TSTP Solution File: LCL795-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL795-1 : 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 : n029.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 : Tue Apr 30 13:49:26 EDT 2024
% Result : Unsatisfiable 1.24s 0.63s
% Output : Refutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 641
% Syntax : Number of formulae : 1111 ( 451 unt; 0 def)
% Number of atoms : 2210 ( 396 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1900 ( 801 ~; 766 |; 0 &)
% ( 333 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 378 ( 376 usr; 334 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 16 con; 0-5 aty)
% Number of variables : 1534 (1534 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5125,plain,
$false,
inference(avatar_sat_refutation,[],[f1124,f1129,f1134,f1139,f1144,f1149,f1154,f1159,f1164,f1169,f1174,f1179,f1184,f1189,f1194,f1199,f1204,f1209,f1214,f1219,f1224,f1229,f1234,f1239,f1244,f1249,f1254,f1259,f1264,f1269,f1274,f1279,f1284,f1289,f1294,f1299,f1303,f1307,f1311,f1315,f1319,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1353,f1359,f1363,f1367,f1371,f1376,f1383,f1387,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1423,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1492,f1496,f1503,f1507,f1511,f1515,f1519,f1523,f1527,f1531,f1535,f1539,f1543,f1547,f1551,f1555,f1560,f1564,f1568,f1573,f1577,f1581,f1585,f1589,f1593,f1597,f1601,f1605,f1620,f1633,f1637,f1641,f1645,f1649,f1653,f1657,f1661,f1665,f1669,f1673,f1677,f1681,f1685,f1689,f1693,f1697,f1701,f1705,f1709,f1713,f1717,f1721,f1725,f1729,f1733,f1737,f1741,f1745,f1749,f1753,f1757,f1761,f1765,f1770,f1774,f1778,f1782,f1906,f1944,f1948,f1952,f1956,f1960,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2134,f2192,f2267,f2279,f2283,f2287,f2291,f2295,f2299,f2303,f2307,f2311,f2323,f2327,f2331,f2335,f2339,f2343,f2347,f2351,f2355,f2359,f2373,f2377,f2381,f2385,f2389,f2393,f2633,f2637,f2641,f2645,f2649,f2653,f2657,f2661,f2665,f2670,f2674,f2678,f2682,f2686,f2690,f2694,f2698,f2702,f2706,f2710,f2714,f2719,f2723,f2728,f2732,f2736,f2740,f2744,f2762,f2958,f3038,f3070,f3074,f3078,f3082,f3086,f3090,f3094,f3098,f3102,f3106,f3110,f3114,f3118,f3122,f3126,f3130,f3134,f3138,f3142,f3146,f3150,f3154,f3158,f3162,f3166,f3170,f3174,f3190,f3194,f3198,f3202,f3206,f3210,f3214,f3218,f3222,f3226,f3236,f3240,f3244,f3248,f3252,f3256,f3260,f3264,f3509,f3736,f3984,f4227,f4256,f4260,f4264,f4268,f4272,f4276,f4280,f4284,f4288,f4292,f4296,f4300,f4304,f4308,f4312,f4316,f4320,f4324,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4391,f4395,f4399,f4403,f4407,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4447,f4451,f4719,f4953,f5124]) ).
fof(f5124,plain,
( ~ spl0_42
| spl0_55
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f5073,f4401,f1380,f1321]) ).
fof(f1321,plain,
( spl0_42
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1380,plain,
( spl0_55
<=> c_Type_Otyping(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat)),v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f4401,plain,
( spl0_319
<=> ! [X51,X21,X6,X2,X26] :
( ~ c_Type_Otyping(X2,X21,X26)
| c_Type_Otyping(c_Type_Oshift(X2,X6,X51,tc_Type_Otype),c_Lambda_Olift(X21,X6),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f5073,plain,
( ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| spl0_55
| ~ spl0_319 ),
inference(resolution,[],[f4402,f1382]) ).
fof(f1382,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat)),v_T____)
| spl0_55 ),
inference(avatar_component_clause,[],[f1380]) ).
fof(f4402,plain,
( ! [X2,X51,X21,X6,X26] :
( c_Type_Otyping(c_Type_Oshift(X2,X6,X51,tc_Type_Otype),c_Lambda_Olift(X21,X6),X26)
| ~ c_Type_Otyping(X2,X21,X26) )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f4401]) ).
fof(f4953,plain,
( spl0_333
| ~ spl0_133
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f4670,f4294,f1719,f4951]) ).
fof(f4951,plain,
( spl0_333
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f1719,plain,
( spl0_133
<=> ! [X6,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X6),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f4294,plain,
( spl0_298
<=> ! [X8,X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat)),X8) = c_Orderings_Oord__class_Omax(X10,X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f4670,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_133
| ~ spl0_298 ),
inference(superposition,[],[f1720,f4295]) ).
fof(f4295,plain,
( ! [X10,X8] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat)),X8) = c_Orderings_Oord__class_Omax(X10,X8,tc_nat)
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f4294]) ).
fof(f1720,plain,
( ! [X6,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X6),X6,tc_nat)
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1719]) ).
fof(f4719,plain,
( spl0_332
| ~ spl0_125
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f4668,f4294,f1687,f4717]) ).
fof(f4717,plain,
( spl0_332
<=> ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f1687,plain,
( spl0_125
<=> ! [X8,X10] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f4668,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_125
| ~ spl0_298 ),
inference(superposition,[],[f1688,f4295]) ).
fof(f1688,plain,
( ! [X10,X8] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10),tc_nat)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1687]) ).
fof(f4451,plain,
spl0_331,
inference(avatar_split_clause,[],[f1078,f4449]) ).
fof(f4449,plain,
( spl0_331
<=> ! [X12,X11] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__Nat__Xnat__Xinduct__1(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f1078,plain,
! [X11,X12] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__Nat__Xnat__Xinduct__1(X11))) ),
inference(forward_demodulation,[],[f812,f815]) ).
fof(f815,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__nat__def_0) ).
fof(f812,axiom,
! [X11,X12] :
( hBOOL(hAPP(X11,X12))
| ~ hBOOL(hAPP(X11,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X11,v_sko__Nat__Xnat__Xinduct__1(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
fof(f4447,plain,
spl0_330,
inference(avatar_split_clause,[],[f1077,f4445]) ).
fof(f4445,plain,
( spl0_330
<=> ! [X12,X11] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__List__Xreplicate__Xinduct__1(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f1077,plain,
! [X11,X12] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__List__Xreplicate__Xinduct__1(X11))) ),
inference(forward_demodulation,[],[f803,f815]) ).
fof(f803,axiom,
! [X11,X12] :
( hBOOL(hAPP(X11,X12))
| ~ hBOOL(hAPP(X11,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X11,v_sko__List__Xreplicate__Xinduct__1(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate_Oinduct_0) ).
fof(f4443,plain,
spl0_329,
inference(avatar_split_clause,[],[f1076,f4441]) ).
fof(f4441,plain,
( spl0_329
<=> ! [X12,X11] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__List__Xupt__Xinduct__1(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f1076,plain,
! [X11,X12] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__List__Xupt__Xinduct__1(X11))) ),
inference(forward_demodulation,[],[f816,f815]) ).
fof(f816,axiom,
! [X11,X12] :
( hBOOL(hAPP(X11,X12))
| ~ hBOOL(hAPP(X11,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X11,v_sko__List__Xupt__Xinduct__1(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
fof(f4439,plain,
spl0_328,
inference(avatar_split_clause,[],[f1075,f4437]) ).
fof(f4437,plain,
( spl0_328
<=> ! [X11,X10] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X10))
| hBOOL(hAPP(X11,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f1075,plain,
! [X10,X11] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X10))
| hBOOL(hAPP(X11,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X11))) ),
inference(forward_demodulation,[],[f786,f815]) ).
fof(f786,axiom,
! [X10,X11] :
( hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(X11,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X11,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__induct_0) ).
fof(f4435,plain,
spl0_327,
inference(avatar_split_clause,[],[f1074,f4433]) ).
fof(f4433,plain,
( spl0_327
<=> ! [X12,X11] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__Nat__Xnat__Xinducts__1(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f1074,plain,
! [X11,X12] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X12))
| hBOOL(hAPP(X11,v_sko__Nat__Xnat__Xinducts__1(X11))) ),
inference(forward_demodulation,[],[f807,f815]) ).
fof(f807,axiom,
! [X11,X12] :
( hBOOL(hAPP(X11,X12))
| ~ hBOOL(hAPP(X11,c_HOL_Ozero__class_Ozero(tc_nat)))
| hBOOL(hAPP(X11,v_sko__Nat__Xnat__Xinducts__1(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinducts_0) ).
fof(f4431,plain,
( spl0_326
| ~ spl0_140
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f2619,f2190,f1747,f4429]) ).
fof(f4429,plain,
( spl0_326
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f1747,plain,
( spl0_140
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X8,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f2190,plain,
( spl0_181
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2619,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_140
| ~ spl0_181 ),
inference(resolution,[],[f2191,f1748]) ).
fof(f1748,plain,
( ! [X10,X8] :
( c_HOL_Oord__class_Oless(X8,c_Suc(X10),tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1747]) ).
fof(f2191,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f2190]) ).
fof(f4427,plain,
spl0_325,
inference(avatar_split_clause,[],[f1073,f4425]) ).
fof(f4425,plain,
( spl0_325
<=> ! [X11,X10] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(X11,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f1073,plain,
! [X10,X11] :
( ~ hBOOL(hAPP(X11,c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(X11,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X11))) ),
inference(forward_demodulation,[],[f819,f815]) ).
fof(f819,axiom,
! [X10,X11] :
( hBOOL(hAPP(X11,X10))
| ~ hBOOL(hAPP(X11,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X11,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_1) ).
fof(f4423,plain,
spl0_324,
inference(avatar_split_clause,[],[f1032,f4421]) ).
fof(f4421,plain,
( spl0_324
<=> ! [X0,X10] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f1032,plain,
! [X10,X0] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
inference(forward_demodulation,[],[f514,f815]) ).
fof(f514,axiom,
! [X10,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| 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(X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f4419,plain,
spl0_323,
inference(avatar_split_clause,[],[f1031,f4417]) ).
fof(f4417,plain,
( spl0_323
<=> ! [X0,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f1031,plain,
! [X10,X0] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
inference(forward_demodulation,[],[f513,f815]) ).
fof(f513,axiom,
! [X10,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ 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(X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f4415,plain,
spl0_322,
inference(avatar_split_clause,[],[f1005,f4413]) ).
fof(f4413,plain,
( spl0_322
<=> ! [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_322])]) ).
fof(f1005,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,[],[f1004,f815]) ).
fof(f1004,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,[],[f717,f815]) ).
fof(f717,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/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
fof(f4411,plain,
spl0_321,
inference(avatar_split_clause,[],[f877,f4409]) ).
fof(f4409,plain,
( spl0_321
<=> ! [X69,X64,X68,X63] :
( X64 = X69
| hAPP(hAPP(c_Type_Otype_OFun,X63),X64) != hAPP(hAPP(c_Type_Otype_OFun,X68),X69) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f877,axiom,
! [X68,X69,X63,X64] :
( X64 = X69
| hAPP(hAPP(c_Type_Otype_OFun,X63),X64) != hAPP(hAPP(c_Type_Otype_OFun,X68),X69) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
fof(f4407,plain,
spl0_320,
inference(avatar_split_clause,[],[f876,f4405]) ).
fof(f4405,plain,
( spl0_320
<=> ! [X64,X63,X69,X68] :
( X63 = X68
| hAPP(hAPP(c_Type_Otype_OFun,X63),X64) != hAPP(hAPP(c_Type_Otype_OFun,X68),X69) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f876,axiom,
! [X68,X69,X63,X64] :
( X63 = X68
| hAPP(hAPP(c_Type_Otype_OFun,X63),X64) != hAPP(hAPP(c_Type_Otype_OFun,X68),X69) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
fof(f4403,plain,
spl0_319,
inference(avatar_split_clause,[],[f875,f4401]) ).
fof(f875,axiom,
! [X2,X21,X51,X6,X26] :
( ~ c_Type_Otyping(X2,X21,X26)
| c_Type_Otyping(c_Type_Oshift(X2,X6,X51,tc_Type_Otype),c_Lambda_Olift(X21,X6),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
fof(f4399,plain,
spl0_318,
inference(avatar_split_clause,[],[f830,f4397]) ).
fof(f4397,plain,
( spl0_318
<=> ! [X0,X16] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X16,X0) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X0),X16,c_HOL_Ozero__class_Ozero(X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f830,axiom,
! [X0,X16] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X16,X0) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X0),X16,c_HOL_Ozero__class_Ozero(X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
fof(f4395,plain,
spl0_317,
inference(avatar_split_clause,[],[f716,f4393]) ).
fof(f4393,plain,
( spl0_317
<=> ! [X8,X19,X10] :
( X8 = X10
| c_HOL_Otimes__class_Otimes(c_Suc(X19),X8,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X19),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f716,axiom,
! [X10,X8,X19] :
( X8 = X10
| c_HOL_Otimes__class_Otimes(c_Suc(X19),X8,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X19),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
fof(f4391,plain,
spl0_316,
inference(avatar_split_clause,[],[f703,f4389]) ).
fof(f4389,plain,
( spl0_316
<=> ! [X8,X19,X10] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X19,X8,tc_nat),c_HOL_Otimes__class_Otimes(X19,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f703,axiom,
! [X10,X8,X19] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X19,X8,tc_nat),c_HOL_Otimes__class_Otimes(X19,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).
fof(f4382,plain,
spl0_315,
inference(avatar_split_clause,[],[f701,f4380]) ).
fof(f4380,plain,
( spl0_315
<=> ! [X6,X9,X19] :
( ~ c_lessequals(X6,X9,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X19,tc_nat),c_HOL_Otimes__class_Otimes(X9,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f701,axiom,
! [X6,X9,X19] :
( ~ c_lessequals(X6,X9,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X19,tc_nat),c_HOL_Otimes__class_Otimes(X9,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
fof(f4378,plain,
spl0_314,
inference(avatar_split_clause,[],[f683,f4376]) ).
fof(f4376,plain,
( spl0_314
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X14,X15,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| c_HOL_Oord__class_Oless(X13,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f683,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X14,X15,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| c_HOL_Oord__class_Oless(X13,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f4374,plain,
spl0_313,
inference(avatar_split_clause,[],[f682,f4372]) ).
fof(f4372,plain,
( spl0_313
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| c_HOL_Oord__class_Oless(X13,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f682,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| c_HOL_Oord__class_Oless(X13,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f4370,plain,
spl0_312,
inference(avatar_split_clause,[],[f622,f4368]) ).
fof(f4368,plain,
( spl0_312
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = c_Orderings_Oord__class_Omax(X13,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f622,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = c_Orderings_Oord__class_Omax(X13,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f4366,plain,
spl0_311,
inference(avatar_split_clause,[],[f617,f4364]) ).
fof(f4364,plain,
( spl0_311
<=> ! [X22,X10,X21,X42] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X22)),X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X10),X42,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f617,axiom,
! [X21,X10,X22,X42] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X22)),X21) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X10),X42,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f4362,plain,
spl0_310,
inference(avatar_split_clause,[],[f576,f4360]) ).
fof(f4360,plain,
( spl0_310
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(X14,X15,X0)
| c_lessequals(X13,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f576,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(X14,X15,X0)
| c_lessequals(X13,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f4358,plain,
spl0_309,
inference(avatar_split_clause,[],[f574,f4356]) ).
fof(f4356,plain,
( spl0_309
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0)
| c_HOL_Oord__class_Oless(X15,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f574,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0)
| c_HOL_Oord__class_Oless(X15,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f4354,plain,
spl0_308,
inference(avatar_split_clause,[],[f573,f4352]) ).
fof(f4352,plain,
( spl0_308
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(X15,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f573,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X15,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(X15,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f4350,plain,
spl0_307,
inference(avatar_split_clause,[],[f572,f4348]) ).
fof(f4348,plain,
( spl0_307
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_lessequals(X15,X14,X0)
| c_lessequals(X15,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f572,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_lessequals(X15,X14,X0)
| c_lessequals(X15,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f4346,plain,
spl0_306,
inference(avatar_split_clause,[],[f506,f4344]) ).
fof(f4344,plain,
( spl0_306
<=> ! [X8,X19,X10] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X19,tc_nat),c_HOL_Otimes__class_Otimes(X10,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f506,axiom,
! [X10,X8,X19] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X19,tc_nat),c_HOL_Otimes__class_Otimes(X10,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
fof(f4324,plain,
spl0_305,
inference(avatar_split_clause,[],[f505,f4322]) ).
fof(f4322,plain,
( spl0_305
<=> ! [X8,X19,X10] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X19,X8,tc_nat),c_HOL_Otimes__class_Otimes(X19,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f505,axiom,
! [X10,X8,X19] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X19,X8,tc_nat),c_HOL_Otimes__class_Otimes(X19,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
fof(f4320,plain,
spl0_304,
inference(avatar_split_clause,[],[f485,f4318]) ).
fof(f4318,plain,
( spl0_304
<=> ! [X0,X8,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f485,axiom,
! [X10,X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f4316,plain,
spl0_303,
inference(avatar_split_clause,[],[f484,f4314]) ).
fof(f4314,plain,
( spl0_303
<=> ! [X0,X8,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f484,axiom,
! [X10,X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f4312,plain,
spl0_302,
inference(avatar_split_clause,[],[f462,f4310]) ).
fof(f4310,plain,
( spl0_302
<=> ! [X22,X21,X7] :
( ~ c_Lambda_Obeta(X22,X21)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X22),X7),hAPP(hAPP(c_Lambda_OdB_OApp,X21),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f462,axiom,
! [X21,X7,X22] :
( ~ c_Lambda_Obeta(X22,X21)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X22),X7),hAPP(hAPP(c_Lambda_OdB_OApp,X21),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
fof(f4308,plain,
spl0_301,
inference(avatar_split_clause,[],[f461,f4306]) ).
fof(f4306,plain,
( spl0_301
<=> ! [X22,X21,X7] :
( ~ c_Lambda_Obeta(X22,X21)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X7),X22),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f461,axiom,
! [X21,X7,X22] :
( ~ c_Lambda_Obeta(X22,X21)
| c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,X7),X22),hAPP(hAPP(c_Lambda_OdB_OApp,X7),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
fof(f4304,plain,
spl0_300,
inference(avatar_split_clause,[],[f369,f4302]) ).
fof(f4302,plain,
( spl0_300
<=> ! [X53,X46,X45,X52] :
( X45 = X52
| hAPP(hAPP(c_Lambda_OdB_OApp,X45),X46) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f369,axiom,
! [X46,X45,X52,X53] :
( X45 = X52
| hAPP(hAPP(c_Lambda_OdB_OApp,X45),X46) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f4300,plain,
spl0_299,
inference(avatar_split_clause,[],[f368,f4298]) ).
fof(f4298,plain,
( spl0_299
<=> ! [X45,X52,X53,X46] :
( X46 = X53
| hAPP(hAPP(c_Lambda_OdB_OApp,X45),X46) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f368,axiom,
! [X46,X45,X52,X53] :
( X46 = X53
| hAPP(hAPP(c_Lambda_OdB_OApp,X45),X46) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f4296,plain,
spl0_298,
inference(avatar_split_clause,[],[f349,f4294]) ).
fof(f349,axiom,
! [X10,X8] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat)),X8) = c_Orderings_Oord__class_Omax(X10,X8,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
fof(f4292,plain,
spl0_297,
inference(avatar_split_clause,[],[f336,f4290]) ).
fof(f4290,plain,
( spl0_297
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X13,X14,X0)
| c_lessequals(X14,X13,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f336,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X13,X14,X0)
| c_lessequals(X14,X13,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f4288,plain,
spl0_296,
inference(avatar_split_clause,[],[f221,f4286]) ).
fof(f4286,plain,
( spl0_296
<=> ! [X25,X8,X10] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X25,tc_nat),c_HOL_Ominus__class_Ominus(X10,X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f221,axiom,
! [X10,X8,X25] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X8,X25,tc_nat),c_HOL_Ominus__class_Ominus(X10,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f4284,plain,
( spl0_295
| ~ spl0_132
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4159,f3234,f1715,f4282]) ).
fof(f4282,plain,
( spl0_295
<=> ! [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_295])]) ).
fof(f1715,plain,
( spl0_132
<=> ! [X6,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X9),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f3234,plain,
( spl0_276
<=> ! [X12] : c_nat_Onat__size(c_Suc(X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X12)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f4159,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_nat_Onat__size(c_Suc(X0)),c_nat_Onat__size(X0),tc_nat)
| ~ spl0_132
| ~ spl0_276 ),
inference(superposition,[],[f1716,f3235]) ).
fof(f3235,plain,
( ! [X12] : c_nat_Onat__size(c_Suc(X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X12)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f3234]) ).
fof(f1716,plain,
( ! [X6,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X9),X6,tc_nat)
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1715]) ).
fof(f4280,plain,
spl0_294,
inference(avatar_split_clause,[],[f220,f4278]) ).
fof(f4278,plain,
( spl0_294
<=> ! [X25,X8,X10] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X25,X10,tc_nat),c_HOL_Ominus__class_Ominus(X25,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f220,axiom,
! [X10,X8,X25] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X25,X10,tc_nat),c_HOL_Ominus__class_Ominus(X25,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f4276,plain,
spl0_293,
inference(avatar_split_clause,[],[f71,f4274]) ).
fof(f4274,plain,
( spl0_293
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0)
| c_HOL_Oord__class_Oless(X15,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f71,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0)
| c_HOL_Oord__class_Oless(X15,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f4272,plain,
spl0_292,
inference(avatar_split_clause,[],[f70,f4270]) ).
fof(f4270,plain,
( spl0_292
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| c_HOL_Oord__class_Oless(X13,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f70,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| c_HOL_Oord__class_Oless(X13,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f4268,plain,
spl0_291,
inference(avatar_split_clause,[],[f63,f4266]) ).
fof(f4266,plain,
( spl0_291
<=> ! [X0,X16] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X16,X0) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0),X16,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f63,axiom,
! [X0,X16] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X16,X0) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0),X16,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
fof(f4264,plain,
spl0_290,
inference(avatar_split_clause,[],[f43,f4262]) ).
fof(f4262,plain,
( spl0_290
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = c_Orderings_Oord__class_Omin(X13,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f43,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = c_Orderings_Oord__class_Omin(X13,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f4260,plain,
spl0_289,
inference(avatar_split_clause,[],[f32,f4258]) ).
fof(f4258,plain,
( spl0_289
<=> ! [X0,X8,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f32,axiom,
! [X10,X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
fof(f4256,plain,
spl0_288,
inference(avatar_split_clause,[],[f31,f4254]) ).
fof(f4254,plain,
( spl0_288
<=> ! [X0,X8,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f31,axiom,
! [X10,X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_Nat_Osemiring__1__class_Oof__nat(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
fof(f4227,plain,
( spl0_287
| ~ spl0_124
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f4157,f3234,f1683,f4225]) ).
fof(f4225,plain,
( spl0_287
<=> ! [X0] : c_lessequals(c_nat_Onat__size(X0),c_nat_Onat__size(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f1683,plain,
( spl0_124
<=> ! [X8,X10] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f4157,plain,
( ! [X0] : c_lessequals(c_nat_Onat__size(X0),c_nat_Onat__size(c_Suc(X0)),tc_nat)
| ~ spl0_124
| ~ spl0_276 ),
inference(superposition,[],[f1684,f3235]) ).
fof(f1684,plain,
( ! [X10,X8] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1683]) ).
fof(f3984,plain,
( spl0_286
| ~ spl0_130
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2536,f2132,f1707,f3982]) ).
fof(f3982,plain,
( spl0_286
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f1707,plain,
( spl0_130
<=> ! [X8,X10] :
( c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(c_Suc(X8),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f2132,plain,
( spl0_180
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f2536,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_130
| ~ spl0_180 ),
inference(resolution,[],[f2133,f1708]) ).
fof(f1708,plain,
( ! [X10,X8] :
( ~ c_lessequals(c_Suc(X8),X10,tc_nat)
| c_lessequals(X8,X10,tc_nat) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1707]) ).
fof(f2133,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f2132]) ).
fof(f3736,plain,
( spl0_285
| ~ spl0_131
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2407,f2049,f1711,f3734]) ).
fof(f3734,plain,
( spl0_285
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f1711,plain,
( spl0_131
<=> ! [X8,X10] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(X8,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f2049,plain,
( spl0_176
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2407,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_131
| ~ spl0_176 ),
inference(resolution,[],[f2050,f1712]) ).
fof(f1712,plain,
( ! [X10,X8] :
( c_lessequals(X8,c_Suc(X10),tc_nat)
| ~ c_lessequals(X8,X10,tc_nat) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f2050,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f3509,plain,
( spl0_284
| ~ spl0_139
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2369,f2005,f1743,f3507]) ).
fof(f3507,plain,
( spl0_284
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f1743,plain,
( spl0_139
<=> ! [X8,X10] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X8),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f2005,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(f2369,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_139
| ~ spl0_165 ),
inference(resolution,[],[f2006,f1744]) ).
fof(f1744,plain,
( ! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X8),X10,tc_nat)
| c_HOL_Oord__class_Oless(X8,X10,tc_nat) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1743]) ).
fof(f2006,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f2005]) ).
fof(f3264,plain,
spl0_283,
inference(avatar_split_clause,[],[f1015,f3262]) ).
fof(f3262,plain,
( spl0_283
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f1015,plain,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X8,tc_nat) ),
inference(forward_demodulation,[],[f1014,f815]) ).
fof(f1014,plain,
! [X10,X8] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f267,f815]) ).
fof(f267,axiom,
! [X10,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
fof(f3260,plain,
spl0_282,
inference(avatar_split_clause,[],[f1013,f3258]) ).
fof(f3258,plain,
( spl0_282
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X8,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_282])]) ).
fof(f1013,plain,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Otimes__class_Otimes(X8,X10,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f1012,f815]) ).
fof(f1012,plain,
! [X10,X8] :
( 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(X8,X10,tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f266,f815]) ).
fof(f266,axiom,
! [X10,X8] :
( 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(X8,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
fof(f3256,plain,
spl0_281,
inference(avatar_split_clause,[],[f1011,f3254]) ).
fof(f3254,plain,
( spl0_281
<=> ! [X8,X10] :
( c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) != c_Suc(c_Orderings_Obot__class_Obot(tc_nat))
| c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f1011,plain,
! [X10,X8] :
( c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) != c_Suc(c_Orderings_Obot__class_Obot(tc_nat))
| c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X8 ),
inference(forward_demodulation,[],[f1010,f815]) ).
fof(f1010,plain,
! [X10,X8] :
( c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X8
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) ),
inference(forward_demodulation,[],[f126,f815]) ).
fof(f126,axiom,
! [X10,X8] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X8
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
fof(f3252,plain,
spl0_280,
inference(avatar_split_clause,[],[f1009,f3250]) ).
fof(f3250,plain,
( spl0_280
<=> ! [X8,X10] :
( c_HOL_Otimes__class_Otimes(X8,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_280])]) ).
fof(f1009,plain,
! [X10,X8] :
( c_HOL_Otimes__class_Otimes(X8,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,[],[f1008,f815]) ).
fof(f1008,plain,
! [X10,X8] :
( c_Suc(c_Orderings_Obot__class_Obot(tc_nat)) = X10
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) ),
inference(forward_demodulation,[],[f127,f815]) ).
fof(f127,axiom,
! [X10,X8] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X10
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
fof(f3248,plain,
spl0_279,
inference(avatar_split_clause,[],[f1003,f3246]) ).
fof(f3246,plain,
( spl0_279
<=> ! [X6,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(X6),tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f1003,plain,
! [X10,X6] :
( ~ 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(X6),tc_nat),X10,tc_nat) ),
inference(forward_demodulation,[],[f729,f815]) ).
fof(f729,axiom,
! [X10,X6] :
( ~ 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(X6),tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f3244,plain,
spl0_278,
inference(avatar_split_clause,[],[f996,f3242]) ).
fof(f3242,plain,
( spl0_278
<=> ! [X8,X10] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f996,plain,
! [X10,X8] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X10 ),
inference(forward_demodulation,[],[f995,f815]) ).
fof(f995,plain,
! [X10,X8] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[],[f790,f815]) ).
fof(f790,axiom,
! [X10,X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f3240,plain,
spl0_277,
inference(avatar_split_clause,[],[f994,f3238]) ).
fof(f3238,plain,
( spl0_277
<=> ! [X8,X10] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f994,plain,
! [X10,X8] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X8 ),
inference(forward_demodulation,[],[f993,f815]) ).
fof(f993,plain,
! [X10,X8] :
( c_Orderings_Obot__class_Obot(tc_nat) = X8
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[],[f791,f815]) ).
fof(f791,axiom,
! [X10,X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f3236,plain,
spl0_276,
inference(avatar_split_clause,[],[f962,f3234]) ).
fof(f962,plain,
! [X12] : c_nat_Onat__size(c_Suc(X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X12)),c_Suc(c_Orderings_Obot__class_Obot(tc_nat))),
inference(forward_demodulation,[],[f470,f815]) ).
fof(f470,axiom,
! [X12] : c_nat_Onat__size(c_Suc(X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_nat_Onat__size(X12)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osize_I2_J_0) ).
fof(f3226,plain,
spl0_275,
inference(avatar_split_clause,[],[f747,f3224]) ).
fof(f3224,plain,
( spl0_275
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| X13 = X14
| ~ c_lessequals(X13,X14,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f747,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| X13 = X14
| ~ c_lessequals(X13,X14,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f3222,plain,
spl0_274,
inference(avatar_split_clause,[],[f745,f3220]) ).
fof(f3220,plain,
( spl0_274
<=> ! [X4,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X4
| ~ c_lessequals(X1,X4,X0)
| c_HOL_Oord__class_Oless(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f745,axiom,
! [X0,X1,X4] :
( ~ class_Orderings_Oorder(X0)
| X1 = X4
| ~ c_lessequals(X1,X4,X0)
| c_HOL_Oord__class_Oless(X1,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
fof(f3218,plain,
spl0_273,
inference(avatar_split_clause,[],[f582,f3216]) ).
fof(f3216,plain,
( spl0_273
<=> ! [X8,X10] :
( c_Suc(X10) = X8
| c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(X8,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f582,axiom,
! [X10,X8] :
( c_Suc(X10) = X8
| c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(X8,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
fof(f3214,plain,
spl0_272,
inference(avatar_split_clause,[],[f488,f3212]) ).
fof(f3212,plain,
( spl0_272
<=> ! [X6,X9,X19] :
( ~ c_HOL_Oord__class_Oless(X6,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X19,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X6),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f488,axiom,
! [X6,X9,X19] :
( ~ c_HOL_Oord__class_Oless(X6,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X19,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X6),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f3210,plain,
spl0_271,
inference(avatar_split_clause,[],[f477,f3208]) ).
fof(f3208,plain,
( spl0_271
<=> ! [X6,X10] :
( ~ c_lessequals(X6,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X10,X6,tc_nat),tc_nat) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f477,axiom,
! [X10,X6] :
( ~ c_lessequals(X6,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X10,c_HOL_Ominus__class_Ominus(X10,X6,tc_nat),tc_nat) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f3206,plain,
spl0_270,
inference(avatar_split_clause,[],[f399,f3204]) ).
fof(f3204,plain,
( spl0_270
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_Suc(X8) = X10
| c_HOL_Oord__class_Oless(c_Suc(X8),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f399,axiom,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_Suc(X8) = X10
| c_HOL_Oord__class_Oless(c_Suc(X8),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f3202,plain,
spl0_269,
inference(avatar_split_clause,[],[f383,f3200]) ).
fof(f3200,plain,
( spl0_269
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f383,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
fof(f3198,plain,
spl0_268,
inference(avatar_split_clause,[],[f382,f3196]) ).
fof(f3196,plain,
( spl0_268
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X15,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f382,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X15,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
fof(f3194,plain,
spl0_267,
inference(avatar_split_clause,[],[f381,f3192]) ).
fof(f3192,plain,
( spl0_267
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X15,X14,X0)
| ~ c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f381,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X15,X14,X0)
| ~ c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f3190,plain,
spl0_266,
inference(avatar_split_clause,[],[f380,f3188]) ).
fof(f3188,plain,
( spl0_266
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X15,X13,X0)
| ~ c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f380,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X15,X13,X0)
| ~ c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f3174,plain,
spl0_265,
inference(avatar_split_clause,[],[f378,f3172]) ).
fof(f3172,plain,
( spl0_265
<=> ! [X22,X20,X42] :
( c_Lambda_OdB_OAbs(X20) = X22
| c_Lambda_OdB_OAbs(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X42,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f378,axiom,
! [X22,X42,X20] :
( c_Lambda_OdB_OAbs(X20) = X22
| c_Lambda_OdB_OAbs(X20) != c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X42,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
fof(f3170,plain,
spl0_264,
inference(avatar_split_clause,[],[f364,f3168]) ).
fof(f3168,plain,
( spl0_264
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| X13 = X14
| c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f364,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| X13 = X14
| c_HOL_Oord__class_Oless(X14,X13,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f3166,plain,
spl0_263,
inference(avatar_split_clause,[],[f360,f3164]) ).
fof(f3164,plain,
( spl0_263
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Oorder(X0)
| X13 = X14
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(X14,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f360,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Oorder(X0)
| X13 = X14
| ~ c_lessequals(X13,X14,X0)
| ~ c_lessequals(X14,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
fof(f3162,plain,
spl0_262,
inference(avatar_split_clause,[],[f331,f3160]) ).
fof(f3160,plain,
( spl0_262
<=> ! [X22,X8,X42] :
( c_Lambda_OdB_OVar(X8) = X22
| c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X42,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f331,axiom,
! [X8,X22,X42] :
( c_Lambda_OdB_OVar(X8) = X22
| c_List_Ofoldl(c_Lambda_OdB_OApp,X22,X42,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
fof(f3158,plain,
spl0_261,
inference(avatar_split_clause,[],[f288,f3156]) ).
fof(f3156,plain,
( spl0_261
<=> ! [X4,X13,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X13,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f288,axiom,
! [X0,X1,X4,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X13,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X4,X0),X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
fof(f3154,plain,
spl0_260,
inference(avatar_split_clause,[],[f286,f3152]) ).
fof(f3152,plain,
( spl0_260
<=> ! [X4,X13,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X1,X0)
| c_lessequals(X13,c_Orderings_Oord__class_Omax(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f286,axiom,
! [X0,X1,X4,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X1,X0)
| c_lessequals(X13,c_Orderings_Oord__class_Omax(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
fof(f3150,plain,
spl0_259,
inference(avatar_split_clause,[],[f285,f3148]) ).
fof(f3148,plain,
( spl0_259
<=> ! [X4,X13,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X4,X0)
| c_lessequals(X13,c_Orderings_Oord__class_Omax(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f285,axiom,
! [X0,X1,X4,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X4,X0)
| c_lessequals(X13,c_Orderings_Oord__class_Omax(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
fof(f3146,plain,
spl0_258,
inference(avatar_split_clause,[],[f281,f3144]) ).
fof(f3144,plain,
( spl0_258
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X15,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X13,X14,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f281,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X15,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X13,X14,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
fof(f3142,plain,
spl0_257,
inference(avatar_split_clause,[],[f259,f3140]) ).
fof(f3140,plain,
( spl0_257
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X13,X14,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f259,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X14,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X13,X14,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f3138,plain,
spl0_256,
inference(avatar_split_clause,[],[f258,f3136]) ).
fof(f3136,plain,
( spl0_256
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X13,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X13,X14,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f258,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X13,X15,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X13,X14,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f3134,plain,
spl0_255,
inference(avatar_split_clause,[],[f256,f3132]) ).
fof(f3132,plain,
( spl0_255
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X15,X13,X0)
| c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f256,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X15,X13,X0)
| c_HOL_Oord__class_Oless(X15,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
fof(f3130,plain,
spl0_254,
inference(avatar_split_clause,[],[f255,f3128]) ).
fof(f3128,plain,
( spl0_254
<=> ! [X4,X13,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X4,X0)
| c_HOL_Oord__class_Oless(X13,c_Orderings_Oord__class_Omax(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f255,axiom,
! [X0,X1,X4,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X4,X0)
| c_HOL_Oord__class_Oless(X13,c_Orderings_Oord__class_Omax(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
fof(f3126,plain,
spl0_253,
inference(avatar_split_clause,[],[f238,f3124]) ).
fof(f3124,plain,
( spl0_253
<=> ! [X10,X13,X0,X16] : c_List_Odrop(c_Suc(X10),c_List_Olist_OCons(X13,X16,X0),X0) = c_List_Odrop(X10,X16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f238,axiom,
! [X10,X0,X16,X13] : c_List_Odrop(c_Suc(X10),c_List_Olist_OCons(X13,X16,X0),X0) = c_List_Odrop(X10,X16,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
fof(f3122,plain,
spl0_252,
inference(avatar_split_clause,[],[f197,f3120]) ).
fof(f3120,plain,
( spl0_252
<=> ! [X8,X19,X10] :
( c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X19),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f197,axiom,
! [X10,X8,X19] :
( c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X19),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f3118,plain,
spl0_251,
inference(avatar_split_clause,[],[f196,f3116]) ).
fof(f3116,plain,
( spl0_251
<=> ! [X8,X19,X10] :
( c_lessequals(X19,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X19),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f196,axiom,
! [X10,X8,X19] :
( c_lessequals(X19,X10,tc_nat)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X19),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f3114,plain,
spl0_250,
inference(avatar_split_clause,[],[f195,f3112]) ).
fof(f3112,plain,
( spl0_250
<=> ! [X6,X9,X8] :
( ~ c_lessequals(X6,X9,tc_nat)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f195,axiom,
! [X8,X6,X9] :
( ~ c_lessequals(X6,X9,tc_nat)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X8),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
fof(f3110,plain,
spl0_249,
inference(avatar_split_clause,[],[f194,f3108]) ).
fof(f3108,plain,
( spl0_249
<=> ! [X6,X9,X8] :
( ~ c_lessequals(X6,X9,tc_nat)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f194,axiom,
! [X8,X6,X9] :
( ~ c_lessequals(X6,X9,tc_nat)
| c_lessequals(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X9),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
fof(f3106,plain,
spl0_248,
inference(avatar_split_clause,[],[f192,f3104]) ).
fof(f3104,plain,
( spl0_248
<=> ! [X13,X0,X10] : c_List_Oreplicate(c_Suc(X10),X13,X0) = c_List_Olist_OCons(X13,c_List_Oreplicate(X10,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f192,axiom,
! [X10,X0,X13] : c_List_Oreplicate(c_Suc(X10),X13,X0) = c_List_Olist_OCons(X13,c_List_Oreplicate(X10,X13,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
fof(f3102,plain,
spl0_247,
inference(avatar_split_clause,[],[f151,f3100]) ).
fof(f3100,plain,
( spl0_247
<=> ! [X4,X13,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X1,X0)
| ~ c_lessequals(X13,c_Orderings_Oord__class_Omin(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f151,axiom,
! [X0,X1,X4,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X1,X0)
| ~ c_lessequals(X13,c_Orderings_Oord__class_Omin(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
fof(f3098,plain,
spl0_246,
inference(avatar_split_clause,[],[f150,f3096]) ).
fof(f3096,plain,
( spl0_246
<=> ! [X4,X13,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X4,X0)
| ~ c_lessequals(X13,c_Orderings_Oord__class_Omin(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f150,axiom,
! [X0,X1,X4,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X4,X0)
| ~ c_lessequals(X13,c_Orderings_Oord__class_Omin(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
fof(f3094,plain,
spl0_245,
inference(avatar_split_clause,[],[f147,f3092]) ).
fof(f3092,plain,
( spl0_245
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X15,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f147,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X15,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
fof(f3090,plain,
spl0_244,
inference(avatar_split_clause,[],[f146,f3088]) ).
fof(f3088,plain,
( spl0_244
<=> ! [X13,X0,X14,X15] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X15,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f146,axiom,
! [X0,X14,X15,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X15,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
fof(f3086,plain,
spl0_243,
inference(avatar_split_clause,[],[f123,f3084]) ).
fof(f3084,plain,
( spl0_243
<=> ! [X8,X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f123,axiom,
! [X10,X8] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f3082,plain,
spl0_242,
inference(avatar_split_clause,[],[f112,f3080]) ).
fof(f3080,plain,
( spl0_242
<=> ! [X6,X9,X19] :
( c_HOL_Oord__class_Oless(X6,X19,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X9),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f112,axiom,
! [X6,X19,X9] :
( c_HOL_Oord__class_Oless(X6,X19,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X9),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f3078,plain,
spl0_241,
inference(avatar_split_clause,[],[f111,f3076]) ).
fof(f3076,plain,
( spl0_241
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f111,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
fof(f3074,plain,
spl0_240,
inference(avatar_split_clause,[],[f110,f3072]) ).
fof(f3072,plain,
( spl0_240
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f110,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f3070,plain,
spl0_239,
inference(avatar_split_clause,[],[f10,f3068]) ).
fof(f3068,plain,
( spl0_239
<=> ! [X0,X10] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X10),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f10,axiom,
! [X10,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X10),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f3038,plain,
( spl0_238
| ~ spl0_99
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f3022,f2716,f1562,f3036]) ).
fof(f3036,plain,
( spl0_238
<=> ! [X0] : v_T____ != c_Type_Otype_OAtom(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1562,plain,
( spl0_99
<=> ! [X64,X12,X63] : c_Type_Otype_OAtom(X12) != hAPP(hAPP(c_Type_Otype_OFun,X63),X64) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2716,plain,
( spl0_229
<=> v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f3022,plain,
( ! [X0] : v_T____ != c_Type_Otype_OAtom(X0)
| ~ spl0_99
| ~ spl0_229 ),
inference(superposition,[],[f1563,f2718]) ).
fof(f2718,plain,
( v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2716]) ).
fof(f1563,plain,
( ! [X63,X12,X64] : c_Type_Otype_OAtom(X12) != hAPP(hAPP(c_Type_Otype_OFun,X63),X64)
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1562]) ).
fof(f2958,plain,
( spl0_237
| ~ spl0_42
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2583,f2379,f1321,f2956]) ).
fof(f2956,plain,
( spl0_237
<=> ! [X0] :
( ~ c_Lambda_Obeta(v_u____,X0)
| c_Type_Otyping(v_e____,X0,v_T____) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2379,plain,
( spl0_204
<=> ! [X61,X21,X2,X26] :
( ~ c_Lambda_Obeta(X21,X61)
| ~ c_Type_Otyping(X2,X21,X26)
| c_Type_Otyping(X2,X61,X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2583,plain,
( ! [X0] :
( ~ c_Lambda_Obeta(v_u____,X0)
| c_Type_Otyping(v_e____,X0,v_T____) )
| ~ spl0_42
| ~ spl0_204 ),
inference(resolution,[],[f2380,f1323]) ).
fof(f1323,plain,
( c_Type_Otyping(v_e____,v_u____,v_T____)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f2380,plain,
( ! [X2,X21,X26,X61] :
( ~ c_Type_Otyping(X2,X21,X26)
| ~ c_Lambda_Obeta(X21,X61)
| c_Type_Otyping(X2,X61,X26) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2379]) ).
fof(f2762,plain,
( spl0_236
| ~ spl0_23
| ~ spl0_50
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1920,f1772,f1356,f1231,f2759]) ).
fof(f2759,plain,
( spl0_236
<=> 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_236])]) ).
fof(f1231,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1356,plain,
( spl0_50
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1772,plain,
( spl0_146
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1920,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_50
| ~ spl0_146 ),
inference(forward_demodulation,[],[f1919,f1358]) ).
fof(f1358,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1356]) ).
fof(f1919,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_146 ),
inference(resolution,[],[f1773,f1233]) ).
fof(f1233,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1231]) ).
fof(f1773,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X0) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f2744,plain,
spl0_235,
inference(avatar_split_clause,[],[f1002,f2742]) ).
fof(f2742,plain,
( spl0_235
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X8,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1002,plain,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X8,X10,tc_nat) ),
inference(forward_demodulation,[],[f706,f815]) ).
fof(f706,axiom,
! [X10,X8] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2740,plain,
spl0_234,
inference(avatar_split_clause,[],[f991,f2738]) ).
fof(f2738,plain,
( spl0_234
<=> ! [X8,X10] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f991,plain,
! [X10,X8] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != X8 ),
inference(forward_demodulation,[],[f802,f815]) ).
fof(f802,axiom,
! [X10,X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10) != X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f2736,plain,
spl0_233,
inference(avatar_split_clause,[],[f982,f2734]) ).
fof(f2734,plain,
( spl0_233
<=> ! [X8,X10] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f982,plain,
! [X10,X8] :
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat) ),
inference(forward_demodulation,[],[f707,f815]) ).
fof(f707,axiom,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X10,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2732,plain,
spl0_232,
inference(avatar_split_clause,[],[f957,f2730]) ).
fof(f2730,plain,
( spl0_232
<=> ! [X22,X21] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X22)),X21),c_Lambda_Osubst(X22,X21,c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f957,plain,
! [X21,X22] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X22)),X21),c_Lambda_Osubst(X22,X21,c_Orderings_Obot__class_Obot(tc_nat))),
inference(forward_demodulation,[],[f344,f815]) ).
fof(f344,axiom,
! [X21,X22] : c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X22)),X21),c_Lambda_Osubst(X22,X21,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f2728,plain,
spl0_231,
inference(avatar_split_clause,[],[f956,f2725]) ).
fof(f2725,plain,
( spl0_231
<=> 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_231])]) ).
fof(f956,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,[],[f325,f815]) ).
fof(f325,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
fof(f2723,plain,
spl0_230,
inference(avatar_split_clause,[],[f955,f2721]) ).
fof(f2721,plain,
( spl0_230
<=> ! [X8,X10] : c_HOL_Ominus__class_Ominus(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f955,plain,
! [X10,X8] : c_HOL_Ominus__class_Ominus(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f224,f815]) ).
fof(f224,axiom,
! [X10,X8] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f2719,plain,
spl0_229,
inference(avatar_split_clause,[],[f874,f2716]) ).
fof(f874,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
fof(f2714,plain,
( spl0_228
| ~ spl0_84
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1873,f1723,f1501,f2712]) ).
fof(f2712,plain,
( spl0_228
<=> ! [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_228])]) ).
fof(f1501,plain,
( spl0_84
<=> ! [X8,X10] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),c_Suc(X8),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1723,plain,
( spl0_134
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1873,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_84
| ~ spl0_134 ),
inference(resolution,[],[f1724,f1502]) ).
fof(f1502,plain,
( ! [X10,X8] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),c_Suc(X8),tc_nat)
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f1724,plain,
( ! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1723]) ).
fof(f2710,plain,
spl0_227,
inference(avatar_split_clause,[],[f698,f2708]) ).
fof(f2708,plain,
( spl0_227
<=> ! [X8,X10] :
( X8 = X10
| ~ c_lessequals(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f698,axiom,
! [X10,X8] :
( X8 = X10
| ~ c_lessequals(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f2706,plain,
spl0_226,
inference(avatar_split_clause,[],[f687,f2704]) ).
fof(f2704,plain,
( spl0_226
<=> ! [X59,X55,X0,X56,X1] :
( X56 = X59
| c_List_Olist_OCons(X55,X56,X0) != c_List_Olist_OCons(X1,X59,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f687,axiom,
! [X59,X0,X56,X1,X55] :
( X56 = X59
| c_List_Olist_OCons(X55,X56,X0) != c_List_Olist_OCons(X1,X59,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
fof(f2702,plain,
spl0_225,
inference(avatar_split_clause,[],[f686,f2700]) ).
fof(f2700,plain,
( spl0_225
<=> ! [X55,X0,X56,X59,X1] :
( X1 = X55
| c_List_Olist_OCons(X55,X56,X0) != c_List_Olist_OCons(X1,X59,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f686,axiom,
! [X0,X59,X1,X56,X55] :
( X1 = X55
| c_List_Olist_OCons(X55,X56,X0) != c_List_Olist_OCons(X1,X59,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
fof(f2698,plain,
spl0_224,
inference(avatar_split_clause,[],[f581,f2696]) ).
fof(f2696,plain,
( spl0_224
<=> ! [X8,X10] : c_Orderings_Oord__class_Omin(c_Suc(X8),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X8,X10,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f581,axiom,
! [X10,X8] : c_Orderings_Oord__class_Omin(c_Suc(X8),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X8,X10,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
fof(f2694,plain,
spl0_223,
inference(avatar_split_clause,[],[f578,f2692]) ).
fof(f2692,plain,
( spl0_223
<=> ! [X6,X9,X19] :
( ~ c_lessequals(X6,X9,tc_nat)
| ~ c_lessequals(X9,X19,tc_nat)
| c_lessequals(X6,X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f578,axiom,
! [X6,X9,X19] :
( ~ c_lessequals(X6,X9,tc_nat)
| ~ c_lessequals(X9,X19,tc_nat)
| c_lessequals(X6,X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2690,plain,
spl0_222,
inference(avatar_split_clause,[],[f537,f2688]) ).
fof(f2688,plain,
( spl0_222
<=> ! [X6,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X9,X6,tc_nat)
| c_Lambda_OdB_OVar(X9) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X9),X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f537,axiom,
! [X6,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X9,X6,tc_nat)
| c_Lambda_OdB_OVar(X9) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X9),X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
fof(f2686,plain,
spl0_221,
inference(avatar_split_clause,[],[f321,f2684]) ).
fof(f2684,plain,
( spl0_221
<=> ! [X8,X10] :
( X8 = X10
| c_HOL_Oord__class_Oless(X10,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f321,axiom,
! [X10,X8] :
( X8 = X10
| c_HOL_Oord__class_Oless(X10,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
fof(f2682,plain,
spl0_220,
inference(avatar_split_clause,[],[f202,f2680]) ).
fof(f2680,plain,
( spl0_220
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X13,X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f202,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X13,X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2678,plain,
spl0_219,
inference(avatar_split_clause,[],[f201,f2676]) ).
fof(f2676,plain,
( spl0_219
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) != X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f201,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) != X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2674,plain,
spl0_218,
inference(avatar_split_clause,[],[f200,f2672]) ).
fof(f2672,plain,
( spl0_218
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f200,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2670,plain,
( spl0_217
| ~ spl0_30
| ~ spl0_50
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1824,f1675,f1356,f1266,f2667]) ).
fof(f2667,plain,
( spl0_217
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1266,plain,
( spl0_30
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1675,plain,
( spl0_122
<=> ! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1824,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat)
| ~ spl0_30
| ~ spl0_50
| ~ spl0_122 ),
inference(forward_demodulation,[],[f1823,f1358]) ).
fof(f1823,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat)
| ~ spl0_30
| ~ spl0_122 ),
inference(resolution,[],[f1676,f1268]) ).
fof(f1268,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f1676,plain,
( ! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1675]) ).
fof(f2665,plain,
spl0_216,
inference(avatar_split_clause,[],[f131,f2663]) ).
fof(f2663,plain,
( spl0_216
<=> ! [X0,X8,X10] :
( ~ class_Nat_Osemiring__char__0(X0)
| X8 = X10
| c_Nat_Osemiring__1__class_Oof__nat(X8,X0) != c_Nat_Osemiring__1__class_Oof__nat(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f131,axiom,
! [X10,X0,X8] :
( ~ class_Nat_Osemiring__char__0(X0)
| X8 = X10
| c_Nat_Osemiring__1__class_Oof__nat(X8,X0) != c_Nat_Osemiring__1__class_Oof__nat(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f2661,plain,
spl0_215,
inference(avatar_split_clause,[],[f75,f2659]) ).
fof(f2659,plain,
( spl0_215
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X13,X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f75,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X14,X13,X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2657,plain,
spl0_214,
inference(avatar_split_clause,[],[f74,f2655]) ).
fof(f2655,plain,
( spl0_214
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) != X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f74,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) != X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2653,plain,
spl0_213,
inference(avatar_split_clause,[],[f73,f2651]) ).
fof(f2651,plain,
( spl0_213
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f73,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X14,X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2649,plain,
spl0_212,
inference(avatar_split_clause,[],[f39,f2647]) ).
fof(f2647,plain,
( spl0_212
<=> ! [X8,X10] : c_Orderings_Oord__class_Omax(c_Suc(X8),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X8,X10,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f39,axiom,
! [X10,X8] : c_Orderings_Oord__class_Omax(c_Suc(X8),c_Suc(X10),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X8,X10,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
fof(f2645,plain,
spl0_211,
inference(avatar_split_clause,[],[f33,f2643]) ).
fof(f2643,plain,
( spl0_211
<=> ! [X20,X21,X6,X22] :
( ~ c_Lambda_Obeta(X20,X22)
| c_Lambda_Obeta(c_Lambda_Osubst(X20,X21,X6),c_Lambda_Osubst(X22,X21,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f33,axiom,
! [X21,X6,X22,X20] :
( ~ c_Lambda_Obeta(X20,X22)
| c_Lambda_Obeta(c_Lambda_Osubst(X20,X21,X6),c_Lambda_Osubst(X22,X21,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
fof(f2641,plain,
spl0_210,
inference(avatar_split_clause,[],[f27,f2639]) ).
fof(f2639,plain,
( spl0_210
<=> ! [X0,X14,X13,X10,X8] :
( X8 = X10
| c_List_Oreplicate(X8,X13,X0) != c_List_Oreplicate(X10,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f27,axiom,
! [X10,X0,X8,X14,X13] :
( X8 = X10
| c_List_Oreplicate(X8,X13,X0) != c_List_Oreplicate(X10,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
fof(f2637,plain,
spl0_209,
inference(avatar_split_clause,[],[f25,f2635]) ).
fof(f2635,plain,
( spl0_209
<=> ! [X18,X0,X16,X17] :
( X17 = X18
| c_List_Oappend(X17,X16,X0) != c_List_Oappend(X18,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f25,axiom,
! [X0,X18,X16,X17] :
( X17 = X18
| c_List_Oappend(X17,X16,X0) != c_List_Oappend(X18,X16,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
fof(f2633,plain,
spl0_208,
inference(avatar_split_clause,[],[f24,f2631]) ).
fof(f2631,plain,
( spl0_208
<=> ! [X18,X0,X16,X17] :
( X17 = X18
| c_List_Oappend(X16,X17,X0) != c_List_Oappend(X16,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f24,axiom,
! [X0,X18,X16,X17] :
( X17 = X18
| c_List_Oappend(X16,X17,X0) != c_List_Oappend(X16,X18,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
fof(f2393,plain,
spl0_207,
inference(avatar_split_clause,[],[f1001,f2391]) ).
fof(f2391,plain,
( spl0_207
<=> ! [X8,X10] :
( c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_lessequals(X8,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1001,plain,
! [X10,X8] :
( c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| c_lessequals(X8,X10,tc_nat) ),
inference(forward_demodulation,[],[f21,f815]) ).
fof(f21,axiom,
! [X10,X8] :
( c_lessequals(X8,X10,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f2389,plain,
spl0_206,
inference(avatar_split_clause,[],[f989,f2387]) ).
fof(f2387,plain,
( spl0_206
<=> ! [X13,X0,X10] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X10,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f989,plain,
! [X10,X0,X13] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X10,X13,X0) ),
inference(forward_demodulation,[],[f517,f815]) ).
fof(f517,axiom,
! [X10,X0,X13] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X10
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X10,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
fof(f2385,plain,
spl0_205,
inference(avatar_split_clause,[],[f973,f2383]) ).
fof(f2383,plain,
( spl0_205
<=> ! [X8,X10] :
( c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_lessequals(X8,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f973,plain,
! [X10,X8] :
( c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_lessequals(X8,X10,tc_nat) ),
inference(forward_demodulation,[],[f20,f815]) ).
fof(f20,axiom,
! [X10,X8] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f2381,plain,
spl0_204,
inference(avatar_split_clause,[],[f834,f2379]) ).
fof(f834,axiom,
! [X2,X21,X26,X61] :
( ~ c_Lambda_Obeta(X21,X61)
| ~ c_Type_Otyping(X2,X21,X26)
| c_Type_Otyping(X2,X61,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f2377,plain,
spl0_203,
inference(avatar_split_clause,[],[f740,f2375]) ).
fof(f2375,plain,
( spl0_203
<=> ! [X8,X10] :
( X8 = X10
| ~ c_lessequals(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X8,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f740,axiom,
! [X10,X8] :
( X8 = X10
| ~ c_lessequals(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X8,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
fof(f2373,plain,
spl0_202,
inference(avatar_split_clause,[],[f674,f2371]) ).
fof(f2371,plain,
( spl0_202
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f674,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f2359,plain,
spl0_201,
inference(avatar_split_clause,[],[f673,f2357]) ).
fof(f2357,plain,
( spl0_201
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f673,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2355,plain,
spl0_200,
inference(avatar_split_clause,[],[f672,f2353]) ).
fof(f2353,plain,
( spl0_200
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f672,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2351,plain,
spl0_199,
inference(avatar_split_clause,[],[f671,f2349]) ).
fof(f2349,plain,
( spl0_199
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f671,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f2347,plain,
spl0_198,
inference(avatar_split_clause,[],[f670,f2345]) ).
fof(f2345,plain,
( spl0_198
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f670,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),c_HOL_Ozero__class_Ozero(X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2343,plain,
spl0_197,
inference(avatar_split_clause,[],[f668,f2341]) ).
fof(f2341,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f668,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f2339,plain,
spl0_196,
inference(avatar_split_clause,[],[f629,f2337]) ).
fof(f2337,plain,
( spl0_196
<=> ! [X8,X10] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),X10,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f629,axiom,
! [X10,X8] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),X10,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f2335,plain,
spl0_195,
inference(avatar_split_clause,[],[f628,f2333]) ).
fof(f2333,plain,
( spl0_195
<=> ! [X8,X10] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10),X10,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f628,axiom,
! [X10,X8] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10),X10,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f2331,plain,
spl0_194,
inference(avatar_split_clause,[],[f478,f2329]) ).
fof(f2329,plain,
( spl0_194
<=> ! [X6,X19] :
( ~ c_HOL_Oord__class_Oless(X6,X19,tc_nat)
| c_Lambda_OdB_OVar(X6) = c_Lambda_Olift(c_Lambda_OdB_OVar(X6),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f478,axiom,
! [X6,X19] :
( ~ c_HOL_Oord__class_Oless(X6,X19,tc_nat)
| c_Lambda_OdB_OVar(X6) = c_Lambda_Olift(c_Lambda_OdB_OVar(X6),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f2327,plain,
spl0_193,
inference(avatar_split_clause,[],[f471,f2325]) ).
fof(f2325,plain,
( spl0_193
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f471,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,c_Orderings_Oord__class_Omin(X13,X14,X0),X0) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f2323,plain,
spl0_192,
inference(avatar_split_clause,[],[f464,f2321]) ).
fof(f2321,plain,
( spl0_192
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = c_Orderings_Oord__class_Omax(X14,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f464,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,X14,X0) = c_Orderings_Oord__class_Omax(X14,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f2311,plain,
spl0_191,
inference(avatar_split_clause,[],[f354,f2309]) ).
fof(f2309,plain,
( spl0_191
<=> ! [X8,X10] :
( X8 = X10
| c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f354,axiom,
! [X10,X8] :
( X8 = X10
| c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X8,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f2307,plain,
spl0_190,
inference(avatar_split_clause,[],[f353,f2305]) ).
fof(f2305,plain,
( spl0_190
<=> ! [X8,X10] :
( X8 = X10
| ~ c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(X10,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f353,axiom,
! [X10,X8] :
( X8 = X10
| ~ c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(X10,X8,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f2303,plain,
spl0_189,
inference(avatar_split_clause,[],[f330,f2301]) ).
fof(f2301,plain,
( spl0_189
<=> ! [X9,X19,X10] :
( ~ c_HOL_Oord__class_Oless(X9,X19,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f330,axiom,
! [X10,X19,X9] :
( ~ c_HOL_Oord__class_Oless(X9,X19,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f2299,plain,
spl0_188,
inference(avatar_split_clause,[],[f315,f2297]) ).
fof(f2297,plain,
( spl0_188
<=> ! [X8,X10] : c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X8),c_Suc(X10),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f315,axiom,
! [X10,X8] : c_HOL_Ominus__class_Ominus(X8,X10,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X8),c_Suc(X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f2295,plain,
spl0_187,
inference(avatar_split_clause,[],[f308,f2293]) ).
fof(f2293,plain,
( spl0_187
<=> ! [X16,X0,X17] :
( c_List_Olist_ONil(X0) = X16
| c_List_Oappend(X16,X17,X0) != c_List_Olist_ONil(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f308,axiom,
! [X0,X16,X17] :
( c_List_Olist_ONil(X0) = X16
| c_List_Oappend(X16,X17,X0) != c_List_Olist_ONil(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
fof(f2291,plain,
spl0_186,
inference(avatar_split_clause,[],[f300,f2289]) ).
fof(f2289,plain,
( spl0_186
<=> ! [X0,X17,X16] :
( c_List_Olist_ONil(X0) = X17
| c_List_Oappend(X16,X17,X0) != c_List_Olist_ONil(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f300,axiom,
! [X0,X16,X17] :
( c_List_Olist_ONil(X0) = X17
| c_List_Oappend(X16,X17,X0) != c_List_Olist_ONil(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
fof(f2287,plain,
spl0_185,
inference(avatar_split_clause,[],[f261,f2285]) ).
fof(f2285,plain,
( spl0_185
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = c_Orderings_Oord__class_Omin(X14,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f261,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,X14,X0) = c_Orderings_Oord__class_Omin(X14,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f2283,plain,
spl0_184,
inference(avatar_split_clause,[],[f230,f2281]) ).
fof(f2281,plain,
( spl0_184
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f230,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f2279,plain,
spl0_183,
inference(avatar_split_clause,[],[f64,f2277]) ).
fof(f2277,plain,
( spl0_183
<=> ! [X13,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X13,X14,X0) = c_HOL_Otimes__class_Otimes(X14,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f64,axiom,
! [X0,X14,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X13,X14,X0) = c_HOL_Otimes__class_Otimes(X14,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f2267,plain,
( spl0_182
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2250,f2041,f2265]) ).
fof(f2265,plain,
( spl0_182
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2041,plain,
( spl0_174
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X14,X0)
| c_lessequals(X14,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f2250,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_174 ),
inference(factoring,[],[f2042]) ).
fof(f2042,plain,
( ! [X0,X14,X13] :
( c_lessequals(X14,X13,X0)
| c_lessequals(X13,X14,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f2041]) ).
fof(f2192,plain,
( spl0_181
| ~ spl0_140
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1961,f1904,f1747,f2190]) ).
fof(f1904,plain,
( spl0_149
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1961,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_140
| ~ spl0_149 ),
inference(resolution,[],[f1905,f1748]) ).
fof(f1905,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1904]) ).
fof(f2134,plain,
( spl0_180
| ~ spl0_110
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1857,f1707,f1618,f2132]) ).
fof(f1618,plain,
( spl0_110
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1857,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_110
| ~ spl0_130 ),
inference(resolution,[],[f1708,f1619]) ).
fof(f1619,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1618]) ).
fof(f2063,plain,
spl0_179,
inference(avatar_split_clause,[],[f988,f2061]) ).
fof(f2061,plain,
( spl0_179
<=> ! [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_179])]) ).
fof(f988,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,[],[f987,f815]) ).
fof(f987,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,[],[f40,f815]) ).
fof(f40,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/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f2059,plain,
spl0_178,
inference(avatar_split_clause,[],[f854,f2057]) ).
fof(f2057,plain,
( spl0_178
<=> ! [X22,X20,X6] :
( ~ c_Lambda_Obeta(X20,X22)
| c_Lambda_Obeta(c_Lambda_Olift(X20,X6),c_Lambda_Olift(X22,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f854,axiom,
! [X6,X22,X20] :
( ~ c_Lambda_Obeta(X20,X22)
| c_Lambda_Obeta(c_Lambda_Olift(X20,X6),c_Lambda_Olift(X22,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
fof(f2055,plain,
spl0_177,
inference(avatar_split_clause,[],[f835,f2053]) ).
fof(f2053,plain,
( spl0_177
<=> ! [X6,X2,X26] :
( ~ c_Type_Otyping(X2,c_Lambda_OdB_OVar(X6),X26)
| hAPP(X2,X6) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f835,axiom,
! [X2,X6,X26] :
( ~ c_Type_Otyping(X2,c_Lambda_OdB_OVar(X6),X26)
| hAPP(X2,X6) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f2051,plain,
( spl0_176
| ~ spl0_110
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1838,f1695,f1618,f2049]) ).
fof(f1695,plain,
( spl0_127
<=> ! [X8,X10] :
( ~ c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(c_Suc(X10),X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1838,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_110
| ~ spl0_127 ),
inference(resolution,[],[f1696,f1619]) ).
fof(f1696,plain,
( ! [X10,X8] :
( ~ c_lessequals(c_Suc(X10),X8,tc_nat)
| ~ c_lessequals(X8,X10,tc_nat) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1695]) ).
fof(f2047,plain,
spl0_175,
inference(avatar_split_clause,[],[f779,f2045]) ).
fof(f2045,plain,
( spl0_175
<=> ! [X4,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f779,axiom,
! [X0,X1,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f2043,plain,
spl0_174,
inference(avatar_split_clause,[],[f777,f2041]) ).
fof(f777,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,X14,X0)
| c_lessequals(X14,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2039,plain,
spl0_173,
inference(avatar_split_clause,[],[f775,f2037]) ).
fof(f2037,plain,
( spl0_173
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f775,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2035,plain,
spl0_172,
inference(avatar_split_clause,[],[f774,f2033]) ).
fof(f2033,plain,
( spl0_172
<=> ! [X4,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f774,axiom,
! [X0,X1,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2031,plain,
spl0_171,
inference(avatar_split_clause,[],[f757,f2029]) ).
fof(f2029,plain,
( spl0_171
<=> ! [X8,X10] :
( ~ c_lessequals(X10,X8,tc_nat)
| c_lessequals(c_Suc(X10),c_Suc(X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f757,axiom,
! [X10,X8] :
( ~ c_lessequals(X10,X8,tc_nat)
| c_lessequals(c_Suc(X10),c_Suc(X8),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f2027,plain,
spl0_170,
inference(avatar_split_clause,[],[f756,f2025]) ).
fof(f2025,plain,
( spl0_170
<=> ! [X8,X10] :
( c_lessequals(X10,X8,tc_nat)
| ~ c_lessequals(c_Suc(X10),c_Suc(X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f756,axiom,
! [X10,X8] :
( c_lessequals(X10,X8,tc_nat)
| ~ c_lessequals(c_Suc(X10),c_Suc(X8),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f2023,plain,
spl0_169,
inference(avatar_split_clause,[],[f652,f2021]) ).
fof(f2021,plain,
( spl0_169
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f652,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f2019,plain,
spl0_168,
inference(avatar_split_clause,[],[f651,f2017]) ).
fof(f2017,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f651,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2015,plain,
spl0_167,
inference(avatar_split_clause,[],[f648,f2013]) ).
fof(f2013,plain,
( spl0_167
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f648,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2011,plain,
spl0_166,
inference(avatar_split_clause,[],[f647,f2009]) ).
fof(f2009,plain,
( spl0_166
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f647,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2007,plain,
( spl0_165
| ~ spl0_110
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1818,f1667,f1618,f2005]) ).
fof(f1667,plain,
( spl0_120
<=> ! [X8,X10] :
( c_HOL_Oord__class_Oless(X10,X8,tc_nat)
| ~ c_lessequals(c_Suc(X10),X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1818,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_110
| ~ spl0_120 ),
inference(resolution,[],[f1668,f1619]) ).
fof(f1668,plain,
( ! [X10,X8] :
( ~ c_lessequals(c_Suc(X10),X8,tc_nat)
| c_HOL_Oord__class_Oless(X10,X8,tc_nat) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1667]) ).
fof(f2003,plain,
spl0_164,
inference(avatar_split_clause,[],[f638,f2001]) ).
fof(f2001,plain,
( spl0_164
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X8),c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f638,axiom,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X8),c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
fof(f1999,plain,
spl0_163,
inference(avatar_split_clause,[],[f637,f1997]) ).
fof(f1997,plain,
( spl0_163
<=> ! [X8,X10] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X8),c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f637,axiom,
! [X10,X8] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X8),c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f1995,plain,
spl0_162,
inference(avatar_split_clause,[],[f632,f1993]) ).
fof(f1993,plain,
( spl0_162
<=> ! [X0,X12,X27,X28] : hAPP(X27,X12) = c_Type_Otype_Otype__case(X27,X28,c_Type_Otype_OAtom(X12),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f632,axiom,
! [X28,X0,X27,X12] : hAPP(X27,X12) = c_Type_Otype_Otype__case(X27,X28,c_Type_Otype_OAtom(X12),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
fof(f1991,plain,
spl0_161,
inference(avatar_split_clause,[],[f610,f1989]) ).
fof(f1989,plain,
( spl0_161
<=> ! [X8] : c_lessequals(X8,c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X8,X8,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f610,axiom,
! [X8] : c_lessequals(X8,c_HOL_Otimes__class_Otimes(X8,c_HOL_Otimes__class_Otimes(X8,X8,tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).
fof(f1987,plain,
spl0_160,
inference(avatar_split_clause,[],[f551,f1985]) ).
fof(f1985,plain,
( spl0_160
<=> ! [X16,X0,X17] :
( c_List_Olist_ONil(X0) = X16
| c_List_Oappend(X16,X17,X0) != X17 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f551,axiom,
! [X0,X16,X17] :
( c_List_Olist_ONil(X0) = X16
| c_List_Oappend(X16,X17,X0) != X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
fof(f1983,plain,
spl0_159,
inference(avatar_split_clause,[],[f549,f1981]) ).
fof(f1981,plain,
( spl0_159
<=> ! [X0,X17,X16] :
( c_List_Olist_ONil(X0) = X17
| c_List_Oappend(X16,X17,X0) != X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f549,axiom,
! [X0,X16,X17] :
( c_List_Olist_ONil(X0) = X17
| c_List_Oappend(X16,X17,X0) != X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
fof(f1979,plain,
spl0_158,
inference(avatar_split_clause,[],[f375,f1977]) ).
fof(f1977,plain,
( spl0_158
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| c_lessequals(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f375,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| c_lessequals(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1975,plain,
spl0_157,
inference(avatar_split_clause,[],[f374,f1973]) ).
fof(f1973,plain,
( spl0_157
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| c_lessequals(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f374,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0)
| c_lessequals(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1971,plain,
spl0_156,
inference(avatar_split_clause,[],[f332,f1969]) ).
fof(f1969,plain,
( spl0_156
<=> ! [X0,X12,X27,X28] : c_Type_Otype_Otype__rec(X27,X28,c_Type_Otype_OAtom(X12),X0) = hAPP(X27,X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f332,axiom,
! [X28,X0,X27,X12] : c_Type_Otype_Otype__rec(X27,X28,c_Type_Otype_OAtom(X12),X0) = hAPP(X27,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
fof(f1967,plain,
spl0_155,
inference(avatar_split_clause,[],[f298,f1965]) ).
fof(f1965,plain,
( spl0_155
<=> ! [X0,X12,X27,X28] : hAPP(X28,X12) = c_Nat_Onat_Onat__case(X27,X28,c_Suc(X12),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f298,axiom,
! [X28,X0,X27,X12] : hAPP(X28,X12) = c_Nat_Onat_Onat__case(X27,X28,c_Suc(X12),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__Suc_0) ).
fof(f1960,plain,
spl0_154,
inference(avatar_split_clause,[],[f212,f1958]) ).
fof(f1958,plain,
( spl0_154
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f212,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X14,X13,X0)
| ~ c_HOL_Oord__class_Oless(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1956,plain,
spl0_153,
inference(avatar_split_clause,[],[f210,f1954]) ).
fof(f1954,plain,
( spl0_153
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f210,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X13,X14,X0)
| ~ c_HOL_Oord__class_Oless(X14,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1952,plain,
spl0_152,
inference(avatar_split_clause,[],[f205,f1950]) ).
fof(f1950,plain,
( spl0_152
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X13,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f205,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,X13,X0)
| c_HOL_Oord__class_Oless(X13,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1948,plain,
spl0_151,
inference(avatar_split_clause,[],[f83,f1946]) ).
fof(f1946,plain,
( spl0_151
<=> ! [X13,X8] : c_HOL_Oord__class_Oless(X8,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X13)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f83,axiom,
! [X8,X13] : c_HOL_Oord__class_Oless(X8,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X13)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f1944,plain,
spl0_150,
inference(avatar_split_clause,[],[f82,f1942]) ).
fof(f1942,plain,
( spl0_150
<=> ! [X6,X8] : c_HOL_Oord__class_Oless(X6,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X6)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f82,axiom,
! [X8,X6] : c_HOL_Oord__class_Oless(X6,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X6)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1906,plain,
( spl0_149
| ~ spl0_38
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1892,f1747,f1305,f1904]) ).
fof(f1305,plain,
( spl0_38
<=> ! [X13] : ~ c_HOL_Oord__class_Oless(X13,X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1892,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_38
| ~ spl0_140 ),
inference(resolution,[],[f1748,f1306]) ).
fof(f1306,plain,
( ! [X13] : ~ c_HOL_Oord__class_Oless(X13,X13,tc_nat)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1305]) ).
fof(f1782,plain,
spl0_148,
inference(avatar_split_clause,[],[f986,f1780]) ).
fof(f1780,plain,
( spl0_148
<=> ! [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_148])]) ).
fof(f986,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,[],[f985,f815]) ).
fof(f985,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,[],[f679,f815]) ).
fof(f679,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/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1778,plain,
spl0_147,
inference(avatar_split_clause,[],[f984,f1776]) ).
fof(f1776,plain,
( spl0_147
<=> ! [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_147])]) ).
fof(f984,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,[],[f983,f815]) ).
fof(f983,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,[],[f785,f815]) ).
fof(f785,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/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1774,plain,
spl0_146,
inference(avatar_split_clause,[],[f971,f1772]) ).
fof(f971,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Osemiring__1(X0) ),
inference(forward_demodulation,[],[f867,f815]) ).
fof(f867,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1770,plain,
spl0_145,
inference(avatar_split_clause,[],[f966,f1767]) ).
fof(f1767,plain,
( spl0_145
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f966,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_T____),
inference(forward_demodulation,[],[f921,f874]) ).
fof(f921,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(definition_unfolding,[],[f871,f162]) ).
fof(f162,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
fof(f871,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_varT_0) ).
fof(f1765,plain,
spl0_144,
inference(avatar_split_clause,[],[f947,f1763]) ).
fof(f1763,plain,
( spl0_144
<=> ! [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_144])]) ).
fof(f947,plain,
! [X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X10) = X10,
inference(forward_demodulation,[],[f827,f815]) ).
fof(f827,axiom,
! [X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X10) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f1761,plain,
spl0_143,
inference(avatar_split_clause,[],[f945,f1759]) ).
fof(f1759,plain,
( spl0_143
<=> ! [X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_Orderings_Obot__class_Obot(tc_nat)) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f945,plain,
! [X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_Orderings_Obot__class_Obot(tc_nat)) = X13,
inference(forward_demodulation,[],[f826,f815]) ).
fof(f826,axiom,
! [X13] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Ozero__class_Ozero(tc_nat)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
fof(f1757,plain,
spl0_142,
inference(avatar_split_clause,[],[f879,f1755]) ).
fof(f1755,plain,
( spl0_142
<=> ! [X13,X2,X0,X26] : hAPP(c_Type_Oshift(X2,X13,X26,X0),X13) = X26 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f879,axiom,
! [X2,X0,X26,X13] : hAPP(c_Type_Oshift(X2,X13,X26,X0),X13) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f1753,plain,
spl0_141,
inference(avatar_split_clause,[],[f850,f1751]) ).
fof(f1751,plain,
( spl0_141
<=> ! [X41,X0,X1,X40] : c_List_Ofoldr(X40,c_List_Olist_ONil(X41),X1,X41,X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f850,axiom,
! [X40,X41,X0,X1] : c_List_Ofoldr(X40,c_List_Olist_ONil(X41),X1,X41,X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
fof(f1749,plain,
spl0_140,
inference(avatar_split_clause,[],[f709,f1747]) ).
fof(f709,axiom,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X8,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1745,plain,
spl0_139,
inference(avatar_split_clause,[],[f708,f1743]) ).
fof(f708,axiom,
! [X10,X8] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X8),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1741,plain,
spl0_138,
inference(avatar_split_clause,[],[f619,f1739]) ).
fof(f1739,plain,
( spl0_138
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f619,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
fof(f1737,plain,
( spl0_137
| ~ spl0_93
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1625,f1566,f1537,f1735]) ).
fof(f1735,plain,
( spl0_137
<=> ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1537,plain,
( spl0_93
<=> ! [X6,X20,X9] :
( ~ c_InductTermi_OIT(X20)
| c_InductTermi_OIT(c_Lambda_Osubst(X20,c_Lambda_OdB_OVar(X6),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1566,plain,
( spl0_100
<=> ! [X22,X21,X19] : c_Lambda_Osubst(c_Lambda_Olift(X21,X19),X22,X19) = X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1625,plain,
( ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) )
| ~ spl0_93
| ~ spl0_100 ),
inference(superposition,[],[f1538,f1567]) ).
fof(f1567,plain,
( ! [X21,X19,X22] : c_Lambda_Osubst(c_Lambda_Olift(X21,X19),X22,X19) = X21
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1566]) ).
fof(f1538,plain,
( ! [X6,X9,X20] :
( c_InductTermi_OIT(c_Lambda_Osubst(X20,c_Lambda_OdB_OVar(X6),X9))
| ~ c_InductTermi_OIT(X20) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f1733,plain,
spl0_136,
inference(avatar_split_clause,[],[f607,f1731]) ).
fof(f1731,plain,
( spl0_136
<=> ! [X6,X21] :
( ~ c_InductTermi_OIT(X21)
| c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,X21),c_Lambda_OdB_OVar(X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f607,axiom,
! [X21,X6] :
( ~ c_InductTermi_OIT(X21)
| c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,X21),c_Lambda_OdB_OVar(X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
fof(f1729,plain,
spl0_135,
inference(avatar_split_clause,[],[f585,f1727]) ).
fof(f1727,plain,
( spl0_135
<=> ! [X8,X10] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f585,axiom,
! [X10,X8] :
( c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1725,plain,
spl0_134,
inference(avatar_split_clause,[],[f584,f1723]) ).
fof(f584,axiom,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,c_Suc(X8),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1721,plain,
spl0_133,
inference(avatar_split_clause,[],[f542,f1719]) ).
fof(f542,axiom,
! [X6,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X6),X6,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1717,plain,
spl0_132,
inference(avatar_split_clause,[],[f541,f1715]) ).
fof(f541,axiom,
! [X6,X9] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X6),X9),X6,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1713,plain,
spl0_131,
inference(avatar_split_clause,[],[f529,f1711]) ).
fof(f529,axiom,
! [X10,X8] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_lessequals(X8,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1709,plain,
spl0_130,
inference(avatar_split_clause,[],[f528,f1707]) ).
fof(f528,axiom,
! [X10,X8] :
( c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(c_Suc(X8),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1705,plain,
spl0_129,
inference(avatar_split_clause,[],[f463,f1703]) ).
fof(f1703,plain,
( spl0_129
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f463,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X8,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1701,plain,
spl0_128,
inference(avatar_split_clause,[],[f401,f1699]) ).
fof(f1699,plain,
( spl0_128
<=> ! [X8,X10] :
( c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_Suc(X10),X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f401,axiom,
! [X10,X8] :
( c_lessequals(X8,X10,tc_nat)
| c_lessequals(c_Suc(X10),X8,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1697,plain,
spl0_127,
inference(avatar_split_clause,[],[f400,f1695]) ).
fof(f400,axiom,
! [X10,X8] :
( ~ c_lessequals(X8,X10,tc_nat)
| ~ c_lessequals(c_Suc(X10),X8,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1693,plain,
( spl0_126
| ~ spl0_33
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f1612,f1529,f1281,f1691]) ).
fof(f1691,plain,
( spl0_126
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1281,plain,
( spl0_33
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1529,plain,
( spl0_91
<=> ! [X13,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,X13,X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1612,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_33
| ~ spl0_91 ),
inference(resolution,[],[f1530,f1283]) ).
fof(f1283,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1281]) ).
fof(f1530,plain,
( ! [X0,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,X13,X0) = X13 )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f1689,plain,
spl0_125,
inference(avatar_split_clause,[],[f347,f1687]) ).
fof(f347,axiom,
! [X10,X8] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f1685,plain,
spl0_124,
inference(avatar_split_clause,[],[f346,f1683]) ).
fof(f346,axiom,
! [X10,X8] : c_lessequals(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X8),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
fof(f1681,plain,
spl0_123,
inference(avatar_split_clause,[],[f296,f1679]) ).
fof(f1679,plain,
( spl0_123
<=> ! [X41,X0,X1,X40] : c_List_Ofoldl(X40,X1,c_List_Olist_ONil(X41),X0,X41) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f296,axiom,
! [X40,X41,X0,X1] : c_List_Ofoldl(X40,X1,c_List_Olist_ONil(X41),X0,X41) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
fof(f1677,plain,
spl0_122,
inference(avatar_split_clause,[],[f260,f1675]) ).
fof(f260,axiom,
! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
fof(f1673,plain,
spl0_121,
inference(avatar_split_clause,[],[f215,f1671]) ).
fof(f1671,plain,
( spl0_121
<=> ! [X11,X26] :
( hBOOL(hAPP(X11,X26))
| ~ hBOOL(hAPP(X11,c_Type_Osko__Type__Xtype__induct__1__1(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f215,axiom,
! [X11,X26] :
( hBOOL(hAPP(X11,X26))
| ~ hBOOL(hAPP(X11,c_Type_Osko__Type__Xtype__induct__1__1(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_2) ).
fof(f1669,plain,
spl0_120,
inference(avatar_split_clause,[],[f109,f1667]) ).
fof(f109,axiom,
! [X10,X8] :
( c_HOL_Oord__class_Oless(X10,X8,tc_nat)
| ~ c_lessequals(c_Suc(X10),X8,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
fof(f1665,plain,
spl0_119,
inference(avatar_split_clause,[],[f106,f1663]) ).
fof(f1663,plain,
( spl0_119
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_lessequals(c_Suc(X8),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f106,axiom,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_lessequals(c_Suc(X8),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
fof(f1661,plain,
spl0_118,
inference(avatar_split_clause,[],[f90,f1659]) ).
fof(f1659,plain,
( spl0_118
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f90,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X14,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1657,plain,
spl0_117,
inference(avatar_split_clause,[],[f89,f1655]) ).
fof(f1655,plain,
( spl0_117
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f89,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X13,c_Orderings_Oord__class_Omax(X13,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1653,plain,
spl0_116,
inference(avatar_split_clause,[],[f65,f1651]) ).
fof(f1651,plain,
( spl0_116
<=> ! [X8,X10] : c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) = c_HOL_Otimes__class_Otimes(X10,X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f65,axiom,
! [X10,X8] : c_HOL_Otimes__class_Otimes(X8,X10,tc_nat) = c_HOL_Otimes__class_Otimes(X10,X8,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1649,plain,
( spl0_115
| ~ spl0_33
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f1611,f1525,f1281,f1647]) ).
fof(f1647,plain,
( spl0_115
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1525,plain,
( spl0_90
<=> ! [X13,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,X13,X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1611,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_33
| ~ spl0_90 ),
inference(resolution,[],[f1526,f1283]) ).
fof(f1526,plain,
( ! [X0,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,X13,X0) = X13 )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1525]) ).
fof(f1645,plain,
spl0_114,
inference(avatar_split_clause,[],[f61,f1643]) ).
fof(f1643,plain,
( spl0_114
<=> ! [X8,X10] :
( c_lessequals(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f61,axiom,
! [X10,X8] :
( c_lessequals(X8,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X8,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1641,plain,
spl0_113,
inference(avatar_split_clause,[],[f60,f1639]) ).
fof(f1639,plain,
( spl0_113
<=> ! [X8,X10] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X8,c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f60,axiom,
! [X10,X8] :
( ~ c_lessequals(X8,X10,tc_nat)
| c_HOL_Oord__class_Oless(X8,c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1637,plain,
spl0_112,
inference(avatar_split_clause,[],[f14,f1635]) ).
fof(f1635,plain,
( spl0_112
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f14,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1633,plain,
spl0_111,
inference(avatar_split_clause,[],[f13,f1631]) ).
fof(f1631,plain,
( spl0_111
<=> ! [X13,X0,X14] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f13,axiom,
! [X0,X14,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X13,X14,X0),X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1620,plain,
( spl0_110
| ~ spl0_45
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1613,f1533,f1334,f1618]) ).
fof(f1334,plain,
( spl0_45
<=> ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1533,plain,
( spl0_92
<=> ! [X8,X10] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_lessequals(X8,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1613,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_45
| ~ spl0_92 ),
inference(resolution,[],[f1534,f1335]) ).
fof(f1335,plain,
( ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f1534,plain,
( ! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_lessequals(X8,X10,tc_nat) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f1605,plain,
spl0_109,
inference(avatar_split_clause,[],[f943,f1603]) ).
fof(f1603,plain,
( spl0_109
<=> ! [X0,X27,X28] : c_Nat_Onat_Onat__case(X27,X28,c_Orderings_Obot__class_Obot(tc_nat),X0) = X27 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f943,plain,
! [X28,X0,X27] : c_Nat_Onat_Onat__case(X27,X28,c_Orderings_Obot__class_Obot(tc_nat),X0) = X27,
inference(forward_demodulation,[],[f793,f815]) ).
fof(f793,axiom,
! [X28,X0,X27] : c_Nat_Onat_Onat__case(X27,X28,c_HOL_Ozero__class_Ozero(tc_nat),X0) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__0_0) ).
fof(f1601,plain,
spl0_108,
inference(avatar_split_clause,[],[f942,f1599]) ).
fof(f1599,plain,
( spl0_108
<=> ! [X0,X27,X28] : c_Nat_Onat_Onat__rec(X27,X28,c_Orderings_Obot__class_Obot(tc_nat),X0) = X27 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f942,plain,
! [X28,X0,X27] : c_Nat_Onat_Onat__rec(X27,X28,c_Orderings_Obot__class_Obot(tc_nat),X0) = X27,
inference(forward_demodulation,[],[f780,f815]) ).
fof(f780,axiom,
! [X28,X0,X27] : c_Nat_Onat_Onat__rec(X27,X28,c_HOL_Ozero__class_Ozero(tc_nat),X0) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__rec__0_0) ).
fof(f1597,plain,
spl0_107,
inference(avatar_split_clause,[],[f940,f1595]) ).
fof(f1595,plain,
( spl0_107
<=> ! [X13,X0] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X13,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f940,plain,
! [X0,X13] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_Orderings_Obot__class_Obot(tc_nat),X13,X0),
inference(forward_demodulation,[],[f469,f815]) ).
fof(f469,axiom,
! [X0,X13] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X13,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
fof(f1593,plain,
spl0_106,
inference(avatar_split_clause,[],[f939,f1591]) ).
fof(f1591,plain,
( spl0_106
<=> ! [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_106])]) ).
fof(f939,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,[],[f788,f815]) ).
fof(f788,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/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f1589,plain,
spl0_105,
inference(avatar_split_clause,[],[f938,f1587]) ).
fof(f1587,plain,
( spl0_105
<=> ! [X8] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Otimes__class_Otimes(X8,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f938,plain,
! [X8] : c_Orderings_Obot__class_Obot(tc_nat) = c_HOL_Otimes__class_Otimes(X8,c_Orderings_Obot__class_Obot(tc_nat),tc_nat),
inference(forward_demodulation,[],[f787,f815]) ).
fof(f787,axiom,
! [X8] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f1585,plain,
spl0_104,
inference(avatar_split_clause,[],[f937,f1583]) ).
fof(f1583,plain,
( spl0_104
<=> ! [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_104])]) ).
fof(f937,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,[],[f818,f815]) ).
fof(f818,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/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1581,plain,
spl0_103,
inference(avatar_split_clause,[],[f936,f1579]) ).
fof(f1579,plain,
( spl0_103
<=> ! [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_103])]) ).
fof(f936,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,[],[f795,f815]) ).
fof(f795,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/sandbox2/benchmark/theBenchmark.p',cls_min__0L_0) ).
fof(f1577,plain,
spl0_102,
inference(avatar_split_clause,[],[f935,f1575]) ).
fof(f1575,plain,
( spl0_102
<=> ! [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_102])]) ).
fof(f935,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,[],[f794,f815]) ).
fof(f794,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/sandbox2/benchmark/theBenchmark.p',cls_min__0R_0) ).
fof(f1573,plain,
spl0_101,
inference(avatar_split_clause,[],[f863,f1570]) ).
fof(f1570,plain,
( spl0_101
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f863,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argT_0) ).
fof(f1568,plain,
spl0_100,
inference(avatar_split_clause,[],[f853,f1566]) ).
fof(f853,axiom,
! [X21,X19,X22] : c_Lambda_Osubst(c_Lambda_Olift(X21,X19),X22,X19) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f1564,plain,
spl0_99,
inference(avatar_split_clause,[],[f840,f1562]) ).
fof(f840,axiom,
! [X63,X12,X64] : c_Type_Otype_OAtom(X12) != hAPP(hAPP(c_Type_Otype_OFun,X63),X64),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
fof(f1560,plain,
spl0_98,
inference(avatar_split_clause,[],[f833,f1557]) ).
fof(f1557,plain,
( spl0_98
<=> c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f833,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).
fof(f1555,plain,
spl0_97,
inference(avatar_split_clause,[],[f776,f1553]) ).
fof(f1553,plain,
( spl0_97
<=> ! [X8,X10] :
( c_lessequals(X8,X10,tc_nat)
| c_lessequals(X10,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f776,axiom,
! [X10,X8] :
( c_lessequals(X8,X10,tc_nat)
| c_lessequals(X10,X8,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1551,plain,
spl0_96,
inference(avatar_split_clause,[],[f695,f1549]) ).
fof(f1549,plain,
( spl0_96
<=> ! [X34,X12] :
( X12 = X34
| c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OVar(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f695,axiom,
! [X34,X12] :
( X12 = X34
| c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OVar(X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f1547,plain,
spl0_95,
inference(avatar_split_clause,[],[f690,f1545]) ).
fof(f1545,plain,
( spl0_95
<=> ! [X52,X53,X35] : c_Lambda_OdB_OAbs(X35) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X53) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f690,axiom,
! [X52,X53,X35] : c_Lambda_OdB_OAbs(X35) != hAPP(hAPP(c_Lambda_OdB_OApp,X52),X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f1543,plain,
spl0_94,
inference(avatar_split_clause,[],[f621,f1541]) ).
fof(f1541,plain,
( spl0_94
<=> ! [X22,X21] :
( ~ c_Lambda_Obeta(X22,X21)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X22),c_Lambda_OdB_OAbs(X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f621,axiom,
! [X21,X22] :
( ~ c_Lambda_Obeta(X22,X21)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X22),c_Lambda_OdB_OAbs(X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f1539,plain,
spl0_93,
inference(avatar_split_clause,[],[f538,f1537]) ).
fof(f538,axiom,
! [X6,X9,X20] :
( ~ c_InductTermi_OIT(X20)
| c_InductTermi_OIT(c_Lambda_Osubst(X20,c_Lambda_OdB_OVar(X6),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
fof(f1535,plain,
spl0_92,
inference(avatar_split_clause,[],[f373,f1533]) ).
fof(f373,axiom,
! [X10,X8] :
( ~ c_HOL_Oord__class_Oless(X8,X10,tc_nat)
| c_lessequals(X8,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
fof(f1531,plain,
spl0_91,
inference(avatar_split_clause,[],[f367,f1529]) ).
fof(f367,axiom,
! [X0,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X13,X13,X0) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1527,plain,
spl0_90,
inference(avatar_split_clause,[],[f343,f1525]) ).
fof(f343,axiom,
! [X0,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X13,X13,X0) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1523,plain,
spl0_89,
inference(avatar_split_clause,[],[f316,f1521]) ).
fof(f1521,plain,
( spl0_89
<=> ! [X45,X12,X46] : c_Lambda_OdB_OVar(X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X45),X46) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f316,axiom,
! [X46,X45,X12] : c_Lambda_OdB_OVar(X12) != hAPP(hAPP(c_Lambda_OdB_OApp,X45),X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
fof(f1519,plain,
spl0_88,
inference(avatar_split_clause,[],[f301,f1517]) ).
fof(f1517,plain,
( spl0_88
<=> ! [X43,X35] :
( X35 = X43
| c_Lambda_OdB_OAbs(X35) != c_Lambda_OdB_OAbs(X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f301,axiom,
! [X35,X43] :
( X35 = X43
| c_Lambda_OdB_OAbs(X35) != c_Lambda_OdB_OAbs(X43) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f1515,plain,
spl0_87,
inference(avatar_split_clause,[],[f155,f1513]) ).
fof(f1513,plain,
( spl0_87
<=> ! [X34,X12] :
( X12 = X34
| c_Suc(X12) != c_Suc(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f155,axiom,
! [X34,X12] :
( X12 = X34
| c_Suc(X12) != c_Suc(X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f1511,plain,
spl0_86,
inference(avatar_split_clause,[],[f139,f1509]) ).
fof(f1509,plain,
( spl0_86
<=> ! [X0,X10] : c_List_Olist_ONil(X0) = c_List_Odrop(X10,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f139,axiom,
! [X10,X0] : c_List_Olist_ONil(X0) = c_List_Odrop(X10,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
fof(f1507,plain,
spl0_85,
inference(avatar_split_clause,[],[f104,f1505]) ).
fof(f1505,plain,
( spl0_85
<=> ! [X34,X12] :
( X12 = X34
| c_Type_Otype_OAtom(X12) != c_Type_Otype_OAtom(X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f104,axiom,
! [X34,X12] :
( X12 = X34
| c_Type_Otype_OAtom(X12) != c_Type_Otype_OAtom(X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
fof(f1503,plain,
spl0_84,
inference(avatar_split_clause,[],[f68,f1501]) ).
fof(f68,axiom,
! [X10,X8] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),c_Suc(X8),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1496,plain,
spl0_83,
inference(avatar_split_clause,[],[f934,f1494]) ).
fof(f1494,plain,
( spl0_83
<=> ! [X16,X0] : c_List_Odrop(c_Orderings_Obot__class_Obot(tc_nat),X16,X0) = X16 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f934,plain,
! [X0,X16] : c_List_Odrop(c_Orderings_Obot__class_Obot(tc_nat),X16,X0) = X16,
inference(forward_demodulation,[],[f817,f815]) ).
fof(f817,axiom,
! [X0,X16] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X16,X0) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
fof(f1492,plain,
spl0_82,
inference(avatar_split_clause,[],[f933,f1490]) ).
fof(f1490,plain,
( spl0_82
<=> ! [X8] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f933,plain,
! [X8] : c_HOL_Ominus__class_Ominus(X8,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X8,
inference(forward_demodulation,[],[f799,f815]) ).
fof(f799,axiom,
! [X8] : c_HOL_Ominus__class_Ominus(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1488,plain,
spl0_81,
inference(avatar_split_clause,[],[f932,f1486]) ).
fof(f1486,plain,
( spl0_81
<=> ! [X10] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f932,plain,
! [X10] : c_Orderings_Oord__class_Omax(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) = X10,
inference(forward_demodulation,[],[f824,f815]) ).
fof(f824,axiom,
! [X10] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
fof(f1484,plain,
spl0_80,
inference(avatar_split_clause,[],[f931,f1482]) ).
fof(f1482,plain,
( spl0_80
<=> ! [X10] : c_Orderings_Oord__class_Omax(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f931,plain,
! [X10] : c_Orderings_Oord__class_Omax(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f823,f815]) ).
fof(f823,axiom,
! [X10] : c_Orderings_Oord__class_Omax(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
fof(f1480,plain,
spl0_79,
inference(avatar_split_clause,[],[f930,f1478]) ).
fof(f1478,plain,
( spl0_79
<=> ! [X8] : c_HOL_Ominus__class_Ominus(X8,X8,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f930,plain,
! [X8] : c_HOL_Ominus__class_Ominus(X8,X8,tc_nat) = c_Orderings_Obot__class_Obot(tc_nat),
inference(forward_demodulation,[],[f800,f815]) ).
fof(f800,axiom,
! [X8] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X8,X8,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1476,plain,
spl0_78,
inference(avatar_split_clause,[],[f920,f1474]) ).
fof(f1474,plain,
( spl0_78
<=> ! [X77,X0,X76] :
( X76 = X77
| ~ c_fequal(X76,X77,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f920,axiom,
! [X0,X76,X77] :
( X76 = X77
| ~ c_fequal(X76,X77,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1472,plain,
spl0_77,
inference(avatar_split_clause,[],[f836,f1470]) ).
fof(f1470,plain,
( spl0_77
<=> ! [X13,X62] : c_Type_Otyping(X62,c_Lambda_OdB_OVar(X13),hAPP(X62,X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f836,axiom,
! [X62,X13] : c_Type_Otyping(X62,c_Lambda_OdB_OVar(X13),hAPP(X62,X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f1468,plain,
spl0_76,
inference(avatar_split_clause,[],[f685,f1466]) ).
fof(f1466,plain,
( spl0_76
<=> ! [X7,X19] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X19),X7,X19) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f685,axiom,
! [X19,X7] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X19),X7,X19) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f1464,plain,
spl0_75,
inference(avatar_split_clause,[],[f472,f1462]) ).
fof(f1462,plain,
( spl0_75
<=> ! [X8] : c_lessequals(X8,c_HOL_Otimes__class_Otimes(X8,X8,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f472,axiom,
! [X8] : c_lessequals(X8,c_HOL_Otimes__class_Otimes(X8,X8,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).
fof(f1460,plain,
spl0_74,
inference(avatar_split_clause,[],[f414,f1458]) ).
fof(f1458,plain,
( spl0_74
<=> ! [X0,X55,X56] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X55,X56,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f414,axiom,
! [X0,X56,X55] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X55,X56,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
fof(f1456,plain,
spl0_73,
inference(avatar_split_clause,[],[f264,f1454]) ).
fof(f1454,plain,
( spl0_73
<=> ! [X8,X10] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f264,axiom,
! [X10,X8] : c_lessequals(c_HOL_Ominus__class_Ominus(X8,X10,tc_nat),X8,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1452,plain,
spl0_72,
inference(avatar_split_clause,[],[f96,f1450]) ).
fof(f1450,plain,
( spl0_72
<=> ! [X13,X0] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f96,axiom,
! [X0,X13] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1448,plain,
spl0_71,
inference(avatar_split_clause,[],[f94,f1446]) ).
fof(f1446,plain,
( spl0_71
<=> ! [X0,X17] : c_List_Oappend(c_List_Olist_ONil(X0),X17,X0) = X17 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f94,axiom,
! [X0,X17] : c_List_Oappend(c_List_Olist_ONil(X0),X17,X0) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
fof(f1444,plain,
spl0_70,
inference(avatar_split_clause,[],[f91,f1442]) ).
fof(f1442,plain,
( spl0_70
<=> ! [X16,X0] : c_List_Oappend(X16,c_List_Olist_ONil(X0),X0) = X16 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f91,axiom,
! [X0,X16] : c_List_Oappend(X16,c_List_Olist_ONil(X0),X0) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
fof(f1440,plain,
spl0_69,
inference(avatar_split_clause,[],[f928,f1438]) ).
fof(f1438,plain,
( spl0_69
<=> ! [X13] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Suc(X13),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f928,plain,
! [X13] : c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),c_Suc(X13),tc_nat),
inference(forward_demodulation,[],[f253,f815]) ).
fof(f253,axiom,
! [X13] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X13),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f1436,plain,
spl0_68,
inference(avatar_split_clause,[],[f927,f1434]) ).
fof(f1434,plain,
( spl0_68
<=> ! [X13] : c_Nitpick_Onat__gcd(X13,c_Orderings_Obot__class_Obot(tc_nat)) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f927,plain,
! [X13] : c_Nitpick_Onat__gcd(X13,c_Orderings_Obot__class_Obot(tc_nat)) = X13,
inference(forward_demodulation,[],[f808,f815]) ).
fof(f808,axiom,
! [X13] : c_Nitpick_Onat__gcd(X13,c_HOL_Ozero__class_Ozero(tc_nat)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__gcd_Osimps_0) ).
fof(f1432,plain,
spl0_67,
inference(avatar_split_clause,[],[f926,f1430]) ).
fof(f1430,plain,
( spl0_67
<=> ! [X3] : c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osize__class_Osize(X3,tc_String_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f926,plain,
! [X3] : c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osize__class_Osize(X3,tc_String_Ochar),
inference(forward_demodulation,[],[f821,f815]) ).
fof(f821,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(X3,tc_String_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_size__char_0) ).
fof(f1428,plain,
spl0_66,
inference(avatar_split_clause,[],[f925,f1425]) ).
fof(f1425,plain,
( spl0_66
<=> 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_66])]) ).
fof(f925,plain,
c_Orderings_Obot__class_Obot(tc_nat) = c_nat_Onat__size(c_Orderings_Obot__class_Obot(tc_nat)),
inference(forward_demodulation,[],[f809,f815]) ).
fof(f809,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_nat_Onat__size(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osize_I1_J_0) ).
fof(f1423,plain,
spl0_65,
inference(avatar_split_clause,[],[f883,f1421]) ).
fof(f1421,plain,
( spl0_65
<=> ! [X75,X74] :
( ~ class_Orderings_Obot(X75)
| class_Orderings_Obot(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f883,axiom,
! [X74,X75] :
( ~ class_Orderings_Obot(X75)
| class_Orderings_Obot(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1419,plain,
spl0_64,
inference(avatar_split_clause,[],[f882,f1417]) ).
fof(f1417,plain,
( spl0_64
<=> ! [X75,X74] :
( ~ class_Orderings_Oorder(X75)
| class_Orderings_Oorder(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f882,axiom,
! [X74,X75] :
( ~ class_Orderings_Oorder(X75)
| class_Orderings_Oorder(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1415,plain,
spl0_63,
inference(avatar_split_clause,[],[f881,f1413]) ).
fof(f1413,plain,
( spl0_63
<=> ! [X75,X74] :
( ~ class_Orderings_Opreorder(X75)
| class_Orderings_Opreorder(tc_fun(X74,X75)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f881,axiom,
! [X74,X75] :
( ~ class_Orderings_Opreorder(X75)
| class_Orderings_Opreorder(tc_fun(X74,X75)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1411,plain,
spl0_62,
inference(avatar_split_clause,[],[f851,f1409]) ).
fof(f1409,plain,
( spl0_62
<=> ! [X6,X21] :
( ~ c_InductTermi_OIT(X21)
| c_InductTermi_OIT(c_Lambda_Olift(X21,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f851,axiom,
! [X21,X6] :
( ~ c_InductTermi_OIT(X21)
| c_InductTermi_OIT(c_Lambda_Olift(X21,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f1407,plain,
spl0_61,
inference(avatar_split_clause,[],[f681,f1405]) ).
fof(f1405,plain,
( spl0_61
<=> ! [X13,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X13,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f681,axiom,
! [X0,X13] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X13,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1403,plain,
spl0_60,
inference(avatar_split_clause,[],[f680,f1401]) ).
fof(f1401,plain,
( spl0_60
<=> ! [X13,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X13,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f680,axiom,
! [X0,X13] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X13,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1399,plain,
spl0_59,
inference(avatar_split_clause,[],[f479,f1397]) ).
fof(f1397,plain,
( spl0_59
<=> ! [X13,X21,X0] : c_List_Olist_OCons(X13,X21,X0) != X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f479,axiom,
! [X21,X0,X13] : c_List_Olist_OCons(X13,X21,X0) != X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f1395,plain,
spl0_58,
inference(avatar_split_clause,[],[f341,f1393]) ).
fof(f1393,plain,
( spl0_58
<=> ! [X13,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f341,axiom,
! [X0,X13] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1391,plain,
spl0_57,
inference(avatar_split_clause,[],[f340,f1389]) ).
fof(f1389,plain,
( spl0_57
<=> ! [X13,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f340,axiom,
! [X0,X13] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1387,plain,
spl0_56,
inference(avatar_split_clause,[],[f339,f1385]) ).
fof(f1385,plain,
( spl0_56
<=> ! [X13,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f339,axiom,
! [X0,X13] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X13,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1383,plain,
( ~ spl0_55
| ~ spl0_50
| spl0_54 ),
inference(avatar_split_clause,[],[f1378,f1373,f1356,f1380]) ).
fof(f1373,plain,
( spl0_54
<=> c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1378,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_Orderings_Obot__class_Obot(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_Orderings_Obot__class_Obot(tc_nat)),v_T____)
| ~ spl0_50
| spl0_54 ),
inference(forward_demodulation,[],[f1377,f1358]) ).
fof(f1377,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),v_T____)
| spl0_54 ),
inference(forward_demodulation,[],[f1375,f874]) ).
fof(f1375,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| spl0_54 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f1376,plain,
~ spl0_54,
inference(avatar_split_clause,[],[f880,f1373]) ).
fof(f880,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1371,plain,
( spl0_53
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f1354,f1351,f1369]) ).
fof(f1369,plain,
( spl0_53
<=> ! [X10] : ~ c_HOL_Oord__class_Oless(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1351,plain,
( spl0_49
<=> ! [X10] : ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1354,plain,
( ! [X10] : ~ c_HOL_Oord__class_Oless(X10,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_49 ),
inference(forward_demodulation,[],[f1352,f815]) ).
fof(f1352,plain,
( ! [X10] : ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f1367,plain,
( spl0_52
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f1349,f1346,f1365]) ).
fof(f1365,plain,
( spl0_52
<=> ! [X34] : c_Suc(X34) != c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1346,plain,
( spl0_48
<=> ! [X34] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1349,plain,
( ! [X34] : c_Suc(X34) != c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1347,f815]) ).
fof(f1347,plain,
( ! [X34] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X34)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f1363,plain,
spl0_51,
inference(avatar_split_clause,[],[f924,f1361]) ).
fof(f1361,plain,
( spl0_51
<=> ! [X10] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f924,plain,
! [X10] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X10,tc_nat),
inference(forward_demodulation,[],[f820,f815]) ).
fof(f820,axiom,
! [X10] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1359,plain,
spl0_50,
inference(avatar_split_clause,[],[f815,f1356]) ).
fof(f1353,plain,
spl0_49,
inference(avatar_split_clause,[],[f814,f1351]) ).
fof(f814,axiom,
! [X10] : ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f1348,plain,
spl0_48,
inference(avatar_split_clause,[],[f805,f1346]) ).
fof(f805,axiom,
! [X34] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f1344,plain,
spl0_47,
inference(avatar_split_clause,[],[f700,f1342]) ).
fof(f1342,plain,
( spl0_47
<=> ! [X12,X35] : c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OAbs(X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f700,axiom,
! [X35,X12] : c_Lambda_OdB_OVar(X12) != c_Lambda_OdB_OAbs(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f1340,plain,
spl0_46,
inference(avatar_split_clause,[],[f533,f1338]) ).
fof(f1338,plain,
( spl0_46
<=> ! [X10] : ~ c_lessequals(c_Suc(X10),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f533,axiom,
! [X10] : ~ c_lessequals(c_Suc(X10),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1336,plain,
spl0_45,
inference(avatar_split_clause,[],[f486,f1334]) ).
fof(f486,axiom,
! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f1332,plain,
spl0_44,
inference(avatar_split_clause,[],[f459,f1330]) ).
fof(f1330,plain,
( spl0_44
<=> ! [X20] :
( ~ c_InductTermi_OIT(X20)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f459,axiom,
! [X20] :
( ~ c_InductTermi_OIT(X20)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f1328,plain,
spl0_43,
inference(avatar_split_clause,[],[f919,f1326]) ).
fof(f1326,plain,
( spl0_43
<=> ! [X13,X0] : c_fequal(X13,X13,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f919,axiom,
! [X0,X13] : c_fequal(X13,X13,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1324,plain,
spl0_42,
inference(avatar_split_clause,[],[f872,f1321]) ).
fof(f872,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
fof(f1319,plain,
spl0_41,
inference(avatar_split_clause,[],[f579,f1317]) ).
fof(f1317,plain,
( spl0_41
<=> ! [X13] : c_lessequals(X13,X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f579,axiom,
! [X13] : c_lessequals(X13,X13,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f1315,plain,
spl0_40,
inference(avatar_split_clause,[],[f560,f1313]) ).
fof(f1313,plain,
( spl0_40
<=> ! [X10] : c_Suc(X10) != X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f560,axiom,
! [X10] : c_Suc(X10) != X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f1311,plain,
spl0_39,
inference(avatar_split_clause,[],[f480,f1309]) ).
fof(f1309,plain,
( spl0_39
<=> ! [X6,X21] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X6),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f480,axiom,
! [X21,X6] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X6),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f1307,plain,
spl0_38,
inference(avatar_split_clause,[],[f337,f1305]) ).
fof(f337,axiom,
! [X13] : ~ c_HOL_Oord__class_Oless(X13,X13,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1303,plain,
spl0_37,
inference(avatar_split_clause,[],[f143,f1301]) ).
fof(f1301,plain,
( spl0_37
<=> ! [X10] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f143,axiom,
! [X10] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
fof(f1299,plain,
spl0_36,
inference(avatar_split_clause,[],[f918,f1296]) ).
fof(f1296,plain,
( spl0_36
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f918,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1294,plain,
spl0_35,
inference(avatar_split_clause,[],[f917,f1291]) ).
fof(f1291,plain,
( spl0_35
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f917,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1289,plain,
spl0_34,
inference(avatar_split_clause,[],[f916,f1286]) ).
fof(f1286,plain,
( spl0_34
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f916,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1284,plain,
spl0_33,
inference(avatar_split_clause,[],[f915,f1281]) ).
fof(f915,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1279,plain,
spl0_32,
inference(avatar_split_clause,[],[f914,f1276]) ).
fof(f1276,plain,
( spl0_32
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f914,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1274,plain,
spl0_31,
inference(avatar_split_clause,[],[f913,f1271]) ).
fof(f1271,plain,
( spl0_31
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f913,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f1269,plain,
spl0_30,
inference(avatar_split_clause,[],[f912,f1266]) ).
fof(f912,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1264,plain,
spl0_29,
inference(avatar_split_clause,[],[f911,f1261]) ).
fof(f1261,plain,
( spl0_29
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f911,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1259,plain,
spl0_28,
inference(avatar_split_clause,[],[f910,f1256]) ).
fof(f1256,plain,
( spl0_28
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f910,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1254,plain,
spl0_27,
inference(avatar_split_clause,[],[f909,f1251]) ).
fof(f1251,plain,
( spl0_27
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f909,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1249,plain,
spl0_26,
inference(avatar_split_clause,[],[f908,f1246]) ).
fof(f1246,plain,
( spl0_26
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f908,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1244,plain,
spl0_25,
inference(avatar_split_clause,[],[f907,f1241]) ).
fof(f1241,plain,
( spl0_25
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f907,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1239,plain,
spl0_24,
inference(avatar_split_clause,[],[f906,f1236]) ).
fof(f1236,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f906,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1234,plain,
spl0_23,
inference(avatar_split_clause,[],[f905,f1231]) ).
fof(f905,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1229,plain,
spl0_22,
inference(avatar_split_clause,[],[f904,f1226]) ).
fof(f1226,plain,
( spl0_22
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f904,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(f1224,plain,
spl0_21,
inference(avatar_split_clause,[],[f903,f1221]) ).
fof(f1221,plain,
( spl0_21
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f903,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1219,plain,
spl0_20,
inference(avatar_split_clause,[],[f902,f1216]) ).
fof(f1216,plain,
( spl0_20
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f902,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1214,plain,
spl0_19,
inference(avatar_split_clause,[],[f901,f1211]) ).
fof(f1211,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f901,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1209,plain,
spl0_18,
inference(avatar_split_clause,[],[f900,f1206]) ).
fof(f1206,plain,
( spl0_18
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f900,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1204,plain,
spl0_17,
inference(avatar_split_clause,[],[f899,f1201]) ).
fof(f1201,plain,
( spl0_17
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f899,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1199,plain,
spl0_16,
inference(avatar_split_clause,[],[f898,f1196]) ).
fof(f1196,plain,
( spl0_16
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f898,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1194,plain,
spl0_15,
inference(avatar_split_clause,[],[f897,f1191]) ).
fof(f1191,plain,
( spl0_15
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f897,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1189,plain,
spl0_14,
inference(avatar_split_clause,[],[f896,f1186]) ).
fof(f1186,plain,
( spl0_14
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f896,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1184,plain,
spl0_13,
inference(avatar_split_clause,[],[f895,f1181]) ).
fof(f1181,plain,
( spl0_13
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f895,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1179,plain,
spl0_12,
inference(avatar_split_clause,[],[f894,f1176]) ).
fof(f1176,plain,
( spl0_12
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f894,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1174,plain,
spl0_11,
inference(avatar_split_clause,[],[f893,f1171]) ).
fof(f1171,plain,
( spl0_11
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f893,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1169,plain,
spl0_10,
inference(avatar_split_clause,[],[f892,f1166]) ).
fof(f1166,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f892,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1164,plain,
spl0_9,
inference(avatar_split_clause,[],[f891,f1161]) ).
fof(f1161,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f891,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1159,plain,
spl0_8,
inference(avatar_split_clause,[],[f890,f1156]) ).
fof(f1156,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f890,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1154,plain,
spl0_7,
inference(avatar_split_clause,[],[f889,f1151]) ).
fof(f1151,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f889,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1149,plain,
spl0_6,
inference(avatar_split_clause,[],[f888,f1146]) ).
fof(f1146,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f888,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1144,plain,
spl0_5,
inference(avatar_split_clause,[],[f887,f1141]) ).
fof(f1141,plain,
( spl0_5
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f887,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1139,plain,
spl0_4,
inference(avatar_split_clause,[],[f886,f1136]) ).
fof(f1136,plain,
( spl0_4
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f886,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1134,plain,
spl0_3,
inference(avatar_split_clause,[],[f885,f1131]) ).
fof(f1131,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f885,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1129,plain,
spl0_2,
inference(avatar_split_clause,[],[f884,f1126]) ).
fof(f1126,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f884,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1124,plain,
spl0_1,
inference(avatar_split_clause,[],[f862,f1121]) ).
fof(f1121,plain,
( spl0_1
<=> c_InductTermi_OIT(v_u____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f862,axiom,
c_InductTermi_OIT(v_u____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL795-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 23:23:50 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (24334)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (24337)WARNING: value z3 for option sas not known
% 0.23/0.45 % (24336)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.45 % (24341)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)
% 0.23/0.45 % (24340)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)
% 0.23/0.45 % (24339)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)
% 0.23/0.45 % (24338)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.45 % (24337)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)
% 0.23/0.45 % (24335)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.11/0.58 TRYING [1]
% 1.24/0.60 TRYING [2]
% 1.24/0.61 % (24339)First to succeed.
% 1.24/0.63 % (24339)Refutation found. Thanks to Tanya!
% 1.24/0.63 % SZS status Unsatisfiable for theBenchmark
% 1.24/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 1.24/0.64 % (24339)------------------------------
% 1.24/0.64 % (24339)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.24/0.64 % (24339)Termination reason: Refutation
% 1.24/0.64
% 1.24/0.64 % (24339)Memory used [KB]: 3376
% 1.24/0.64 % (24339)Time elapsed: 0.180 s
% 1.24/0.64 % (24339)Instructions burned: 286 (million)
% 1.24/0.64 % (24339)------------------------------
% 1.24/0.64 % (24339)------------------------------
% 1.24/0.64 % (24334)Success in time 0.258 s
%------------------------------------------------------------------------------