c_Type_Osko__Type__Xtype__induct__1__1(X9) != c_Type_Otype_OFun(X61,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_0) ).
fof(f4698,plain,
spl0_330,
inference(avatar_split_clause,[],[f877,f4696]) ).
fof(f4696,plain,
( spl0_330
<=> ! [X59,X60,X23,X9] :
( hBOOL(hAPP(X9,X60))
| hBOOL(hAPP(X9,X23))
| c_Type_Osko__Type__Xtype__induct__1__1(X9) != c_Type_Otype_OFun(X59,X60) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f877,axiom,
! [X59,X9,X60,X23] :
( hBOOL(hAPP(X9,X60))
| hBOOL(hAPP(X9,X23))
| c_Type_Osko__Type__Xtype__induct__1__1(X9) != c_Type_Otype_OFun(X59,X60) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_1) ).
fof(f4694,plain,
spl0_329,
inference(avatar_split_clause,[],[f742,f4692]) ).
fof(f4692,plain,
( spl0_329
<=> ! [X1,X3,X10] :
( X1 = X10
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f742,axiom,
! [X3,X10,X1] :
( X1 = X10
| c_HOL_Otimes__class_Otimes(c_Suc(X3),X1,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X3),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
fof(f4690,plain,
spl0_328,
inference(avatar_split_clause,[],[f729,f4688]) ).
fof(f4688,plain,
( spl0_328
<=> ! [X4,X0,X3] :
( ~ c_lessequals(X0,X4,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f729,axiom,
! [X3,X0,X4] :
( ~ c_lessequals(X0,X4,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X0,tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
fof(f4680,plain,
spl0_327,
inference(avatar_split_clause,[],[f728,f4678]) ).
fof(f4678,plain,
( spl0_327
<=> ! [X4,X0,X3] :
( ~ c_lessequals(X0,X4,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,tc_nat),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f728,axiom,
! [X3,X0,X4] :
( ~ c_lessequals(X0,X4,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X0,X3,tc_nat),c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
fof(f4676,plain,
spl0_326,
inference(avatar_split_clause,[],[f710,f4674]) ).
fof(f4674,plain,
( spl0_326
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X16,X17,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| c_HOL_Oord__class_Oless(X2,X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f710,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X16,X17,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| c_HOL_Oord__class_Oless(X2,X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f4672,plain,
spl0_325,
inference(avatar_split_clause,[],[f709,f4670]) ).
fof(f4670,plain,
( spl0_325
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X2,X16,X5)
| ~ c_HOL_Oord__class_Oless(X16,X17,X5)
| c_HOL_Oord__class_Oless(X2,X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f709,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X2,X16,X5)
| ~ c_HOL_Oord__class_Oless(X16,X17,X5)
| c_HOL_Oord__class_Oless(X2,X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f4668,plain,
spl0_324,
inference(avatar_split_clause,[],[f645,f4666]) ).
fof(f4666,plain,
( spl0_324
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f645,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f4664,plain,
spl0_323,
inference(avatar_split_clause,[],[f603,f4662]) ).
fof(f4662,plain,
( spl0_323
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X2,X16,X5)
| ~ c_lessequals(X16,X17,X5)
| c_lessequals(X2,X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f603,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X2,X16,X5)
| ~ c_lessequals(X16,X17,X5)
| c_lessequals(X2,X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f4660,plain,
spl0_322,
inference(avatar_split_clause,[],[f601,f4658]) ).
fof(f4658,plain,
( spl0_322
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X17,X16,X5)
| c_HOL_Oord__class_Oless(X17,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f601,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X17,X16,X5)
| c_HOL_Oord__class_Oless(X17,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f4656,plain,
spl0_321,
inference(avatar_split_clause,[],[f600,f4654]) ).
fof(f4654,plain,
( spl0_321
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X17,X16,X5)
| ~ c_HOL_Oord__class_Oless(X16,X2,X5)
| c_HOL_Oord__class_Oless(X17,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f600,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X17,X16,X5)
| ~ c_HOL_Oord__class_Oless(X16,X2,X5)
| c_HOL_Oord__class_Oless(X17,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f4652,plain,
spl0_320,
inference(avatar_split_clause,[],[f599,f4650]) ).
fof(f4650,plain,
( spl0_320
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_lessequals(X17,X16,X5)
| c_lessequals(X17,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f599,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_lessequals(X17,X16,X5)
| c_lessequals(X17,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f4648,plain,
spl0_319,
inference(avatar_split_clause,[],[f587,f4646]) ).
fof(f4646,plain,
( spl0_319
<=> ! [X1,X10] : c_Divides_Odiv__class_Omod(c_Suc(X1),X10,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X10,tc_nat)),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f587,axiom,
! [X10,X1] : c_Divides_Odiv__class_Omod(c_Suc(X1),X10,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X1,X10,tc_nat)),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
fof(f4644,plain,
spl0_318,
inference(avatar_split_clause,[],[f528,f4642]) ).
fof(f4642,plain,
( spl0_318
<=> ! [X1,X3,X10] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X10,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f528,axiom,
! [X3,X10,X1] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),c_HOL_Otimes__class_Otimes(X10,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
fof(f4622,plain,
spl0_317,
inference(avatar_split_clause,[],[f527,f4620]) ).
fof(f4620,plain,
( spl0_317
<=> ! [X1,X3,X10] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f527,axiom,
! [X3,X10,X1] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,tc_nat),c_HOL_Otimes__class_Otimes(X3,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
fof(f4618,plain,
spl0_316,
inference(avatar_split_clause,[],[f506,f4616]) ).
fof(f4616,plain,
( spl0_316
<=> ! [X5,X1,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f506,axiom,
! [X10,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f4614,plain,
spl0_315,
inference(avatar_split_clause,[],[f470,f4612]) ).
fof(f4612,plain,
( spl0_315
<=> ! [X1,X3,X10] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Odiv(X1,X3,tc_nat),c_Divides_Odiv__class_Odiv(X10,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f470,axiom,
! [X3,X10,X1] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Odiv(X1,X3,tc_nat),c_Divides_Odiv__class_Odiv(X10,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__mono_0) ).
fof(f4610,plain,
spl0_314,
inference(avatar_split_clause,[],[f405,f4608]) ).
fof(f4608,plain,
( spl0_314
<=> ! [X5,X1,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f405,axiom,
! [X10,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f4606,plain,
spl0_313,
inference(avatar_split_clause,[],[f376,f4604]) ).
fof(f376,axiom,
! [X10,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat)),X1) = c_Orderings_Oord__class_Omax(X10,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
fof(f4602,plain,
spl0_312,
inference(avatar_split_clause,[],[f362,f4600]) ).
fof(f4600,plain,
( spl0_312
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X2,X16,X5)
| c_lessequals(X16,X2,X5)
| c_HOL_Oord__class_Oless(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f362,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X2,X16,X5)
| c_lessequals(X16,X2,X5)
| c_HOL_Oord__class_Oless(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f4598,plain,
spl0_311,
inference(avatar_split_clause,[],[f356,f4596]) ).
fof(f4596,plain,
( spl0_311
<=> ! [X5,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5),X10,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f356,axiom,
! [X10,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(X5),c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5),X10,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Opower__one_0) ).
fof(f4594,plain,
spl0_310,
inference(avatar_split_clause,[],[f241,f4592]) ).
fof(f4592,plain,
( spl0_310
<=> ! [X22,X1,X10] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X22,tc_nat),c_HOL_Ominus__class_Ominus(X10,X22,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f241,axiom,
! [X10,X1,X22] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X22,tc_nat),c_HOL_Ominus__class_Ominus(X10,X22,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f4590,plain,
spl0_309,
inference(avatar_split_clause,[],[f240,f4588]) ).
fof(f4588,plain,
( spl0_309
<=> ! [X22,X1,X10] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X22,X10,tc_nat),c_HOL_Ominus__class_Ominus(X22,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f240,axiom,
! [X10,X1,X22] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X22,X10,tc_nat),c_HOL_Ominus__class_Ominus(X22,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f4586,plain,
spl0_308,
inference(avatar_split_clause,[],[f89,f4584]) ).
fof(f4584,plain,
( spl0_308
<=> ! [X11,X13,X23,X19] :
( ~ c_Type_Otyping(X11,c_Lambda_OdB_OApp(X19,X13),X23)
| c_Type_Otyping(X11,X13,c_Type_Osko__Type__Xtyping__elims__2__1(X23,X11,X19,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f89,axiom,
! [X11,X19,X23,X13] :
( ~ c_Type_Otyping(X11,c_Lambda_OdB_OApp(X19,X13),X23)
| c_Type_Otyping(X11,X13,c_Type_Osko__Type__Xtyping__elims__2__1(X23,X11,X19,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
fof(f4582,plain,
( spl0_307
| ~ spl0_131
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4456,f3474,f1765,f4580]) ).
fof(f4580,plain,
( spl0_307
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_nat_Onat__size(c_Suc(X0)),c_nat_Onat__size(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f1765,plain,
( spl0_131
<=> ! [X4,X0] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X4),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f3474,plain,
( spl0_287
<=> ! [X15] : c_nat_Onat__size(c_Suc(X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X15)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f4456,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_nat_Onat__size(c_Suc(X0)),c_nat_Onat__size(X0),tc_nat)
| ~ spl0_131
| ~ spl0_287 ),
inference(superposition,[],[f1766,f3475]) ).
fof(f3475,plain,
( ! [X15] : c_nat_Onat__size(c_Suc(X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X15)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f3474]) ).
fof(f1766,plain,
( ! [X0,X4] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X4),X0,tc_nat)
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1765]) ).
fof(f4578,plain,
spl0_306,
inference(avatar_split_clause,[],[f88,f4576]) ).
fof(f4576,plain,
( spl0_306
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X17,X16,X5)
| c_HOL_Oord__class_Oless(X17,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f88,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X17,X16,X5)
| c_HOL_Oord__class_Oless(X17,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f4574,plain,
spl0_305,
inference(avatar_split_clause,[],[f87,f4572]) ).
fof(f4572,plain,
( spl0_305
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| ~ c_HOL_Oord__class_Oless(X16,X17,X5)
| c_HOL_Oord__class_Oless(X2,X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f87,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| ~ c_HOL_Oord__class_Oless(X16,X17,X5)
| c_HOL_Oord__class_Oless(X2,X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f4570,plain,
spl0_304,
inference(avatar_split_clause,[],[f55,f4568]) ).
fof(f4568,plain,
( spl0_304
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f55,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f4566,plain,
spl0_303,
inference(avatar_split_clause,[],[f43,f4564]) ).
fof(f4564,plain,
( spl0_303
<=> ! [X5,X1,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f43,axiom,
! [X10,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
fof(f4562,plain,
spl0_302,
inference(avatar_split_clause,[],[f42,f4560]) ).
fof(f4560,plain,
( spl0_302
<=> ! [X5,X1,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f42,axiom,
! [X10,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
fof(f4558,plain,
spl0_301,
inference(avatar_split_clause,[],[f41,f4556]) ).
fof(f4556,plain,
( spl0_301
<=> ! [X6,X5,X7] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X6,X7,X5) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X6,X7,X5),X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f41,axiom,
! [X6,X7,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X6,X7,X5) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X6,X7,X5),X7,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f4522,plain,
( spl0_300
| ~ spl0_121
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f4454,f3474,f1725,f4520]) ).
fof(f4520,plain,
( spl0_300
<=> ! [X0] : c_lessequals(c_nat_Onat__size(X0),c_nat_Onat__size(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f1725,plain,
( spl0_121
<=> ! [X1,X10] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f4454,plain,
( ! [X0] : c_lessequals(c_nat_Onat__size(X0),c_nat_Onat__size(c_Suc(X0)),tc_nat)
| ~ spl0_121
| ~ spl0_287 ),
inference(superposition,[],[f1726,f3475]) ).
fof(f1726,plain,
( ! [X10,X1] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),tc_nat)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1725]) ).
fof(f4306,plain,
( spl0_299
| ~ spl0_129
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2518,f2153,f1757,f4304]) ).
fof(f4304,plain,
( spl0_299
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f1757,plain,
( spl0_129
<=> ! [X1,X10] :
( c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(c_Suc(X1),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2153,plain,
( spl0_187
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f2518,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_129
| ~ spl0_187 ),
inference(resolution,[],[f2154,f1758]) ).
fof(f1758,plain,
( ! [X10,X1] :
( ~ c_lessequals(c_Suc(X1),X10,tc_nat)
| c_lessequals(X1,X10,tc_nat) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1757]) ).
fof(f2154,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2153]) ).
fof(f3950,plain,
( spl0_298
| ~ spl0_130
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2476,f2109,f1761,f3948]) ).
fof(f3948,plain,
( spl0_298
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f1761,plain,
( spl0_130
<=> ! [X1,X10] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(X1,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f2109,plain,
( spl0_176
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2476,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_130
| ~ spl0_176 ),
inference(resolution,[],[f2110,f1762]) ).
fof(f1762,plain,
( ! [X10,X1] :
( c_lessequals(X1,c_Suc(X10),tc_nat)
| ~ c_lessequals(X1,X10,tc_nat) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1761]) ).
fof(f2110,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f2109]) ).
fof(f3721,plain,
( spl0_297
| ~ spl0_136
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2426,f2065,f1785,f3719]) ).
fof(f3719,plain,
( spl0_297
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f1785,plain,
( spl0_136
<=> ! [X1,X10] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f2065,plain,
( spl0_165
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2426,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_136
| ~ spl0_165 ),
inference(resolution,[],[f2066,f1786]) ).
fof(f1786,plain,
( ! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X1),X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1785]) ).
fof(f2066,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f2065]) ).
fof(f3516,plain,
spl0_296,
inference(avatar_split_clause,[],[f1057,f3514]) ).
fof(f3514,plain,
( spl0_296
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f1057,plain,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f1056,f855]) ).
fof(f1056,plain,
! [X10,X1] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f282,f855]) ).
fof(f282,axiom,
! [X10,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
fof(f3510,plain,
spl0_295,
inference(avatar_split_clause,[],[f1055,f3508]) ).
fof(f3508,plain,
( spl0_295
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f1055,plain,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat) ),
inference(forward_demodulation,[],[f1054,f855]) ).
fof(f1054,plain,
! [X10,X1] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f283,f855]) ).
fof(f283,axiom,
! [X10,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
fof(f3505,plain,
spl0_294,
inference(avatar_split_clause,[],[f1053,f3503]) ).
fof(f3503,plain,
( spl0_294
<=> ! [X9,X10] :
( ~ hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f1053,plain,
! [X10,X9] :
( ~ hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat))) ),
inference(forward_demodulation,[],[f1052,f855]) ).
fof(f1052,plain,
! [X10,X9] :
( hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(forward_demodulation,[],[f818,f855]) ).
fof(f818,axiom,
! [X10,X9] :
( hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_0) ).
fof(f3501,plain,
spl0_293,
inference(avatar_split_clause,[],[f1051,f3499]) ).
fof(f3499,plain,
( spl0_293
<=> ! [X1,X10] :
( c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_Orderings_Obot__class_Obot(tc_nat))
| c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f1051,plain,
! [X10,X1] :
( c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_Orderings_Obot__class_Obot(tc_nat))
| c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X1 ),
inference(forward_demodulation,[],[f1050,f855]) ).
fof(f1050,plain,
! [X10,X1] :
( c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X1
| c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(forward_demodulation,[],[f142,f855]) ).
fof(f142,axiom,
! [X10,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
fof(f3497,plain,
spl0_292,
inference(avatar_split_clause,[],[f1049,f3495]) ).
fof(f3495,plain,
( spl0_292
<=> ! [X1,X10] :
( c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_Orderings_Obot__class_Obot(tc_nat))
| c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f1049,plain,
! [X10,X1] :
( c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_Orderings_Obot__class_Obot(tc_nat))
| c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X10 ),
inference(forward_demodulation,[],[f1048,f855]) ).
fof(f1048,plain,
! [X10,X1] :
( c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X10
| c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(forward_demodulation,[],[f143,f855]) ).
fof(f143,axiom,
! [X10,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X10
| c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
fof(f3493,plain,
spl0_291,
inference(avatar_split_clause,[],[f1038,f3491]) ).
fof(f3491,plain,
( spl0_291
<=> ! [X0,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,c_Suc(X0),tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f1038,plain,
! [X10,X0] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,c_Suc(X0),tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f756,f855]) ).
fof(f756,axiom,
! [X10,X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,c_Suc(X0),tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f3488,plain,
spl0_290,
inference(avatar_split_clause,[],[f1033,f3486]) ).
fof(f3486,plain,
( spl0_290
<=> ! [X9,X1] :
( hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f1033,plain,
! [X1,X9] :
( hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat))) ),
inference(forward_demodulation,[],[f1032,f855]) ).
fof(f1032,plain,
! [X1,X9] :
( ~ hBOOL(hAPP(X9,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
inference(forward_demodulation,[],[f816,f855]) ).
fof(f816,axiom,
! [X1,X9] :
( ~ hBOOL(hAPP(X9,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X9,c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_H_6) ).
fof(f3484,plain,
spl0_289,
inference(avatar_split_clause,[],[f1022,f3482]) ).
fof(f3482,plain,
( spl0_289
<=> ! [X1,X10] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f1022,plain,
! [X10,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X1 ),
inference(forward_demodulation,[],[f1021,f855]) ).
fof(f1021,plain,
! [X10,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) ),
inference(forward_demodulation,[],[f831,f855]) ).
fof(f831,axiom,
! [X10,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f3480,plain,
spl0_288,
inference(avatar_split_clause,[],[f1020,f3478]) ).
fof(f3478,plain,
( spl0_288
<=> ! [X1,X10] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f1020,plain,
! [X10,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ),
inference(forward_demodulation,[],[f1019,f855]) ).
fof(f1019,plain,
! [X10,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) ),
inference(forward_demodulation,[],[f830,f855]) ).
fof(f830,axiom,
! [X10,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f3476,plain,
spl0_287,
inference(avatar_split_clause,[],[f988,f3474]) ).
fof(f988,plain,
! [X15] : c_nat_Onat__size(c_Suc(X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X15)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat))),
inference(forward_demodulation,[],[f488,f855]) ).
fof(f488,axiom,
! [X15] : c_nat_Onat__size(c_Suc(X15)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X15)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osize_I2_J_0) ).
fof(f3472,plain,
spl0_286,
inference(avatar_split_clause,[],[f885,f3470]) ).
fof(f3470,plain,
( spl0_286
<=> ! [X20,X19,X3] : c_Lambda_Olift(c_Lambda_OdB_OApp(X20,X19),X3) = c_Lambda_OdB_OApp(c_Lambda_Olift(X20,X3),c_Lambda_Olift(X19,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f885,axiom,
! [X3,X19,X20] : c_Lambda_Olift(c_Lambda_OdB_OApp(X20,X19),X3) = c_Lambda_OdB_OApp(c_Lambda_Olift(X20,X3),c_Lambda_Olift(X19,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
fof(f3465,plain,
spl0_285,
inference(avatar_split_clause,[],[f880,f3463]) ).
fof(f3463,plain,
( spl0_285
<=> ! [X62,X63,X5,X25,X24] : hAPP(hAPP(X25,X62),X63) = c_Type_Otype_Otype__case(X24,X25,c_Type_Otype_OFun(X62,X63),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f880,axiom,
! [X62,X63,X24,X5,X25] : hAPP(hAPP(X25,X62),X63) = c_Type_Otype_Otype__case(X24,X25,c_Type_Otype_OFun(X62,X63),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
fof(f3461,plain,
spl0_284,
inference(avatar_split_clause,[],[f775,f3459]) ).
fof(f3459,plain,
( spl0_284
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| X2 = X16
| ~ c_lessequals(X2,X16,X5)
| c_HOL_Oord__class_Oless(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f775,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| X2 = X16
| ~ c_lessequals(X2,X16,X5)
| c_HOL_Oord__class_Oless(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f3457,plain,
spl0_283,
inference(avatar_split_clause,[],[f773,f3455]) ).
fof(f3455,plain,
( spl0_283
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Oorder(X5)
| X6 = X7
| ~ c_lessequals(X6,X7,X5)
| c_HOL_Oord__class_Oless(X6,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f773,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Oorder(X5)
| X6 = X7
| ~ c_lessequals(X6,X7,X5)
| c_HOL_Oord__class_Oless(X6,X7,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
fof(f3453,plain,
spl0_282,
inference(avatar_split_clause,[],[f509,f3451]) ).
fof(f3451,plain,
( spl0_282
<=> ! [X4,X0,X3] :
( ~ c_HOL_Oord__class_Oless(X0,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f509,axiom,
! [X3,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f3449,plain,
spl0_281,
inference(avatar_split_clause,[],[f498,f3447]) ).
fof(f3447,plain,
( spl0_281
<=> ! [X1,X10] :
( c_Suc(X10) = X1
| c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(X1,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f498,axiom,
! [X10,X1] :
( c_Suc(X10) = X1
| c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(X1,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
fof(f3445,plain,
spl0_280,
inference(avatar_split_clause,[],[f495,f3443]) ).
fof(f3443,plain,
( spl0_280
<=> ! [X0,X10] :
( ~ c_lessequals(X0,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X10,X0,tc_nat),tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f495,axiom,
! [X10,X0] :
( ~ c_lessequals(X0,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X10,X0,tc_nat),tc_nat) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f3441,plain,
spl0_279,
inference(avatar_split_clause,[],[f414,f3439]) ).
fof(f3439,plain,
( spl0_279
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_Suc(X1) = X10
| c_HOL_Oord__class_Oless(c_Suc(X1),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f414,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_Suc(X1) = X10
| c_HOL_Oord__class_Oless(c_Suc(X1),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f3437,plain,
spl0_278,
inference(avatar_split_clause,[],[f386,f3435]) ).
fof(f3435,plain,
( spl0_278
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Oorder(X5)
| X2 = X16
| ~ c_lessequals(X16,X2,X5)
| ~ c_lessequals(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f386,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Oorder(X5)
| X2 = X16
| ~ c_lessequals(X16,X2,X5)
| ~ c_lessequals(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f3433,plain,
spl0_277,
inference(avatar_split_clause,[],[f384,f3431]) ).
fof(f3431,plain,
( spl0_277
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| X2 = X16
| c_HOL_Oord__class_Oless(X2,X16,X5)
| c_HOL_Oord__class_Oless(X16,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f384,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| X2 = X16
| c_HOL_Oord__class_Oless(X2,X16,X5)
| c_HOL_Oord__class_Oless(X16,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f3429,plain,
spl0_276,
inference(avatar_split_clause,[],[f312,f3427]) ).
fof(f3427,plain,
( spl0_276
<=> ! [X5,X7,X6,X2] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X6,X2,X5)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X6,X7,X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f312,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X6,X2,X5)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X6,X7,X5),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
fof(f3419,plain,
spl0_275,
inference(avatar_split_clause,[],[f311,f3417]) ).
fof(f3417,plain,
( spl0_275
<=> ! [X6,X2,X5,X7] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X7,X2,X5)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X6,X7,X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f311,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X7,X2,X5)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X6,X7,X5),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
fof(f3415,plain,
spl0_274,
inference(avatar_split_clause,[],[f309,f3413]) ).
fof(f3413,plain,
( spl0_274
<=> ! [X5,X7,X6,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X6,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f309,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X7,X5)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X6,X7,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
fof(f3411,plain,
spl0_273,
inference(avatar_split_clause,[],[f308,f3409]) ).
fof(f3409,plain,
( spl0_273
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X17,X2,X5)
| c_lessequals(X17,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f308,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X17,X2,X5)
| c_lessequals(X17,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
fof(f3407,plain,
spl0_272,
inference(avatar_split_clause,[],[f296,f3405]) ).
fof(f3405,plain,
( spl0_272
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X17,X5)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X16,X5),X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f296,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X17,X5)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X2,X16,X5),X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
fof(f3403,plain,
spl0_271,
inference(avatar_split_clause,[],[f295,f3401]) ).
fof(f3401,plain,
( spl0_271
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X17,X16,X5)
| ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f295,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X17,X16,X5)
| ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f3399,plain,
spl0_270,
inference(avatar_split_clause,[],[f294,f3397]) ).
fof(f3397,plain,
( spl0_270
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X17,X2,X5)
| ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f294,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X17,X2,X5)
| ~ c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f3395,plain,
spl0_269,
inference(avatar_split_clause,[],[f293,f3393]) ).
fof(f3393,plain,
( spl0_269
<=> ! [X6,X2,X5,X7] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X7,X2,X5)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X6,X7,X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f293,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X7,X2,X5)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X6,X7,X5),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
fof(f3391,plain,
spl0_268,
inference(avatar_split_clause,[],[f277,f3389]) ).
fof(f3389,plain,
( spl0_268
<=> ! [X2,X5,X17,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X16,X17,X5)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X16,X5),X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f277,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X16,X17,X5)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X16,X5),X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f3387,plain,
spl0_267,
inference(avatar_split_clause,[],[f276,f3385]) ).
fof(f3385,plain,
( spl0_267
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X2,X17,X5)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X16,X5),X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f276,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_HOL_Oord__class_Oless(X2,X17,X5)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X2,X16,X5),X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f3383,plain,
spl0_266,
inference(avatar_split_clause,[],[f275,f3381]) ).
fof(f3381,plain,
( spl0_266
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X17,X16,X5)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f275,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X17,X16,X5)
| c_HOL_Oord__class_Oless(X17,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
fof(f3374,plain,
spl0_265,
inference(avatar_split_clause,[],[f272,f3372]) ).
fof(f3372,plain,
( spl0_265
<=> ! [X5,X7,X6,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X6,X5)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X6,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f272,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X6,X5)
| c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X6,X7,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
fof(f3370,plain,
spl0_264,
inference(avatar_split_clause,[],[f214,f3368]) ).
fof(f3368,plain,
( spl0_264
<=> ! [X2,X16,X17] :
( ~ c_lessequals(X2,X16,tc_nat)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f214,axiom,
! [X2,X16,X17] :
( ~ c_lessequals(X2,X16,tc_nat)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X16),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
fof(f3366,plain,
spl0_263,
inference(avatar_split_clause,[],[f212,f3364]) ).
fof(f3364,plain,
( spl0_263
<=> ! [X1,X3,X10] :
( c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f212,axiom,
! [X3,X10,X1] :
( c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f3362,plain,
spl0_262,
inference(avatar_split_clause,[],[f211,f3360]) ).
fof(f3360,plain,
( spl0_262
<=> ! [X1,X3,X10] :
( c_lessequals(X3,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f211,axiom,
! [X3,X10,X1] :
( c_lessequals(X3,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f3358,plain,
spl0_261,
inference(avatar_split_clause,[],[f209,f3356]) ).
fof(f3356,plain,
( spl0_261
<=> ! [X4,X0,X1] :
( ~ c_lessequals(X0,X4,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f209,axiom,
! [X0,X1,X4] :
( ~ c_lessequals(X0,X4,tc_nat)
| c_lessequals(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
fof(f3354,plain,
spl0_260,
inference(avatar_split_clause,[],[f173,f3352]) ).
fof(f3352,plain,
( spl0_260
<=> ! [X5,X7,X6,X2] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X6,X5)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X6,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f173,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X6,X5)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X6,X7,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
fof(f3350,plain,
spl0_259,
inference(avatar_split_clause,[],[f172,f3348]) ).
fof(f3348,plain,
( spl0_259
<=> ! [X5,X7,X6,X2] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X6,X7,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f172,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X7,X5)
| ~ c_lessequals(X2,c_Orderings_Oord__class_Omin(X6,X7,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
fof(f3346,plain,
spl0_258,
inference(avatar_split_clause,[],[f170,f3344]) ).
fof(f3344,plain,
( spl0_258
<=> ! [X6,X2,X5,X7] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X7,X2,X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X6,X7,X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f170,axiom,
! [X2,X6,X7,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X7,X2,X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X6,X7,X5),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
fof(f3342,plain,
spl0_257,
inference(avatar_split_clause,[],[f169,f3340]) ).
fof(f3340,plain,
( spl0_257
<=> ! [X17,X16,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X17,X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X16,X5),X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f169,axiom,
! [X2,X16,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X17,X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X16,X5),X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
fof(f3338,plain,
spl0_256,
inference(avatar_split_clause,[],[f139,f3336]) ).
fof(f3336,plain,
( spl0_256
<=> ! [X1,X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f139,axiom,
! [X10,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f3331,plain,
spl0_255,
inference(avatar_split_clause,[],[f130,f3329]) ).
fof(f3329,plain,
( spl0_255
<=> ! [X4,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X4,tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f130,axiom,
! [X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X4,tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f3327,plain,
spl0_254,
inference(avatar_split_clause,[],[f129,f3325]) ).
fof(f3325,plain,
( spl0_254
<=> ! [X4,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X4,tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f129,axiom,
! [X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X0,X4,tc_nat)
| c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
fof(f3323,plain,
spl0_253,
inference(avatar_split_clause,[],[f128,f3321]) ).
fof(f3321,plain,
( spl0_253
<=> ! [X4,X0,X3] :
( c_HOL_Oord__class_Oless(X0,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f128,axiom,
! [X3,X0,X4] :
( c_HOL_Oord__class_Oless(X0,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X4),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f3319,plain,
spl0_252,
inference(avatar_split_clause,[],[f19,f3317]) ).
fof(f3317,plain,
( spl0_252
<=> ! [X5,X10] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X5),c_Suc(X10),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f19,axiom,
! [X10,X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X5),c_Suc(X10),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f3245,plain,
( spl0_251
| ~ spl0_45
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2734,f2528,f1391,f3243]) ).
fof(f3243,plain,
( spl0_251
<=> ! [X0] :
( ~ c_Lambda_Obeta(v_ta____,X0)
| c_Type_Otyping(v_ea____,X0,v_Ta____) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2528,plain,
( spl0_212
<=> ! [X55,X11,X23,X19] :
( ~ c_Lambda_Obeta(X19,X55)
| ~ c_Type_Otyping(X11,X19,X23)
| c_Type_Otyping(X11,X55,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2734,plain,
( ! [X0] :
( ~ c_Lambda_Obeta(v_ta____,X0)
| c_Type_Otyping(v_ea____,X0,v_Ta____) )
| ~ spl0_45
| ~ spl0_212 ),
inference(resolution,[],[f2529,f1393]) ).
fof(f1393,plain,
( c_Type_Otyping(v_ea____,v_ta____,v_Ta____)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1391]) ).
fof(f2529,plain,
( ! [X11,X19,X55,X23] :
( ~ c_Type_Otyping(X11,X19,X23)
| ~ c_Lambda_Obeta(X19,X55)
| c_Type_Otyping(X11,X55,X23) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2528]) ).
fof(f2934,plain,
( spl0_250
| ~ spl0_49
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2249,f2029,f1408,f2932]) ).
fof(f2932,plain,
( spl0_250
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1408,plain,
( spl0_49
<=> ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2029,plain,
( spl0_156
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X10,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f2249,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0
| ~ spl0_49
| ~ spl0_156 ),
inference(resolution,[],[f2030,f1409]) ).
fof(f1409,plain,
( ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1408]) ).
fof(f2030,plain,
( ! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X10,tc_nat) = X1 )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f2925,plain,
spl0_249,
inference(avatar_split_clause,[],[f1037,f2923]) ).
fof(f2923,plain,
( spl0_249
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f1037,plain,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f221,f855]) ).
fof(f221,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f2921,plain,
spl0_248,
inference(avatar_split_clause,[],[f1036,f2919]) ).
fof(f2919,plain,
( spl0_248
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1036,plain,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f144,f855]) ).
fof(f144,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
fof(f2917,plain,
spl0_247,
inference(avatar_split_clause,[],[f1031,f2915]) ).
fof(f2915,plain,
( spl0_247
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1031,plain,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat) ),
inference(forward_demodulation,[],[f732,f855]) ).
fof(f732,axiom,
! [X10,X1] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2912,plain,
spl0_246,
inference(avatar_split_clause,[],[f1025,f2910]) ).
fof(f2910,plain,
( spl0_246
<=> ! [X9,X10] :
( ~ hBOOL(hAPP(X9,c_Divides_Odiv__class_Omod(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| hBOOL(hAPP(X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1025,plain,
! [X10,X9] :
( ~ hBOOL(hAPP(X9,c_Divides_Odiv__class_Omod(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| hBOOL(hAPP(X9,X10)) ),
inference(forward_demodulation,[],[f806,f855]) ).
fof(f806,axiom,
! [X10,X9] :
( hBOOL(hAPP(X9,X10))
| ~ hBOOL(hAPP(X9,c_Divides_Odiv__class_Omod(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).
fof(f2908,plain,
spl0_245,
inference(avatar_split_clause,[],[f1017,f2906]) ).
fof(f2906,plain,
( spl0_245
<=> ! [X1,X10] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f1017,plain,
! [X10,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) != X1 ),
inference(forward_demodulation,[],[f842,f855]) ).
fof(f842,axiom,
! [X10,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f2904,plain,
spl0_244,
inference(avatar_split_clause,[],[f1010,f2902]) ).
fof(f2902,plain,
( spl0_244
<=> ! [X1,X10] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1010,plain,
! [X10,X1] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat) ),
inference(forward_demodulation,[],[f733,f855]) ).
fof(f733,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X10,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2899,plain,
spl0_243,
inference(avatar_split_clause,[],[f999,f2897]) ).
fof(f2897,plain,
( spl0_243
<=> ! [X9,X10] :
( hBOOL(hAPP(X9,c_Divides_Odiv__class_Omod(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X9,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f999,plain,
! [X10,X9] :
( hBOOL(hAPP(X9,c_Divides_Odiv__class_Omod(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)))
| ~ hBOOL(hAPP(X9,X10)) ),
inference(forward_demodulation,[],[f705,f855]) ).
fof(f705,axiom,
! [X10,X9] :
( ~ hBOOL(hAPP(X9,X10))
| hBOOL(hAPP(X9,c_Divides_Odiv__class_Omod(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).
fof(f2895,plain,
spl0_242,
inference(avatar_split_clause,[],[f983,f2892]) ).
fof(f2892,plain,
( spl0_242
<=> c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f983,plain,
c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),
inference(forward_demodulation,[],[f348,f855]) ).
fof(f348,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/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
fof(f2890,plain,
spl0_241,
inference(avatar_split_clause,[],[f982,f2888]) ).
fof(f2888,plain,
( spl0_241
<=> ! [X1,X10] : c_HOL_Ominus__class_Ominus(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f982,plain,
! [X10,X1] : c_HOL_Ominus__class_Ominus(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f244,f855]) ).
fof(f244,axiom,
! [X10,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f2886,plain,
( spl0_240
| ~ spl0_23
| ~ spl0_53
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1974,f1818,f1426,f1285,f2883]) ).
fof(f2883,plain,
( spl0_240
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1285,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1426,plain,
( spl0_53
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1818,plain,
( spl0_144
<=> ! [X5] :
( c_HOL_Ozero__class_Ozero(X5) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X5)
| ~ class_Ring__and__Field_Osemiring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1974,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_23
| ~ spl0_53
| ~ spl0_144 ),
inference(forward_demodulation,[],[f1973,f1428]) ).
fof(f1428,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1426]) ).
fof(f1973,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_23
| ~ spl0_144 ),
inference(resolution,[],[f1819,f1287]) ).
fof(f1287,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f1819,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X5) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1818]) ).
fof(f2881,plain,
spl0_239,
inference(avatar_split_clause,[],[f724,f2879]) ).
fof(f2879,plain,
( spl0_239
<=> ! [X1,X10] :
( X1 = X10
| ~ c_lessequals(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f724,axiom,
! [X10,X1] :
( X1 = X10
| ~ c_lessequals(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f2877,plain,
spl0_238,
inference(avatar_split_clause,[],[f719,f2875]) ).
fof(f2875,plain,
( spl0_238
<=> ! [X6,X5,X7] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X6,X5),X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f719,axiom,
! [X6,X7,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X6,X5),X7,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f2873,plain,
spl0_237,
inference(avatar_split_clause,[],[f718,f2871]) ).
fof(f2871,plain,
( spl0_237
<=> ! [X6,X5,X7] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X7,X5),X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f718,axiom,
! [X6,X7,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X7,X5),X7,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f2869,plain,
spl0_236,
inference(avatar_split_clause,[],[f605,f2867]) ).
fof(f2867,plain,
( spl0_236
<=> ! [X4,X0,X3] :
( ~ c_lessequals(X0,X4,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat)
| c_lessequals(X0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f605,axiom,
! [X3,X0,X4] :
( ~ c_lessequals(X0,X4,tc_nat)
| ~ c_lessequals(X4,X3,tc_nat)
| c_lessequals(X0,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2865,plain,
spl0_235,
inference(avatar_split_clause,[],[f563,f2863]) ).
fof(f2863,plain,
( spl0_235
<=> ! [X13,X4,X0] :
( ~ c_HOL_Oord__class_Oless(X4,X0,tc_nat)
| c_Lambda_OdB_OVar(X4) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X4),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f563,axiom,
! [X0,X4,X13] :
( ~ c_HOL_Oord__class_Oless(X4,X0,tc_nat)
| c_Lambda_OdB_OVar(X4) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X4),X13,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
fof(f2861,plain,
spl0_234,
inference(avatar_split_clause,[],[f497,f2859]) ).
fof(f2859,plain,
( spl0_234
<=> ! [X1,X10] : c_Orderings_Oord__class_Omin(c_Suc(X1),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X1,X10,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f497,axiom,
! [X10,X1] : c_Orderings_Oord__class_Omin(c_Suc(X1),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X1,X10,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
fof(f2857,plain,
spl0_233,
inference(avatar_split_clause,[],[f483,f2855]) ).
fof(f2855,plain,
( spl0_233
<=> ! [X0,X3,X10] :
( ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat)
| c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X10,c_Lambda_OdB_OVar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f483,axiom,
! [X3,X10,X0] :
( ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat)
| c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X10,c_Lambda_OdB_OVar(X0),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
fof(f2853,plain,
spl0_232,
inference(avatar_split_clause,[],[f343,f2851]) ).
fof(f2851,plain,
( spl0_232
<=> ! [X1,X10] :
( X1 = X10
| c_HOL_Oord__class_Oless(X10,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f343,axiom,
! [X10,X1] :
( X1 = X10
| c_HOL_Oord__class_Oless(X10,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
fof(f2849,plain,
spl0_231,
inference(avatar_split_clause,[],[f219,f2847]) ).
fof(f2847,plain,
( spl0_231
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X16,X2,X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f219,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X16,X2,X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2845,plain,
spl0_230,
inference(avatar_split_clause,[],[f218,f2843]) ).
fof(f2843,plain,
( spl0_230
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f218,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2841,plain,
( spl0_229
| ~ spl0_31
| ~ spl0_53
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1938,f1781,f1426,f1325,f2839]) ).
fof(f2839,plain,
( spl0_229
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1325,plain,
( spl0_31
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1781,plain,
( spl0_135
<=> ! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X6,c_HOL_Ozero__class_Ozero(X5),X5) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1938,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_53
| ~ spl0_135 ),
inference(forward_demodulation,[],[f1937,f1428]) ).
fof(f1937,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_135 ),
inference(resolution,[],[f1782,f1327]) ).
fof(f1327,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f1782,plain,
( ! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X6,c_HOL_Ozero__class_Ozero(X5),X5) = X6 )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1781]) ).
fof(f2837,plain,
spl0_228,
inference(avatar_split_clause,[],[f217,f2835]) ).
fof(f2835,plain,
( spl0_228
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f217,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2833,plain,
spl0_227,
inference(avatar_split_clause,[],[f163,f2831]) ).
fof(f2831,plain,
( spl0_227
<=> ! [X19,X3,X10] : c_Lambda_Oliftn(c_Suc(X10),X19,X3) = c_Lambda_Olift(c_Lambda_Oliftn(X10,X19,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f163,axiom,
! [X3,X10,X19] : c_Lambda_Oliftn(c_Suc(X10),X19,X3) = c_Lambda_Olift(c_Lambda_Oliftn(X10,X19,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
fof(f2829,plain,
spl0_226,
inference(avatar_split_clause,[],[f150,f2827]) ).
fof(f2827,plain,
( spl0_226
<=> ! [X6,X5,X7] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X6,X7,X5),X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f150,axiom,
! [X6,X7,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X6,X7,X5),X7,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f2825,plain,
spl0_225,
inference(avatar_split_clause,[],[f148,f2823]) ).
fof(f2823,plain,
( spl0_225
<=> ! [X5,X1,X10] :
( ~ class_Nat_Osemiring__char__0(X5)
| X1 = X10
| c_Nat_Osemiring__1__class_Oof__nat(X1,X5) != c_Nat_Osemiring__1__class_Oof__nat(X10,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f148,axiom,
! [X10,X1,X5] :
( ~ class_Nat_Osemiring__char__0(X5)
| X1 = X10
| c_Nat_Osemiring__1__class_Oof__nat(X1,X5) != c_Nat_Osemiring__1__class_Oof__nat(X10,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f2821,plain,
spl0_224,
inference(avatar_split_clause,[],[f92,f2819]) ).
fof(f2819,plain,
( spl0_224
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X16,X2,X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f92,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X16,X2,X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2817,plain,
spl0_223,
inference(avatar_split_clause,[],[f91,f2815]) ).
fof(f2815,plain,
( spl0_223
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) != X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f91,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) != X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2813,plain,
spl0_222,
inference(avatar_split_clause,[],[f90,f2811]) ).
fof(f2811,plain,
( spl0_222
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f90,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X2,X16,X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2809,plain,
spl0_221,
inference(avatar_split_clause,[],[f50,f2807]) ).
fof(f2807,plain,
( spl0_221
<=> ! [X1,X10] : c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X10,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f50,axiom,
! [X10,X1] : c_Orderings_Oord__class_Omax(c_Suc(X1),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X1,X10,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
fof(f2805,plain,
spl0_220,
inference(avatar_split_clause,[],[f44,f2803]) ).
fof(f2803,plain,
( spl0_220
<=> ! [X18,X20,X0,X19] :
( ~ c_Lambda_Obeta(X18,X20)
| c_Lambda_Obeta(c_Lambda_Osubst(X18,X19,X0),c_Lambda_Osubst(X20,X19,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f44,axiom,
! [X0,X18,X19,X20] :
( ~ c_Lambda_Obeta(X18,X20)
| c_Lambda_Obeta(c_Lambda_Osubst(X18,X19,X0),c_Lambda_Osubst(X20,X19,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
fof(f2801,plain,
spl0_219,
inference(avatar_split_clause,[],[f37,f2799]) ).
fof(f2799,plain,
( spl0_219
<=> ! [X2,X16,X10,X5,X1] :
( X1 = X10
| c_List_Oreplicate(X1,X2,X5) != c_List_Oreplicate(X10,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f37,axiom,
! [X2,X10,X1,X16,X5] :
( X1 = X10
| c_List_Oreplicate(X1,X2,X5) != c_List_Oreplicate(X10,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
fof(f2797,plain,
( spl0_218
| ~ spl0_31
| ~ spl0_53
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1936,f1777,f1426,f1325,f2795]) ).
fof(f2795,plain,
( spl0_218
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1777,plain,
( spl0_134
<=> ! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X6,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1936,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_31
| ~ spl0_53
| ~ spl0_134 ),
inference(forward_demodulation,[],[f1935,f1428]) ).
fof(f1935,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_31
| ~ spl0_134 ),
inference(resolution,[],[f1778,f1327]) ).
fof(f1778,plain,
( ! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X6,X6,X5) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1777]) ).
fof(f2695,plain,
( spl0_217
| ~ spl0_89
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1897,f1745,f1576,f2693]) ).
fof(f2693,plain,
( spl0_217
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1576,plain,
( spl0_89
<=> ! [X1,X10] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X10,tc_nat),c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1745,plain,
( spl0_126
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1897,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_89
| ~ spl0_126 ),
inference(resolution,[],[f1746,f1577]) ).
fof(f1577,plain,
( ! [X10,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X10,tc_nat),c_Suc(X1),tc_nat)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1576]) ).
fof(f1746,plain,
( ! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1745]) ).
fof(f2546,plain,
spl0_216,
inference(avatar_split_clause,[],[f1030,f2544]) ).
fof(f2544,plain,
( spl0_216
<=> ! [X1,X10] :
( c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_lessequals(X1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1030,plain,
! [X10,X1] :
( c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_lessequals(X1,X10,tc_nat) ),
inference(forward_demodulation,[],[f31,f855]) ).
fof(f31,axiom,
! [X10,X1] :
( c_lessequals(X1,X10,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f2542,plain,
spl0_215,
inference(avatar_split_clause,[],[f1009,f2540]) ).
fof(f2540,plain,
( spl0_215
<=> ! [X1,X10] :
( c_Divides_Odiv__class_Odiv(X1,X10,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1009,plain,
! [X10,X1] :
( c_Divides_Odiv__class_Odiv(X1,X10,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat) ),
inference(forward_demodulation,[],[f471,f855]) ).
fof(f471,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X1,X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).
fof(f2538,plain,
spl0_214,
inference(avatar_split_clause,[],[f1000,f2536]) ).
fof(f2536,plain,
( spl0_214
<=> ! [X1,X10] :
( c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_lessequals(X1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1000,plain,
! [X10,X1] :
( c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_lessequals(X1,X10,tc_nat) ),
inference(forward_demodulation,[],[f30,f855]) ).
fof(f30,axiom,
! [X10,X1] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f2534,plain,
spl0_213,
inference(avatar_split_clause,[],[f981,f2532]) ).
fof(f2532,plain,
( spl0_213
<=> ! [X2,X5,X16] : c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X2,X5) = c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X16,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f981,plain,
! [X2,X16,X5] : c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X2,X5) = c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X16,X5),
inference(forward_demodulation,[],[f862,f855]) ).
fof(f862,axiom,
! [X2,X16,X5] : c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X2,X5) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X16,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
fof(f2530,plain,
spl0_212,
inference(avatar_split_clause,[],[f870,f2528]) ).
fof(f870,axiom,
! [X11,X19,X55,X23] :
( ~ c_Lambda_Obeta(X19,X55)
| ~ c_Type_Otyping(X11,X19,X23)
| c_Type_Otyping(X11,X55,X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f2526,plain,
spl0_211,
inference(avatar_split_clause,[],[f767,f2524]) ).
fof(f2524,plain,
( spl0_211
<=> ! [X1,X10] :
( X1 = X10
| ~ c_lessequals(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f767,axiom,
! [X10,X1] :
( X1 = X10
| ~ c_lessequals(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
fof(f2516,plain,
spl0_210,
inference(avatar_split_clause,[],[f703,f2514]) ).
fof(f2514,plain,
( spl0_210
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f703,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f2512,plain,
spl0_209,
inference(avatar_split_clause,[],[f702,f2510]) ).
fof(f2510,plain,
( spl0_209
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f702,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2508,plain,
spl0_208,
inference(avatar_split_clause,[],[f701,f2506]) ).
fof(f2506,plain,
( spl0_208
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f701,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2504,plain,
spl0_207,
inference(avatar_split_clause,[],[f700,f2502]) ).
fof(f2502,plain,
( spl0_207
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f700,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f2500,plain,
spl0_206,
inference(avatar_split_clause,[],[f699,f2498]) ).
fof(f2498,plain,
( spl0_206
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f699,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2496,plain,
spl0_205,
inference(avatar_split_clause,[],[f697,f2494]) ).
fof(f2494,plain,
( spl0_205
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f697,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f2492,plain,
spl0_204,
inference(avatar_split_clause,[],[f652,f2490]) ).
fof(f2490,plain,
( spl0_204
<=> ! [X1,X10] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),X10,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f652,axiom,
! [X10,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),X10,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f2488,plain,
spl0_203,
inference(avatar_split_clause,[],[f651,f2486]) ).
fof(f2486,plain,
( spl0_203
<=> ! [X1,X10] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10),X10,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f651,axiom,
! [X10,X1] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10),X10,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f2484,plain,
spl0_202,
inference(avatar_split_clause,[],[f496,f2482]) ).
fof(f2482,plain,
( spl0_202
<=> ! [X0,X3] :
( ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat)
| c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f496,axiom,
! [X3,X0] :
( ~ c_HOL_Oord__class_Oless(X0,X3,tc_nat)
| c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f2480,plain,
spl0_201,
inference(avatar_split_clause,[],[f489,f2478]) ).
fof(f2478,plain,
( spl0_201
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f489,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omin(X2,X16,X5),X5) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f2468,plain,
spl0_200,
inference(avatar_split_clause,[],[f481,f2466]) ).
fof(f2466,plain,
( spl0_200
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = c_Orderings_Oord__class_Omax(X16,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f481,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,X16,X5) = c_Orderings_Oord__class_Omax(X16,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f2464,plain,
spl0_199,
inference(avatar_split_clause,[],[f382,f2462]) ).
fof(f2462,plain,
( spl0_199
<=> ! [X2,X16] :
( X2 = X16
| c_HOL_Oord__class_Oless(X2,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f382,axiom,
! [X2,X16] :
( X2 = X16
| c_HOL_Oord__class_Oless(X2,X16,tc_nat)
| c_HOL_Oord__class_Oless(X16,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f2460,plain,
spl0_198,
inference(avatar_split_clause,[],[f379,f2458]) ).
fof(f2458,plain,
( spl0_198
<=> ! [X1,X10] :
( X1 = X10
| ~ c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(X10,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f379,axiom,
! [X10,X1] :
( X1 = X10
| ~ c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(X10,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f2456,plain,
spl0_197,
inference(avatar_split_clause,[],[f357,f2454]) ).
fof(f2454,plain,
( spl0_197
<=> ! [X4,X3,X10] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f357,axiom,
! [X3,X10,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X10,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f2452,plain,
spl0_196,
inference(avatar_split_clause,[],[f335,f2450]) ).
fof(f2450,plain,
( spl0_196
<=> ! [X1,X10] : c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X10),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f335,axiom,
! [X10,X1] : c_HOL_Ominus__class_Ominus(X1,X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X1),c_Suc(X10),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f2448,plain,
spl0_195,
inference(avatar_split_clause,[],[f278,f2446]) ).
fof(f2446,plain,
( spl0_195
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = c_Orderings_Oord__class_Omin(X16,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f278,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,X16,X5) = c_Orderings_Oord__class_Omin(X16,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f2444,plain,
spl0_194,
inference(avatar_split_clause,[],[f250,f2442]) ).
fof(f2442,plain,
( spl0_194
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f250,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f2440,plain,
spl0_193,
inference(avatar_split_clause,[],[f81,f2438]) ).
fof(f2438,plain,
( spl0_193
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X6,X7,X5) = c_HOL_Otimes__class_Otimes(X7,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f81,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Otimes__class_Otimes(X6,X7,X5) = c_HOL_Otimes__class_Otimes(X7,X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2352,plain,
( spl0_192
| ~ spl0_137
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2021,f1969,f1789,f2350]) ).
fof(f1969,plain,
( spl0_148
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2021,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_137
| ~ spl0_148 ),
inference(resolution,[],[f1970,f1790]) ).
fof(f1970,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1969]) ).
fof(f2248,plain,
( spl0_191
| ~ spl0_58
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2221,f2010,f1447,f2246]) ).
fof(f2246,plain,
( spl0_191
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1447,plain,
( spl0_58
<=> ! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f2010,plain,
( spl0_152
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X16,X2,X5)
| c_HOL_Oord__class_Oless(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f2221,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_58
| ~ spl0_152 ),
inference(duplicate_literal_removal,[],[f2214]) ).
fof(f2214,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_58
| ~ spl0_152 ),
inference(resolution,[],[f2011,f1448]) ).
fof(f1448,plain,
( ! [X2,X5] :
( ~ c_HOL_Oord__class_Oless(X2,X2,X5)
| ~ class_Orderings_Olinorder(X5) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f2011,plain,
( ! [X2,X16,X5] :
( c_HOL_Oord__class_Oless(X2,X16,X5)
| c_lessequals(X16,X2,X5)
| ~ class_Orderings_Olinorder(X5) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f2010]) ).
fof(f2167,plain,
spl0_190,
inference(avatar_split_clause,[],[f1016,f2165]) ).
fof(f2165,plain,
( spl0_190
<=> ! [X10] :
( ~ c_HOL_Oord__class_Oless(X10,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1016,plain,
! [X10] :
( ~ c_HOL_Oord__class_Oless(X10,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ),
inference(forward_demodulation,[],[f1015,f855]) ).
fof(f1015,plain,
! [X10] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
inference(forward_demodulation,[],[f51,f855]) ).
fof(f51,axiom,
! [X10] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f2163,plain,
spl0_189,
inference(avatar_split_clause,[],[f997,f2161]) ).
fof(f2161,plain,
( spl0_189
<=> ! [X5,X0,X37] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X37,c_Orderings_Obot__class_Obot(tc_nat),X0,X5) = X0
| ~ class_Ring__and__Field_Osemiring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f997,plain,
! [X0,X37,X5] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X37,c_Orderings_Obot__class_Obot(tc_nat),X0,X5) = X0
| ~ class_Ring__and__Field_Osemiring__1(X5) ),
inference(forward_demodulation,[],[f811,f855]) ).
fof(f811,axiom,
! [X0,X37,X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X37,c_HOL_Ozero__class_Ozero(tc_nat),X0,X5) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I1_J_0) ).
fof(f2159,plain,
spl0_188,
inference(avatar_split_clause,[],[f975,f2157]) ).
fof(f2157,plain,
( spl0_188
<=> ! [X20,X19] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X20),X19),c_Lambda_Osubst(X20,X19,c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f975,plain,
! [X19,X20] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X20),X19),c_Lambda_Osubst(X20,X19,c_Orderings_Obot__class_Obot(tc_nat))),
inference(forward_demodulation,[],[f371,f855]) ).
fof(f371,axiom,
! [X19,X20] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X20),X19),c_Lambda_Osubst(X20,X19,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f2155,plain,
( spl0_187
| ~ spl0_110
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1915,f1757,f1679,f2153]) ).
fof(f1679,plain,
( spl0_110
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1915,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_110
| ~ spl0_129 ),
inference(resolution,[],[f1758,f1680]) ).
fof(f1680,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1679]) ).
fof(f2151,plain,
spl0_186,
inference(avatar_split_clause,[],[f974,f2149]) ).
fof(f2149,plain,
( spl0_186
<=> ! [X2,X12] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X12,X2,tc_nat),X12,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f974,plain,
! [X2,X12] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X12,X2,tc_nat),X12,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f720,f855]) ).
fof(f720,axiom,
! [X2,X12] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X12,X2,tc_nat),X12,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
fof(f2147,plain,
spl0_185,
inference(avatar_split_clause,[],[f903,f2145]) ).
fof(f2145,plain,
( spl0_185
<=> ! [X58,X57,X62,X63] :
( X58 = X63
| c_Type_Otype_OFun(X57,X58) != c_Type_Otype_OFun(X62,X63) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f903,axiom,
! [X58,X57,X62,X63] :
( X58 = X63
| c_Type_Otype_OFun(X57,X58) != c_Type_Otype_OFun(X62,X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
fof(f2143,plain,
spl0_184,
inference(avatar_split_clause,[],[f902,f2141]) ).
fof(f2141,plain,
( spl0_184
<=> ! [X62,X57,X63,X58] :
( X57 = X62
| c_Type_Otype_OFun(X57,X58) != c_Type_Otype_OFun(X62,X63) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f902,axiom,
! [X58,X57,X62,X63] :
( X57 = X62
| c_Type_Otype_OFun(X57,X58) != c_Type_Otype_OFun(X62,X63) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
fof(f2139,plain,
spl0_183,
inference(avatar_split_clause,[],[f887,f2137]) ).
fof(f2137,plain,
( spl0_183
<=> ! [X20,X0,X18] :
( ~ c_Lambda_Obeta(X18,X20)
| c_Lambda_Obeta(c_Lambda_Olift(X18,X0),c_Lambda_Olift(X20,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f887,axiom,
! [X0,X18,X20] :
( ~ c_Lambda_Obeta(X18,X20)
| c_Lambda_Obeta(c_Lambda_Olift(X18,X0),c_Lambda_Olift(X20,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
fof(f2135,plain,
spl0_182,
inference(avatar_split_clause,[],[f871,f2133]) ).
fof(f2133,plain,
( spl0_182
<=> ! [X0,X11,X23] :
( ~ c_Type_Otyping(X11,c_Lambda_OdB_OVar(X0),X23)
| hAPP(X11,X0) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f871,axiom,
! [X0,X11,X23] :
( ~ c_Type_Otyping(X11,c_Lambda_OdB_OVar(X0),X23)
| hAPP(X11,X0) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f2131,plain,
spl0_181,
inference(avatar_split_clause,[],[f805,f2129]) ).
fof(f2129,plain,
( spl0_181
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X6,X7,X5)
| ~ c_HOL_Oord__class_Oless(X7,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f805,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X6,X7,X5)
| ~ c_HOL_Oord__class_Oless(X7,X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f2127,plain,
spl0_180,
inference(avatar_split_clause,[],[f803,f2125]) ).
fof(f2125,plain,
( spl0_180
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X16,X5)
| c_lessequals(X16,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f803,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,X16,X5)
| c_lessequals(X16,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2123,plain,
spl0_179,
inference(avatar_split_clause,[],[f801,f2121]) ).
fof(f2121,plain,
( spl0_179
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f801,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2119,plain,
spl0_178,
inference(avatar_split_clause,[],[f800,f2117]) ).
fof(f2117,plain,
( spl0_178
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X7,X6,X5)
| ~ c_HOL_Oord__class_Oless(X6,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f800,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X7,X6,X5)
| ~ c_HOL_Oord__class_Oless(X6,X7,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2115,plain,
spl0_177,
inference(avatar_split_clause,[],[f787,f2113]) ).
fof(f2113,plain,
( spl0_177
<=> ! [X1,X10] :
( ~ c_lessequals(X10,X1,tc_nat)
| c_lessequals(c_Suc(X10),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f787,axiom,
! [X10,X1] :
( ~ c_lessequals(X10,X1,tc_nat)
| c_lessequals(c_Suc(X10),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f2111,plain,
( spl0_176
| ~ spl0_110
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1885,f1733,f1679,f2109]) ).
fof(f1733,plain,
( spl0_123
<=> ! [X1,X10] :
( ~ c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(c_Suc(X10),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1885,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_110
| ~ spl0_123 ),
inference(resolution,[],[f1734,f1680]) ).
fof(f1734,plain,
( ! [X10,X1] :
( ~ c_lessequals(c_Suc(X10),X1,tc_nat)
| ~ c_lessequals(X1,X10,tc_nat) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1733]) ).
fof(f2107,plain,
spl0_175,
inference(avatar_split_clause,[],[f786,f2105]) ).
fof(f2105,plain,
( spl0_175
<=> ! [X1,X10] :
( c_lessequals(X10,X1,tc_nat)
| ~ c_lessequals(c_Suc(X10),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f786,axiom,
! [X10,X1] :
( c_lessequals(X10,X1,tc_nat)
| ~ c_lessequals(c_Suc(X10),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f2103,plain,
spl0_174,
inference(avatar_split_clause,[],[f691,f2101]) ).
fof(f2101,plain,
( spl0_174
<=> ! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X5),X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f691,axiom,
! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X5),X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f2099,plain,
spl0_173,
inference(avatar_split_clause,[],[f681,f2097]) ).
fof(f2097,plain,
( spl0_173
<=> ! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X5),X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f681,axiom,
! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X5),X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f2095,plain,
spl0_172,
inference(avatar_split_clause,[],[f680,f2093]) ).
fof(f2093,plain,
( spl0_172
<=> ! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(X6,c_HOL_Ozero__class_Ozero(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f680,axiom,
! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Odiv(X6,c_HOL_Ozero__class_Ozero(X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f2091,plain,
spl0_171,
inference(avatar_split_clause,[],[f675,f2089]) ).
fof(f2089,plain,
( spl0_171
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f675,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2087,plain,
spl0_170,
inference(avatar_split_clause,[],[f672,f2085]) ).
fof(f2085,plain,
( spl0_170
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f672,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2083,plain,
spl0_169,
inference(avatar_split_clause,[],[f671,f2081]) ).
fof(f2081,plain,
( spl0_169
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f671,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2079,plain,
spl0_168,
inference(avatar_split_clause,[],[f670,f2077]) ).
fof(f2077,plain,
( spl0_168
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f670,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X5),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f2075,plain,
spl0_167,
inference(avatar_split_clause,[],[f662,f2073]) ).
fof(f2073,plain,
( spl0_167
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f662,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
fof(f2071,plain,
spl0_166,
inference(avatar_split_clause,[],[f661,f2069]) ).
fof(f2069,plain,
( spl0_166
<=> ! [X1,X10] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f661,axiom,
! [X10,X1] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f2067,plain,
( spl0_165
| ~ spl0_110
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1867,f1717,f1679,f2065]) ).
fof(f1717,plain,
( spl0_119
<=> ! [X1,X10] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_lessequals(c_Suc(X1),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1867,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_110
| ~ spl0_119 ),
inference(resolution,[],[f1718,f1680]) ).
fof(f1718,plain,
( ! [X10,X1] :
( ~ c_lessequals(c_Suc(X1),X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,X10,tc_nat) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1717]) ).
fof(f2063,plain,
spl0_164,
inference(avatar_split_clause,[],[f654,f2061]) ).
fof(f2061,plain,
( spl0_164
<=> ! [X15,X24,X5,X25] : hAPP(X24,X15) = c_Type_Otype_Otype__case(X24,X25,c_Type_Otype_OAtom(X15),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f654,axiom,
! [X24,X15,X25,X5] : hAPP(X24,X15) = c_Type_Otype_Otype__case(X24,X25,c_Type_Otype_OAtom(X15),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
fof(f2059,plain,
spl0_163,
inference(avatar_split_clause,[],[f631,f2057]) ).
fof(f2057,plain,
( spl0_163
<=> ! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f631,axiom,
! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).
fof(f2055,plain,
spl0_162,
inference(avatar_split_clause,[],[f479,f2053]) ).
fof(f2053,plain,
( spl0_162
<=> ! [X13,X20,X19] :
( ~ c_Lambda_Obeta(X20,X19)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X20,X13),c_Lambda_OdB_OApp(X19,X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f479,axiom,
! [X19,X13,X20] :
( ~ c_Lambda_Obeta(X20,X19)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X20,X13),c_Lambda_OdB_OApp(X19,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
fof(f2051,plain,
spl0_161,
inference(avatar_split_clause,[],[f478,f2049]) ).
fof(f2049,plain,
( spl0_161
<=> ! [X13,X20,X19] :
( ~ c_Lambda_Obeta(X20,X19)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X13,X20),c_Lambda_OdB_OApp(X13,X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f478,axiom,
! [X19,X13,X20] :
( ~ c_Lambda_Obeta(X20,X19)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X13,X20),c_Lambda_OdB_OApp(X13,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
fof(f2047,plain,
spl0_160,
inference(avatar_split_clause,[],[f400,f2045]) ).
fof(f2045,plain,
( spl0_160
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| c_lessequals(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f400,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| c_lessequals(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2043,plain,
spl0_159,
inference(avatar_split_clause,[],[f399,f2041]) ).
fof(f2041,plain,
( spl0_159
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| c_lessequals(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f399,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5)
| c_lessequals(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2039,plain,
spl0_158,
inference(avatar_split_clause,[],[f394,f2037]) ).
fof(f2037,plain,
( spl0_158
<=> ! [X44,X50,X49,X43] :
( X43 = X49
| c_Lambda_OdB_OApp(X43,X44) != c_Lambda_OdB_OApp(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f394,axiom,
! [X50,X49,X44,X43] :
( X43 = X49
| c_Lambda_OdB_OApp(X43,X44) != c_Lambda_OdB_OApp(X49,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f2035,plain,
spl0_157,
inference(avatar_split_clause,[],[f393,f2033]) ).
fof(f2033,plain,
( spl0_157
<=> ! [X50,X44,X43,X49] :
( X44 = X50
| c_Lambda_OdB_OApp(X43,X44) != c_Lambda_OdB_OApp(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f393,axiom,
! [X50,X49,X44,X43] :
( X44 = X50
| c_Lambda_OdB_OApp(X43,X44) != c_Lambda_OdB_OApp(X49,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f2031,plain,
spl0_156,
inference(avatar_split_clause,[],[f360,f2029]) ).
fof(f360,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_Divides_Odiv__class_Omod(X1,X10,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f2027,plain,
spl0_155,
inference(avatar_split_clause,[],[f358,f2025]) ).
fof(f2025,plain,
( spl0_155
<=> ! [X15,X24,X5,X25] : c_Type_Otype_Otype__rec(X24,X25,c_Type_Otype_OAtom(X15),X5) = hAPP(X24,X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f358,axiom,
! [X24,X15,X25,X5] : c_Type_Otype_Otype__rec(X24,X25,c_Type_Otype_OAtom(X15),X5) = hAPP(X24,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
fof(f2020,plain,
spl0_154,
inference(avatar_split_clause,[],[f320,f2018]) ).
fof(f2018,plain,
( spl0_154
<=> ! [X15,X24,X5,X25] : hAPP(X25,X15) = c_Nat_Onat_Onat__case(X24,X25,c_Suc(X15),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f320,axiom,
! [X15,X24,X25,X5] : hAPP(X25,X15) = c_Nat_Onat_Onat__case(X24,X25,c_Suc(X15),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__case__Suc_0) ).
fof(f2016,plain,
spl0_153,
inference(avatar_split_clause,[],[f229,f2014]) ).
fof(f2014,plain,
( spl0_153
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f229,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2012,plain,
spl0_152,
inference(avatar_split_clause,[],[f226,f2010]) ).
fof(f226,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X16,X2,X5)
| c_HOL_Oord__class_Oless(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f2008,plain,
spl0_151,
inference(avatar_split_clause,[],[f225,f2006]) ).
fof(f2006,plain,
( spl0_151
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f225,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X16,X2,X5)
| ~ c_HOL_Oord__class_Oless(X2,X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f2004,plain,
spl0_150,
inference(avatar_split_clause,[],[f3,f2002]) ).
fof(f2002,plain,
( spl0_150
<=> ! [X2,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f3,axiom,
! [X2,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f2000,plain,
spl0_149,
inference(avatar_split_clause,[],[f2,f1998]) ).
fof(f1998,plain,
( spl0_149
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f2,axiom,
! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1971,plain,
( spl0_148
| ~ spl0_41
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1944,f1789,f1375,f1969]) ).
fof(f1375,plain,
( spl0_41
<=> ! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1944,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_41
| ~ spl0_137 ),
inference(resolution,[],[f1790,f1376]) ).
fof(f1376,plain,
( ! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f1835,plain,
( spl0_147
| ~ spl0_96
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1674,f1620,f1604,f1833]) ).
fof(f1833,plain,
( spl0_147
<=> ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1604,plain,
( spl0_96
<=> ! [X18,X0,X4] :
( ~ c_InductTermi_OIT(X18)
| c_InductTermi_OIT(c_Lambda_Osubst(X18,c_Lambda_OdB_OVar(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1620,plain,
( spl0_100
<=> ! [X20,X3,X19] : c_Lambda_Osubst(c_Lambda_Olift(X19,X3),X20,X3) = X19 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1674,plain,
( ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) )
| ~ spl0_96
| ~ spl0_100 ),
inference(superposition,[],[f1605,f1621]) ).
fof(f1621,plain,
( ! [X3,X19,X20] : c_Lambda_Osubst(c_Lambda_Olift(X19,X3),X20,X3) = X19
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1620]) ).
fof(f1605,plain,
( ! [X0,X18,X4] :
( c_InductTermi_OIT(c_Lambda_Osubst(X18,c_Lambda_OdB_OVar(X0),X4))
| ~ c_InductTermi_OIT(X18) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1604]) ).
fof(f1828,plain,
spl0_146,
inference(avatar_split_clause,[],[f1014,f1826]) ).
fof(f1826,plain,
( spl0_146
<=> ! [X10] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1014,plain,
! [X10] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ),
inference(forward_demodulation,[],[f1013,f855]) ).
fof(f1013,plain,
! [X10] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f819,f855]) ).
fof(f819,axiom,
! [X10] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1824,plain,
spl0_145,
inference(avatar_split_clause,[],[f1012,f1822]) ).
fof(f1822,plain,
( spl0_145
<=> ! [X10] :
( ~ c_lessequals(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1012,plain,
! [X10] :
( ~ c_lessequals(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ),
inference(forward_demodulation,[],[f1011,f855]) ).
fof(f1011,plain,
! [X10] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f825,f855]) ).
fof(f825,axiom,
! [X10] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| ~ c_lessequals(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1820,plain,
spl0_144,
inference(avatar_split_clause,[],[f996,f1818]) ).
fof(f996,plain,
! [X5] :
( c_HOL_Ozero__class_Ozero(X5) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X5)
| ~ class_Ring__and__Field_Osemiring__1(X5) ),
inference(forward_demodulation,[],[f893,f855]) ).
fof(f893,axiom,
! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1816,plain,
spl0_143,
inference(avatar_split_clause,[],[f991,f1813]) ).
fof(f1813,plain,
( spl0_143
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Odiv(c_Orderings_Obot__class_Obot(tc_nat),c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f991,plain,
c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Odiv(c_Orderings_Obot__class_Obot(tc_nat),c_Orderings_Obot__class_Obot(tc_nat),tc_nat),
inference(forward_demodulation,[],[f990,f964]) ).
fof(f964,plain,
! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Otimes__class_Otimes(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat),
inference(forward_demodulation,[],[f828,f855]) ).
fof(f828,axiom,
! [X10] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f990,plain,
! [X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat),c_Orderings_Obot__class_Obot(tc_nat),tc_nat),
inference(forward_demodulation,[],[f989,f964]) ).
fof(f989,plain,
! [X10,X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat),tc_nat),
inference(forward_demodulation,[],[f541,f855]) ).
fof(f541,axiom,
! [X10,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).
fof(f1811,plain,
spl0_142,
inference(avatar_split_clause,[],[f973,f1809]) ).
fof(f1809,plain,
( spl0_142
<=> ! [X6,X33,X5,X32] : c_Power_Opower_Opower(X32,X33,X6,c_Orderings_Obot__class_Obot(tc_nat),X5) = X32 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f973,plain,
! [X6,X5,X32,X33] : c_Power_Opower_Opower(X32,X33,X6,c_Orderings_Obot__class_Obot(tc_nat),X5) = X32,
inference(forward_demodulation,[],[f807,f855]) ).
fof(f807,axiom,
! [X6,X5,X32,X33] : c_Power_Opower_Opower(X32,X33,X6,c_HOL_Ozero__class_Ozero(tc_nat),X5) = X32,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power_Opower_Opower__0_0) ).
fof(f1807,plain,
spl0_141,
inference(avatar_split_clause,[],[f972,f1805]) ).
fof(f1805,plain,
( spl0_141
<=> ! [X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X10) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f972,plain,
! [X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X10) = X10,
inference(forward_demodulation,[],[f867,f855]) ).
fof(f867,axiom,
! [X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f1803,plain,
spl0_140,
inference(avatar_split_clause,[],[f970,f1801]) ).
fof(f1801,plain,
( spl0_140
<=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Orderings_Obot__class_Obot(tc_nat)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f970,plain,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_Orderings_Obot__class_Obot(tc_nat)) = X2,
inference(forward_demodulation,[],[f866,f855]) ).
fof(f866,axiom,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
fof(f1799,plain,
spl0_139,
inference(avatar_split_clause,[],[f969,f1797]) ).
fof(f1797,plain,
( spl0_139
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f969,plain,
! [X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),
inference(forward_demodulation,[],[f355,f855]) ).
fof(f355,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1795,plain,
spl0_138,
inference(avatar_split_clause,[],[f904,f1793]) ).
fof(f1793,plain,
( spl0_138
<=> ! [X2,X5,X11,X23] : hAPP(c_Type_Oshift(X11,X2,X23,X5),X2) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f904,axiom,
! [X2,X11,X5,X23] : hAPP(c_Type_Oshift(X11,X2,X23,X5),X2) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f1791,plain,
spl0_137,
inference(avatar_split_clause,[],[f735,f1789]) ).
fof(f735,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1787,plain,
spl0_136,
inference(avatar_split_clause,[],[f734,f1785]) ).
fof(f734,axiom,
! [X10,X1] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1783,plain,
spl0_135,
inference(avatar_split_clause,[],[f690,f1781]) ).
fof(f690,axiom,
! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_Divides_Odiv__class_Omod(X6,c_HOL_Ozero__class_Ozero(X5),X5) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1779,plain,
spl0_134,
inference(avatar_split_clause,[],[f689,f1777]) ).
fof(f689,axiom,
! [X6,X5] :
( ~ class_Divides_Osemiring__div(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X6,X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1775,plain,
spl0_133,
inference(avatar_split_clause,[],[f641,f1773]) ).
fof(f1773,plain,
( spl0_133
<=> ! [X5,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f641,axiom,
! [X10,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_HOL_Ozero__class_Ozero(X5),c_Nat_Osemiring__1__class_Oof__nat(X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
fof(f1771,plain,
spl0_132,
inference(avatar_split_clause,[],[f568,f1769]) ).
fof(f1769,plain,
( spl0_132
<=> ! [X4,X0] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f568,axiom,
! [X0,X4] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1767,plain,
spl0_131,
inference(avatar_split_clause,[],[f567,f1765]) ).
fof(f567,axiom,
! [X0,X4] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X4),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1763,plain,
spl0_130,
inference(avatar_split_clause,[],[f555,f1761]) ).
fof(f555,axiom,
! [X10,X1] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_lessequals(X1,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1759,plain,
spl0_129,
inference(avatar_split_clause,[],[f554,f1757]) ).
fof(f554,axiom,
! [X10,X1] :
( c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(c_Suc(X1),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1755,plain,
spl0_128,
inference(avatar_split_clause,[],[f501,f1753]) ).
fof(f1753,plain,
( spl0_128
<=> ! [X1,X10] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f501,axiom,
! [X10,X1] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1751,plain,
( spl0_127
| ~ spl0_34
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1661,f1596,f1340,f1749]) ).
fof(f1749,plain,
( spl0_127
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1340,plain,
( spl0_34
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1596,plain,
( spl0_94
<=> ! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,X2,X5) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1661,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_34
| ~ spl0_94 ),
inference(resolution,[],[f1597,f1342]) ).
fof(f1342,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1597,plain,
( ! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,X2,X5) = X2 )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1596]) ).
fof(f1747,plain,
spl0_126,
inference(avatar_split_clause,[],[f500,f1745]) ).
fof(f500,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1743,plain,
spl0_125,
inference(avatar_split_clause,[],[f480,f1741]) ).
fof(f1741,plain,
( spl0_125
<=> ! [X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_HOL_Ozero__class_Ozero(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f480,axiom,
! [X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1739,plain,
spl0_124,
inference(avatar_split_clause,[],[f416,f1737]) ).
fof(f1737,plain,
( spl0_124
<=> ! [X1,X10] :
( c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_Suc(X10),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f416,axiom,
! [X10,X1] :
( c_lessequals(X1,X10,tc_nat)
| c_lessequals(c_Suc(X10),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1735,plain,
spl0_123,
inference(avatar_split_clause,[],[f415,f1733]) ).
fof(f415,axiom,
! [X10,X1] :
( ~ c_lessequals(X1,X10,tc_nat)
| ~ c_lessequals(c_Suc(X10),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1731,plain,
spl0_122,
inference(avatar_split_clause,[],[f374,f1729]) ).
fof(f374,axiom,
! [X10,X1] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X10),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f1727,plain,
spl0_121,
inference(avatar_split_clause,[],[f373,f1725]) ).
fof(f373,axiom,
! [X10,X1] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).
fof(f1723,plain,
spl0_120,
inference(avatar_split_clause,[],[f235,f1721]) ).
fof(f1721,plain,
( spl0_120
<=> ! [X9,X23] :
( hBOOL(hAPP(X9,X23))
| ~ hBOOL(hAPP(X9,c_Type_Osko__Type__Xtype__induct__1__1(X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f235,axiom,
! [X9,X23] :
( hBOOL(hAPP(X9,X23))
| ~ hBOOL(hAPP(X9,c_Type_Osko__Type__Xtype__induct__1__1(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_2) ).
fof(f1719,plain,
spl0_119,
inference(avatar_split_clause,[],[f123,f1717]) ).
fof(f123,axiom,
! [X10,X1] :
( c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| ~ c_lessequals(c_Suc(X1),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
fof(f1715,plain,
spl0_118,
inference(avatar_split_clause,[],[f122,f1713]) ).
fof(f1713,plain,
( spl0_118
<=> ! [X1,X10] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_lessequals(c_Suc(X1),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f122,axiom,
! [X10,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X10,tc_nat)
| c_lessequals(c_Suc(X1),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
fof(f1711,plain,
spl0_117,
inference(avatar_split_clause,[],[f110,f1709]) ).
fof(f1709,plain,
( spl0_117
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X16,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f110,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X16,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1707,plain,
spl0_116,
inference(avatar_split_clause,[],[f109,f1705]) ).
fof(f1705,plain,
( spl0_116
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f109,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X2,X16,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1703,plain,
spl0_115,
inference(avatar_split_clause,[],[f79,f1701]) ).
fof(f1701,plain,
( spl0_115
<=> ! [X1,X10] : c_HOL_Otimes__class_Otimes(X10,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f79,axiom,
! [X10,X1] : c_HOL_Otimes__class_Otimes(X10,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1699,plain,
spl0_114,
inference(avatar_split_clause,[],[f76,f1697]) ).
fof(f1697,plain,
( spl0_114
<=> ! [X1,X10] :
( c_lessequals(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f76,axiom,
! [X10,X1] :
( c_lessequals(X1,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1695,plain,
spl0_113,
inference(avatar_split_clause,[],[f75,f1693]) ).
fof(f1693,plain,
( spl0_113
<=> ! [X1,X10] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f75,axiom,
! [X10,X1] :
( ~ c_lessequals(X1,X10,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1691,plain,
spl0_112,
inference(avatar_split_clause,[],[f24,f1689]) ).
fof(f1689,plain,
( spl0_112
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X16,X5),X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f24,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X16,X5),X16,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1687,plain,
spl0_111,
inference(avatar_split_clause,[],[f23,f1685]) ).
fof(f1685,plain,
( spl0_111
<=> ! [X2,X5,X16] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X16,X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f23,axiom,
! [X2,X16,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X16,X5),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1681,plain,
( spl0_110
| ~ spl0_49
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1666,f1600,f1408,f1679]) ).
fof(f1600,plain,
( spl0_95
<=> ! [X2,X16] :
( ~ c_HOL_Oord__class_Oless(X2,X16,tc_nat)
| c_lessequals(X2,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1666,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_49
| ~ spl0_95 ),
inference(resolution,[],[f1601,f1409]) ).
fof(f1601,plain,
( ! [X2,X16] :
( ~ c_HOL_Oord__class_Oless(X2,X16,tc_nat)
| c_lessequals(X2,X16,tc_nat) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1600]) ).
fof(f1665,plain,
( spl0_109
| ~ spl0_34
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1660,f1592,f1340,f1663]) ).
fof(f1663,plain,
( spl0_109
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1592,plain,
( spl0_93
<=> ! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,X2,X5) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1660,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_34
| ~ spl0_93 ),
inference(resolution,[],[f1593,f1342]) ).
fof(f1593,plain,
( ! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,X2,X5) = X2 )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1592]) ).
fof(f1654,plain,
spl0_108,
inference(avatar_split_clause,[],[f967,f1652]) ).
fof(f1652,plain,
( spl0_108
<=> ! [X25,X5,X24] : c_Nat_Onat_Onat__case(X24,X25,c_Orderings_Obot__class_Obot(tc_nat),X5) = X24 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f967,plain,
! [X24,X5,X25] : c_Nat_Onat_Onat__case(X24,X25,c_Orderings_Obot__class_Obot(tc_nat),X5) = X24,
inference(forward_demodulation,[],[f833,f855]) ).
fof(f833,axiom,
! [X24,X5,X25] : c_Nat_Onat_Onat__case(X24,X25,c_HOL_Ozero__class_Ozero(tc_nat),X5) = X24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__case__0_0) ).
fof(f1650,plain,
spl0_107,
inference(avatar_split_clause,[],[f966,f1648]) ).
fof(f1648,plain,
( spl0_107
<=> ! [X25,X5,X24] : c_Nat_Onat_Onat__rec(X24,X25,c_Orderings_Obot__class_Obot(tc_nat),X5) = X24 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f966,plain,
! [X24,X5,X25] : c_Nat_Onat_Onat__rec(X24,X25,c_Orderings_Obot__class_Obot(tc_nat),X5) = X24,
inference(forward_demodulation,[],[f820,f855]) ).
fof(f820,axiom,
! [X24,X5,X25] : c_Nat_Onat_Onat__rec(X24,X25,c_HOL_Ozero__class_Ozero(tc_nat),X5) = X24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__rec__0_0) ).
fof(f1646,plain,
spl0_106,
inference(avatar_split_clause,[],[f965,f1644]) ).
fof(f1644,plain,
( spl0_106
<=> ! [X1] : c_Divides_Odiv__class_Odiv(X1,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f965,plain,
! [X1] : c_Divides_Odiv__class_Odiv(X1,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),tc_nat) = X1,
inference(forward_demodulation,[],[f646,f855]) ).
fof(f646,axiom,
! [X1] : c_Divides_Odiv__class_Odiv(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).
fof(f1642,plain,
spl0_105,
inference(avatar_split_clause,[],[f964,f1640]) ).
fof(f1640,plain,
( spl0_105
<=> ! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Otimes__class_Otimes(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1638,plain,
spl0_104,
inference(avatar_split_clause,[],[f963,f1636]) ).
fof(f1636,plain,
( spl0_104
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f963,plain,
! [X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat),
inference(forward_demodulation,[],[f827,f855]) ).
fof(f827,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f1634,plain,
spl0_103,
inference(avatar_split_clause,[],[f962,f1632]) ).
fof(f1632,plain,
( spl0_103
<=> ! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f962,plain,
! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat),
inference(forward_demodulation,[],[f858,f855]) ).
fof(f858,axiom,
! [X10] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1630,plain,
spl0_102,
inference(avatar_split_clause,[],[f961,f1628]) ).
fof(f1628,plain,
( spl0_102
<=> ! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_Orderings_Oord__class_Omin(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f961,plain,
! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_Orderings_Oord__class_Omin(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat),
inference(forward_demodulation,[],[f835,f855]) ).
fof(f835,axiom,
! [X10] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0L_0) ).
fof(f1626,plain,
spl0_101,
inference(avatar_split_clause,[],[f960,f1624]) ).
fof(f1624,plain,
( spl0_101
<=> ! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_Orderings_Oord__class_Omin(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f960,plain,
! [X10] : c_Orderings_Obot__class_Obot(tc_nat) = c_Orderings_Oord__class_Omin(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat),
inference(forward_demodulation,[],[f834,f855]) ).
fof(f834,axiom,
! [X10] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0R_0) ).
fof(f1622,plain,
spl0_100,
inference(avatar_split_clause,[],[f886,f1620]) ).
fof(f886,axiom,
! [X3,X19,X20] : c_Lambda_Osubst(c_Lambda_Olift(X19,X3),X20,X3) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f1618,plain,
spl0_99,
inference(avatar_split_clause,[],[f802,f1616]) ).
fof(f1616,plain,
( spl0_99
<=> ! [X1,X10] :
( c_lessequals(X1,X10,tc_nat)
| c_lessequals(X10,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f802,axiom,
! [X10,X1] :
( c_lessequals(X1,X10,tc_nat)
| c_lessequals(X10,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1614,plain,
spl0_98,
inference(avatar_split_clause,[],[f721,f1612]) ).
fof(f1612,plain,
( spl0_98
<=> ! [X15,X31] :
( X15 = X31
| c_Lambda_OdB_OVar(X15) != c_Lambda_OdB_OVar(X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f721,axiom,
! [X31,X15] :
( X15 = X31
| c_Lambda_OdB_OVar(X15) != c_Lambda_OdB_OVar(X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f1610,plain,
spl0_97,
inference(avatar_split_clause,[],[f644,f1608]) ).
fof(f1608,plain,
( spl0_97
<=> ! [X20,X19] :
( ~ c_Lambda_Obeta(X20,X19)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X20),c_Lambda_OdB_OAbs(X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f644,axiom,
! [X19,X20] :
( ~ c_Lambda_Obeta(X20,X19)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X20),c_Lambda_OdB_OAbs(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f1606,plain,
spl0_96,
inference(avatar_split_clause,[],[f564,f1604]) ).
fof(f564,axiom,
! [X0,X18,X4] :
( ~ c_InductTermi_OIT(X18)
| c_InductTermi_OIT(c_Lambda_Osubst(X18,c_Lambda_OdB_OVar(X0),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
fof(f1602,plain,
spl0_95,
inference(avatar_split_clause,[],[f397,f1600]) ).
fof(f397,axiom,
! [X2,X16] :
( ~ c_HOL_Oord__class_Oless(X2,X16,tc_nat)
| c_lessequals(X2,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
fof(f1598,plain,
spl0_94,
inference(avatar_split_clause,[],[f392,f1596]) ).
fof(f392,axiom,
! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omax(X2,X2,X5) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1594,plain,
spl0_93,
inference(avatar_split_clause,[],[f369,f1592]) ).
fof(f369,axiom,
! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Orderings_Oord__class_Omin(X2,X2,X5) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1590,plain,
spl0_92,
inference(avatar_split_clause,[],[f322,f1588]) ).
fof(f1588,plain,
( spl0_92
<=> ! [X34,X41] :
( X34 = X41
| c_Lambda_OdB_OAbs(X34) != c_Lambda_OdB_OAbs(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f322,axiom,
! [X41,X34] :
( X34 = X41
| c_Lambda_OdB_OAbs(X34) != c_Lambda_OdB_OAbs(X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f1586,plain,
spl0_91,
inference(avatar_split_clause,[],[f180,f1584]) ).
fof(f1584,plain,
( spl0_91
<=> ! [X15,X31] :
( X15 = X31
| c_Suc(X15) != c_Suc(X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f180,axiom,
! [X31,X15] :
( X15 = X31
| c_Suc(X15) != c_Suc(X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f1582,plain,
spl0_90,
inference(avatar_split_clause,[],[f120,f1580]) ).
fof(f1580,plain,
( spl0_90
<=> ! [X15,X31] :
( X15 = X31
| c_Type_Otype_OAtom(X15) != c_Type_Otype_OAtom(X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f120,axiom,
! [X31,X15] :
( X15 = X31
| c_Type_Otype_OAtom(X15) != c_Type_Otype_OAtom(X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
fof(f1578,plain,
spl0_89,
inference(avatar_split_clause,[],[f82,f1576]) ).
fof(f82,axiom,
! [X10,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X10,tc_nat),c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1571,plain,
spl0_88,
inference(avatar_split_clause,[],[f959,f1569]) ).
fof(f1569,plain,
( spl0_88
<=> ! [X3,X19] : c_Lambda_Oliftn(c_Orderings_Obot__class_Obot(tc_nat),X19,X3) = X19 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f959,plain,
! [X3,X19] : c_Lambda_Oliftn(c_Orderings_Obot__class_Obot(tc_nat),X19,X3) = X19,
inference(forward_demodulation,[],[f815,f855]) ).
fof(f815,axiom,
! [X3,X19] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X19,X3) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
fof(f1567,plain,
spl0_87,
inference(avatar_split_clause,[],[f958,f1565]) ).
fof(f1565,plain,
( spl0_87
<=> ! [X52,X5] : c_List_Odrop(c_Orderings_Obot__class_Obot(tc_nat),X52,X5) = X52 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f958,plain,
! [X52,X5] : c_List_Odrop(c_Orderings_Obot__class_Obot(tc_nat),X52,X5) = X52,
inference(forward_demodulation,[],[f857,f855]) ).
fof(f857,axiom,
! [X52,X5] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X52,X5) = X52,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).
fof(f1563,plain,
spl0_86,
inference(avatar_split_clause,[],[f957,f1561]) ).
fof(f1561,plain,
( spl0_86
<=> ! [X1] : c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f957,plain,
! [X1] : c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X1,
inference(forward_demodulation,[],[f839,f855]) ).
fof(f839,axiom,
! [X1] : c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1559,plain,
spl0_85,
inference(avatar_split_clause,[],[f956,f1557]) ).
fof(f1557,plain,
( spl0_85
<=> ! [X10] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f956,plain,
! [X10] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) = X10,
inference(forward_demodulation,[],[f864,f855]) ).
fof(f864,axiom,
! [X10] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0L_0) ).
fof(f1555,plain,
spl0_84,
inference(avatar_split_clause,[],[f955,f1553]) ).
fof(f1553,plain,
( spl0_84
<=> ! [X10] : c_Orderings_Oord__class_Omax(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f955,plain,
! [X10] : c_Orderings_Oord__class_Omax(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f863,f855]) ).
fof(f863,axiom,
! [X10] : c_Orderings_Oord__class_Omax(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0R_0) ).
fof(f1551,plain,
spl0_83,
inference(avatar_split_clause,[],[f954,f1549]) ).
fof(f1549,plain,
( spl0_83
<=> ! [X1] : c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f954,plain,
! [X1] : c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f840,f855]) ).
fof(f840,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1547,plain,
spl0_82,
inference(avatar_split_clause,[],[f946,f1545]) ).
fof(f1545,plain,
( spl0_82
<=> ! [X5,X69,X68] :
( X68 = X69
| ~ c_fequal(X68,X69,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f946,axiom,
! [X68,X69,X5] :
( X68 = X69
| ~ c_fequal(X68,X69,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1543,plain,
spl0_81,
inference(avatar_split_clause,[],[f872,f1541]) ).
fof(f1541,plain,
( spl0_81
<=> ! [X2,X56] : c_Type_Otyping(X56,c_Lambda_OdB_OVar(X2),hAPP(X56,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f872,axiom,
! [X2,X56] : c_Type_Otyping(X56,c_Lambda_OdB_OVar(X2),hAPP(X56,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f1539,plain,
spl0_80,
inference(avatar_split_clause,[],[f712,f1537]) ).
fof(f1537,plain,
( spl0_80
<=> ! [X13,X3] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X3),X13,X3) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f712,axiom,
! [X3,X13] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X3),X13,X3) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f1535,plain,
spl0_79,
inference(avatar_split_clause,[],[f625,f1533]) ).
fof(f1533,plain,
( spl0_79
<=> ! [X0,X19] :
( ~ c_InductTermi_OIT(X19)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(X19,c_Lambda_OdB_OVar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f625,axiom,
! [X0,X19] :
( ~ c_InductTermi_OIT(X19)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(X19,c_Lambda_OdB_OVar(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
fof(f1531,plain,
spl0_78,
inference(avatar_split_clause,[],[f490,f1529]) ).
fof(f1529,plain,
( spl0_78
<=> ! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f490,axiom,
! [X1] : c_lessequals(X1,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).
fof(f1527,plain,
spl0_77,
inference(avatar_split_clause,[],[f424,f1525]) ).
fof(f1525,plain,
( spl0_77
<=> ! [X1,X10] : c_lessequals(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f424,axiom,
! [X10,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X1,X10,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
fof(f1523,plain,
spl0_76,
inference(avatar_split_clause,[],[f281,f1521]) ).
fof(f1521,plain,
( spl0_76
<=> ! [X1,X10] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X10,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f281,axiom,
! [X10,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X10,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1519,plain,
spl0_75,
inference(avatar_split_clause,[],[f111,f1517]) ).
fof(f1517,plain,
( spl0_75
<=> ! [X2,X5] :
( ~ class_Orderings_Obot(X5)
| c_lessequals(c_Orderings_Obot__class_Obot(X5),X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f111,axiom,
! [X2,X5] :
( ~ class_Orderings_Obot(X5)
| c_lessequals(c_Orderings_Obot__class_Obot(X5),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1515,plain,
spl0_74,
inference(avatar_split_clause,[],[f54,f1513]) ).
fof(f1513,plain,
( spl0_74
<=> ! [X1,X10] : c_lessequals(c_Divides_Odiv__class_Odiv(X1,X10,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f54,axiom,
! [X10,X1] : c_lessequals(c_Divides_Odiv__class_Odiv(X1,X10,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__dividend_0) ).
fof(f1511,plain,
spl0_73,
inference(avatar_split_clause,[],[f952,f1509]) ).
fof(f1509,plain,
( spl0_73
<=> ! [X2] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Suc(X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f952,plain,
! [X2] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Suc(X2),tc_nat),
inference(forward_demodulation,[],[f271,f855]) ).
fof(f271,axiom,
! [X2] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f1507,plain,
spl0_72,
inference(avatar_split_clause,[],[f951,f1505]) ).
fof(f1505,plain,
( spl0_72
<=> ! [X2] : c_Nitpick_Onat__gcd(X2,c_Orderings_Obot__class_Obot(tc_nat)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f951,plain,
! [X2] : c_Nitpick_Onat__gcd(X2,c_Orderings_Obot__class_Obot(tc_nat)) = X2,
inference(forward_demodulation,[],[f848,f855]) ).
fof(f848,axiom,
! [X2] : c_Nitpick_Onat__gcd(X2,c_HOL_Ozero__class_Ozero(tc_nat)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__gcd_Osimps_0) ).
fof(f1503,plain,
spl0_71,
inference(avatar_split_clause,[],[f950,f1501]) ).
fof(f1501,plain,
( spl0_71
<=> ! [X8] : c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osize__class_Osize(X8,tc_String_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f950,plain,
! [X8] : c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osize__class_Osize(X8,tc_String_Ochar),
inference(forward_demodulation,[],[f861,f855]) ).
fof(f861,axiom,
! [X8] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(X8,tc_String_Ochar),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_size__char_0) ).
fof(f1499,plain,
spl0_70,
inference(avatar_split_clause,[],[f949,f1496]) ).
fof(f1496,plain,
( spl0_70
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_nat_Onat__size(c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f949,plain,
c_Orderings_Obot__class_Obot(tc_nat) = c_nat_Onat__size(c_Orderings_Obot__class_Obot(tc_nat)),
inference(forward_demodulation,[],[f849,f855]) ).
fof(f849,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osize_I1_J_0) ).
fof(f1494,plain,
spl0_69,
inference(avatar_split_clause,[],[f909,f1492]) ).
fof(f1492,plain,
( spl0_69
<=> ! [X66,X67] :
( ~ class_Orderings_Obot(X67)
| class_Orderings_Obot(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f909,axiom,
! [X66,X67] :
( ~ class_Orderings_Obot(X67)
| class_Orderings_Obot(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1490,plain,
spl0_68,
inference(avatar_split_clause,[],[f908,f1488]) ).
fof(f1488,plain,
( spl0_68
<=> ! [X66,X67] :
( ~ class_Orderings_Oorder(X67)
| class_Orderings_Oorder(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f908,axiom,
! [X66,X67] :
( ~ class_Orderings_Oorder(X67)
| class_Orderings_Oorder(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1486,plain,
spl0_67,
inference(avatar_split_clause,[],[f907,f1484]) ).
fof(f1484,plain,
( spl0_67
<=> ! [X66,X67] :
( ~ class_Orderings_Opreorder(X67)
| class_Orderings_Opreorder(tc_fun(X66,X67)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f907,axiom,
! [X66,X67] :
( ~ class_Orderings_Opreorder(X67)
| class_Orderings_Opreorder(tc_fun(X66,X67)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1482,plain,
spl0_66,
inference(avatar_split_clause,[],[f899,f1479]) ).
fof(f1479,plain,
( spl0_66
<=> c_Type_Otyping(v_ea____,v_s____,c_Type_Otype_OFun(v_Ta____,v_U____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f899,axiom,
c_Type_Otyping(v_ea____,v_s____,c_Type_Otype_OFun(v_Ta____,v_U____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I1_J_0) ).
fof(f1477,plain,
spl0_65,
inference(avatar_split_clause,[],[f884,f1475]) ).
fof(f1475,plain,
( spl0_65
<=> ! [X0,X19] :
( ~ c_InductTermi_OIT(X19)
| c_InductTermi_OIT(c_Lambda_Olift(X19,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f884,axiom,
! [X0,X19] :
( ~ c_InductTermi_OIT(X19)
| c_InductTermi_OIT(c_Lambda_Olift(X19,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f1473,plain,
spl0_64,
inference(avatar_split_clause,[],[f876,f1471]) ).
fof(f1471,plain,
( spl0_64
<=> ! [X15,X57,X58] : c_Type_Otype_OAtom(X15) != c_Type_Otype_OFun(X57,X58) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f876,axiom,
! [X58,X57,X15] : c_Type_Otype_OAtom(X15) != c_Type_Otype_OFun(X57,X58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
fof(f1469,plain,
spl0_63,
inference(avatar_split_clause,[],[f725,f1467]) ).
fof(f1467,plain,
( spl0_63
<=> ! [X34,X50,X49] : c_Lambda_OdB_OAbs(X34) != c_Lambda_OdB_OApp(X49,X50) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f725,axiom,
! [X50,X49,X34] : c_Lambda_OdB_OAbs(X34) != c_Lambda_OdB_OApp(X49,X50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f1465,plain,
spl0_62,
inference(avatar_split_clause,[],[f708,f1463]) ).
fof(f1463,plain,
( spl0_62
<=> ! [X2,X5] :
( ~ class_Orderings_Opreorder(X5)
| c_lessequals(X2,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f708,axiom,
! [X2,X5] :
( ~ class_Orderings_Opreorder(X5)
| c_lessequals(X2,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1461,plain,
spl0_61,
inference(avatar_split_clause,[],[f707,f1459]) ).
fof(f1459,plain,
( spl0_61
<=> ! [X2,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X2,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f707,axiom,
! [X2,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X2,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1457,plain,
spl0_60,
inference(avatar_split_clause,[],[f659,f1455]) ).
fof(f1455,plain,
( spl0_60
<=> ! [X44,X43,X15] : c_Lambda_OdB_OVar(X15) != c_Lambda_OdB_OApp(X43,X44) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f659,axiom,
! [X44,X15,X43] : c_Lambda_OdB_OVar(X15) != c_Lambda_OdB_OApp(X43,X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
fof(f1453,plain,
spl0_59,
inference(avatar_split_clause,[],[f367,f1451]) ).
fof(f1451,plain,
( spl0_59
<=> ! [X2,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f367,axiom,
! [X2,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1449,plain,
spl0_58,
inference(avatar_split_clause,[],[f366,f1447]) ).
fof(f366,axiom,
! [X2,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1445,plain,
spl0_57,
inference(avatar_split_clause,[],[f365,f1443]) ).
fof(f1443,plain,
( spl0_57
<=> ! [X2,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f365,axiom,
! [X2,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_HOL_Oord__class_Oless(X2,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1441,plain,
( spl0_56
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f1424,f1421,f1439]) ).
fof(f1439,plain,
( spl0_56
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1421,plain,
( spl0_52
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1424,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1422,f855]) ).
fof(f1422,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1437,plain,
( spl0_55
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f1419,f1416,f1435]) ).
fof(f1435,plain,
( spl0_55
<=> ! [X31] : c_Suc(X31) != c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1416,plain,
( spl0_51
<=> ! [X31] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X31) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1419,plain,
( ! [X31] : c_Suc(X31) != c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_51 ),
inference(forward_demodulation,[],[f1417,f855]) ).
fof(f1417,plain,
( ! [X31] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X31)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f1433,plain,
spl0_54,
inference(avatar_split_clause,[],[f948,f1431]) ).
fof(f1431,plain,
( spl0_54
<=> ! [X10] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f948,plain,
! [X10] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat),
inference(forward_demodulation,[],[f860,f855]) ).
fof(f860,axiom,
! [X10] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1429,plain,
spl0_53,
inference(avatar_split_clause,[],[f855,f1426]) ).
fof(f1423,plain,
spl0_52,
inference(avatar_split_clause,[],[f853,f1421]) ).
fof(f853,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f1418,plain,
spl0_51,
inference(avatar_split_clause,[],[f845,f1416]) ).
fof(f845,axiom,
! [X31] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f1414,plain,
spl0_50,
inference(avatar_split_clause,[],[f558,f1412]) ).
fof(f1412,plain,
( spl0_50
<=> ! [X10] : ~ c_lessequals(c_Suc(X10),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f558,axiom,
! [X10] : ~ c_lessequals(c_Suc(X10),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1410,plain,
spl0_49,
inference(avatar_split_clause,[],[f507,f1408]) ).
fof(f507,axiom,
! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f1406,plain,
spl0_48,
inference(avatar_split_clause,[],[f476,f1404]) ).
fof(f1404,plain,
( spl0_48
<=> ! [X18] :
( ~ c_InductTermi_OIT(X18)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f476,axiom,
! [X18] :
( ~ c_InductTermi_OIT(X18)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f1402,plain,
spl0_47,
inference(avatar_split_clause,[],[f181,f1400]) ).
fof(f1400,plain,
( spl0_47
<=> ! [X34,X15] : c_Lambda_OdB_OVar(X15) != c_Lambda_OdB_OAbs(X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f181,axiom,
! [X34,X15] : c_Lambda_OdB_OVar(X15) != c_Lambda_OdB_OAbs(X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f1398,plain,
spl0_46,
inference(avatar_split_clause,[],[f945,f1396]) ).
fof(f1396,plain,
( spl0_46
<=> ! [X2,X5] : c_fequal(X2,X2,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f945,axiom,
! [X2,X5] : c_fequal(X2,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1394,plain,
spl0_45,
inference(avatar_split_clause,[],[f905,f1391]) ).
fof(f905,axiom,
c_Type_Otyping(v_ea____,v_ta____,v_Ta____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I3_J_0) ).
fof(f1389,plain,
spl0_44,
inference(avatar_split_clause,[],[f706,f1387]) ).
fof(f1387,plain,
( spl0_44
<=> ! [X2] : c_lessequals(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f706,axiom,
! [X2] : c_lessequals(X2,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f1385,plain,
spl0_43,
inference(avatar_split_clause,[],[f586,f1383]) ).
fof(f1383,plain,
( spl0_43
<=> ! [X10] : c_Suc(X10) != X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f586,axiom,
! [X10] : c_Suc(X10) != X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f1381,plain,
spl0_42,
inference(avatar_split_clause,[],[f401,f1379]) ).
fof(f1379,plain,
( spl0_42
<=> ! [X0,X19] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X0),X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f401,axiom,
! [X0,X19] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X0),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f1377,plain,
spl0_41,
inference(avatar_split_clause,[],[f363,f1375]) ).
fof(f363,axiom,
! [X2] : ~ c_HOL_Oord__class_Oless(X2,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1373,plain,
( ~ spl0_40
| spl0_39 ),
inference(avatar_split_clause,[],[f1368,f1364,f1370]) ).
fof(f1364,plain,
( spl0_39
<=> c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1368,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_Orderings_Obot__class_Obot(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_Orderings_Obot__class_Obot(tc_nat)),v_Ta____)
| spl0_39 ),
inference(forward_demodulation,[],[f1366,f855]) ).
fof(f1366,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____)
| spl0_39 ),
inference(avatar_component_clause,[],[f1364]) ).
fof(f1367,plain,
~ spl0_39,
inference(avatar_split_clause,[],[f906,f1364]) ).
fof(f906,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Otype_OFun(v_Ta____,v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1362,plain,
spl0_38,
inference(avatar_split_clause,[],[f165,f1360]) ).
fof(f1360,plain,
( spl0_38
<=> ! [X10] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f165,axiom,
! [X10] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
fof(f1358,plain,
spl0_37,
inference(avatar_split_clause,[],[f944,f1355]) ).
fof(f1355,plain,
( spl0_37
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f944,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1353,plain,
spl0_36,
inference(avatar_split_clause,[],[f943,f1350]) ).
fof(f1350,plain,
( spl0_36
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f943,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1348,plain,
spl0_35,
inference(avatar_split_clause,[],[f942,f1345]) ).
fof(f1345,plain,
( spl0_35
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f942,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1343,plain,
spl0_34,
inference(avatar_split_clause,[],[f941,f1340]) ).
fof(f941,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1338,plain,
spl0_33,
inference(avatar_split_clause,[],[f940,f1335]) ).
fof(f1335,plain,
( spl0_33
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f940,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1333,plain,
spl0_32,
inference(avatar_split_clause,[],[f939,f1330]) ).
fof(f1330,plain,
( spl0_32
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f939,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f1328,plain,
spl0_31,
inference(avatar_split_clause,[],[f938,f1325]) ).
fof(f938,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f1323,plain,
spl0_30,
inference(avatar_split_clause,[],[f937,f1320]) ).
fof(f1320,plain,
( spl0_30
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f937,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1318,plain,
spl0_29,
inference(avatar_split_clause,[],[f936,f1315]) ).
fof(f1315,plain,
( spl0_29
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f936,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1313,plain,
spl0_28,
inference(avatar_split_clause,[],[f935,f1310]) ).
fof(f1310,plain,
( spl0_28
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f935,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1308,plain,
spl0_27,
inference(avatar_split_clause,[],[f934,f1305]) ).
fof(f1305,plain,
( spl0_27
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f934,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1303,plain,
spl0_26,
inference(avatar_split_clause,[],[f933,f1300]) ).
fof(f1300,plain,
( spl0_26
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f933,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1298,plain,
spl0_25,
inference(avatar_split_clause,[],[f932,f1295]) ).
fof(f1295,plain,
( spl0_25
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f932,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1293,plain,
spl0_24,
inference(avatar_split_clause,[],[f931,f1290]) ).
fof(f1290,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f931,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1288,plain,
spl0_23,
inference(avatar_split_clause,[],[f930,f1285]) ).
fof(f930,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1283,plain,
spl0_22,
inference(avatar_split_clause,[],[f929,f1280]) ).
fof(f1280,plain,
( spl0_22
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f929,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1278,plain,
spl0_21,
inference(avatar_split_clause,[],[f928,f1275]) ).
fof(f1275,plain,
( spl0_21
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f928,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1273,plain,
spl0_20,
inference(avatar_split_clause,[],[f927,f1270]) ).
fof(f1270,plain,
( spl0_20
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f927,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1268,plain,
spl0_19,
inference(avatar_split_clause,[],[f926,f1265]) ).
fof(f1265,plain,
( spl0_19
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f926,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1263,plain,
spl0_18,
inference(avatar_split_clause,[],[f925,f1260]) ).
fof(f1260,plain,
( spl0_18
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f925,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1258,plain,
spl0_17,
inference(avatar_split_clause,[],[f924,f1255]) ).
fof(f1255,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f924,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1253,plain,
spl0_16,
inference(avatar_split_clause,[],[f923,f1250]) ).
fof(f1250,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f923,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1248,plain,
spl0_15,
inference(avatar_split_clause,[],[f922,f1245]) ).
fof(f1245,plain,
( spl0_15
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f922,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1243,plain,
spl0_14,
inference(avatar_split_clause,[],[f921,f1240]) ).
fof(f1240,plain,
( spl0_14
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f921,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1238,plain,
spl0_13,
inference(avatar_split_clause,[],[f920,f1235]) ).
fof(f1235,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f920,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1233,plain,
spl0_12,
inference(avatar_split_clause,[],[f919,f1230]) ).
fof(f1230,plain,
( spl0_12
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f919,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1228,plain,
spl0_11,
inference(avatar_split_clause,[],[f918,f1225]) ).
fof(f1225,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f918,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1223,plain,
spl0_10,
inference(avatar_split_clause,[],[f917,f1220]) ).
fof(f1220,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f917,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1218,plain,
spl0_9,
inference(avatar_split_clause,[],[f916,f1215]) ).
fof(f1215,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f916,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1213,plain,
spl0_8,
inference(avatar_split_clause,[],[f915,f1210]) ).
fof(f1210,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f915,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1208,plain,
spl0_7,
inference(avatar_split_clause,[],[f914,f1205]) ).
fof(f1205,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f914,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1203,plain,
spl0_6,
inference(avatar_split_clause,[],[f913,f1200]) ).
fof(f1200,plain,
( spl0_6
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f913,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1198,plain,
spl0_5,
inference(avatar_split_clause,[],[f912,f1195]) ).
fof(f1195,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f912,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1193,plain,
spl0_4,
inference(avatar_split_clause,[],[f911,f1190]) ).
fof(f1190,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f911,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1188,plain,
spl0_3,
inference(avatar_split_clause,[],[f910,f1185]) ).
fof(f1185,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f910,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1183,plain,
spl0_2,
inference(avatar_split_clause,[],[f894,f1180]) ).
fof(f1180,plain,
( spl0_2
<=> c_InductTermi_OIT(v_ta____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f894,axiom,
c_InductTermi_OIT(v_ta____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
fof(f1178,plain,
spl0_1,
inference(avatar_split_clause,[],[f321,f1175]) ).
fof(f1175,plain,
( spl0_1
<=> c_InductTermi_OIT(v_s____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f321,axiom,
c_InductTermi_OIT(v_s____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL851-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 14:03:42 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (18535)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.41 % (18538)WARNING: value z3 for option sas not known
% 0.13/0.41 % (18541)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)
% 0.13/0.41 % (18536)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.41 % (18539)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.41 % (18540)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)
% 0.13/0.41 % (18537)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.41 % (18538)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)
% 0.13/0.41 % (18542)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)
% 0.19/0.54 TRYING [1]
% 0.19/0.55 TRYING [2]
% 0.19/0.56 % (18540)First to succeed.
% 1.34/0.57 % (18540)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18535"
% 1.34/0.57 % (18540)Refutation found. Thanks to Tanya!
% 1.34/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.34/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.34/0.58 % (18540)------------------------------
% 1.34/0.58 % (18540)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.34/0.58 % (18540)Termination reason: Refutation
% 1.34/0.58
% 1.34/0.58 % (18540)Memory used [KB]: 3565
% 1.34/0.58 % (18540)Time elapsed: 0.158 s
% 1.34/0.58 % (18540)Instructions burned: 312 (million)
% 1.34/0.58 % (18535)Success in time 0.21 s
%------------------------------------------------------------------------------