TSTP Solution File: SWV972-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV972-1 : 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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:13:02 EDT 2024
% Result : Unsatisfiable 0.21s 0.56s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 668
% Syntax : Number of formulae : 1075 ( 473 unt; 0 def)
% Number of atoms : 2084 ( 540 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 1676 ( 667 ~; 663 |; 0 &)
% ( 346 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 390 ( 388 usr; 348 prp; 0-8 aty)
% Number of functors : 52 ( 52 usr; 17 con; 0-5 aty)
% Number of variables : 1712 (1712 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4827,plain,
$false,
inference(avatar_sat_refutation,[],[f541,f546,f551,f556,f561,f566,f571,f576,f581,f586,f591,f596,f601,f606,f611,f616,f621,f626,f631,f636,f641,f646,f651,f656,f661,f666,f671,f676,f681,f686,f691,f696,f701,f706,f711,f716,f721,f726,f731,f736,f741,f746,f751,f756,f761,f766,f771,f776,f781,f786,f791,f796,f800,f804,f808,f812,f816,f820,f824,f828,f832,f837,f841,f845,f849,f853,f857,f861,f865,f869,f873,f877,f881,f885,f889,f893,f897,f901,f905,f909,f913,f917,f928,f932,f936,f940,f944,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f988,f998,f1002,f1006,f1011,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1067,f1071,f1075,f1079,f1083,f1087,f1091,f1117,f1158,f1163,f1167,f1171,f1175,f1179,f1183,f1187,f1191,f1196,f1200,f1205,f1209,f1213,f1217,f1221,f1226,f1230,f1234,f1241,f1271,f1283,f1287,f1291,f1295,f1300,f1304,f1308,f1312,f1316,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1380,f1384,f1388,f1392,f1396,f1400,f1404,f1408,f1413,f1473,f1524,f1550,f1554,f1559,f1563,f1567,f1571,f1575,f1579,f1583,f1587,f1591,f1595,f1599,f1603,f1607,f1611,f1615,f1619,f1623,f1627,f1631,f1641,f1719,f1763,f1767,f1771,f1775,f1779,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1812,f1940,f1944,f1948,f1952,f1956,f1960,f1964,f1968,f1973,f1977,f1981,f1985,f1989,f1993,f1997,f2001,f2005,f2009,f2013,f2018,f2022,f2026,f2030,f2034,f2038,f2042,f2046,f2050,f2054,f2058,f2063,f2067,f2071,f2075,f2079,f2084,f2535,f2539,f2543,f2547,f2551,f2555,f2559,f2563,f2567,f2571,f2585,f2589,f2593,f2597,f2601,f2605,f2609,f2613,f2617,f2621,f2626,f2630,f2634,f2638,f2642,f2646,f2650,f3385,f3389,f3393,f3397,f3401,f3405,f3409,f3413,f3417,f3421,f3425,f3429,f3433,f3437,f3441,f3445,f3449,f3453,f3457,f3461,f3465,f3611,f3797,f3817,f3821,f3825,f3829,f3833,f3837,f3841,f3845,f3858,f3862,f3866,f3870,f3874,f3878,f3889,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4371,f4375,f4379,f4383,f4391,f4395,f4399,f4403,f4407,f4412,f4813,f4817,f4821,f4825,f4826]) ).
fof(f4826,plain,
( ~ spl0_177
| ~ spl0_58
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4807,f4409,f818,f1410]) ).
fof(f1410,plain,
( spl0_177
<=> c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f818,plain,
( spl0_58
<=> ! [X1] :
( ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,X1)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X1,v_Us____,tc_Type_Oty,tc_Type_Oty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f4409,plain,
( spl0_342
<=> c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____),v_Us____,tc_Type_Oty,tc_Type_Oty) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f4807,plain,
( ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____))
| ~ spl0_58
| ~ spl0_342 ),
inference(resolution,[],[f4411,f819]) ).
fof(f819,plain,
( ! [X1] :
( ~ c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X1,v_Us____,tc_Type_Oty,tc_Type_Oty)
| ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,X1) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f4411,plain,
( c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____),v_Us____,tc_Type_Oty,tc_Type_Oty)
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4409]) ).
fof(f4825,plain,
spl0_346,
inference(avatar_split_clause,[],[f108,f4823]) ).
fof(f4823,plain,
( spl0_346
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X23,X29,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| c_lessequals(X23,c_HOL_Oplus__class_Oplus(X5,X29,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f108,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_lessequals(X23,X29,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| c_lessequals(X23,c_HOL_Oplus__class_Oplus(X5,X29,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f4821,plain,
spl0_345,
inference(avatar_split_clause,[],[f37,f4819]) ).
fof(f4819,plain,
( spl0_345
<=> ! [X31,X4,X30,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X30,X2) = X31
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,X2),X2) != c_HOL_Oplus__class_Oplus(X4,X31,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f37,axiom,
! [X2,X31,X1,X4,X30] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Oplus__class_Oplus(X1,X30,X2) = X31
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,X2),X2) != c_HOL_Oplus__class_Oplus(X4,X31,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f4817,plain,
spl0_344,
inference(avatar_split_clause,[],[f24,f4815]) ).
fof(f4815,plain,
( spl0_344
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X23,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X5,X23,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f24,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X23,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X5,X23,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f4813,plain,
spl0_343,
inference(avatar_split_clause,[],[f19,f4811]) ).
fof(f4811,plain,
( spl0_343
<=> ! [X24,X29,X23,X5,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X5,X23,X2)
| ~ c_lessequals(X29,X24,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X24,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f19,axiom,
! [X2,X29,X24,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X5,X23,X2)
| ~ c_lessequals(X29,X24,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X24,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f4412,plain,
spl0_342,
inference(avatar_split_clause,[],[f450,f4409]) ).
fof(f450,axiom,
c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____),v_Us____,tc_Type_Oty,tc_Type_Oty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f4407,plain,
spl0_341,
inference(avatar_split_clause,[],[f327,f4405]) ).
fof(f4405,plain,
( spl0_341
<=> ! [X2,X7,X25] : c_List_Orev(c_List_Otake(X25,X7,X2),X2) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X25,tc_nat),c_List_Orev(X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f327,axiom,
! [X2,X7,X25] : c_List_Orev(c_List_Otake(X25,X7,X2),X2) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X25,tc_nat),c_List_Orev(X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__take_0) ).
fof(f4403,plain,
spl0_340,
inference(avatar_split_clause,[],[f326,f4401]) ).
fof(f4401,plain,
( spl0_340
<=> ! [X2,X7,X25] : c_List_Orev(c_List_Odrop(X25,X7,X2),X2) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X25,tc_nat),c_List_Orev(X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f326,axiom,
! [X2,X7,X25] : c_List_Orev(c_List_Odrop(X25,X7,X2),X2) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X25,tc_nat),c_List_Orev(X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__drop_0) ).
fof(f4399,plain,
spl0_339,
inference(avatar_split_clause,[],[f248,f4397]) ).
fof(f4397,plain,
( spl0_339
<=> ! [X43,X45,X4,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X4,X1,X2)
| c_lessequals(X45,X43,X2)
| c_HOL_Ominus__class_Ominus(X1,X4,X2) != c_HOL_Ominus__class_Ominus(X43,X45,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f248,axiom,
! [X2,X1,X45,X4,X43] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X4,X1,X2)
| c_lessequals(X45,X43,X2)
| c_HOL_Ominus__class_Ominus(X1,X4,X2) != c_HOL_Ominus__class_Ominus(X43,X45,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f4395,plain,
spl0_338,
inference(avatar_split_clause,[],[f208,f4393]) ).
fof(f4393,plain,
( spl0_338
<=> ! [X2,X1,X25] : c_List_Oappend(c_List_Oreplicate(X25,X1,X2),c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Oreplicate(X25,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f208,axiom,
! [X2,X1,X25] : c_List_Oappend(c_List_Oreplicate(X25,X1,X2),c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Oreplicate(X25,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
fof(f4391,plain,
spl0_337,
inference(avatar_split_clause,[],[f167,f4389]) ).
fof(f4389,plain,
( spl0_337
<=> ! [X2,X5,X3] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X5,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f167,axiom,
! [X2,X3,X5] :
( ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X5,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f4383,plain,
spl0_336,
inference(avatar_split_clause,[],[f163,f4381]) ).
fof(f4381,plain,
( spl0_336
<=> ! [X25,X27,X26] :
( ~ c_lessequals(X26,X27,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X27,X25,tc_nat),X26,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f163,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(X26,X27,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X27,X25,tc_nat),X26,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X25,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
fof(f4379,plain,
spl0_335,
inference(avatar_split_clause,[],[f162,f4377]) ).
fof(f4377,plain,
( spl0_335
<=> ! [X25,X27,X26] :
( ~ c_lessequals(X26,X27,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X25,X27,tc_nat),X26,tc_nat) = c_HOL_Oplus__class_Oplus(X25,c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f162,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(X26,X27,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X25,X27,tc_nat),X26,tc_nat) = c_HOL_Oplus__class_Oplus(X25,c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
fof(f4375,plain,
spl0_334,
inference(avatar_split_clause,[],[f134,f4373]) ).
fof(f4373,plain,
( spl0_334
<=> ! [X25,X27,X26] :
( ~ c_lessequals(X26,X27,tc_nat)
| c_HOL_Ominus__class_Ominus(X25,c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),X27,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f134,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(X26,X27,tc_nat)
| c_HOL_Ominus__class_Ominus(X25,c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),X27,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
fof(f4371,plain,
spl0_333,
inference(avatar_split_clause,[],[f79,f4369]) ).
fof(f4369,plain,
( spl0_333
<=> ! [X2,X1,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otl(c_List_Oreplicate(X3,X1,X2),X2) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f79,axiom,
! [X2,X3,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otl(c_List_Oreplicate(X3,X1,X2),X2) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__replicate_0) ).
fof(f4075,plain,
spl0_332,
inference(avatar_split_clause,[],[f526,f4073]) ).
fof(f4073,plain,
( spl0_332
<=> ! [X26,X3,X2,X1] : c_List_Oappend(c_List_Oreplicate(X3,X1,X2),c_List_Oreplicate(X26,X1,X2),X2) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f526,plain,
! [X2,X3,X1,X26] : c_List_Oappend(c_List_Oreplicate(X3,X1,X2),c_List_Oreplicate(X26,X1,X2),X2) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),X1,X2),
inference(forward_demodulation,[],[f148,f165]) ).
fof(f165,axiom,
! [X2,X3,X0,X1] : c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X1,X2) = c_List_Oappend(c_List_Oreplicate(X3,X1,X2),c_List_Oreplicate(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).
fof(f148,axiom,
! [X2,X3,X1,X26] : c_List_Oappend(c_List_Oreplicate(X3,X1,X2),c_List_Oreplicate(X26,X1,X2),X2) = c_List_Oappend(c_List_Oreplicate(X26,X1,X2),c_List_Oreplicate(X3,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
fof(f4071,plain,
spl0_331,
inference(avatar_split_clause,[],[f439,f4069]) ).
fof(f4069,plain,
( spl0_331
<=> ! [X2,X44,X4,X34,X7,X8,X1] :
( hBOOL(hAPP(hAPP(X8,X1),X4))
| ~ c_List_Olist__all2(X8,c_List_Olist_OCons(X1,X7,X2),c_List_Olist_OCons(X4,X34,X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f439,axiom,
! [X2,X1,X8,X44,X7,X4,X34] :
( hBOOL(hAPP(hAPP(X8,X1),X4))
| ~ c_List_Olist__all2(X8,c_List_Olist_OCons(X1,X7,X2),c_List_Olist_OCons(X4,X34,X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_0) ).
fof(f4067,plain,
spl0_330,
inference(avatar_split_clause,[],[f429,f4065]) ).
fof(f4065,plain,
( spl0_330
<=> ! [X44,X34,X7,X8,X3,X2] :
( ~ c_List_Olist__all2(X8,X7,X34,X2,X44)
| c_List_Olist__all2(X8,c_List_Otake(X3,X7,X2),c_List_Otake(X3,X34,X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f429,axiom,
! [X2,X3,X8,X44,X7,X34] :
( ~ c_List_Olist__all2(X8,X7,X34,X2,X44)
| c_List_Olist__all2(X8,c_List_Otake(X3,X7,X2),c_List_Otake(X3,X34,X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__takeI_0) ).
fof(f4063,plain,
spl0_329,
inference(avatar_split_clause,[],[f427,f4061]) ).
fof(f4061,plain,
( spl0_329
<=> ! [X44,X4,X34,X7,X8,X2,X1] :
( c_List_Olist__all2(X8,X7,X34,X2,X44)
| ~ c_List_Olist__all2(X8,c_List_Olist_OCons(X1,X7,X2),c_List_Olist_OCons(X4,X34,X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f427,axiom,
! [X2,X1,X8,X44,X7,X4,X34] :
( c_List_Olist__all2(X8,X7,X34,X2,X44)
| ~ c_List_Olist__all2(X8,c_List_Olist_OCons(X1,X7,X2),c_List_Olist_OCons(X4,X34,X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Cons_1) ).
fof(f4059,plain,
spl0_328,
inference(avatar_split_clause,[],[f413,f4057]) ).
fof(f4057,plain,
( spl0_328
<=> ! [X44,X8,X71,X3,X70,X2] :
( ~ c_List_Olist__all2(X8,X70,X71,X2,X44)
| c_List_Olist__all2(X8,c_List_Odrop(X3,X70,X2),c_List_Odrop(X3,X71,X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f413,axiom,
! [X2,X3,X70,X71,X8,X44] :
( ~ c_List_Olist__all2(X8,X70,X71,X2,X44)
| c_List_Olist__all2(X8,c_List_Odrop(X3,X70,X2),c_List_Odrop(X3,X71,X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__dropI_0) ).
fof(f4055,plain,
spl0_327,
inference(avatar_split_clause,[],[f231,f4053]) ).
fof(f4053,plain,
( spl0_327
<=> ! [X0,X3,X2,X7] : c_List_Odrop(X3,c_List_Otake(X0,X7,X2),X2) = c_List_Otake(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),c_List_Odrop(X3,X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f231,axiom,
! [X2,X3,X0,X7] : c_List_Odrop(X3,c_List_Otake(X0,X7,X2),X2) = c_List_Otake(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),c_List_Odrop(X3,X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__take_0) ).
fof(f4051,plain,
spl0_326,
inference(avatar_split_clause,[],[f204,f4049]) ).
fof(f4049,plain,
( spl0_326
<=> ! [X0,X3,X2,X7] : c_List_Otake(X3,c_List_Odrop(X0,X7,X2),X2) = c_List_Odrop(X0,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f204,axiom,
! [X2,X3,X0,X7] : c_List_Otake(X3,c_List_Odrop(X0,X7,X2),X2) = c_List_Odrop(X0,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__drop_0) ).
fof(f4047,plain,
spl0_325,
inference(avatar_split_clause,[],[f201,f4045]) ).
fof(f4045,plain,
( spl0_325
<=> ! [X34,X2,X7] : c_Nat_Osize__class_Osize(c_List_Oappend(X7,X34,X2),tc_List_Olist(X2)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X34,tc_List_Olist(X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f201,axiom,
! [X2,X7,X34] : c_Nat_Osize__class_Osize(c_List_Oappend(X7,X34,X2),tc_List_Olist(X2)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X34,tc_List_Olist(X2)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__append_0) ).
fof(f4043,plain,
spl0_324,
inference(avatar_split_clause,[],[f165,f4041]) ).
fof(f4041,plain,
( spl0_324
<=> ! [X0,X3,X2,X1] : c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X1,X2) = c_List_Oappend(c_List_Oreplicate(X3,X1,X2),c_List_Oreplicate(X0,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f4039,plain,
spl0_323,
inference(avatar_split_clause,[],[f106,f4037]) ).
fof(f4037,plain,
( spl0_323
<=> ! [X25,X27,X26] :
( ~ c_lessequals(X26,X27,tc_nat)
| ~ c_lessequals(X25,c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),X27,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f106,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(X26,X27,tc_nat)
| ~ c_lessequals(X25,c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),X27,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
fof(f4035,plain,
spl0_322,
inference(avatar_split_clause,[],[f99,f4033]) ).
fof(f4033,plain,
( spl0_322
<=> ! [X17,X12,X20,X0,X14,X16,X8,X2] :
( ~ c_TypeRel_OMethod(X8,X17,X12,X16,X14,X0,X20,X2)
| c_TypeRel_OMethod(X8,X20,X12,X16,X14,X0,X20,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f99,axiom,
! [X2,X0,X8,X16,X14,X17,X12,X20] :
( ~ c_TypeRel_OMethod(X8,X17,X12,X16,X14,X0,X20,X2)
| c_TypeRel_OMethod(X8,X20,X12,X16,X14,X0,X20,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sees__method__idemp_0) ).
fof(f4031,plain,
spl0_321,
inference(avatar_split_clause,[],[f44,f4029]) ).
fof(f4029,plain,
( spl0_321
<=> ! [X2,X7,X27,X25,X1] :
( X25 = X27
| hAPP(c_List_Onth(c_List_Olist__update(X7,X25,X1,X2),X2),X27) = hAPP(c_List_Onth(X7,X2),X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f44,axiom,
! [X2,X1,X7,X27,X25] :
( X25 = X27
| hAPP(c_List_Onth(c_List_Olist__update(X7,X25,X1,X2),X2),X27) = hAPP(c_List_Onth(X7,X2),X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).
fof(f4027,plain,
spl0_320,
inference(avatar_split_clause,[],[f18,f4025]) ).
fof(f4025,plain,
( spl0_320
<=> ! [X28,X27,X25,X26] :
( ~ c_lessequals(X25,X27,tc_nat)
| ~ c_lessequals(X26,X28,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),c_HOL_Oplus__class_Oplus(X27,X28,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f18,axiom,
! [X28,X26,X27,X25] :
( ~ c_lessequals(X25,X27,tc_nat)
| ~ c_lessequals(X26,X28,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),c_HOL_Oplus__class_Oplus(X27,X28,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
fof(f4023,plain,
( ~ spl0_318
| spl0_203
| ~ spl0_319
| ~ spl0_92
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2486,f2048,f962,f4020,f1717,f4016]) ).
fof(f4016,plain,
( spl0_318
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1717,plain,
( spl0_203
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f4020,plain,
( spl0_319
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f962,plain,
( spl0_92
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2048,plain,
( spl0_244
<=> ! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| X1 = X4
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X1,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2486,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_92
| ~ spl0_244 ),
inference(trivial_inequality_removal,[],[f2483]) ).
fof(f2483,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_92
| ~ spl0_244 ),
inference(superposition,[],[f2049,f963]) ).
fof(f963,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f962]) ).
fof(f2049,plain,
( ! [X2,X1,X4] :
( c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X1,X4,X2)
| ~ class_Int_Onumber__ring(X2)
| X1 = X4
| ~ class_Ring__and__Field_Oidom(X2) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2048]) ).
fof(f3889,plain,
( spl0_317
| ~ spl0_33
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1253,f1177,f698,f3887]) ).
fof(f3887,plain,
( spl0_317
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f698,plain,
( spl0_33
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1177,plain,
( spl0_129
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1253,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_33
| ~ spl0_129 ),
inference(resolution,[],[f1178,f700]) ).
fof(f700,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f1178,plain,
( ! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1177]) ).
fof(f3878,plain,
spl0_316,
inference(avatar_split_clause,[],[f521,f3876]) ).
fof(f3876,plain,
( spl0_316
<=> ! [X2] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f521,plain,
! [X2] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
inference(duplicate_literal_removal,[],[f22]) ).
fof(f22,axiom,
! [X2] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f3874,plain,
spl0_315,
inference(avatar_split_clause,[],[f356,f3872]) ).
fof(f3872,plain,
( spl0_315
<=> ! [X2,X1,X7] : c_List_Orev(c_List_Olist_OCons(X1,X7,X2),X2) = c_List_Oappend(c_List_Orev(X7,X2),c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f356,axiom,
! [X2,X1,X7] : c_List_Orev(c_List_Olist_OCons(X1,X7,X2),X2) = c_List_Oappend(c_List_Orev(X7,X2),c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
fof(f3870,plain,
spl0_314,
inference(avatar_split_clause,[],[f264,f3868]) ).
fof(f3868,plain,
( spl0_314
<=> ! [X0,X3] :
( X0 = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f264,axiom,
! [X3,X0] :
( X0 = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f3866,plain,
spl0_313,
inference(avatar_split_clause,[],[f218,f3864]) ).
fof(f3864,plain,
( spl0_313
<=> ! [X2,X7,X3] : c_List_Otl(c_List_Otake(X3,X7,X2),X2) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f218,axiom,
! [X2,X3,X7] : c_List_Otl(c_List_Otake(X3,X7,X2),X2) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__take_0) ).
fof(f3862,plain,
spl0_312,
inference(avatar_split_clause,[],[f215,f3860]) ).
fof(f3860,plain,
( spl0_312
<=> ! [X36,X2,X1,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Nat_Onat_Onat__case(X1,X36,X3,X2) = hAPP(X36,c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f215,axiom,
! [X2,X3,X36,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Nat_Onat_Onat__case(X1,X36,X3,X2) = hAPP(X36,c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_1) ).
fof(f3858,plain,
spl0_311,
inference(avatar_split_clause,[],[f199,f3856]) ).
fof(f3856,plain,
( spl0_311
<=> ! [X34,X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Otl(c_List_Oappend(X7,X34,X2),X2) = c_List_Oappend(c_List_Otl(X7,X2),X34,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f199,axiom,
! [X2,X7,X34] :
( c_List_Olist_ONil(X2) = X7
| c_List_Otl(c_List_Oappend(X7,X34,X2),X2) = c_List_Oappend(c_List_Otl(X7,X2),X34,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).
fof(f3845,plain,
spl0_310,
inference(avatar_split_clause,[],[f188,f3843]) ).
fof(f3843,plain,
( spl0_310
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f188,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X2) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
fof(f3841,plain,
spl0_309,
inference(avatar_split_clause,[],[f34,f3839]) ).
fof(f3839,plain,
( spl0_309
<=> ! [X5,X24,X29,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X29,X24,X2),X2) = c_HOL_Oplus__class_Oplus(X29,c_HOL_Oplus__class_Oplus(X5,X24,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f34,axiom,
! [X2,X29,X24,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X29,X24,X2),X2) = c_HOL_Oplus__class_Oplus(X29,c_HOL_Oplus__class_Oplus(X5,X24,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f3837,plain,
spl0_308,
inference(avatar_split_clause,[],[f33,f3835]) ).
fof(f3835,plain,
( spl0_308
<=> ! [X5,X23,X29,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X29,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X29,X2),X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f33,axiom,
! [X2,X29,X5,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X29,X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X29,X2),X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f3833,plain,
spl0_307,
inference(avatar_split_clause,[],[f31,f3831]) ).
fof(f3831,plain,
( spl0_307
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Oab__semigroup__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X29,X2) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f31,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Oab__semigroup__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X29,X2) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f3829,plain,
spl0_306,
inference(avatar_split_clause,[],[f30,f3827]) ).
fof(f3827,plain,
( spl0_306
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) = c_HOL_Oplus__class_Oplus(X23,c_HOL_Oplus__class_Oplus(X5,X29,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f30,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) = c_HOL_Oplus__class_Oplus(X23,c_HOL_Oplus__class_Oplus(X5,X29,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f3825,plain,
spl0_305,
inference(avatar_split_clause,[],[f29,f3823]) ).
fof(f3823,plain,
( spl0_305
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X29,X2) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f29,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X29,X2) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f3821,plain,
spl0_304,
inference(avatar_split_clause,[],[f28,f3819]) ).
fof(f3819,plain,
( spl0_304
<=> ! [X4,X30,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X2),X30,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f28,axiom,
! [X2,X1,X4,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,X2),X2) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X4,X2),X30,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f3817,plain,
spl0_303,
inference(avatar_split_clause,[],[f25,f3815]) ).
fof(f3815,plain,
( spl0_303
<=> ! [X4,X30,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,X2),X2) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X1,X30,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f25,axiom,
! [X2,X1,X4,X30] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,X2),X2) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X1,X30,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f3797,plain,
( spl0_302
| ~ spl0_82
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3762,f3443,f915,f3795]) ).
fof(f3795,plain,
( spl0_302
<=> ! [X2,X0,X1] : c_List_Olist__all2(c_fequal(X0),X1,X1,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f915,plain,
( spl0_82
<=> ! [X2,X1] : hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f3443,plain,
( spl0_295
<=> ! [X2,X7,X8] :
( c_List_Olist__all2(X8,X7,X7,X2,X2)
| ~ hBOOL(hAPP(hAPP(X8,c_List_Osko__List__Xlist__all2__refl__1__1(X8,X2)),c_List_Osko__List__Xlist__all2__refl__1__1(X8,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3762,plain,
( ! [X2,X0,X1] : c_List_Olist__all2(c_fequal(X0),X1,X1,X2,X2)
| ~ spl0_82
| ~ spl0_295 ),
inference(resolution,[],[f3444,f916]) ).
fof(f916,plain,
( ! [X2,X1] : hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1))
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f3444,plain,
( ! [X2,X8,X7] :
( ~ hBOOL(hAPP(hAPP(X8,c_List_Osko__List__Xlist__all2__refl__1__1(X8,X2)),c_List_Osko__List__Xlist__all2__refl__1__1(X8,X2)))
| c_List_Olist__all2(X8,X7,X7,X2,X2) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3443]) ).
fof(f3611,plain,
( spl0_301
| ~ spl0_9
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1252,f1177,f578,f3609]) ).
fof(f3609,plain,
( spl0_301
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f578,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1252,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_9
| ~ spl0_129 ),
inference(resolution,[],[f1178,f580]) ).
fof(f580,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f3465,plain,
spl0_300,
inference(avatar_split_clause,[],[f449,f3463]) ).
fof(f3463,plain,
( spl0_300
<=> ! [X44,X34,X7,X8,X2] :
( ~ c_List_Olist__all2(X8,c_List_Orev(X7,X2),X34,X2,X44)
| c_List_Olist__all2(X8,X7,c_List_Orev(X34,X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f449,axiom,
! [X2,X8,X44,X7,X34] :
( ~ c_List_Olist__all2(X8,c_List_Orev(X7,X2),X34,X2,X44)
| c_List_Olist__all2(X8,X7,c_List_Orev(X34,X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_0) ).
fof(f3461,plain,
spl0_299,
inference(avatar_split_clause,[],[f448,f3459]) ).
fof(f3459,plain,
( spl0_299
<=> ! [X44,X34,X7,X8,X2] :
( ~ c_List_Olist__all2(X8,X7,c_List_Orev(X34,X44),X2,X44)
| c_List_Olist__all2(X8,c_List_Orev(X7,X2),X34,X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f448,axiom,
! [X2,X8,X44,X7,X34] :
( ~ c_List_Olist__all2(X8,X7,c_List_Orev(X34,X44),X2,X44)
| c_List_Olist__all2(X8,c_List_Orev(X7,X2),X34,X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev1_1) ).
fof(f3457,plain,
spl0_298,
inference(avatar_split_clause,[],[f425,f3455]) ).
fof(f3455,plain,
( spl0_298
<=> ! [X44,X34,X7,X8,X2] :
( c_List_Olist__all2(X8,X7,X34,X2,X44)
| ~ c_List_Olist__all2(X8,c_List_Orev(X7,X2),c_List_Orev(X34,X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f425,axiom,
! [X2,X8,X44,X7,X34] :
( c_List_Olist__all2(X8,X7,X34,X2,X44)
| ~ c_List_Olist__all2(X8,c_List_Orev(X7,X2),c_List_Orev(X34,X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_0) ).
fof(f3453,plain,
( spl0_297
| ~ spl0_41
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1236,f1161,f738,f3451]) ).
fof(f3451,plain,
( spl0_297
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f738,plain,
( spl0_41
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1161,plain,
( spl0_125
<=> ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1236,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X0,tc_Int_Oint)
| ~ spl0_41
| ~ spl0_125 ),
inference(resolution,[],[f1162,f740]) ).
fof(f740,plain,
( class_OrderedGroup_Omonoid__mult(tc_Int_Oint)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f1162,plain,
( ! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X2),X3,X2) )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1161]) ).
fof(f3449,plain,
spl0_296,
inference(avatar_split_clause,[],[f424,f3447]) ).
fof(f3447,plain,
( spl0_296
<=> ! [X44,X34,X7,X8,X2] :
( ~ c_List_Olist__all2(X8,X7,X34,X2,X44)
| c_List_Olist__all2(X8,c_List_Orev(X7,X2),c_List_Orev(X34,X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f424,axiom,
! [X2,X8,X44,X7,X34] :
( ~ c_List_Olist__all2(X8,X7,X34,X2,X44)
| c_List_Olist__all2(X8,c_List_Orev(X7,X2),c_List_Orev(X34,X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__rev_1) ).
fof(f3445,plain,
spl0_295,
inference(avatar_split_clause,[],[f405,f3443]) ).
fof(f405,axiom,
! [X2,X8,X7] :
( c_List_Olist__all2(X8,X7,X7,X2,X2)
| ~ hBOOL(hAPP(hAPP(X8,c_List_Osko__List__Xlist__all2__refl__1__1(X8,X2)),c_List_Osko__List__Xlist__all2__refl__1__1(X8,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__refl_0) ).
fof(f3441,plain,
spl0_294,
inference(avatar_split_clause,[],[f372,f3439]) ).
fof(f3439,plain,
( spl0_294
<=> ! [X2,X1,X7] :
( c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = X7
| c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) != c_List_Orev(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f372,axiom,
! [X2,X1,X7] :
( c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = X7
| c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) != c_List_Orev(X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
fof(f3437,plain,
spl0_293,
inference(avatar_split_clause,[],[f210,f3435]) ).
fof(f3435,plain,
( spl0_293
<=> ! [X34,X7,X2,X1] : hAPP(c_List_Onth(c_List_Oappend(X7,c_List_Olist_OCons(X1,X34,X2),X2),X2),c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f210,axiom,
! [X2,X1,X7,X34] : hAPP(c_List_Onth(c_List_Oappend(X7,c_List_Olist_OCons(X1,X34,X2),X2),X2),c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append__length_0) ).
fof(f3433,plain,
spl0_292,
inference(avatar_split_clause,[],[f202,f3431]) ).
fof(f3431,plain,
( spl0_292
<=> ! [X4,X34,X7,X3,X2] :
( hAPP(c_List_Onth(X7,X2),X3) = X4
| c_List_Odrop(X3,X7,X2) != c_List_Olist_OCons(X4,X34,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f202,axiom,
! [X2,X3,X7,X4,X34] :
( hAPP(c_List_Onth(X7,X2),X3) = X4
| c_List_Odrop(X3,X7,X2) != c_List_Olist_OCons(X4,X34,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).
fof(f3429,plain,
spl0_291,
inference(avatar_split_clause,[],[f171,f3427]) ).
fof(f3427,plain,
( spl0_291
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X2) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f171,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X2) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f3425,plain,
spl0_290,
inference(avatar_split_clause,[],[f154,f3423]) ).
fof(f3423,plain,
( spl0_290
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X29,X5,X2),c_HOL_Oplus__class_Oplus(X29,X23,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f154,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X29,X5,X2),c_HOL_Oplus__class_Oplus(X29,X23,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f3421,plain,
spl0_289,
inference(avatar_split_clause,[],[f153,f3419]) ).
fof(f3419,plain,
( spl0_289
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f153,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f3417,plain,
spl0_288,
inference(avatar_split_clause,[],[f152,f3415]) ).
fof(f3415,plain,
( spl0_288
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X5,X23,X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X29,X5,X2),c_HOL_Oplus__class_Oplus(X29,X23,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f152,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X5,X23,X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X29,X5,X2),c_HOL_Oplus__class_Oplus(X29,X23,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f3413,plain,
spl0_287,
inference(avatar_split_clause,[],[f151,f3411]) ).
fof(f3411,plain,
( spl0_287
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X29,X5,X2),c_HOL_Oplus__class_Oplus(X29,X23,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f151,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X29,X5,X2),c_HOL_Oplus__class_Oplus(X29,X23,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f3409,plain,
( spl0_286
| ~ spl0_16
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1235,f1161,f613,f3407]) ).
fof(f3407,plain,
( spl0_286
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f613,plain,
( spl0_16
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1235,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_16
| ~ spl0_125 ),
inference(resolution,[],[f1162,f615]) ).
fof(f615,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f3405,plain,
spl0_285,
inference(avatar_split_clause,[],[f150,f3403]) ).
fof(f3403,plain,
( spl0_285
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X5,X23,X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f150,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| c_lessequals(X5,X23,X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f3401,plain,
spl0_284,
inference(avatar_split_clause,[],[f149,f3399]) ).
fof(f3399,plain,
( spl0_284
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f149,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X29,X2),c_HOL_Oplus__class_Oplus(X23,X29,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f3397,plain,
spl0_283,
inference(avatar_split_clause,[],[f80,f3395]) ).
fof(f3395,plain,
( spl0_283
<=> ! [X2,X4,X0,X3,X1] :
( X1 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Oreplicate(X0,X1,X2) != c_List_Oreplicate(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f80,axiom,
! [X2,X3,X0,X1,X4] :
( X1 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_List_Oreplicate(X0,X1,X2) != c_List_Oreplicate(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
fof(f3393,plain,
spl0_282,
inference(avatar_split_clause,[],[f72,f3391]) ).
fof(f3391,plain,
( spl0_282
<=> ! [X7,X3,X2,X1] : hAPP(c_List_Onth(c_List_Olist_OCons(X1,X7,X2),X2),X3) = c_Nat_Onat_Onat__case(X1,c_List_Onth(X7,X2),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f72,axiom,
! [X2,X3,X1,X7] : hAPP(c_List_Onth(c_List_Olist_OCons(X1,X7,X2),X2),X3) = c_Nat_Onat_Onat__case(X1,c_List_Onth(X7,X2),X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth_Osimps_0) ).
fof(f3389,plain,
spl0_281,
inference(avatar_split_clause,[],[f64,f3387]) ).
fof(f3387,plain,
( spl0_281
<=> ! [X4,X30,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| X4 = X30
| c_HOL_Oplus__class_Oplus(X1,X30,X2) != c_HOL_Oplus__class_Oplus(X1,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f64,axiom,
! [X2,X1,X4,X30] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| X4 = X30
| c_HOL_Oplus__class_Oplus(X1,X30,X2) != c_HOL_Oplus__class_Oplus(X1,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f3385,plain,
spl0_280,
inference(avatar_split_clause,[],[f36,f3383]) ).
fof(f3383,plain,
( spl0_280
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f36,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| ~ class_Ring__and__Field_Omult__zero(X2)
| ~ class_Ring__and__Field_Ozero__neq__one(X2)
| ~ class_Power_Opower(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f2650,plain,
spl0_279,
inference(avatar_split_clause,[],[f524,f2648]) ).
fof(f2648,plain,
( spl0_279
<=> ! [X34,X2,X4] : c_List_Olist_OCons(X4,X34,X2) = c_List_Orev(c_List_Orotate1(c_List_Olist_OCons(X4,c_List_Orev(X34,X2),X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f524,plain,
! [X2,X4,X34] : c_List_Olist_OCons(X4,X34,X2) = c_List_Orev(c_List_Orotate1(c_List_Olist_OCons(X4,c_List_Orev(X34,X2),X2),X2),X2),
inference(forward_demodulation,[],[f338,f207]) ).
fof(f207,axiom,
! [X1,X44,X7] : c_List_Orotate1(c_List_Olist_OCons(X1,X7,X44),X44) = c_List_Oappend(X7,c_List_Olist_OCons(X1,c_List_Olist_ONil(X44),X44),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
fof(f338,axiom,
! [X2,X4,X34] : c_List_Olist_OCons(X4,X34,X2) = c_List_Orev(c_List_Oappend(c_List_Orev(X34,X2),c_List_Olist_OCons(X4,c_List_Olist_ONil(X2),X2),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
fof(f2646,plain,
spl0_278,
inference(avatar_split_clause,[],[f523,f2644]) ).
fof(f2644,plain,
( spl0_278
<=> ! [X25,X27,X26] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X27,tc_nat),X26,tc_nat) = c_HOL_Ominus__class_Ominus(X25,c_HOL_Oplus__class_Oplus(X26,X27,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f523,plain,
! [X26,X27,X25] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X27,tc_nat),X26,tc_nat) = c_HOL_Ominus__class_Ominus(X25,c_HOL_Oplus__class_Oplus(X26,X27,tc_nat),tc_nat),
inference(forward_demodulation,[],[f299,f47]) ).
fof(f47,axiom,
! [X26,X27,X25] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X27,tc_nat),X26,tc_nat) = c_HOL_Ominus__class_Ominus(X25,c_HOL_Oplus__class_Oplus(X27,X26,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f299,axiom,
! [X26,X27,X25] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X27,tc_nat),X26,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X26,tc_nat),X27,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f2642,plain,
spl0_277,
inference(avatar_split_clause,[],[f438,f2640]) ).
fof(f2640,plain,
( spl0_277
<=> ! [X10,X13,X8,X63,X9,X16] :
( ~ c_Objects_Ohext(X9,X63)
| ~ c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16)
| c_WellTypeRT_OWTrts(X8,X63,X10,X13,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f438,axiom,
! [X10,X8,X9,X16,X63,X13] :
( ~ c_Objects_Ohext(X9,X63)
| ~ c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16)
| c_WellTypeRT_OWTrts(X8,X63,X10,X13,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrts__hext__mono_0) ).
fof(f2638,plain,
spl0_276,
inference(avatar_split_clause,[],[f416,f2636]) ).
fof(f2636,plain,
( spl0_276
<=> ! [X44,X34,X7,X8,X2] :
( ~ c_List_Olist__all2(X8,X7,X34,X2,X44)
| c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X34,tc_List_Olist(X44)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f416,axiom,
! [X2,X8,X44,X7,X34] :
( ~ c_List_Olist__all2(X8,X7,X34,X2,X44)
| c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X34,tc_List_Olist(X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__def_0) ).
fof(f2634,plain,
spl0_275,
inference(avatar_split_clause,[],[f403,f2632]) ).
fof(f2632,plain,
( spl0_275
<=> ! [X7,X67,X2,X1] : c_List_Oappend(X7,c_List_Oappend(X1,X67,X2),X2) = c_List_Oappend(c_List_Oappend(X7,X1,X2),X67,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f403,axiom,
! [X2,X1,X7,X67] : c_List_Oappend(X7,c_List_Oappend(X1,X67,X2),X2) = c_List_Oappend(c_List_Oappend(X7,X1,X2),X67,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
fof(f2630,plain,
spl0_274,
inference(avatar_split_clause,[],[f348,f2628]) ).
fof(f2628,plain,
( spl0_274
<=> ! [X10,X11,X14,X63,X9,X8] :
( ~ c_Objects_Ohext(X9,X63)
| ~ c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14)
| c_WellTypeRT_OWTrt(X8,X63,X10,X11,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f348,axiom,
! [X10,X11,X8,X9,X14,X63] :
( ~ c_Objects_Ohext(X9,X63)
| ~ c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14)
| c_WellTypeRT_OWTrt(X8,X63,X10,X11,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTrt__hext__mono_0) ).
fof(f2626,plain,
spl0_273,
inference(avatar_split_clause,[],[f343,f2624]) ).
fof(f2624,plain,
( spl0_273
<=> ! [X35,X50,X2,X1] : c_List_Olist_OCons(X1,c_List_Oappend(X50,X35,X2),X2) = c_List_Oappend(c_List_Olist_OCons(X1,X50,X2),X35,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f343,axiom,
! [X50,X2,X1,X35] : c_List_Olist_OCons(X1,c_List_Oappend(X50,X35,X2),X2) = c_List_Oappend(c_List_Olist_OCons(X1,X50,X2),X35,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
fof(f2621,plain,
spl0_272,
inference(avatar_split_clause,[],[f328,f2619]) ).
fof(f2619,plain,
( spl0_272
<=> ! [X34,X2,X7] : c_List_Orev(c_List_Oappend(X7,X34,X2),X2) = c_List_Oappend(c_List_Orev(X34,X2),c_List_Orev(X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f328,axiom,
! [X2,X7,X34] : c_List_Orev(c_List_Oappend(X7,X34,X2),X2) = c_List_Oappend(c_List_Orev(X34,X2),c_List_Orev(X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
fof(f2617,plain,
spl0_271,
inference(avatar_split_clause,[],[f237,f2615]) ).
fof(f2615,plain,
( spl0_271
<=> ! [X2,X7,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Otake(X3,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f237,axiom,
! [X2,X3,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Otake(X3,X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
fof(f2613,plain,
spl0_270,
inference(avatar_split_clause,[],[f232,f2611]) ).
fof(f2611,plain,
( spl0_270
<=> ! [X2,X7,X3] : c_Nat_Osize__class_Osize(c_List_Odrop(X3,X7,X2),tc_List_Olist(X2)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f232,axiom,
! [X2,X3,X7] : c_Nat_Osize__class_Osize(c_List_Odrop(X3,X7,X2),tc_List_Olist(X2)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__drop_0) ).
fof(f2609,plain,
spl0_269,
inference(avatar_split_clause,[],[f216,f2607]) ).
fof(f2607,plain,
( spl0_269
<=> ! [X2,X7] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otl(X7,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f216,axiom,
! [X2,X7] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otl(X7,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__tl_0) ).
fof(f2605,plain,
spl0_268,
inference(avatar_split_clause,[],[f207,f2603]) ).
fof(f2603,plain,
( spl0_268
<=> ! [X44,X1,X7] : c_List_Orotate1(c_List_Olist_OCons(X1,X7,X44),X44) = c_List_Oappend(X7,c_List_Olist_OCons(X1,c_List_Olist_ONil(X44),X44),X44) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2601,plain,
spl0_267,
inference(avatar_split_clause,[],[f190,f2599]) ).
fof(f2599,plain,
( spl0_267
<=> ! [X4,X7,X25,X2,X1] : c_List_Olist__update(c_List_Olist__update(X7,X25,X1,X2),X25,X4,X2) = c_List_Olist__update(X7,X25,X4,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f190,axiom,
! [X2,X1,X7,X4,X25] : c_List_Olist__update(c_List_Olist__update(X7,X25,X1,X2),X25,X4,X2) = c_List_Olist__update(X7,X25,X4,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
fof(f2597,plain,
spl0_266,
inference(avatar_split_clause,[],[f179,f2595]) ).
fof(f2595,plain,
( spl0_266
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X5,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f179,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X2),X2)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X5,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f2593,plain,
spl0_265,
inference(avatar_split_clause,[],[f178,f2591]) ).
fof(f2591,plain,
( spl0_265
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X5,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f178,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X2),X2)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X5,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f2589,plain,
spl0_264,
inference(avatar_split_clause,[],[f164,f2587]) ).
fof(f2587,plain,
( spl0_264
<=> ! [X0,X3,X2,X7] : c_List_Odrop(X3,c_List_Odrop(X0,X7,X2),X2) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X7,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f164,axiom,
! [X2,X3,X0,X7] : c_List_Odrop(X3,c_List_Odrop(X0,X7,X2),X2) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X7,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__drop_0) ).
fof(f2585,plain,
spl0_263,
inference(avatar_split_clause,[],[f97,f2583]) ).
fof(f2583,plain,
( spl0_263
<=> ! [X0,X3,X2,X7] : c_List_Orotate(X0,c_List_Orotate(X3,X7,X2),X2) = c_List_Orotate(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X7,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f97,axiom,
! [X2,X3,X0,X7] : c_List_Orotate(X0,c_List_Orotate(X3,X7,X2),X2) = c_List_Orotate(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X7,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__rotate_0) ).
fof(f2571,plain,
spl0_262,
inference(avatar_split_clause,[],[f74,f2569]) ).
fof(f2569,plain,
( spl0_262
<=> ! [X26,X25,X2,X1] : c_List_Odrop(X25,c_List_Oreplicate(X26,X1,X2),X2) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X26,X25,tc_nat),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f74,axiom,
! [X2,X1,X26,X25] : c_List_Odrop(X25,c_List_Oreplicate(X26,X1,X2),X2) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X26,X25,tc_nat),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
fof(f2567,plain,
spl0_261,
inference(avatar_split_clause,[],[f54,f2565]) ).
fof(f2565,plain,
( spl0_261
<=> ! [X0,X3,X26] : c_HOL_Ominus__class_Ominus(X0,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X26,X0,tc_nat),c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f54,axiom,
! [X3,X0,X26] : c_HOL_Ominus__class_Ominus(X0,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X26,X0,tc_nat),c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f2563,plain,
spl0_260,
inference(avatar_split_clause,[],[f53,f2561]) ).
fof(f2561,plain,
( spl0_260
<=> ! [X0,X3,X26] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X26,tc_nat),c_HOL_Oplus__class_Oplus(X3,X26,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f53,axiom,
! [X3,X0,X26] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X26,tc_nat),c_HOL_Oplus__class_Oplus(X3,X26,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f2559,plain,
spl0_259,
inference(avatar_split_clause,[],[f47,f2557]) ).
fof(f2557,plain,
( spl0_259
<=> ! [X25,X27,X26] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X25,X27,tc_nat),X26,tc_nat) = c_HOL_Ominus__class_Ominus(X25,c_HOL_Oplus__class_Oplus(X27,X26,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2555,plain,
spl0_258,
inference(avatar_split_clause,[],[f27,f2553]) ).
fof(f2553,plain,
( spl0_258
<=> ! [X0,X3,X26] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X26,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X3,X26,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f27,axiom,
! [X3,X0,X26] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X26,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X3,X26,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f2551,plain,
spl0_257,
inference(avatar_split_clause,[],[f26,f2549]) ).
fof(f2549,plain,
( spl0_257
<=> ! [X4,X1,X30] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X1,X30,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f26,axiom,
! [X1,X4,X30] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X4,X30,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X1,X30,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f2547,plain,
spl0_256,
inference(avatar_split_clause,[],[f12,f2545]) ).
fof(f2545,plain,
( spl0_256
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X5,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f12,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X5,X5,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f2543,plain,
spl0_255,
inference(avatar_split_clause,[],[f11,f2541]) ).
fof(f2541,plain,
( spl0_255
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X5,X5,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f11,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oplus__class_Oplus(X5,X5,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f2539,plain,
spl0_254,
inference(avatar_split_clause,[],[f4,f2537]) ).
fof(f2537,plain,
( spl0_254
<=> ! [X2,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X5,X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X5,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f4,axiom,
! [X2,X3,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),X5,X2)
| c_lessequals(c_HOL_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X5,X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f2535,plain,
spl0_253,
inference(avatar_split_clause,[],[f2,f2533]) ).
fof(f2533,plain,
( spl0_253
<=> ! [X2,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X5,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2,axiom,
! [X2,X3,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X2),X5,X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X5,X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f2084,plain,
spl0_252,
inference(avatar_split_clause,[],[f422,f2081]) ).
fof(f2081,plain,
( spl0_252
<=> c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_Us____,v_Ts____,tc_Type_Oty,tc_Type_Oty) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f422,axiom,
c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),v_Us____,v_Ts____,tc_Type_Oty,tc_Type_Oty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_I4_J_0) ).
fof(f2079,plain,
spl0_251,
inference(avatar_split_clause,[],[f394,f2077]) ).
fof(f2077,plain,
( spl0_251
<=> ! [X5,X44,X23,X61,X2,X66] :
( X23 = X66
| c_Pair(X5,X23,X2,X44) != c_Pair(X61,X66,X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f394,axiom,
! [X2,X44,X66,X5,X23,X61] :
( X23 = X66
| c_Pair(X5,X23,X2,X44) != c_Pair(X61,X66,X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
fof(f2075,plain,
spl0_250,
inference(avatar_split_clause,[],[f393,f2073]) ).
fof(f2073,plain,
( spl0_250
<=> ! [X61,X23,X44,X5,X2,X66] :
( X5 = X61
| c_Pair(X5,X23,X2,X44) != c_Pair(X61,X66,X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f393,axiom,
! [X2,X44,X5,X66,X61,X23] :
( X5 = X61
| c_Pair(X5,X23,X2,X44) != c_Pair(X61,X66,X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
fof(f2071,plain,
spl0_249,
inference(avatar_split_clause,[],[f313,f2069]) ).
fof(f2069,plain,
( spl0_249
<=> ! [X2,X7,X3] :
( c_List_Odrop(X3,X7,X2) != c_List_Olist_ONil(X2)
| c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f313,axiom,
! [X2,X3,X7] :
( c_List_Odrop(X3,X7,X2) != c_List_Olist_ONil(X2)
| c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
fof(f2067,plain,
spl0_248,
inference(avatar_split_clause,[],[f312,f2065]) ).
fof(f2065,plain,
( spl0_248
<=> ! [X2,X7,X3] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat)
| c_List_Odrop(X3,X7,X2) = c_List_Olist_ONil(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f312,axiom,
! [X2,X3,X7] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat)
| c_List_Odrop(X3,X7,X2) = c_List_Olist_ONil(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__all_0) ).
fof(f2063,plain,
spl0_247,
inference(avatar_split_clause,[],[f311,f2060]) ).
fof(f2060,plain,
( spl0_247
<=> c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OCall(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_M____,v_esa____,tc_List_Olist(tc_String_Ochar)),v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f311,axiom,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OCall(c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),v_M____,v_esa____,tc_List_Olist(tc_String_Ochar)),v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt_0) ).
fof(f2058,plain,
( spl0_246
| ~ spl0_43
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1152,f1077,f748,f2056]) ).
fof(f2056,plain,
( spl0_246
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f748,plain,
( spl0_43
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1077,plain,
( spl0_119
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X1,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1152,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
| ~ spl0_43
| ~ spl0_119 ),
inference(resolution,[],[f1078,f750]) ).
fof(f750,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f1078,plain,
( ! [X2,X1] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X1,X1,X2) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f2054,plain,
spl0_245,
inference(avatar_split_clause,[],[f305,f2052]) ).
fof(f2052,plain,
( spl0_245
<=> ! [X2,X1,X7] : c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f305,axiom,
! [X2,X1,X7] : c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
fof(f2050,plain,
spl0_244,
inference(avatar_split_clause,[],[f295,f2048]) ).
fof(f295,axiom,
! [X2,X1,X4] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| X1 = X4
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X1,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f2046,plain,
spl0_243,
inference(avatar_split_clause,[],[f291,f2044]) ).
fof(f2044,plain,
( spl0_243
<=> ! [X48,X51,X53,X47,X49,X2,X52] :
( X49 = X53
| c_Expr_Oexp_OCall(X47,X48,X49,X2) != c_Expr_Oexp_OCall(X51,X52,X53,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f291,axiom,
! [X2,X51,X48,X49,X47,X52,X53] :
( X49 = X53
| c_Expr_Oexp_OCall(X47,X48,X49,X2) != c_Expr_Oexp_OCall(X51,X52,X53,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_2) ).
fof(f2042,plain,
spl0_242,
inference(avatar_split_clause,[],[f290,f2040]) ).
fof(f2040,plain,
( spl0_242
<=> ! [X2,X48,X51,X53,X49,X52,X47] :
( X48 = X52
| c_Expr_Oexp_OCall(X47,X48,X49,X2) != c_Expr_Oexp_OCall(X51,X52,X53,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f290,axiom,
! [X2,X51,X48,X49,X47,X52,X53] :
( X48 = X52
| c_Expr_Oexp_OCall(X47,X48,X49,X2) != c_Expr_Oexp_OCall(X51,X52,X53,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_1) ).
fof(f2038,plain,
spl0_241,
inference(avatar_split_clause,[],[f289,f2036]) ).
fof(f2036,plain,
( spl0_241
<=> ! [X52,X48,X51,X53,X49,X2,X47] :
( X47 = X51
| c_Expr_Oexp_OCall(X47,X48,X49,X2) != c_Expr_Oexp_OCall(X51,X52,X53,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f289,axiom,
! [X2,X51,X48,X49,X47,X52,X53] :
( X47 = X51
| c_Expr_Oexp_OCall(X47,X48,X49,X2) != c_Expr_Oexp_OCall(X51,X52,X53,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I9_J_0) ).
fof(f2034,plain,
spl0_240,
inference(avatar_split_clause,[],[f285,f2032]) ).
fof(f2032,plain,
( spl0_240
<=> ! [X4,X50,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X4 = X50
| c_HOL_Ominus__class_Ominus(X1,X1,X2) != c_HOL_Ominus__class_Ominus(X50,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f285,axiom,
! [X50,X2,X1,X4] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X4 = X50
| c_HOL_Ominus__class_Ominus(X1,X1,X2) != c_HOL_Ominus__class_Ominus(X50,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
fof(f2030,plain,
spl0_239,
inference(avatar_split_clause,[],[f282,f2028]) ).
fof(f2028,plain,
( spl0_239
<=> ! [X0,X28,X3] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X28,tc_nat),c_HOL_Ominus__class_Ominus(X3,X28,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f282,axiom,
! [X3,X28,X0] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X28,tc_nat),c_HOL_Ominus__class_Ominus(X3,X28,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f2026,plain,
spl0_238,
inference(avatar_split_clause,[],[f281,f2024]) ).
fof(f2024,plain,
( spl0_238
<=> ! [X0,X28,X3] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X28,X3,tc_nat),c_HOL_Ominus__class_Ominus(X28,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f281,axiom,
! [X3,X28,X0] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X28,X3,tc_nat),c_HOL_Ominus__class_Ominus(X28,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f2022,plain,
spl0_237,
inference(avatar_split_clause,[],[f260,f2020]) ).
fof(f2020,plain,
( spl0_237
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X5,X23,X2)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X23,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f260,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| c_lessequals(X5,X23,X2)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X23,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f2018,plain,
spl0_236,
inference(avatar_split_clause,[],[f259,f2016]) ).
fof(f2016,plain,
( spl0_236
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X23,X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f259,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X5,X23,X2)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X23,X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f2013,plain,
spl0_235,
inference(avatar_split_clause,[],[f257,f2011]) ).
fof(f2011,plain,
( spl0_235
<=> ! [X4,X30,X2,X1] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X4,X1,X2)
| ~ c_lessequals(X30,X4,X2)
| c_lessequals(X30,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f257,axiom,
! [X2,X1,X4,X30] :
( ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X4,X1,X2)
| ~ c_lessequals(X30,X4,X2)
| c_lessequals(X30,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2009,plain,
spl0_234,
inference(avatar_split_clause,[],[f256,f2007]) ).
fof(f2007,plain,
( spl0_234
<=> ! [X4,X30,X2,X1] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X1,X4,X2)
| ~ c_lessequals(X4,X30,X2)
| c_lessequals(X1,X30,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f256,axiom,
! [X2,X1,X4,X30] :
( ~ class_Orderings_Opreorder(X2)
| ~ c_lessequals(X1,X4,X2)
| ~ c_lessequals(X4,X30,X2)
| c_lessequals(X1,X30,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2005,plain,
spl0_233,
inference(avatar_split_clause,[],[f214,f2003]) ).
fof(f2003,plain,
( spl0_233
<=> ! [X2,X7,X3] :
( c_List_Orotate(X3,X7,X2) = X7
| ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f214,axiom,
! [X2,X3,X7] :
( c_List_Orotate(X3,X7,X2) = X7
| ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__length01_0) ).
fof(f2001,plain,
spl0_232,
inference(avatar_split_clause,[],[f158,f1999]) ).
fof(f1999,plain,
( spl0_232
<=> ! [X2,X7,X25,X1] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X25,tc_nat)
| c_List_Olist__update(X7,X25,X1,X2) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f158,axiom,
! [X2,X1,X7,X25] :
( ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X25,tc_nat)
| c_List_Olist__update(X7,X25,X1,X2) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
fof(f1997,plain,
spl0_231,
inference(avatar_split_clause,[],[f157,f1995]) ).
fof(f1995,plain,
( spl0_231
<=> ! [X0,X3,X26] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X26,X0,tc_nat),c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f157,axiom,
! [X3,X0,X26] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X26,X0,tc_nat),c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
fof(f1993,plain,
spl0_230,
inference(avatar_split_clause,[],[f156,f1991]) ).
fof(f1991,plain,
( spl0_230
<=> ! [X0,X3,X26] :
( c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X26,X0,tc_nat),c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f156,axiom,
! [X3,X0,X26] :
( c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X26,X0,tc_nat),c_HOL_Oplus__class_Oplus(X26,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
fof(f1989,plain,
spl0_229,
inference(avatar_split_clause,[],[f155,f1987]) ).
fof(f1987,plain,
( spl0_229
<=> ! [X25,X27,X26] :
( ~ c_lessequals(X25,X27,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),c_HOL_Oplus__class_Oplus(X27,X26,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f155,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(X25,X27,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),c_HOL_Oplus__class_Oplus(X27,X26,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
fof(f1985,plain,
spl0_228,
inference(avatar_split_clause,[],[f130,f1983]) ).
fof(f1983,plain,
( spl0_228
<=> ! [X25,X27,X26] :
( ~ c_lessequals(X27,c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f130,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(X27,c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X25,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
fof(f1981,plain,
spl0_227,
inference(avatar_split_clause,[],[f129,f1979]) ).
fof(f1979,plain,
( spl0_227
<=> ! [X25,X27,X26] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X25,tc_nat)
| c_lessequals(X27,c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f129,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X27,X26,tc_nat),X25,tc_nat)
| c_lessequals(X27,c_HOL_Oplus__class_Oplus(X25,X26,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
fof(f1977,plain,
spl0_226,
inference(avatar_split_clause,[],[f117,f1975]) ).
fof(f1975,plain,
( spl0_226
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Oplus__class_Oplus(X1,X5,X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f117,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Oplus__class_Oplus(X1,X5,X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f1973,plain,
( spl0_225
| ~ spl0_62
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1757,f1625,f834,f1970]) ).
fof(f1970,plain,
( spl0_225
<=> c_Progress_OWTrts_H(v_P,v_ha____,v_E____,v_esa____,v_Us____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f834,plain,
( spl0_62
<=> c_WellTypeRT_OWTrts(v_P,v_ha____,v_E____,v_esa____,v_Us____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1625,plain,
( spl0_199
<=> ! [X10,X13,X8,X9,X16] :
( ~ c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16)
| c_Progress_OWTrts_H(X8,X9,X10,X13,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1757,plain,
( c_Progress_OWTrts_H(v_P,v_ha____,v_E____,v_esa____,v_Us____)
| ~ spl0_62
| ~ spl0_199 ),
inference(resolution,[],[f1626,f836]) ).
fof(f836,plain,
( c_WellTypeRT_OWTrts(v_P,v_ha____,v_E____,v_esa____,v_Us____)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f834]) ).
fof(f1626,plain,
( ! [X10,X8,X9,X16,X13] :
( ~ c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16)
| c_Progress_OWTrts_H(X8,X9,X10,X13,X16) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1625]) ).
fof(f1968,plain,
spl0_224,
inference(avatar_split_clause,[],[f77,f1966]) ).
fof(f1966,plain,
( spl0_224
<=> ! [X2,X1,X7,X4] : c_List_Olist__update(c_List_Olist_OCons(X1,X7,X2),c_HOL_Ozero__class_Ozero(tc_nat),X4,X2) = c_List_Olist_OCons(X4,X7,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f77,axiom,
! [X2,X1,X7,X4] : c_List_Olist__update(c_List_Olist_OCons(X1,X7,X2),c_HOL_Ozero__class_Ozero(tc_nat),X4,X2) = c_List_Olist_OCons(X4,X7,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
fof(f1964,plain,
spl0_223,
inference(avatar_split_clause,[],[f68,f1962]) ).
fof(f1962,plain,
( spl0_223
<=> ! [X0,X3,X26] :
( ~ c_lessequals(X26,X3,tc_nat)
| c_lessequals(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X26,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f68,axiom,
! [X3,X0,X26] :
( ~ c_lessequals(X26,X3,tc_nat)
| c_lessequals(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X26,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
fof(f1960,plain,
spl0_222,
inference(avatar_split_clause,[],[f67,f1958]) ).
fof(f1958,plain,
( spl0_222
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X23 = X29
| c_HOL_Oplus__class_Oplus(X23,X5,X2) != c_HOL_Oplus__class_Oplus(X29,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f67,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X23 = X29
| c_HOL_Oplus__class_Oplus(X23,X5,X2) != c_HOL_Oplus__class_Oplus(X29,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f1956,plain,
spl0_221,
inference(avatar_split_clause,[],[f66,f1954]) ).
fof(f1954,plain,
( spl0_221
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X23 = X29
| c_HOL_Oplus__class_Oplus(X5,X29,X2) != c_HOL_Oplus__class_Oplus(X5,X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f66,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X2)
| X23 = X29
| c_HOL_Oplus__class_Oplus(X5,X29,X2) != c_HOL_Oplus__class_Oplus(X5,X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f1952,plain,
spl0_220,
inference(avatar_split_clause,[],[f65,f1950]) ).
fof(f1950,plain,
( spl0_220
<=> ! [X5,X23,X29,X2] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2)
| X23 = X29
| c_HOL_Oplus__class_Oplus(X5,X29,X2) != c_HOL_Oplus__class_Oplus(X5,X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f65,axiom,
! [X2,X29,X5,X23] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2)
| X23 = X29
| c_HOL_Oplus__class_Oplus(X5,X29,X2) != c_HOL_Oplus__class_Oplus(X5,X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f1948,plain,
spl0_219,
inference(avatar_split_clause,[],[f50,f1946]) ).
fof(f1946,plain,
( spl0_219
<=> ! [X2,X1,X4] :
( ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2)
| X1 = X4
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f50,axiom,
! [X2,X1,X4] :
( ~ class_Int_Oring__char__0(X2)
| ~ class_Int_Onumber__ring(X2)
| X1 = X4
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f1944,plain,
spl0_218,
inference(avatar_split_clause,[],[f7,f1942]) ).
fof(f1942,plain,
( spl0_218
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f7,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(X0,X3,tc_nat)
| c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
fof(f1940,plain,
spl0_217,
inference(avatar_split_clause,[],[f6,f1938]) ).
fof(f1938,plain,
( spl0_217
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f6,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X0,X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
fof(f1812,plain,
( ~ spl0_216
| spl0_203
| ~ spl0_92
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1696,f1593,f962,f1717,f1809]) ).
fof(f1809,plain,
( spl0_216
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1593,plain,
( spl0_191
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X5 = X23
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X5,X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1696,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_92
| ~ spl0_191 ),
inference(trivial_inequality_removal,[],[f1693]) ).
fof(f1693,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_92
| ~ spl0_191 ),
inference(superposition,[],[f1594,f963]) ).
fof(f1594,plain,
( ! [X2,X5,X23] :
( c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X5,X23,X2)
| X5 = X23
| ~ class_OrderedGroup_Oab__group__add(X2) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1593]) ).
fof(f1807,plain,
spl0_215,
inference(avatar_split_clause,[],[f331,f1805]) ).
fof(f1805,plain,
( spl0_215
<=> ! [X2,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f331,axiom,
! [X2,X1] : c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2) = c_List_Orev(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
fof(f1803,plain,
spl0_214,
inference(avatar_split_clause,[],[f303,f1801]) ).
fof(f1801,plain,
( spl0_214
<=> ! [X25,X3] :
( ~ c_lessequals(X25,X3,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X3,X25,tc_nat),tc_nat) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f303,axiom,
! [X3,X25] :
( ~ c_lessequals(X25,X3,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X3,X25,tc_nat),tc_nat) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f1799,plain,
spl0_213,
inference(avatar_split_clause,[],[f263,f1797]) ).
fof(f1797,plain,
( spl0_213
<=> ! [X2,X1,X4] :
( ~ class_Orderings_Oorder(X2)
| X1 = X4
| ~ c_lessequals(X1,X4,X2)
| ~ c_lessequals(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f263,axiom,
! [X2,X1,X4] :
( ~ class_Orderings_Oorder(X2)
| X1 = X4
| ~ c_lessequals(X1,X4,X2)
| ~ c_lessequals(X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f1795,plain,
spl0_212,
inference(avatar_split_clause,[],[f244,f1793]) ).
fof(f1793,plain,
( spl0_212
<=> ! [X34,X2,X1] : ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X34,X2),tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X34,tc_List_Olist(X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f244,axiom,
! [X2,X1,X34] : ~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X34,X2),tc_List_Olist(X2)),c_Nat_Osize__class_Osize(X34,tc_List_Olist(X2)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
fof(f1791,plain,
spl0_211,
inference(avatar_split_clause,[],[f233,f1789]) ).
fof(f1789,plain,
( spl0_211
<=> ! [X2,X7,X3] :
( c_List_Otake(X3,X7,X2) = X7
| ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f233,axiom,
! [X2,X3,X7] :
( c_List_Otake(X3,X7,X2) = X7
| ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__all_0) ).
fof(f1787,plain,
spl0_210,
inference(avatar_split_clause,[],[f213,f1785]) ).
fof(f1785,plain,
( spl0_210
<=> ! [X2,X7] :
( c_List_Orotate1(X7,X2) = X7
| ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f213,axiom,
! [X2,X7] :
( c_List_Orotate1(X7,X2) = X7
| ~ c_lessequals(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__length01_0) ).
fof(f1783,plain,
spl0_209,
inference(avatar_split_clause,[],[f189,f1781]) ).
fof(f1781,plain,
( spl0_209
<=> ! [X2,X7,X3] : c_List_Orotate1(c_List_Orotate(X3,X7,X2),X2) = c_List_Orotate(X3,c_List_Orotate1(X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f189,axiom,
! [X2,X3,X7] : c_List_Orotate1(c_List_Orotate(X3,X7,X2),X2) = c_List_Orotate(X3,c_List_Orotate1(X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__rotate__swap_0) ).
fof(f1779,plain,
spl0_208,
inference(avatar_split_clause,[],[f166,f1777]) ).
fof(f1777,plain,
( spl0_208
<=> ! [X2,X5,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X5,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f166,axiom,
! [X2,X3,X5] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Ozero__class_Ozero(X2) != c_Power_Opower__class_Opower(X5,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f1775,plain,
spl0_207,
inference(avatar_split_clause,[],[f160,f1773]) ).
fof(f1773,plain,
( spl0_207
<=> ! [X0,X3] :
( ~ c_lessequals(X3,X0,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f160,axiom,
! [X3,X0] :
( ~ c_lessequals(X3,X0,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),tc_nat) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
fof(f1771,plain,
spl0_206,
inference(avatar_split_clause,[],[f126,f1769]) ).
fof(f1769,plain,
( spl0_206
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oplus__class_Oplus(X5,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f126,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = X5
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oplus__class_Oplus(X5,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f1767,plain,
spl0_205,
inference(avatar_split_clause,[],[f78,f1765]) ).
fof(f1765,plain,
( spl0_205
<=> ! [X7,X25,X2,X1] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X7,X25,X1,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f78,axiom,
! [X2,X1,X7,X25] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X7,X25,X1,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).
fof(f1763,plain,
spl0_204,
inference(avatar_split_clause,[],[f52,f1761]) ).
fof(f1761,plain,
( spl0_204
<=> ! [X2,X7,X3] : c_List_Odrop(X3,c_List_Otl(X7,X2),X2) = c_List_Otl(c_List_Odrop(X3,X7,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f52,axiom,
! [X2,X3,X7] : c_List_Odrop(X3,c_List_Otl(X7,X2),X2) = c_List_Otl(c_List_Odrop(X3,X7,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__drop_0) ).
fof(f1719,plain,
( ~ spl0_202
| spl0_203
| ~ spl0_92
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1688,f1589,f962,f1717,f1713]) ).
fof(f1713,plain,
( spl0_202
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1589,plain,
( spl0_190
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| X5 = X23
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X5,X23,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1688,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_92
| ~ spl0_190 ),
inference(trivial_inequality_removal,[],[f1685]) ).
fof(f1685,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_92
| ~ spl0_190 ),
inference(superposition,[],[f1590,f963]) ).
fof(f1590,plain,
( ! [X2,X5,X23] :
( c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X5,X23,X2)
| X5 = X23
| ~ class_OrderedGroup_Ogroup__add(X2) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1589]) ).
fof(f1641,plain,
( spl0_201
| ~ spl0_43
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1151,f1073,f748,f1639]) ).
fof(f1639,plain,
( spl0_201
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1073,plain,
( spl0_118
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1151,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_43
| ~ spl0_118 ),
inference(resolution,[],[f1074,f750]) ).
fof(f1074,plain,
( ! [X2,X5] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f1631,plain,
spl0_200,
inference(avatar_split_clause,[],[f435,f1629]) ).
fof(f1629,plain,
( spl0_200
<=> ! [X10,X13,X8,X9,X16] :
( ~ c_Progress_OWTrts_H(X8,X9,X10,X13,X16)
| c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f435,axiom,
! [X10,X8,X9,X16,X13] :
( ~ c_Progress_OWTrts_H(X8,X9,X10,X13,X16)
| c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wts_H__wts_0) ).
fof(f1627,plain,
spl0_199,
inference(avatar_split_clause,[],[f434,f1625]) ).
fof(f434,axiom,
! [X10,X8,X9,X16,X13] :
( ~ c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16)
| c_Progress_OWTrts_H(X8,X9,X10,X13,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wts__wts_H_0) ).
fof(f1623,plain,
spl0_198,
inference(avatar_split_clause,[],[f392,f1621]) ).
fof(f1621,plain,
( spl0_198
<=> ! [X61,X32,X5,X2,X65] :
( X32 = X65
| c_List_Olist_OCons(X61,X32,X2) != c_List_Olist_OCons(X5,X65,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f392,axiom,
! [X2,X65,X5,X32,X61] :
( X32 = X65
| c_List_Olist_OCons(X61,X32,X2) != c_List_Olist_OCons(X5,X65,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
fof(f1619,plain,
spl0_197,
inference(avatar_split_clause,[],[f391,f1617]) ).
fof(f1617,plain,
( spl0_197
<=> ! [X61,X32,X5,X2,X65] :
( X5 = X61
| c_List_Olist_OCons(X61,X32,X2) != c_List_Olist_OCons(X5,X65,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f391,axiom,
! [X2,X65,X5,X61,X32] :
( X5 = X61
| c_List_Olist_OCons(X61,X32,X2) != c_List_Olist_OCons(X5,X65,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
fof(f1615,plain,
spl0_196,
inference(avatar_split_clause,[],[f370,f1613]) ).
fof(f1613,plain,
( spl0_196
<=> ! [X34,X2,X7] : c_List_Otake(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_List_Oappend(X7,X34,X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f370,axiom,
! [X2,X7,X34] : c_List_Otake(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_List_Oappend(X7,X34,X2),X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
fof(f1611,plain,
spl0_195,
inference(avatar_split_clause,[],[f360,f1609]) ).
fof(f1609,plain,
( spl0_195
<=> ! [X35,X34,X7,X2] :
( X34 = X35
| c_List_Oappend(X7,X34,X2) != c_List_Oappend(X7,X35,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f360,axiom,
! [X2,X7,X34,X35] :
( X34 = X35
| c_List_Oappend(X7,X34,X2) != c_List_Oappend(X7,X35,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
fof(f1607,plain,
spl0_194,
inference(avatar_split_clause,[],[f359,f1605]) ).
fof(f1605,plain,
( spl0_194
<=> ! [X35,X34,X7,X2] :
( X34 = X35
| c_List_Oappend(X34,X7,X2) != c_List_Oappend(X35,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f359,axiom,
! [X2,X7,X34,X35] :
( X34 = X35
| c_List_Oappend(X34,X7,X2) != c_List_Oappend(X35,X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
fof(f1603,plain,
spl0_193,
inference(avatar_split_clause,[],[f349,f1601]) ).
fof(f1601,plain,
( spl0_193
<=> ! [X34,X2,X7] : c_List_Odrop(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_List_Oappend(X7,X34,X2),X2) = X34 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f349,axiom,
! [X2,X7,X34] : c_List_Odrop(c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)),c_List_Oappend(X7,X34,X2),X2) = X34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
fof(f1599,plain,
spl0_192,
inference(avatar_split_clause,[],[f339,f1597]) ).
fof(f1597,plain,
( spl0_192
<=> ! [X2,X7,X3] : c_List_Oappend(c_List_Otake(X3,X7,X2),c_List_Odrop(X3,X7,X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f339,axiom,
! [X2,X3,X7] : c_List_Oappend(c_List_Otake(X3,X7,X2),c_List_Odrop(X3,X7,X2),X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
fof(f1595,plain,
spl0_191,
inference(avatar_split_clause,[],[f297,f1593]) ).
fof(f297,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| X5 = X23
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X5,X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f1591,plain,
spl0_190,
inference(avatar_split_clause,[],[f296,f1589]) ).
fof(f296,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| X5 = X23
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Ominus__class_Ominus(X5,X23,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f1587,plain,
spl0_189,
inference(avatar_split_clause,[],[f254,f1585]) ).
fof(f1585,plain,
( spl0_189
<=> ! [X25,X27,X26] :
( ~ c_lessequals(X25,X27,tc_nat)
| ~ c_lessequals(X27,X26,tc_nat)
| c_lessequals(X25,X26,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f254,axiom,
! [X26,X27,X25] :
( ~ c_lessequals(X25,X27,tc_nat)
| ~ c_lessequals(X27,X26,tc_nat)
| c_lessequals(X25,X26,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f1583,plain,
spl0_188,
inference(avatar_split_clause,[],[f135,f1581]) ).
fof(f1581,plain,
( spl0_188
<=> ! [X2,X7,X3] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orotate(X3,X7,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f135,axiom,
! [X2,X3,X7] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orotate(X3,X7,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate_0) ).
fof(f1579,plain,
spl0_187,
inference(avatar_split_clause,[],[f115,f1577]) ).
fof(f1577,plain,
( spl0_187
<=> ! [X2,X0,X3] :
( ~ class_Nat_Osemiring__char__0(X2)
| X0 = X3
| c_Nat_Osemiring__1__class_Oof__nat(X0,X2) != c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f115,axiom,
! [X2,X3,X0] :
( ~ class_Nat_Osemiring__char__0(X2)
| X0 = X3
| c_Nat_Osemiring__1__class_Oof__nat(X0,X2) != c_Nat_Osemiring__1__class_Oof__nat(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f1575,plain,
spl0_186,
inference(avatar_split_clause,[],[f98,f1573]) ).
fof(f1573,plain,
( spl0_186
<=> ! [X26,X7,X2,X1] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Olist__update(X7,X26,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f98,axiom,
! [X2,X1,X26,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Olist__update(X7,X26,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
fof(f1571,plain,
spl0_185,
inference(avatar_split_clause,[],[f63,f1569]) ).
fof(f1569,plain,
( spl0_185
<=> ! [X0,X3,X26] :
( X0 = X3
| c_HOL_Oplus__class_Oplus(X26,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X26,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f63,axiom,
! [X3,X0,X26] :
( X0 = X3
| c_HOL_Oplus__class_Oplus(X26,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X26,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
fof(f1567,plain,
spl0_184,
inference(avatar_split_clause,[],[f62,f1565]) ).
fof(f1565,plain,
( spl0_184
<=> ! [X0,X3,X26] :
( X0 = X3
| c_HOL_Oplus__class_Oplus(X3,X26,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X26,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f62,axiom,
! [X3,X0,X26] :
( X0 = X3
| c_HOL_Oplus__class_Oplus(X3,X26,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X26,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f1563,plain,
spl0_183,
inference(avatar_split_clause,[],[f9,f1561]) ).
fof(f1561,plain,
( spl0_183
<=> ! [X10,X11,X14,X9,X8] :
( ~ c_Progress_OWTrt_H(X8,X9,X10,X11,X14)
| c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f9,axiom,
! [X10,X11,X8,X9,X14] :
( ~ c_Progress_OWTrt_H(X8,X9,X10,X11,X14)
| c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt_H__wt_0) ).
fof(f1559,plain,
( ~ spl0_182
| spl0_102
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1546,f1406,f1008,f1556]) ).
fof(f1556,plain,
( spl0_182
<=> c_WellType_OWTs(v_P,v_E____,v_es_Ha____,v_Us____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1008,plain,
( spl0_102
<=> c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,v_Us____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1406,plain,
( spl0_176
<=> ! [X10,X9,X13,X16,X8] :
( ~ c_WellType_OWTs(X8,X10,X13,X16)
| c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1546,plain,
( ~ c_WellType_OWTs(v_P,v_E____,v_es_Ha____,v_Us____)
| spl0_102
| ~ spl0_176 ),
inference(resolution,[],[f1407,f1010]) ).
fof(f1010,plain,
( ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,v_Us____)
| spl0_102 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f1407,plain,
( ! [X10,X8,X9,X16,X13] :
( c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16)
| ~ c_WellType_OWTs(X8,X10,X13,X16) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1406]) ).
fof(f1554,plain,
spl0_181,
inference(avatar_split_clause,[],[f8,f1552]) ).
fof(f1552,plain,
( spl0_181
<=> ! [X10,X11,X14,X9,X8] :
( ~ c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14)
| c_Progress_OWTrt_H(X8,X9,X10,X11,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f8,axiom,
! [X10,X11,X8,X9,X14] :
( ~ c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14)
| c_Progress_OWTrt_H(X8,X9,X10,X11,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wt__wt_H_0) ).
fof(f1550,plain,
spl0_180,
inference(avatar_split_clause,[],[f1,f1548]) ).
fof(f1548,plain,
( spl0_180
<=> ! [X4,X0,X3,X2,X1] :
( X0 = X3
| c_List_Oreplicate(X0,X1,X2) != c_List_Oreplicate(X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X4] :
( X0 = X3
| c_List_Oreplicate(X0,X1,X2) != c_List_Oreplicate(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
fof(f1524,plain,
( spl0_179
| ~ spl0_33
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1140,f1053,f698,f1522]) ).
fof(f1522,plain,
( spl0_179
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1053,plain,
( spl0_113
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1140,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X0
| ~ spl0_33
| ~ spl0_113 ),
inference(resolution,[],[f1054,f700]) ).
fof(f1054,plain,
( ! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1473,plain,
( spl0_178
| ~ spl0_9
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1139,f1053,f578,f1471]) ).
fof(f1471,plain,
( spl0_178
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1139,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_9
| ~ spl0_113 ),
inference(resolution,[],[f1054,f580]) ).
fof(f1413,plain,
spl0_177,
inference(avatar_split_clause,[],[f451,f1410]) ).
fof(f451,axiom,
c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,v_sko__CHAINED__1(v_E____,v_P,v_Us____,v_es_Ha____,v_h_Ha____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1408,plain,
spl0_176,
inference(avatar_split_clause,[],[f436,f1406]) ).
fof(f436,axiom,
! [X10,X8,X9,X16,X13] :
( ~ c_WellType_OWTs(X8,X10,X13,X16)
| c_WellTypeRT_OWTrts(X8,X9,X10,X13,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__implies__WTrts_0) ).
fof(f1404,plain,
spl0_175,
inference(avatar_split_clause,[],[f412,f1402]) ).
fof(f1402,plain,
( spl0_175
<=> ! [X34,X44,X8,X2] :
( c_List_Olist_ONil(X44) = X34
| ~ c_List_Olist__all2(X8,c_List_Olist_ONil(X2),X34,X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f412,axiom,
! [X2,X8,X44,X34] :
( c_List_Olist_ONil(X44) = X34
| ~ c_List_Olist__all2(X8,c_List_Olist_ONil(X2),X34,X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_0) ).
fof(f1400,plain,
spl0_174,
inference(avatar_split_clause,[],[f411,f1398]) ).
fof(f1398,plain,
( spl0_174
<=> ! [X2,X44,X7,X8] :
( c_List_Olist_ONil(X2) = X7
| ~ c_List_Olist__all2(X8,X7,c_List_Olist_ONil(X44),X2,X44) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f411,axiom,
! [X2,X8,X44,X7] :
( c_List_Olist_ONil(X2) = X7
| ~ c_List_Olist__all2(X8,X7,c_List_Olist_ONil(X44),X2,X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil2_0) ).
fof(f1396,plain,
spl0_173,
inference(avatar_split_clause,[],[f396,f1394]) ).
fof(f1394,plain,
( spl0_173
<=> ! [X2,X7] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orev(X7,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f396,axiom,
! [X2,X7] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orev(X7,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).
fof(f1392,plain,
spl0_172,
inference(avatar_split_clause,[],[f377,f1390]) ).
fof(f1390,plain,
( spl0_172
<=> ! [X34,X2,X7] :
( c_List_Olist_ONil(X2) = X34
| c_List_Olist_ONil(X2) != c_List_Oappend(X7,X34,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f377,axiom,
! [X2,X7,X34] :
( c_List_Olist_ONil(X2) = X34
| c_List_Olist_ONil(X2) != c_List_Oappend(X7,X34,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
fof(f1388,plain,
spl0_171,
inference(avatar_split_clause,[],[f376,f1386]) ).
fof(f1386,plain,
( spl0_171
<=> ! [X34,X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Oappend(X7,X34,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f376,axiom,
! [X2,X7,X34] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Oappend(X7,X34,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
fof(f1384,plain,
( spl0_170
| ~ spl0_35
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1099,f1021,f708,f1382]) ).
fof(f1382,plain,
( spl0_170
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f708,plain,
( spl0_35
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1021,plain,
( spl0_105
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1099,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_35
| ~ spl0_105 ),
inference(resolution,[],[f1022,f710]) ).
fof(f710,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f1022,plain,
( ! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1380,plain,
spl0_169,
inference(avatar_split_clause,[],[f280,f1378]) ).
fof(f1378,plain,
( spl0_169
<=> ! [X0,X3] :
( c_lessequals(X0,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f280,axiom,
! [X3,X0] :
( c_lessequals(X0,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f1376,plain,
spl0_168,
inference(avatar_split_clause,[],[f279,f1374]) ).
fof(f1374,plain,
( spl0_168
<=> ! [X0,X3] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f279,axiom,
! [X3,X0] :
( ~ c_lessequals(X0,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f1372,plain,
spl0_167,
inference(avatar_split_clause,[],[f273,f1370]) ).
fof(f1370,plain,
( spl0_167
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X1,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f273,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f1368,plain,
spl0_166,
inference(avatar_split_clause,[],[f265,f1366]) ).
fof(f1366,plain,
( spl0_166
<=> ! [X0,X3] :
( X0 = X3
| ~ c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(X3,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f265,axiom,
! [X3,X0] :
( X0 = X3
| ~ c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(X3,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1364,plain,
spl0_165,
inference(avatar_split_clause,[],[f242,f1362]) ).
fof(f1362,plain,
( spl0_165
<=> ! [X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f242,axiom,
! [X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
fof(f1360,plain,
spl0_164,
inference(avatar_split_clause,[],[f176,f1358]) ).
fof(f1358,plain,
( spl0_164
<=> ! [X2,X7,X3] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Orotate(X3,X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f176,axiom,
! [X2,X3,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Orotate(X3,X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_0) ).
fof(f1356,plain,
spl0_163,
inference(avatar_split_clause,[],[f175,f1354]) ).
fof(f1354,plain,
( spl0_163
<=> ! [X2,X7,X25] : c_List_Olist__update(X7,X25,hAPP(c_List_Onth(X7,X2),X25),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f175,axiom,
! [X2,X7,X25] : c_List_Olist__update(X7,X25,hAPP(c_List_Onth(X7,X2),X25),X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__id_0) ).
fof(f1352,plain,
spl0_162,
inference(avatar_split_clause,[],[f170,f1350]) ).
fof(f1350,plain,
( spl0_162
<=> ! [X2,X1,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X2) != c_List_Oreplicate(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f170,axiom,
! [X2,X3,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X2) != c_List_Oreplicate(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
fof(f1348,plain,
spl0_161,
inference(avatar_split_clause,[],[f137,f1346]) ).
fof(f1346,plain,
( spl0_161
<=> ! [X2,X7] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X7,X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f137,axiom,
! [X2,X7] : c_Nat_Osize__class_Osize(X7,tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X7,X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
fof(f1344,plain,
spl0_160,
inference(avatar_split_clause,[],[f125,f1342]) ).
fof(f1342,plain,
( spl0_160
<=> ! [X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f125,axiom,
! [X3,X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1340,plain,
( spl0_159
| ~ spl0_35
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1097,f1017,f708,f1338]) ).
fof(f1338,plain,
( spl0_159
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1017,plain,
( spl0_104
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1097,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X0,tc_Int_Oint) = X0
| ~ spl0_35
| ~ spl0_104 ),
inference(resolution,[],[f1018,f710]) ).
fof(f1018,plain,
( ! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1336,plain,
spl0_158,
inference(avatar_split_clause,[],[f124,f1334]) ).
fof(f1334,plain,
( spl0_158
<=> ! [X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f124,axiom,
! [X3,X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1332,plain,
spl0_157,
inference(avatar_split_clause,[],[f116,f1330]) ).
fof(f1330,plain,
( spl0_157
<=> ! [X2,X1,X7] : hAPP(c_List_Onth(c_List_Olist_OCons(X1,X7,X2),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f116,axiom,
! [X2,X1,X7] : hAPP(c_List_Onth(c_List_Olist_OCons(X1,X7,X2),X2),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).
fof(f1328,plain,
spl0_156,
inference(avatar_split_clause,[],[f114,f1326]) ).
fof(f1326,plain,
( spl0_156
<=> ! [X2,X1,X3] : c_List_Oreplicate(X3,X1,X2) = c_List_Orev(c_List_Oreplicate(X3,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f114,axiom,
! [X2,X3,X1] : c_List_Oreplicate(X3,X1,X2) = c_List_Orev(c_List_Oreplicate(X3,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
fof(f1324,plain,
spl0_155,
inference(avatar_split_clause,[],[f111,f1322]) ).
fof(f1322,plain,
( spl0_155
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,X23,X2) = c_HOL_Oplus__class_Oplus(X23,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f111,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,X23,X2) = c_HOL_Oplus__class_Oplus(X23,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1320,plain,
spl0_154,
inference(avatar_split_clause,[],[f110,f1318]) ).
fof(f1318,plain,
( spl0_154
<=> ! [X29,X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,X29,X2) = c_HOL_Oplus__class_Oplus(X29,X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f110,axiom,
! [X2,X29,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,X29,X2) = c_HOL_Oplus__class_Oplus(X29,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f1316,plain,
spl0_153,
inference(avatar_split_clause,[],[f96,f1314]) ).
fof(f1314,plain,
( spl0_153
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X23,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f96,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X23,X2),X23,X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f1312,plain,
spl0_152,
inference(avatar_split_clause,[],[f88,f1310]) ).
fof(f1310,plain,
( spl0_152
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f88,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f1308,plain,
spl0_151,
inference(avatar_split_clause,[],[f57,f1306]) ).
fof(f1306,plain,
( spl0_151
<=> ! [X9,X11,X14,X10,X8] :
( ~ c_WellType_OWT(X8,X10,X11,X14)
| c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f57,axiom,
! [X10,X11,X8,X9,X14] :
( ~ c_WellType_OWT(X8,X10,X11,X14)
| c_WellTypeRT_OWTrt(X8,X9,X10,X11,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__implies__WTrt_0) ).
fof(f1304,plain,
spl0_150,
inference(avatar_split_clause,[],[f43,f1302]) ).
fof(f1302,plain,
( spl0_150
<=> ! [X4,X1,X30] :
( ~ c_lessequals(X1,X4,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,X30,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f43,axiom,
! [X1,X4,X30] :
( ~ c_lessequals(X1,X4,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,X30,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
fof(f1300,plain,
spl0_149,
inference(avatar_split_clause,[],[f42,f1298]) ).
fof(f1298,plain,
( spl0_149
<=> ! [X4,X1,X30] :
( ~ c_lessequals(X1,X30,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,X30,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f42,axiom,
! [X1,X4,X30] :
( ~ c_lessequals(X1,X30,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X4,X30,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
fof(f1295,plain,
spl0_148,
inference(avatar_split_clause,[],[f41,f1293]) ).
fof(f1293,plain,
( spl0_148
<=> ! [X0,X3,X26] :
( c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X26,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f41,axiom,
! [X3,X0,X26] :
( c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X26,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f1291,plain,
spl0_147,
inference(avatar_split_clause,[],[f40,f1289]) ).
fof(f1289,plain,
( spl0_147
<=> ! [X0,X3,X26] :
( c_lessequals(X26,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X26,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f40,axiom,
! [X3,X0,X26] :
( c_lessequals(X26,X3,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X26,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f1287,plain,
spl0_146,
inference(avatar_split_clause,[],[f20,f1285]) ).
fof(f1285,plain,
( spl0_146
<=> ! [X2] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f20,axiom,
! [X2] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f1283,plain,
spl0_145,
inference(avatar_split_clause,[],[f15,f1281]) ).
fof(f1281,plain,
( spl0_145
<=> ! [X2,X5,X23] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X23,X2),X23,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f15,axiom,
! [X2,X5,X23] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X23,X2),X23,X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f1271,plain,
( spl0_144
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1260,f1189,f1269]) ).
fof(f1269,plain,
( spl0_144
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1189,plain,
( spl0_132
<=> ! [X2,X1,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,X4,X2)
| c_lessequals(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1260,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_132 ),
inference(factoring,[],[f1190]) ).
fof(f1190,plain,
( ! [X2,X1,X4] :
( c_lessequals(X4,X1,X2)
| c_lessequals(X1,X4,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f1241,plain,
( spl0_143
| ~ spl0_37
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1095,f1000,f718,f1238]) ).
fof(f1238,plain,
( spl0_143
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f718,plain,
( spl0_37
<=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1000,plain,
( spl0_100
<=> ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1095,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_37
| ~ spl0_100 ),
inference(resolution,[],[f1001,f720]) ).
fof(f720,plain,
( class_Ring__and__Field_Osemiring__1(tc_Int_Oint)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f1001,plain,
( ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1000]) ).
fof(f1234,plain,
spl0_142,
inference(avatar_split_clause,[],[f508,f1232]) ).
fof(f1232,plain,
( spl0_142
<=> ! [X2,X80,X81] :
( X80 = X81
| ~ hBOOL(hAPP(hAPP(c_fequal(X2),X80),X81)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f508,axiom,
! [X2,X80,X81] :
( X80 = X81
| ~ hBOOL(hAPP(hAPP(c_fequal(X2),X80),X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1230,plain,
spl0_141,
inference(avatar_split_clause,[],[f430,f1228]) ).
fof(f1228,plain,
( spl0_141
<=> ! [X34,X2,X7] :
( X7 = X34
| ~ c_List_Olist__all2(c_fequal(X2),X7,X34,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f430,axiom,
! [X2,X7,X34] :
( X7 = X34
| ~ c_List_Olist__all2(c_fequal(X2),X7,X34,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_1) ).
fof(f1226,plain,
spl0_140,
inference(avatar_split_clause,[],[f417,f1223]) ).
fof(f1223,plain,
( spl0_140
<=> c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OClass(v_C____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f417,axiom,
c_WellTypeRT_OWTrt(v_P,v_h_Ha____,v_E____,c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OClass(v_C____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_I5_J_0) ).
fof(f1221,plain,
spl0_139,
inference(avatar_split_clause,[],[f404,f1219]) ).
fof(f1219,plain,
( spl0_139
<=> ! [X2,X46,X68] :
( X46 = X68
| c_Expr_Oexp_OVal(X46,X2) != c_Expr_Oexp_OVal(X68,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f404,axiom,
! [X2,X46,X68] :
( X46 = X68
| c_Expr_Oexp_OVal(X46,X2) != c_Expr_Oexp_OVal(X68,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I3_J_0) ).
fof(f1217,plain,
spl0_138,
inference(avatar_split_clause,[],[f387,f1215]) ).
fof(f1215,plain,
( spl0_138
<=> ! [X34,X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Oappend(X7,X34,X2) != X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f387,axiom,
! [X2,X7,X34] :
( c_List_Olist_ONil(X2) = X7
| c_List_Oappend(X7,X34,X2) != X34 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
fof(f1213,plain,
spl0_137,
inference(avatar_split_clause,[],[f386,f1211]) ).
fof(f1211,plain,
( spl0_137
<=> ! [X34,X2,X7] :
( c_List_Olist_ONil(X2) = X34
| c_List_Oappend(X7,X34,X2) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f386,axiom,
! [X2,X7,X34] :
( c_List_Olist_ONil(X2) = X34
| c_List_Oappend(X7,X34,X2) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
fof(f1209,plain,
spl0_136,
inference(avatar_split_clause,[],[f382,f1207]) ).
fof(f1207,plain,
( spl0_136
<=> ! [X34,X2,X7] :
( X7 = X34
| c_List_Orev(X7,X2) != c_List_Orev(X34,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f382,axiom,
! [X2,X7,X34] :
( X7 = X34
| c_List_Orev(X7,X2) != c_List_Orev(X34,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
fof(f1205,plain,
spl0_135,
inference(avatar_split_clause,[],[f337,f1202]) ).
fof(f1202,plain,
( spl0_135
<=> c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OClass(v_C____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f337,axiom,
c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OVal(v_v____,tc_List_Olist(tc_String_Ochar)),c_Type_Oty_OClass(v_C____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wte_0) ).
fof(f1200,plain,
spl0_134,
inference(avatar_split_clause,[],[f336,f1198]) ).
fof(f1198,plain,
( spl0_134
<=> ! [X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Orev(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f336,axiom,
! [X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Orev(X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
fof(f1196,plain,
( spl0_133
| ~ spl0_13
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1094,f1000,f598,f1193]) ).
fof(f1193,plain,
( spl0_133
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f598,plain,
( spl0_13
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1094,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_13
| ~ spl0_100 ),
inference(resolution,[],[f1001,f600]) ).
fof(f600,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f1191,plain,
spl0_132,
inference(avatar_split_clause,[],[f245,f1189]) ).
fof(f245,axiom,
! [X2,X1,X4] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,X4,X2)
| c_lessequals(X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1187,plain,
spl0_131,
inference(avatar_split_clause,[],[f235,f1185]) ).
fof(f1185,plain,
( spl0_131
<=> ! [X2,X1,X7] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X7,X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f235,axiom,
! [X2,X1,X7] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X1,X7,X2),X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
fof(f1183,plain,
spl0_130,
inference(avatar_split_clause,[],[f169,f1181]) ).
fof(f1181,plain,
( spl0_130
<=> ! [X2,X5] :
( ~ class_Power_Opower(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f169,axiom,
! [X2,X5] :
( ~ class_Power_Opower(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f1179,plain,
spl0_129,
inference(avatar_split_clause,[],[f168,f1177]) ).
fof(f168,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f1175,plain,
spl0_128,
inference(avatar_split_clause,[],[f118,f1173]) ).
fof(f1173,plain,
( spl0_128
<=> ! [X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f118,axiom,
! [X3,X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f1171,plain,
spl0_127,
inference(avatar_split_clause,[],[f105,f1169]) ).
fof(f1169,plain,
( spl0_127
<=> ! [X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Orotate1(X7,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f105,axiom,
! [X2,X7] :
( c_List_Olist_ONil(X2) = X7
| c_List_Olist_ONil(X2) != c_List_Orotate1(X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
fof(f1167,plain,
spl0_126,
inference(avatar_split_clause,[],[f46,f1165]) ).
fof(f1165,plain,
( spl0_126
<=> ! [X0,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f46,axiom,
! [X3,X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f1163,plain,
spl0_125,
inference(avatar_split_clause,[],[f45,f1161]) ).
fof(f45,axiom,
! [X2,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_HOL_Oone__class_Oone(X2) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X2),X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1158,plain,
( spl0_124
| ~ spl0_37
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1093,f996,f718,f1155]) ).
fof(f1155,plain,
( spl0_124
<=> c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f996,plain,
( spl0_99
<=> ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1093,plain,
( c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint)
| ~ spl0_37
| ~ spl0_99 ),
inference(resolution,[],[f997,f720]) ).
fof(f997,plain,
( ! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f1117,plain,
( spl0_123
| ~ spl0_13
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1092,f996,f598,f1114]) ).
fof(f1114,plain,
( spl0_123
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1092,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_13
| ~ spl0_99 ),
inference(resolution,[],[f997,f600]) ).
fof(f1091,plain,
spl0_122,
inference(avatar_split_clause,[],[f347,f1089]) ).
fof(f1089,plain,
( spl0_122
<=> ! [X9,X64,X63] :
( ~ c_Objects_Ohext(X9,X63)
| ~ c_Objects_Ohext(X63,X64)
| c_Objects_Ohext(X9,X64) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f347,axiom,
! [X9,X63,X64] :
( ~ c_Objects_Ohext(X9,X63)
| ~ c_Objects_Ohext(X63,X64)
| c_Objects_Ohext(X9,X64) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__trans_0) ).
fof(f1087,plain,
spl0_121,
inference(avatar_split_clause,[],[f301,f1085]) ).
fof(f1085,plain,
( spl0_121
<=> ! [X48,X47,X46,X49,X2] : c_Expr_Oexp_OVal(X46,X2) != c_Expr_Oexp_OCall(X47,X48,X49,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f301,axiom,
! [X2,X48,X46,X49,X47] : c_Expr_Oexp_OVal(X46,X2) != c_Expr_Oexp_OCall(X47,X48,X49,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp_Osimps_I81_J_0) ).
fof(f1083,plain,
spl0_120,
inference(avatar_split_clause,[],[f277,f1081]) ).
fof(f1081,plain,
( spl0_120
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X1,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f277,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1079,plain,
spl0_119,
inference(avatar_split_clause,[],[f276,f1077]) ).
fof(f276,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_HOL_Ominus__class_Ominus(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f1075,plain,
spl0_118,
inference(avatar_split_clause,[],[f275,f1073]) ).
fof(f275,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1071,plain,
spl0_117,
inference(avatar_split_clause,[],[f268,f1069]) ).
fof(f1069,plain,
( spl0_117
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f268,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1067,plain,
spl0_116,
inference(avatar_split_clause,[],[f203,f1065]) ).
fof(f1065,plain,
( spl0_116
<=> ! [X2,X17,X8] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X8,X2),c_Type_Oty_ONT),c_Type_Oty_OClass(X17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f203,axiom,
! [X2,X8,X17] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X8,X2),c_Type_Oty_ONT),c_Type_Oty_OClass(X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__Class_2) ).
fof(f1063,plain,
spl0_115,
inference(avatar_split_clause,[],[f173,f1061]) ).
fof(f1061,plain,
( spl0_115
<=> ! [X2,X1,X3] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X1,X2),tc_List_Olist(X2)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f173,axiom,
! [X2,X3,X1] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X1,X2),tc_List_Olist(X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).
fof(f1059,plain,
spl0_114,
inference(avatar_split_clause,[],[f128,f1057]) ).
fof(f1057,plain,
( spl0_114
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f128,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X2)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
fof(f1055,plain,
spl0_113,
inference(avatar_split_clause,[],[f127,f1053]) ).
fof(f127,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1051,plain,
spl0_112,
inference(avatar_split_clause,[],[f113,f1049]) ).
fof(f1049,plain,
( spl0_112
<=> ! [X0,X3] : c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f113,axiom,
! [X3,X0] : c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f1047,plain,
spl0_111,
inference(avatar_split_clause,[],[f95,f1045]) ).
fof(f1045,plain,
( spl0_111
<=> ! [X0,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X3,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f95,axiom,
! [X3,X0] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),X3,tc_nat) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1043,plain,
spl0_110,
inference(avatar_split_clause,[],[f94,f1041]) ).
fof(f1041,plain,
( spl0_110
<=> ! [X0,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X3,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f94,axiom,
! [X3,X0] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X3,tc_nat) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f1039,plain,
spl0_109,
inference(avatar_split_clause,[],[f93,f1037]) ).
fof(f1037,plain,
( spl0_109
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f93,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1035,plain,
spl0_108,
inference(avatar_split_clause,[],[f92,f1033]) ).
fof(f1033,plain,
( spl0_108
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f92,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1031,plain,
spl0_107,
inference(avatar_split_clause,[],[f91,f1029]) ).
fof(f1029,plain,
( spl0_107
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f91,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1027,plain,
spl0_106,
inference(avatar_split_clause,[],[f90,f1025]) ).
fof(f1025,plain,
( spl0_106
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f90,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1023,plain,
spl0_105,
inference(avatar_split_clause,[],[f89,f1021]) ).
fof(f89,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X2),X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1019,plain,
spl0_104,
inference(avatar_split_clause,[],[f86,f1017]) ).
fof(f86,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X2),X5,X2) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1015,plain,
spl0_103,
inference(avatar_split_clause,[],[f81,f1013]) ).
fof(f1013,plain,
( spl0_103
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f81,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_Nat_Osemiring__1__class_Oof__nat(X3,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
fof(f1011,plain,
( ~ spl0_102
| ~ spl0_58
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f994,f986,f818,f1008]) ).
fof(f986,plain,
( spl0_98
<=> ! [X2,X7,X8] : c_List_Olist__all2(c_TypeRel_Owiden(X8,X2),X7,X7,tc_Type_Oty,tc_Type_Oty) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f994,plain,
( ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,v_Us____)
| ~ spl0_58
| ~ spl0_98 ),
inference(resolution,[],[f987,f819]) ).
fof(f987,plain,
( ! [X2,X8,X7] : c_List_Olist__all2(c_TypeRel_Owiden(X8,X2),X7,X7,tc_Type_Oty,tc_Type_Oty)
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f1006,plain,
spl0_101,
inference(avatar_split_clause,[],[f58,f1004]) ).
fof(f1004,plain,
( spl0_101
<=> ! [X2,X1,X26] : c_List_Olist_ONil(X2) = c_List_Olist__update(c_List_Olist_ONil(X2),X26,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f58,axiom,
! [X2,X1,X26] : c_List_Olist_ONil(X2) = c_List_Olist__update(c_List_Olist_ONil(X2),X26,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
fof(f1002,plain,
spl0_100,
inference(avatar_split_clause,[],[f56,f1000]) ).
fof(f56,axiom,
! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Ozero__class_Ozero(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f998,plain,
spl0_99,
inference(avatar_split_clause,[],[f49,f996]) ).
fof(f49,axiom,
! [X2] :
( ~ class_Ring__and__Field_Osemiring__1(X2)
| c_HOL_Oone__class_Oone(X2) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
fof(f988,plain,
spl0_98,
inference(avatar_split_clause,[],[f445,f986]) ).
fof(f445,axiom,
! [X2,X8,X7] : c_List_Olist__all2(c_TypeRel_Owiden(X8,X2),X7,X7,tc_Type_Oty,tc_Type_Oty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widens__refl_0) ).
fof(f984,plain,
spl0_97,
inference(avatar_split_clause,[],[f431,f982]) ).
fof(f982,plain,
( spl0_97
<=> ! [X2,X8,X14] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X8,X2),X14),X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f431,axiom,
! [X2,X8,X14] : hBOOL(hAPP(hAPP(c_TypeRel_Owiden(X8,X2),X14),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_widen__refl_0) ).
fof(f980,plain,
spl0_96,
inference(avatar_split_clause,[],[f407,f978]) ).
fof(f978,plain,
( spl0_96
<=> ! [X2,X44,X8] : c_List_Olist__all2(X8,c_List_Olist_ONil(X2),c_List_Olist_ONil(X44),X2,X44) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f407,axiom,
! [X2,X8,X44] : c_List_Olist__all2(X8,c_List_Olist_ONil(X2),c_List_Olist_ONil(X44),X2,X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__Nil_1) ).
fof(f976,plain,
spl0_95,
inference(avatar_split_clause,[],[f373,f974]) ).
fof(f974,plain,
( spl0_95
<=> ! [X2,X3] : c_List_Olist_ONil(X2) = c_List_Odrop(X3,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f373,axiom,
! [X2,X3] : c_List_Olist_ONil(X2) = c_List_Odrop(X3,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
fof(f972,plain,
spl0_94,
inference(avatar_split_clause,[],[f371,f970]) ).
fof(f970,plain,
( spl0_94
<=> ! [X32,X65] :
( X32 = X65
| c_Type_Oty_OClass(X32) != c_Type_Oty_OClass(X65) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f371,axiom,
! [X65,X32] :
( X32 = X65
| c_Type_Oty_OClass(X32) != c_Type_Oty_OClass(X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Oinject_0) ).
fof(f968,plain,
spl0_93,
inference(avatar_split_clause,[],[f361,f966]) ).
fof(f966,plain,
( spl0_93
<=> ! [X2,X3] : c_List_Olist_ONil(X2) = c_List_Otake(X3,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f361,axiom,
! [X2,X3] : c_List_Olist_ONil(X2) = c_List_Otake(X3,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
fof(f964,plain,
spl0_92,
inference(avatar_split_clause,[],[f293,f962]) ).
fof(f293,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f960,plain,
spl0_91,
inference(avatar_split_clause,[],[f269,f958]) ).
fof(f958,plain,
( spl0_91
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f269,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| c_lessequals(c_HOL_Ozero__class_Ozero(X2),c_HOL_Oone__class_Oone(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f956,plain,
spl0_90,
inference(avatar_split_clause,[],[f266,f954]) ).
fof(f954,plain,
( spl0_90
<=> ! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f266,axiom,
! [X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X2),c_HOL_Ozero__class_Ozero(X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f952,plain,
spl0_89,
inference(avatar_split_clause,[],[f246,f950]) ).
fof(f950,plain,
( spl0_89
<=> ! [X0,X3] :
( c_lessequals(X0,X3,tc_nat)
| c_lessequals(X3,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f246,axiom,
! [X3,X0] :
( c_lessequals(X0,X3,tc_nat)
| c_lessequals(X3,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f948,plain,
spl0_88,
inference(avatar_split_clause,[],[f243,f946]) ).
fof(f946,plain,
( spl0_88
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X2),tc_List_Olist(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f243,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X2),tc_List_Olist(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
fof(f944,plain,
spl0_87,
inference(avatar_split_clause,[],[f236,f942]) ).
fof(f942,plain,
( spl0_87
<=> ! [X2,X7] : c_List_Olist_ONil(X2) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X7,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f236,axiom,
! [X2,X7] : c_List_Olist_ONil(X2) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X7,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).
fof(f940,plain,
spl0_86,
inference(avatar_split_clause,[],[f142,f938]) ).
fof(f938,plain,
( spl0_86
<=> ! [X2,X1,X7] : c_List_Otl(c_List_Olist_OCons(X1,X7,X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f142,axiom,
! [X2,X1,X7] : c_List_Otl(c_List_Olist_OCons(X1,X7,X2),X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
fof(f936,plain,
spl0_85,
inference(avatar_split_clause,[],[f120,f934]) ).
fof(f934,plain,
( spl0_85
<=> ! [X22,X2,X21] : c_Nat_Onat_Onat__case(X21,X22,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f120,axiom,
! [X2,X21,X22] : c_Nat_Onat_Onat__case(X21,X22,c_HOL_Ozero__class_Ozero(tc_nat),X2) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__case__0_0) ).
fof(f932,plain,
spl0_84,
inference(avatar_split_clause,[],[f76,f930]) ).
fof(f930,plain,
( spl0_84
<=> ! [X2,X3] : c_List_Olist_ONil(X2) = c_List_Orotate(X3,c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f76,axiom,
! [X2,X3] : c_List_Olist_ONil(X2) = c_List_Orotate(X3,c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__is__Nil__conv_1) ).
fof(f928,plain,
spl0_83,
inference(avatar_split_clause,[],[f75,f926]) ).
fof(f926,plain,
( spl0_83
<=> ! [X2,X1] : c_List_Olist_ONil(X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f75,axiom,
! [X2,X1] : c_List_Olist_ONil(X2) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
fof(f917,plain,
spl0_82,
inference(avatar_split_clause,[],[f507,f915]) ).
fof(f507,axiom,
! [X2,X1] : hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f913,plain,
spl0_81,
inference(avatar_split_clause,[],[f406,f911]) ).
fof(f911,plain,
( spl0_81
<=> ! [X2,X1] : c_List_Olist__all2(c_fequal(X2),X1,X1,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f406,axiom,
! [X2,X1] : c_List_Olist__all2(c_fequal(X2),X1,X1,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__all2__eq_0) ).
fof(f909,plain,
spl0_80,
inference(avatar_split_clause,[],[f395,f907]) ).
fof(f907,plain,
( spl0_80
<=> ! [X2] : c_List_Olist_ONil(X2) = c_List_Orev(c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f395,axiom,
! [X2] : c_List_Olist_ONil(X2) = c_List_Orev(c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
fof(f905,plain,
spl0_79,
inference(avatar_split_clause,[],[f381,f903]) ).
fof(f903,plain,
( spl0_79
<=> ! [X61,X2,X32] : c_List_Olist_ONil(X2) != c_List_Olist_OCons(X61,X32,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f381,axiom,
! [X2,X61,X32] : c_List_Olist_ONil(X2) != c_List_Olist_OCons(X61,X32,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
fof(f901,plain,
spl0_78,
inference(avatar_split_clause,[],[f369,f899]) ).
fof(f899,plain,
( spl0_78
<=> ! [X2,X7] : c_List_Orev(c_List_Orev(X7,X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f369,axiom,
! [X2,X7] : c_List_Orev(c_List_Orev(X7,X2),X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
fof(f897,plain,
spl0_77,
inference(avatar_split_clause,[],[f366,f895]) ).
fof(f895,plain,
( spl0_77
<=> ! [X34,X2] : c_List_Oappend(c_List_Olist_ONil(X2),X34,X2) = X34 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f366,axiom,
! [X2,X34] : c_List_Oappend(c_List_Olist_ONil(X2),X34,X2) = X34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
fof(f893,plain,
spl0_76,
inference(avatar_split_clause,[],[f362,f891]) ).
fof(f891,plain,
( spl0_76
<=> ! [X2,X7] : c_List_Oappend(X7,c_List_Olist_ONil(X2),X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f362,axiom,
! [X2,X7] : c_List_Oappend(X7,c_List_Olist_ONil(X2),X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
fof(f889,plain,
spl0_75,
inference(avatar_split_clause,[],[f294,f887]) ).
fof(f887,plain,
( spl0_75
<=> ! [X0,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f294,axiom,
! [X3,X0] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X3,tc_nat),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f885,plain,
spl0_74,
inference(avatar_split_clause,[],[f292,f883]) ).
fof(f883,plain,
( spl0_74
<=> ! [X2,X7] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X7,X2) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f292,axiom,
! [X2,X7] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X7,X2) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).
fof(f881,plain,
spl0_73,
inference(avatar_split_clause,[],[f272,f879]) ).
fof(f879,plain,
( spl0_73
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f272,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f877,plain,
spl0_72,
inference(avatar_split_clause,[],[f271,f875]) ).
fof(f875,plain,
( spl0_72
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f271,axiom,
! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f873,plain,
spl0_71,
inference(avatar_split_clause,[],[f270,f871]) ).
fof(f871,plain,
( spl0_71
<=> ! [X2] :
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f270,axiom,
! [X2] :
( ~ class_Ring__and__Field_Ozero__neq__one(X2)
| c_HOL_Ozero__class_Ozero(X2) != c_HOL_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f869,plain,
spl0_70,
inference(avatar_split_clause,[],[f177,f867]) ).
fof(f867,plain,
( spl0_70
<=> ! [X2] : c_List_Olist_ONil(X2) = c_List_Otl(c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f177,axiom,
! [X2] : c_List_Olist_ONil(X2) = c_List_Otl(c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
fof(f865,plain,
spl0_69,
inference(avatar_split_clause,[],[f140,f863]) ).
fof(f863,plain,
( spl0_69
<=> ! [X0,X3] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f140,axiom,
! [X3,X0] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f861,plain,
spl0_68,
inference(avatar_split_clause,[],[f139,f859]) ).
fof(f859,plain,
( spl0_68
<=> ! [X0,X3] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f139,axiom,
! [X3,X0] : c_lessequals(X3,c_HOL_Oplus__class_Oplus(X3,X0,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).
fof(f857,plain,
spl0_67,
inference(avatar_split_clause,[],[f84,f855]) ).
fof(f855,plain,
( spl0_67
<=> ! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f84,axiom,
! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f853,plain,
spl0_66,
inference(avatar_split_clause,[],[f83,f851]) ).
fof(f851,plain,
( spl0_66
<=> ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f83,axiom,
! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
fof(f849,plain,
spl0_65,
inference(avatar_split_clause,[],[f14,f847]) ).
fof(f847,plain,
( spl0_65
<=> ! [X2] : c_List_Olist_ONil(X2) = c_List_Orotate1(c_List_Olist_ONil(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f14,axiom,
! [X2] : c_List_Olist_ONil(X2) = c_List_Orotate1(c_List_Olist_ONil(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
fof(f845,plain,
spl0_64,
inference(avatar_split_clause,[],[f455,f843]) ).
fof(f843,plain,
( spl0_64
<=> ! [X78,X79] :
( ~ class_Orderings_Oorder(X79)
| class_Orderings_Oorder(tc_fun(X78,X79)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f455,axiom,
! [X78,X79] :
( ~ class_Orderings_Oorder(X79)
| class_Orderings_Oorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f841,plain,
spl0_63,
inference(avatar_split_clause,[],[f454,f839]) ).
fof(f839,plain,
( spl0_63
<=> ! [X78,X79] :
( ~ class_Orderings_Opreorder(X79)
| class_Orderings_Opreorder(tc_fun(X78,X79)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f454,axiom,
! [X78,X79] :
( ~ class_Orderings_Opreorder(X79)
| class_Orderings_Opreorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f837,plain,
spl0_62,
inference(avatar_split_clause,[],[f447,f834]) ).
fof(f447,axiom,
c_WellTypeRT_OWTrts(v_P,v_ha____,v_E____,v_esa____,v_Us____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wtes_0) ).
fof(f832,plain,
spl0_61,
inference(avatar_split_clause,[],[f334,f830]) ).
fof(f830,plain,
( spl0_61
<=> ! [X2,X1,X58] : c_List_Olist_OCons(X1,X58,X2) != X58 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f334,axiom,
! [X2,X58,X1] : c_List_Olist_OCons(X1,X58,X2) != X58,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
fof(f828,plain,
spl0_60,
inference(avatar_split_clause,[],[f252,f826]) ).
fof(f826,plain,
( spl0_60
<=> ! [X2,X1] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f252,axiom,
! [X2,X1] :
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f824,plain,
spl0_59,
inference(avatar_split_clause,[],[f251,f822]) ).
fof(f822,plain,
( spl0_59
<=> ! [X2,X1] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f251,axiom,
! [X2,X1] :
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f820,plain,
( spl0_58
| spl0_1 ),
inference(avatar_split_clause,[],[f453,f538,f818]) ).
fof(f538,plain,
( spl0_1
<=> v_thesis____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f453,axiom,
! [X1] :
( v_thesis____
| ~ c_WellTypeRT_OWTrts(v_P,v_h_Ha____,v_E____,v_es_Ha____,X1)
| ~ c_List_Olist__all2(c_TypeRel_Owiden(v_P,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))),X1,v_Us____,tc_Type_Oty,tc_Type_Oty) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f816,plain,
spl0_57,
inference(avatar_split_clause,[],[f357,f814]) ).
fof(f814,plain,
( spl0_57
<=> ! [X2,X8] : c_COMBI(X8,X2) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f357,axiom,
! [X2,X8] : c_COMBI(X8,X2) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
fof(f812,plain,
spl0_56,
inference(avatar_split_clause,[],[f300,f810]) ).
fof(f810,plain,
( spl0_56
<=> ! [X3] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f300,axiom,
! [X3] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f808,plain,
spl0_55,
inference(avatar_split_clause,[],[f253,f806]) ).
fof(f806,plain,
( spl0_55
<=> ! [X1] : c_lessequals(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f253,axiom,
! [X1] : c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f804,plain,
spl0_54,
inference(avatar_split_clause,[],[f55,f802]) ).
fof(f802,plain,
( spl0_54
<=> ! [X32] : c_Type_Oty_OClass(X32) != c_Type_Oty_ONT ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f55,axiom,
! [X32] : c_Type_Oty_OClass(X32) != c_Type_Oty_ONT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ty_Osimps_I21_J_0) ).
fof(f800,plain,
spl0_53,
inference(avatar_split_clause,[],[f345,f798]) ).
fof(f798,plain,
( spl0_53
<=> ! [X9] : c_Objects_Ohext(X9,X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f345,axiom,
! [X9] : c_Objects_Ohext(X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hext__refl_0) ).
fof(f796,plain,
spl0_52,
inference(avatar_split_clause,[],[f506,f793]) ).
fof(f793,plain,
( spl0_52
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f506,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
fof(f791,plain,
spl0_51,
inference(avatar_split_clause,[],[f505,f788]) ).
fof(f788,plain,
( spl0_51
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f505,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f786,plain,
spl0_50,
inference(avatar_split_clause,[],[f504,f783]) ).
fof(f783,plain,
( spl0_50
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f504,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f781,plain,
spl0_49,
inference(avatar_split_clause,[],[f503,f778]) ).
fof(f778,plain,
( spl0_49
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f503,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f776,plain,
spl0_48,
inference(avatar_split_clause,[],[f502,f773]) ).
fof(f773,plain,
( spl0_48
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f502,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f771,plain,
spl0_47,
inference(avatar_split_clause,[],[f501,f768]) ).
fof(f768,plain,
( spl0_47
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f501,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f766,plain,
spl0_46,
inference(avatar_split_clause,[],[f500,f763]) ).
fof(f763,plain,
( spl0_46
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f500,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f761,plain,
spl0_45,
inference(avatar_split_clause,[],[f499,f758]) ).
fof(f758,plain,
( spl0_45
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f499,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f756,plain,
spl0_44,
inference(avatar_split_clause,[],[f498,f753]) ).
fof(f753,plain,
( spl0_44
<=> class_Ring__and__Field_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f498,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
fof(f751,plain,
spl0_43,
inference(avatar_split_clause,[],[f497,f748]) ).
fof(f497,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f746,plain,
spl0_42,
inference(avatar_split_clause,[],[f496,f743]) ).
fof(f743,plain,
( spl0_42
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f496,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f741,plain,
spl0_41,
inference(avatar_split_clause,[],[f495,f738]) ).
fof(f495,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f736,plain,
spl0_40,
inference(avatar_split_clause,[],[f494,f733]) ).
fof(f733,plain,
( spl0_40
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f494,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f731,plain,
spl0_39,
inference(avatar_split_clause,[],[f493,f728]) ).
fof(f728,plain,
( spl0_39
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f493,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f726,plain,
spl0_38,
inference(avatar_split_clause,[],[f492,f723]) ).
fof(f723,plain,
( spl0_38
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f492,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(f721,plain,
spl0_37,
inference(avatar_split_clause,[],[f491,f718]) ).
fof(f491,axiom,
class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
fof(f716,plain,
spl0_36,
inference(avatar_split_clause,[],[f490,f713]) ).
fof(f713,plain,
( spl0_36
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f490,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f711,plain,
spl0_35,
inference(avatar_split_clause,[],[f489,f708]) ).
fof(f489,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f706,plain,
spl0_34,
inference(avatar_split_clause,[],[f488,f703]) ).
fof(f703,plain,
( spl0_34
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f488,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f701,plain,
spl0_33,
inference(avatar_split_clause,[],[f487,f698]) ).
fof(f487,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f696,plain,
spl0_32,
inference(avatar_split_clause,[],[f486,f693]) ).
fof(f693,plain,
( spl0_32
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f486,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f691,plain,
spl0_31,
inference(avatar_split_clause,[],[f485,f688]) ).
fof(f688,plain,
( spl0_31
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f485,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f686,plain,
spl0_30,
inference(avatar_split_clause,[],[f484,f683]) ).
fof(f683,plain,
( spl0_30
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f484,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f681,plain,
spl0_29,
inference(avatar_split_clause,[],[f483,f678]) ).
fof(f678,plain,
( spl0_29
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f483,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f676,plain,
spl0_28,
inference(avatar_split_clause,[],[f482,f673]) ).
fof(f673,plain,
( spl0_28
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f482,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f671,plain,
spl0_27,
inference(avatar_split_clause,[],[f481,f668]) ).
fof(f668,plain,
( spl0_27
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f481,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f666,plain,
spl0_26,
inference(avatar_split_clause,[],[f480,f663]) ).
fof(f663,plain,
( spl0_26
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f480,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f661,plain,
spl0_25,
inference(avatar_split_clause,[],[f479,f658]) ).
fof(f658,plain,
( spl0_25
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f479,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f656,plain,
spl0_24,
inference(avatar_split_clause,[],[f478,f653]) ).
fof(f653,plain,
( spl0_24
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f478,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f651,plain,
spl0_23,
inference(avatar_split_clause,[],[f477,f648]) ).
fof(f648,plain,
( spl0_23
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f477,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f646,plain,
spl0_22,
inference(avatar_split_clause,[],[f476,f643]) ).
fof(f643,plain,
( spl0_22
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f476,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f641,plain,
spl0_21,
inference(avatar_split_clause,[],[f475,f638]) ).
fof(f638,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f475,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f636,plain,
spl0_20,
inference(avatar_split_clause,[],[f474,f633]) ).
fof(f633,plain,
( spl0_20
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f474,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f631,plain,
spl0_19,
inference(avatar_split_clause,[],[f473,f628]) ).
fof(f628,plain,
( spl0_19
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f473,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f626,plain,
spl0_18,
inference(avatar_split_clause,[],[f472,f623]) ).
fof(f623,plain,
( spl0_18
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f472,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f621,plain,
spl0_17,
inference(avatar_split_clause,[],[f471,f618]) ).
fof(f618,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f471,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f616,plain,
spl0_16,
inference(avatar_split_clause,[],[f470,f613]) ).
fof(f470,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f611,plain,
spl0_15,
inference(avatar_split_clause,[],[f469,f608]) ).
fof(f608,plain,
( spl0_15
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f469,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f606,plain,
spl0_14,
inference(avatar_split_clause,[],[f468,f603]) ).
fof(f603,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f468,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f601,plain,
spl0_13,
inference(avatar_split_clause,[],[f467,f598]) ).
fof(f467,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f596,plain,
spl0_12,
inference(avatar_split_clause,[],[f466,f593]) ).
fof(f593,plain,
( spl0_12
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f466,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f591,plain,
spl0_11,
inference(avatar_split_clause,[],[f465,f588]) ).
fof(f588,plain,
( spl0_11
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f465,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f586,plain,
spl0_10,
inference(avatar_split_clause,[],[f464,f583]) ).
fof(f583,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f464,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f581,plain,
spl0_9,
inference(avatar_split_clause,[],[f463,f578]) ).
fof(f463,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f576,plain,
spl0_8,
inference(avatar_split_clause,[],[f462,f573]) ).
fof(f573,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f462,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f571,plain,
spl0_7,
inference(avatar_split_clause,[],[f461,f568]) ).
fof(f568,plain,
( spl0_7
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f461,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f566,plain,
spl0_6,
inference(avatar_split_clause,[],[f460,f563]) ).
fof(f563,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f460,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f561,plain,
spl0_5,
inference(avatar_split_clause,[],[f459,f558]) ).
fof(f558,plain,
( spl0_5
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f459,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f556,plain,
spl0_4,
inference(avatar_split_clause,[],[f458,f553]) ).
fof(f553,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f458,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f551,plain,
spl0_3,
inference(avatar_split_clause,[],[f457,f548]) ).
fof(f548,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f457,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f546,plain,
spl0_2,
inference(avatar_split_clause,[],[f456,f543]) ).
fof(f543,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f456,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f541,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f452,f538]) ).
fof(f452,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV972-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 20:55:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (10096)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (10099)WARNING: value z3 for option sas not known
% 0.14/0.40 % (10097)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (10098)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (10099)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)
% 0.14/0.40 % (10100)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (10101)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)
% 0.14/0.40 % (10103)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)
% 0.14/0.40 % (10102)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)
% 0.21/0.47 TRYING [1]
% 0.21/0.49 TRYING [2]
% 0.21/0.55 % (10101)First to succeed.
% 0.21/0.56 % (10101)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10096"
% 0.21/0.56 % (10101)Refutation found. Thanks to Tanya!
% 0.21/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.57 % (10101)------------------------------
% 0.21/0.57 % (10101)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.57 % (10101)Termination reason: Refutation
% 0.21/0.57
% 0.21/0.57 % (10101)Memory used [KB]: 3313
% 0.21/0.57 % (10101)Time elapsed: 0.165 s
% 0.21/0.57 % (10101)Instructions burned: 295 (million)
% 0.21/0.57 % (10096)Success in time 0.206 s
%------------------------------------------------------------------------------