TSTP Solution File: SWV972-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------