TSTP Solution File: LCL817-1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL817-1 : 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 : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 13:50:11 EDT 2024

% Result   : Unsatisfiable 0.11s 0.34s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  477
% Syntax   : Number of formulae    :  806 ( 303 unt;   0 def)
%            Number of atoms       : 1697 ( 344 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 1567 ( 676   ~; 641   |;   0   &)
%                                         ( 250 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :  275 ( 273 usr; 251 prp; 0-4 aty)
%            Number of functors    :   48 (  48 usr;  23 con; 0-5 aty)
%            Number of variables   : 1618 (1618   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2482,plain,
    $false,
    inference(avatar_sat_refutation,[],[f315,f320,f325,f330,f335,f340,f345,f350,f355,f360,f365,f370,f375,f380,f385,f390,f395,f400,f405,f410,f414,f419,f424,f429,f433,f437,f441,f445,f449,f453,f457,f461,f465,f469,f474,f478,f482,f487,f491,f495,f499,f504,f508,f512,f516,f521,f525,f529,f533,f537,f541,f545,f550,f555,f560,f566,f570,f574,f578,f582,f586,f590,f594,f598,f603,f609,f622,f626,f630,f635,f639,f643,f647,f651,f662,f668,f672,f676,f680,f684,f688,f692,f697,f701,f705,f709,f713,f717,f721,f762,f766,f770,f774,f778,f782,f787,f791,f795,f809,f828,f832,f836,f840,f845,f849,f882,f886,f891,f895,f899,f903,f907,f911,f915,f919,f924,f928,f932,f936,f940,f944,f948,f952,f956,f961,f993,f1040,f1044,f1048,f1052,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1124,f1165,f1169,f1173,f1177,f1181,f1185,f1189,f1193,f1197,f1238,f1242,f1246,f1250,f1254,f1258,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1335,f1353,f1392,f1396,f1400,f1404,f1408,f1412,f1416,f1436,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1526,f1530,f1534,f1680,f1800,f1833,f1837,f1841,f1845,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1946,f2063,f2067,f2082,f2086,f2090,f2094,f2100,f2104,f2108,f2225,f2229,f2233,f2237,f2241,f2245,f2249,f2253,f2276,f2298,f2313,f2325,f2329,f2347,f2363,f2367,f2371,f2375,f2388,f2392,f2411,f2415,f2459,f2464,f2468,f2472,f2476,f2481]) ).

fof(f2481,plain,
    ( ~ spl0_24
    | spl0_1
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2477,f2457,f312,f426]) ).

fof(f426,plain,
    ( spl0_24
  <=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f312,plain,
    ( spl0_1
  <=> c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f2457,plain,
    ( spl0_246
  <=> ! [X0] :
        ( c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,X0,v_n____),v_T_H_H____)
        | ~ c_Type_Otyping(v_e____,X0,v_T____) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2477,plain,
    ( ~ c_Type_Otyping(v_e____,v_u____,v_T____)
    | spl0_1
    | ~ spl0_246 ),
    inference(resolution,[],[f2458,f314]) ).

fof(f314,plain,
    ( ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f312]) ).

fof(f2458,plain,
    ( ! [X0] :
        ( c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,X0,v_n____),v_T_H_H____)
        | ~ c_Type_Otyping(v_e____,X0,v_T____) )
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f2457]) ).

fof(f2476,plain,
    ( spl0_250
    | ~ spl0_50
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1814,f1532,f535,f2474]) ).

fof(f2474,plain,
    ( spl0_250
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2) != c_Lambda_OdB_OVar(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f535,plain,
    ( spl0_50
  <=> ! [X33,X46,X47] : c_Lambda_OdB_OVar(X33) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X47) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f1532,plain,
    ( spl0_197
  <=> ! [X48,X16,X26,X30] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26),X30,X48) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X16,X30,X48)),c_Lambda_Osubst(X26,X30,X48)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f1814,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2) != c_Lambda_OdB_OVar(X4)
    | ~ spl0_50
    | ~ spl0_197 ),
    inference(superposition,[],[f536,f1533]) ).

fof(f1533,plain,
    ( ! [X48,X26,X16,X30] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26),X30,X48) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X16,X30,X48)),c_Lambda_Osubst(X26,X30,X48))
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f1532]) ).

fof(f536,plain,
    ( ! [X46,X47,X33] : c_Lambda_OdB_OVar(X33) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X47)
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f535]) ).

fof(f2472,plain,
    ( spl0_249
    | ~ spl0_47
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1813,f1532,f523,f2470]) ).

fof(f2470,plain,
    ( spl0_249
  <=> ! [X4,X0,X3,X2,X1] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2) != c_Lambda_OdB_OAbs(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f523,plain,
    ( spl0_47
  <=> ! [X34,X32,X35] : c_Lambda_OdB_OAbs(X32) != hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f1813,plain,
    ( ! [X2,X3,X0,X1,X4] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X3),X1,X2) != c_Lambda_OdB_OAbs(X4)
    | ~ spl0_47
    | ~ spl0_197 ),
    inference(superposition,[],[f524,f1533]) ).

fof(f524,plain,
    ( ! [X34,X35,X32] : c_Lambda_OdB_OAbs(X32) != hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35)
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f523]) ).

fof(f2468,plain,
    ( spl0_248
    | ~ spl0_41
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1601,f1468,f497,f2466]) ).

fof(f2466,plain,
    ( spl0_248
  <=> ! [X4,X0,X3,X2,X1] : ~ hBOOL(c_List_Ofoldr(c_Lambda_Obeta,c_List_Olist_OCons(c_Lambda_OdB_OVar(X0),X1,X3),X2,X3,X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f497,plain,
    ( spl0_41
  <=> ! [X16,X37] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X37)),X16)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1468,plain,
    ( spl0_181
  <=> ! [X11,X13,X0,X12,X3,X1] : c_List_Ofoldr(X11,c_List_Olist_OCons(X1,X0,X12),X13,X12,X3) = hAPP(hAPP(X11,X1),c_List_Ofoldr(X11,X0,X13,X12,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f1601,plain,
    ( ! [X2,X3,X0,X1,X4] : ~ hBOOL(c_List_Ofoldr(c_Lambda_Obeta,c_List_Olist_OCons(c_Lambda_OdB_OVar(X0),X1,X3),X2,X3,X4))
    | ~ spl0_41
    | ~ spl0_181 ),
    inference(superposition,[],[f498,f1469]) ).

fof(f1469,plain,
    ( ! [X3,X0,X11,X1,X12,X13] : c_List_Ofoldr(X11,c_List_Olist_OCons(X1,X0,X12),X13,X12,X3) = hAPP(hAPP(X11,X1),c_List_Ofoldr(X11,X0,X13,X12,X3))
    | ~ spl0_181 ),
    inference(avatar_component_clause,[],[f1468]) ).

fof(f498,plain,
    ( ! [X37,X16] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X37)),X16))
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f497]) ).

fof(f2464,plain,
    ( spl0_247
    | ~ spl0_96
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1596,f1468,f784,f2461]) ).

fof(f2461,plain,
    ( spl0_247
  <=> v_T____ = c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f784,plain,
    ( spl0_96
  <=> v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1596,plain,
    ( v_T____ = c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)
    | ~ spl0_96
    | ~ spl0_181 ),
    inference(superposition,[],[f1469,f786]) ).

fof(f786,plain,
    ( v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f784]) ).

fof(f2459,plain,
    ( spl0_246
    | ~ spl0_54
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1442,f1414,f552,f2457]) ).

fof(f552,plain,
    ( spl0_54
  <=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f1414,plain,
    ( spl0_174
  <=> ! [X59,X16,X44,X36,X26,X37] :
        ( ~ c_Type_Otyping(X59,X26,X44)
        | c_Type_Otyping(X59,c_Lambda_Osubst(X16,X26,X37),X36)
        | ~ c_Type_Otyping(c_Type_Oshift(X59,X37,X44,tc_Type_Otype),X16,X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f1442,plain,
    ( ! [X0] :
        ( c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,X0,v_n____),v_T_H_H____)
        | ~ c_Type_Otyping(v_e____,X0,v_T____) )
    | ~ spl0_54
    | ~ spl0_174 ),
    inference(resolution,[],[f1415,f554]) ).

fof(f554,plain,
    ( c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____)
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f552]) ).

fof(f1415,plain,
    ( ! [X59,X36,X37,X44,X26,X16] :
        ( ~ c_Type_Otyping(c_Type_Oshift(X59,X37,X44,tc_Type_Otype),X16,X36)
        | c_Type_Otyping(X59,c_Lambda_Osubst(X16,X26,X37),X36)
        | ~ c_Type_Otyping(X59,X26,X44) )
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f1414]) ).

fof(f2415,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f310,f2413]) ).

fof(f2413,plain,
    ( spl0_245
  <=> ! [X15,X37,X7,X44,X36,X17,X2] :
        ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),c_List_Oappend(X2,X7,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),X36)
        | ~ c_Type_Otypings(X15,X2,X17)
        | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44)
        | c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X44,X15,X7),X36,tc_Type_Otype,tc_Type_Otype) = X44 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f310,plain,
    ! [X2,X36,X37,X44,X7,X17,X15] :
      ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),c_List_Oappend(X2,X7,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),X36)
      | ~ c_Type_Otypings(X15,X2,X17)
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44)
      | c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X44,X15,X7),X36,tc_Type_Otype,tc_Type_Otype) = X44 ),
    inference(forward_demodulation,[],[f248,f41]) ).

fof(f41,axiom,
    ! [X3,X0,X11,X5,X12,X13] : c_List_Ofoldl(X11,X13,c_List_Oappend(X0,X5,X12),X3,X12) = c_List_Ofoldl(X11,c_List_Ofoldl(X11,X13,X0,X3,X12),X5,X3,X12),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).

fof(f248,axiom,
    ! [X2,X36,X37,X44,X7,X17,X15] :
      ( ~ c_Type_Otypings(X15,X2,X17)
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44)
      | c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X44,X15,X7),X36,tc_Type_Otype,tc_Type_Otype) = X44
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).

fof(f2411,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f308,f2409]) ).

fof(f2409,plain,
    ( spl0_244
  <=> ! [X39,X30,X10] :
        ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),c_List_Olist_OCons(X30,X39,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
        | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X30,tc_Lambda_OdB)
        | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X30,c_HOL_Ozero__class_Ozero(tc_nat)),X39,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f308,plain,
    ! [X10,X39,X30] :
      ( c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),c_List_Olist_OCons(X30,X39,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X30,tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X30,c_HOL_Ozero__class_Ozero(tc_nat)),X39,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    inference(forward_demodulation,[],[f181,f67]) ).

fof(f67,axiom,
    ! [X3,X0,X11,X1,X12,X13] : c_List_Ofoldl(X11,X13,c_List_Olist_OCons(X1,X0,X12),X3,X12) = c_List_Ofoldl(X11,hAPP(hAPP(X11,X13),X1),X0,X3,X12),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).

fof(f181,axiom,
    ! [X10,X39,X30] :
      ( ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X30,tc_Lambda_OdB)
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X30,c_HOL_Ozero__class_Ozero(tc_nat)),X39,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
      | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10)),X30),X39,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).

fof(f2392,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f309,f2390]) ).

fof(f2390,plain,
    ( spl0_243
  <=> ! [X15,X37,X7,X44,X36,X17,X2] :
        ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),c_List_Oappend(X2,X7,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),X36)
        | ~ c_Type_Otypings(X15,X2,X17)
        | c_Type_Otypings(X15,X7,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X44,X15,X7))
        | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f309,plain,
    ! [X2,X36,X37,X44,X7,X17,X15] :
      ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),c_List_Oappend(X2,X7,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),X36)
      | ~ c_Type_Otypings(X15,X2,X17)
      | c_Type_Otypings(X15,X7,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X44,X15,X7))
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    inference(forward_demodulation,[],[f193,f41]) ).

fof(f193,axiom,
    ! [X2,X36,X37,X44,X7,X17,X15] :
      ( ~ c_Type_Otypings(X15,X2,X17)
      | c_Type_Otypings(X15,X7,c_Type_Osko__Type__Xvar__app__types__1__1(X36,X44,X15,X7))
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44)
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X7,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).

fof(f2388,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f55,f2386]) ).

fof(f2386,plain,
    ( spl0_242
  <=> ! [X20,X21,X13,X3,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X22)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f55,axiom,
    ! [X21,X3,X22,X13,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f2375,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f306,f2373]) ).

fof(f2373,plain,
    ( spl0_241
  <=> ! [X18,X30,X10] :
        ( c_List_Ofoldl(c_Lambda_OdB_OApp,X10,c_List_Olist_OCons(X30,X18,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) != X10
        | hAPP(hAPP(c_Lambda_OdB_OApp,X10),X30) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X30),c_List_Oappend(X18,c_List_Olist_OCons(X30,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f306,plain,
    ! [X10,X18,X30] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,X10,c_List_Olist_OCons(X30,X18,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) != X10
      | hAPP(hAPP(c_Lambda_OdB_OApp,X10),X30) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X30),c_List_Oappend(X18,c_List_Olist_OCons(X30,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    inference(forward_demodulation,[],[f108,f67]) ).

fof(f108,axiom,
    ! [X10,X18,X30] :
      ( c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X30),X18,tc_Lambda_OdB,tc_Lambda_OdB) != X10
      | hAPP(hAPP(c_Lambda_OdB_OApp,X10),X30) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,X10),X30),c_List_Oappend(X18,c_List_Olist_OCons(X30,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).

fof(f2371,plain,
    ( spl0_240
    | ~ spl0_185
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1738,f1492,f1484,f2369]) ).

fof(f2369,plain,
    ( spl0_240
  <=> ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f1484,plain,
    ( spl0_185
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
        | c_HOL_Oord__class_Oless(X13,X20,X3)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f1492,plain,
    ( spl0_187
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
        | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X20),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f1738,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1) )
    | ~ spl0_185
    | ~ spl0_187 ),
    inference(duplicate_literal_removal,[],[f1719]) ).

fof(f1719,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
        | c_HOL_Oord__class_Oless(X2,X2,X1)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
    | ~ spl0_185
    | ~ spl0_187 ),
    inference(resolution,[],[f1493,f1485]) ).

fof(f1485,plain,
    ( ! [X21,X3,X13,X20] :
        ( ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21),X3)
        | c_HOL_Oord__class_Oless(X13,X20,X3)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f1484]) ).

fof(f1493,plain,
    ( ! [X21,X3,X13,X20] :
        ( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X20),X3)
        | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
        | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3) )
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f1492]) ).

fof(f2367,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f235,f2365]) ).

fof(f2365,plain,
    ( spl0_239
  <=> ! [X26,X37,X51,X53,X16,X15,X52] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
        | ~ c_Type_Otyping(X15,X26,X52)
        | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X51),X52)
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X16,X26,X37)))
        | ~ c_Type_Otyping(c_Type_Oshift(X15,X37,X52,tc_Type_Otype),X16,X53) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f235,axiom,
    ! [X51,X37,X26,X16,X52,X15,X53] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
      | ~ c_Type_Otyping(X15,X26,X52)
      | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X51),X52)
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X16,X26,X37)))
      | ~ c_Type_Otyping(c_Type_Oshift(X15,X37,X52,tc_Type_Otype),X16,X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).

fof(f2363,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f234,f2361]) ).

fof(f2361,plain,
    ( spl0_238
  <=> ! [X52,X37,X51,X53,X16,X15,X26] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
        | ~ c_Type_Otyping(X15,X26,X51)
        | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X51),X52)
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X16,X26,X37)))
        | ~ c_Type_Otyping(c_Type_Oshift(X15,X37,X51,tc_Type_Otype),X16,X53) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f234,axiom,
    ! [X51,X37,X26,X16,X52,X15,X53] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
      | ~ c_Type_Otyping(X15,X26,X51)
      | v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X51),X52)
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X16,X26,X37)))
      | ~ c_Type_Otyping(c_Type_Oshift(X15,X37,X51,tc_Type_Otype),X16,X53) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).

fof(f2347,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f211,f2345]) ).

fof(f2345,plain,
    ( spl0_237
  <=> ! [X49,X16,X43,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X43))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X49))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X49))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f211,axiom,
    ! [X49,X16,X30,X43] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X43))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X49))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X49))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).

fof(f2329,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f307,f2327]) ).

fof(f2327,plain,
    ( spl0_236
  <=> ! [X39,X30,X10] :
        ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),c_List_Olist_OCons(X30,X39,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,X30))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X30,c_HOL_Ozero__class_Ozero(tc_nat)),X39,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f307,plain,
    ! [X10,X39,X30] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),c_List_Olist_OCons(X30,X39,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,X30))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X30,c_HOL_Ozero__class_Ozero(tc_nat)),X39,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(forward_demodulation,[],[f173,f67]) ).

fof(f173,axiom,
    ! [X10,X39,X30] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X30))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X10,X30,c_HOL_Ozero__class_Ozero(tc_nat)),X39,tc_Lambda_OdB,tc_Lambda_OdB)))
      | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10)),X30),X39,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).

fof(f2325,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f32,f2323]) ).

fof(f2323,plain,
    ( spl0_235
  <=> ! [X10,X0,X8,X5,X3,X1] :
        ( c_ListOrder_Ostep1(X10,X5,X0,X3)
        | hBOOL(hAPP(hAPP(X10,X8),X1))
        | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f32,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( c_ListOrder_Ostep1(X10,X5,X0,X3)
      | hBOOL(hAPP(hAPP(X10,X8),X1))
      | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).

fof(f2313,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f19,f2311]) ).

fof(f2311,plain,
    ( spl0_234
  <=> ! [X5,X10,X8,X0,X3,X1] :
        ( X1 = X8
        | hBOOL(hAPP(hAPP(X10,X8),X1))
        | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f19,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( X1 = X8
      | hBOOL(hAPP(hAPP(X10,X8),X1))
      | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).

fof(f2298,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f39,f2296]) ).

fof(f2296,plain,
    ( spl0_233
  <=> ! [X10,X0,X8,X5,X3,X1] :
        ( X0 = X5
        | c_ListOrder_Ostep1(X10,X5,X0,X3)
        | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f39,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( X0 = X5
      | c_ListOrder_Ostep1(X10,X5,X0,X3)
      | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).

fof(f2276,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f149,f2274]) ).

fof(f2274,plain,
    ( spl0_232
  <=> ! [X39,X30,X10] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X39,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f149,axiom,
    ! [X10,X39,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X39,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).

fof(f2253,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f304,f2251]) ).

fof(f2251,plain,
    ( spl0_231
  <=> ! [X4,X8,X3,X1] :
        ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X8,X4,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X1,c_List_Olist_OCons(X8,X4,X3),X3,X3)
        | ~ class_OrderedGroup_Osemigroup__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f304,plain,
    ! [X3,X1,X8,X4] :
      ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X8,X4,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X1,c_List_Olist_OCons(X8,X4,X3),X3,X3)
      | ~ class_OrderedGroup_Osemigroup__add(X3) ),
    inference(forward_demodulation,[],[f95,f67]) ).

fof(f95,axiom,
    ! [X3,X1,X8,X4] :
      ( ~ class_OrderedGroup_Osemigroup__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X8),X4,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X8,X4,X3,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).

fof(f2249,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f82,f2247]) ).

fof(f2247,plain,
    ( spl0_230
  <=> ! [X8,X3,X25,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X8)),X25) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f82,axiom,
    ! [X3,X1,X8,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X8)),X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

fof(f2245,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f80,f2243]) ).

fof(f2243,plain,
    ( spl0_229
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f80,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f2241,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f79,f2239]) ).

fof(f2239,plain,
    ( spl0_228
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f79,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f2237,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f78,f2235]) ).

fof(f2235,plain,
    ( spl0_227
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f78,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f2233,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f76,f2231]) ).

fof(f2231,plain,
    ( spl0_226
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21)),X20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f76,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20)),X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21)),X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f2229,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f75,f2227]) ).

fof(f2227,plain,
    ( spl0_225
  <=> ! [X13,X21,X3,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X22)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f75,axiom,
    ! [X21,X3,X22,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X22)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X22)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f2225,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f14,f2223]) ).

fof(f2223,plain,
    ( spl0_224
  <=> ! [X3,X10,X0,X5,X8,X1] :
        ( X0 = X5
        | X1 = X8
        | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f14,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( X0 = X5
      | X1 = X8
      | ~ c_ListOrder_Ostep1(X10,c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3),c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).

fof(f2108,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f220,f2106]) ).

fof(f2106,plain,
    ( spl0_223
  <=> ! [X15,X37,X36,X2] :
        ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
        | c_Type_Otyping(X15,c_Lambda_OdB_OVar(X37),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X36,X15,X37,X2),X36,tc_Type_Otype,tc_Type_Otype)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f220,axiom,
    ! [X2,X36,X37,X15] :
      ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
      | c_Type_Otyping(X15,c_Lambda_OdB_OVar(X37),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X36,X15,X37,X2),X36,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).

fof(f2104,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f217,f2102]) ).

fof(f2102,plain,
    ( spl0_222
  <=> ! [X45,X29,X40] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X40,tc_Lambda_OdB,tc_Lambda_OdB)),X45))
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X29,X40,X45),tc_Lambda_OdB,tc_Lambda_OdB) = X45 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f217,axiom,
    ! [X40,X29,X45] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X40,tc_Lambda_OdB,tc_Lambda_OdB)),X45))
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X29,X40,X45),tc_Lambda_OdB,tc_Lambda_OdB) = X45 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).

fof(f2100,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f213,f2098]) ).

fof(f2098,plain,
    ( spl0_221
  <=> ! [X16,X30,X49] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X49))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16)),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X49))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f213,axiom,
    ! [X49,X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X49))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16)),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X49))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).

fof(f2094,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f212,f2092]) ).

fof(f2092,plain,
    ( spl0_220
  <=> ! [X16,X43,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X43))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X16))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f212,axiom,
    ! [X16,X30,X43] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X43))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16)),hAPP(hAPP(c_Lambda_OdB_OApp,X43),X16))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).

fof(f2090,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f176,f2088]) ).

fof(f2088,plain,
    ( spl0_219
  <=> ! [X10,X8,X3,X25,X1] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X8))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X8),X25))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X25)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f176,axiom,
    ! [X3,X10,X1,X8,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X8))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X8),X25))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X25)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).

fof(f2086,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f130,f2084]) ).

fof(f2084,plain,
    ( spl0_218
  <=> ! [X2,X16,X26] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X26) = c_List_Ofoldl(c_Lambda_OdB_OApp,X16,c_List_Oappend(X2,c_List_Olist_OCons(X26,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f130,axiom,
    ! [X2,X26,X16] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X26) = c_List_Ofoldl(c_Lambda_OdB_OApp,X16,c_List_Oappend(X2,c_List_Olist_OCons(X26,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).

fof(f2082,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f112,f2080]) ).

fof(f2080,plain,
    ( spl0_217
  <=> ! [X13,X21,X3,X22,X20] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
        | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
        | ~ c_HOL_Oord__class_Oless(X21,X22,X3)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X22),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f112,axiom,
    ! [X21,X3,X22,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
      | ~ c_HOL_Oord__class_Oless(X21,X22,X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X22),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

fof(f2067,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f242,f2065]) ).

fof(f2065,plain,
    ( spl0_216
  <=> ! [X15,X37,X44,X36,X2] :
        ( X36 = X44
        | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
        | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f242,axiom,
    ! [X2,X36,X37,X44,X15] :
      ( X36 = X44
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X44) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).

fof(f2063,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f106,f2061]) ).

fof(f2061,plain,
    ( spl0_215
  <=> ! [X4,X1,X3] :
        ( ~ class_OrderedGroup_Omonoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X4,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X1,X4,X3,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f106,axiom,
    ! [X3,X1,X4] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X4,X3,X3)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X1,X4,X3,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).

fof(f1946,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f239,f1944]) ).

fof(f1944,plain,
    ( spl0_214
  <=> ! [X39,X30,X10] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X39,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f239,axiom,
    ! [X10,X39,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X39,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).

fof(f1935,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f230,f1933]) ).

fof(f1933,plain,
    ( spl0_213
  <=> ! [X37,X10,X16,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X16,X10,X37)),c_Lambda_Osubst(X16,X30,X37))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f230,axiom,
    ! [X10,X37,X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X16,X10,X37)),c_Lambda_Osubst(X16,X30,X37))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).

fof(f1931,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f229,f1929]) ).

fof(f1929,plain,
    ( spl0_212
  <=> ! [X37,X10,X16,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X10,X16,X37)),c_Lambda_Osubst(X30,X16,X37))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f229,axiom,
    ! [X10,X37,X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X10,X16,X37)),c_Lambda_Osubst(X30,X16,X37))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).

fof(f1927,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f222,f1925]) ).

fof(f1925,plain,
    ( spl0_211
  <=> ! [X2,X15,X36,X16] :
        ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
        | c_Type_Otyping(X15,X16,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X36,X15,X16,X2),X36,tc_Type_Otype,tc_Type_Otype)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f222,axiom,
    ! [X2,X36,X16,X15] :
      ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
      | c_Type_Otyping(X15,X16,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X36,X15,X16,X2),X36,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).

fof(f1923,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f218,f1921]) ).

fof(f1921,plain,
    ( spl0_210
  <=> ! [X15,X17,X16,X36,X2] :
        ( ~ c_Type_Otypings(X15,X2,X17)
        | ~ c_Type_Otyping(X15,X16,c_List_Ofoldr(c_Type_Otype_OFun,X17,X36,tc_Type_Otype,tc_Type_Otype))
        | c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f218,axiom,
    ! [X2,X36,X16,X17,X15] :
      ( ~ c_Type_Otypings(X15,X2,X17)
      | ~ c_Type_Otyping(X15,X16,c_List_Ofoldr(c_Type_Otype_OFun,X17,X36,tc_Type_Otype,tc_Type_Otype))
      | c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).

fof(f1919,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f205,f1917]) ).

fof(f1917,plain,
    ( spl0_209
  <=> ! [X2,X15,X36,X16] :
        ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
        | c_Type_Otyping(X15,X16,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X36,X15,X16,X2),X36,tc_Type_Otype,tc_Type_Otype)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f205,axiom,
    ! [X2,X36,X16,X15] :
      ( ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36)
      | c_Type_Otyping(X15,X16,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X36,X15,X16,X2),X36,tc_Type_Otype,tc_Type_Otype)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).

fof(f1915,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f139,f1913]) ).

fof(f1913,plain,
    ( spl0_208
  <=> ! [X3,X13,X10,X21,X20] :
        ( ~ hBOOL(hAPP(hAPP(X10,X13),X20))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X20),X21))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X13),X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f139,axiom,
    ! [X21,X3,X10,X13,X20] :
      ( ~ hBOOL(hAPP(hAPP(X10,X13),X20))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X20),X21))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X13),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).

fof(f1911,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f138,f1909]) ).

fof(f1909,plain,
    ( spl0_207
  <=> ! [X3,X13,X10,X21,X20] :
        ( ~ hBOOL(hAPP(hAPP(X10,X20),X21))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X13),X20))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X13),X21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f138,axiom,
    ! [X21,X3,X10,X13,X20] :
      ( ~ hBOOL(hAPP(hAPP(X10,X20),X21))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X13),X20))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X13),X21)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).

fof(f1907,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f128,f1905]) ).

fof(f1905,plain,
    ( spl0_206
  <=> ! [X10,X0,X8,X5,X3,X1] :
        ( c_ListOrder_Ostep1(X10,X5,X0,X3)
        | hBOOL(hAPP(hAPP(X10,X8),X1))
        | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f128,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( c_ListOrder_Ostep1(X10,X5,X0,X3)
      | hBOOL(hAPP(hAPP(X10,X8),X1))
      | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).

fof(f1903,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f110,f1901]) ).

fof(f1901,plain,
    ( spl0_205
  <=> ! [X13,X20,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X13,X3)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X20,X3)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f110,axiom,
    ! [X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X13,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X20,X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

fof(f1899,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f63,f1897]) ).

fof(f1897,plain,
    ( spl0_204
  <=> ! [X13,X20,X3] :
        ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
        | ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X3),X3)
        | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X3),X3)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f63,axiom,
    ! [X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
      | ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(X3),X3)
      | ~ c_HOL_Oord__class_Oless(X20,c_HOL_Ozero__class_Ozero(X3),X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

fof(f1845,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f305,f1843]) ).

fof(f1843,plain,
    ( spl0_203
  <=> ! [X13,X0,X3] :
        ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X13,X0,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),c_List_Olist_OCons(X13,X0,X3),c_HOL_Ozero__class_Ozero(X3),X3,X3)
        | ~ class_OrderedGroup_Omonoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f305,plain,
    ! [X3,X0,X13] :
      ( c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X13,X0,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),c_List_Olist_OCons(X13,X0,X3),c_HOL_Ozero__class_Ozero(X3),X3,X3)
      | ~ class_OrderedGroup_Omonoid__add(X3) ),
    inference(forward_demodulation,[],[f190,f118]) ).

fof(f118,axiom,
    ! [X3,X0,X11,X1,X12,X13] : c_List_Ofoldr(X11,c_List_Olist_OCons(X1,X0,X12),X13,X12,X3) = hAPP(hAPP(X11,X1),c_List_Ofoldr(X11,X0,X13,X12,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).

fof(f190,axiom,
    ! [X3,X0,X13] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X13,X0,X3,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X0,c_HOL_Ozero__class_Ozero(X3),X3,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).

fof(f1841,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f164,f1839]) ).

fof(f1839,plain,
    ( spl0_202
  <=> ! [X40,X39,X10] :
        ( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X40,X39,tc_Lambda_OdB)
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X40,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X39,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f164,axiom,
    ! [X40,X39,X10] :
      ( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X40,X39,tc_Lambda_OdB)
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X40,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X39,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).

fof(f1837,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f41,f1835]) ).

fof(f1835,plain,
    ( spl0_201
  <=> ! [X11,X0,X13,X12,X5,X3] : c_List_Ofoldl(X11,X13,c_List_Oappend(X0,X5,X12),X3,X12) = c_List_Ofoldl(X11,c_List_Ofoldl(X11,X13,X0,X3,X12),X5,X3,X12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f1833,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f20,f1831]) ).

fof(f1831,plain,
    ( spl0_200
  <=> ! [X11,X13,X0,X12,X5,X3] : c_List_Ofoldr(X11,c_List_Oappend(X0,X5,X12),X13,X12,X3) = c_List_Ofoldr(X11,X0,c_List_Ofoldr(X11,X5,X13,X12,X3),X12,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f20,axiom,
    ! [X3,X0,X11,X5,X12,X13] : c_List_Ofoldr(X11,c_List_Oappend(X0,X5,X12),X13,X12,X3) = c_List_Ofoldr(X11,X0,c_List_Ofoldr(X11,X5,X13,X12,X3),X12,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).

fof(f1800,plain,
    ( spl0_199
    | ~ spl0_50
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1274,f1256,f535,f1798]) ).

fof(f1798,plain,
    ( spl0_199
  <=> ! [X2,X0,X1,X3] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1) != c_Lambda_OdB_OVar(X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f1256,plain,
    ( spl0_153
  <=> ! [X48,X16,X30] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16),X48) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X30,X48)),c_Lambda_Olift(X16,X48)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f1274,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1) != c_Lambda_OdB_OVar(X3)
    | ~ spl0_50
    | ~ spl0_153 ),
    inference(superposition,[],[f536,f1257]) ).

fof(f1257,plain,
    ( ! [X48,X16,X30] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16),X48) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X30,X48)),c_Lambda_Olift(X16,X48))
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1256]) ).

fof(f1680,plain,
    ( spl0_198
    | ~ spl0_47
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1273,f1256,f523,f1678]) ).

fof(f1678,plain,
    ( spl0_198
  <=> ! [X2,X0,X1,X3] : c_Lambda_OdB_OAbs(X3) != c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f1273,plain,
    ( ! [X2,X3,X0,X1] : c_Lambda_OdB_OAbs(X3) != c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X0),X2),X1)
    | ~ spl0_47
    | ~ spl0_153 ),
    inference(superposition,[],[f524,f1257]) ).

fof(f1534,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f258,f1532]) ).

fof(f258,axiom,
    ! [X48,X26,X16,X30] : c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26),X30,X48) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(X16,X30,X48)),c_Lambda_Osubst(X26,X30,X48)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).

fof(f1530,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f246,f1528]) ).

fof(f1528,plain,
    ( spl0_196
  <=> ! [X44,X50,X36,X16,X30] :
        ( ~ c_Type_Otyping(X50,X16,X36)
        | ~ c_Type_Otyping(X50,X30,hAPP(hAPP(c_Type_Otype_OFun,X36),X44))
        | c_Type_Otyping(X50,hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16),X44) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f246,axiom,
    ! [X50,X36,X44,X16,X30] :
      ( ~ c_Type_Otyping(X50,X16,X36)
      | ~ c_Type_Otyping(X50,X30,hAPP(hAPP(c_Type_Otype_OFun,X36),X44))
      | c_Type_Otyping(X50,hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16),X44) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).

fof(f1526,plain,
    ( spl0_195
    | ~ spl0_59
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1141,f1071,f576,f1524]) ).

fof(f1524,plain,
    ( spl0_195
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OAbs(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f576,plain,
    ( spl0_59
  <=> ! [X13,X12,X11,X3] : c_List_Ofoldl(X11,X13,c_List_Olist_ONil(X12),X3,X12) = X13 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f1071,plain,
    ( spl0_135
  <=> ! [X29,X2,X39,X10] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X39,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f1141,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OAbs(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_59
    | ~ spl0_135 ),
    inference(superposition,[],[f1072,f577]) ).

fof(f577,plain,
    ( ! [X3,X11,X12,X13] : c_List_Ofoldl(X11,X13,c_List_Olist_ONil(X12),X3,X12) = X13
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f576]) ).

fof(f1072,plain,
    ( ! [X2,X10,X29,X39] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X39,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1071]) ).

fof(f1522,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f241,f1520]) ).

fof(f1520,plain,
    ( spl0_194
  <=> ! [X37,X30,X10] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X10,X37)),c_Lambda_Olift(X30,X37))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f241,axiom,
    ! [X10,X37,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X10),X30))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Olift(X10,X37)),c_Lambda_Olift(X30,X37))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).

fof(f1518,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f226,f1516]) ).

fof(f1516,plain,
    ( spl0_193
  <=> ! [X37,X10,X16,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X16,X10,X37)),c_Lambda_Osubst(X16,X30,X37))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f226,axiom,
    ! [X10,X37,X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(X16,X10,X37)),c_Lambda_Osubst(X16,X30,X37))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).

fof(f1514,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f210,f1512]) ).

fof(f1512,plain,
    ( spl0_192
  <=> ! [X16,X30,X26] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X16))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X30)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X16))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f210,axiom,
    ! [X26,X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X16))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X30)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X16))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).

fof(f1510,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f209,f1508]) ).

fof(f1508,plain,
    ( spl0_191
  <=> ! [X16,X30,X26] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X16))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X30),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f209,axiom,
    ! [X26,X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X16))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X30),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).

fof(f1506,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f203,f1504]) ).

fof(f1504,plain,
    ( spl0_190
  <=> ! [X16,X36,X15,X26] :
        ( ~ c_Type_Otyping(X15,hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26),X36)
        | c_Type_Otyping(X15,X16,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X36,X15,X16,X26)),X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f203,axiom,
    ! [X36,X26,X16,X15] :
      ( ~ c_Type_Otyping(X15,hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26),X36)
      | c_Type_Otyping(X15,X16,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X36,X15,X16,X26)),X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).

fof(f1502,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f198,f1500]) ).

fof(f1500,plain,
    ( spl0_189
  <=> ! [X45,X29,X40] :
        ( c_ListOrder_Ostep1(c_Lambda_Obeta,X40,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X29,X40,X45),tc_Lambda_OdB)
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X40,tc_Lambda_OdB,tc_Lambda_OdB)),X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f198,axiom,
    ! [X40,X29,X45] :
      ( c_ListOrder_Ostep1(c_Lambda_Obeta,X40,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X29,X40,X45),tc_Lambda_OdB)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X40,tc_Lambda_OdB,tc_Lambda_OdB)),X45)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).

fof(f1498,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f125,f1496]) ).

fof(f1496,plain,
    ( spl0_188
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
        | c_HOL_Oord__class_Oless(X13,X20,X3)
        | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X20),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f125,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X13,X20,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X20),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

fof(f1494,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f124,f1492]) ).

fof(f124,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X20),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

fof(f1490,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f123,f1488]) ).

fof(f1488,plain,
    ( spl0_186
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
        | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X20),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f123,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X20),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

fof(f1486,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f122,f1484]) ).

fof(f122,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | c_HOL_Oord__class_Oless(X13,X20,X3)
      | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

fof(f1482,plain,
    ( spl0_184
    | ~ spl0_59
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1140,f1071,f576,f1480]) ).

fof(f1480,plain,
    ( spl0_184
  <=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f1140,plain,
    ( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)
    | ~ spl0_59
    | ~ spl0_135 ),
    inference(superposition,[],[f1072,f577]) ).

fof(f1478,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f121,f1476]) ).

fof(f1476,plain,
    ( spl0_183
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
        | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f121,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
      | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

fof(f1474,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f120,f1472]) ).

fof(f1472,plain,
    ( spl0_182
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
        | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
        | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f120,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
      | ~ c_HOL_Oord__class_Oless(X13,X20,X3)
      | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X21),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

fof(f1470,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f118,f1468]) ).

fof(f1466,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f117,f1464]) ).

fof(f1464,plain,
    ( spl0_180
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X3)
        | ~ c_HOL_Oord__class_Oless(X20,X21,X3)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X13,X3)
        | c_HOL_Oord__class_Oless(X20,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f117,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(X20,X21,X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X13,X3)
      | c_HOL_Oord__class_Oless(X20,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

fof(f1462,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f67,f1460]) ).

fof(f1460,plain,
    ( spl0_179
  <=> ! [X3,X11,X0,X13,X12,X1] : c_List_Ofoldl(X11,X13,c_List_Olist_OCons(X1,X0,X12),X3,X12) = c_List_Ofoldl(X11,hAPP(hAPP(X11,X13),X1),X0,X3,X12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1458,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f56,f1456]) ).

fof(f1456,plain,
    ( spl0_178
  <=> ! [X5,X10,X8,X0,X3,X1] :
        ( X1 = X8
        | hBOOL(hAPP(hAPP(X10,X8),X1))
        | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f56,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( X1 = X8
      | hBOOL(hAPP(hAPP(X10,X8),X1))
      | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).

fof(f1454,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f7,f1452]) ).

fof(f1452,plain,
    ( spl0_177
  <=> ! [X3,X0,X5,X8,X1] :
        ( X0 = X5
        | c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f7,axiom,
    ! [X3,X0,X1,X8,X5] :
      ( X0 = X5
      | c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).

fof(f1450,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f6,f1448]) ).

fof(f1448,plain,
    ( spl0_176
  <=> ! [X3,X0,X8,X5,X1] :
        ( X1 = X8
        | c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f6,axiom,
    ! [X3,X0,X1,X8,X5] :
      ( X1 = X8
      | c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3) != c_List_Oappend(X5,c_List_Olist_OCons(X8,c_List_Olist_ONil(X3),X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).

fof(f1436,plain,
    ( spl0_175
    | ~ spl0_96
    | ~ spl0_122 ),
    inference(avatar_split_clause,[],[f1033,f946,f784,f1434]) ).

fof(f1434,plain,
    ( spl0_175
  <=> ! [X0,X1] :
        ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X0),X1)
        | v_T_H_H____ = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f946,plain,
    ( spl0_122
  <=> ! [X55,X54,X56,X57] :
        ( X54 = X56
        | hAPP(hAPP(c_Type_Otype_OFun,X54),X55) != hAPP(hAPP(c_Type_Otype_OFun,X56),X57) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f1033,plain,
    ( ! [X0,X1] :
        ( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X0),X1)
        | v_T_H_H____ = X0 )
    | ~ spl0_96
    | ~ spl0_122 ),
    inference(superposition,[],[f947,f786]) ).

fof(f947,plain,
    ( ! [X56,X54,X57,X55] :
        ( hAPP(hAPP(c_Type_Otype_OFun,X54),X55) != hAPP(hAPP(c_Type_Otype_OFun,X56),X57)
        | X54 = X56 )
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f946]) ).

fof(f1416,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f269,f1414]) ).

fof(f269,axiom,
    ! [X59,X36,X37,X44,X26,X16] :
      ( ~ c_Type_Otyping(X59,X26,X44)
      | c_Type_Otyping(X59,c_Lambda_Osubst(X16,X26,X37),X36)
      | ~ c_Type_Otyping(c_Type_Oshift(X59,X37,X44,tc_Type_Otype),X16,X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).

fof(f1412,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f152,f1410]) ).

fof(f1410,plain,
    ( spl0_173
  <=> ! [X0,X3] :
        ( ~ class_OrderedGroup_Omonoid__add(X3)
        | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X0,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X0,c_HOL_Ozero__class_Ozero(X3),X3,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f152,axiom,
    ! [X3,X0] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3),X0,X3,X3) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X0,c_HOL_Ozero__class_Ozero(X3),X3,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).

fof(f1408,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f111,f1406]) ).

fof(f1406,plain,
    ( spl0_172
  <=> ! [X10,X0,X8,X5,X3,X1] :
        ( X0 = X5
        | c_ListOrder_Ostep1(X10,X5,X0,X3)
        | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f111,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( X0 = X5
      | c_ListOrder_Ostep1(X10,X5,X0,X3)
      | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).

fof(f1404,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f66,f1402]) ).

fof(f1402,plain,
    ( spl0_171
  <=> ! [X10,X8,X3,X1] :
        ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X8),X1))
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X1),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f66,axiom,
    ! [X3,X10,X1,X8] :
      ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X8),X1))
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X1),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).

fof(f1400,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f65,f1398]) ).

fof(f1398,plain,
    ( spl0_170
  <=> ! [X10,X8,X3,X1] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X8),X1))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X1),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f65,axiom,
    ! [X3,X10,X1,X8] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X8),X1))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(X10,X3,X3),X3),X1),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).

fof(f1396,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f33,f1394]) ).

fof(f1394,plain,
    ( spl0_169
  <=> ! [X15,X17,X16,X2] :
        ( c_Type_Otyping(X15,X16,c_Type_Osko__Type__Xtypes__snocE__1__2(X17,X15,X16,X2))
        | ~ c_Type_Otypings(X15,c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X17) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f33,axiom,
    ! [X2,X16,X17,X15] :
      ( c_Type_Otyping(X15,X16,c_Type_Osko__Type__Xtypes__snocE__1__2(X17,X15,X16,X2))
      | ~ c_Type_Otypings(X15,c_List_Oappend(X2,c_List_Olist_OCons(X16,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_types__snocE_2) ).

fof(f1392,plain,
    ( spl0_168
    | ~ spl0_52
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f824,f793,f543,f1390]) ).

fof(f1390,plain,
    ( spl0_168
  <=> ! [X0,X1] :
        ( hBOOL(hAPP(c_InductTermi_OIT,X0))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f543,plain,
    ( spl0_52
  <=> ! [X48,X16,X30] : c_Lambda_Osubst(c_Lambda_Olift(X16,X48),X30,X48) = X16 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f793,plain,
    ( spl0_98
  <=> ! [X38,X37,X10] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X10))
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X10,c_Lambda_OdB_OVar(X37),X38))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f824,plain,
    ( ! [X0,X1] :
        ( hBOOL(hAPP(c_InductTermi_OIT,X0))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X0,X1))) )
    | ~ spl0_52
    | ~ spl0_98 ),
    inference(superposition,[],[f794,f544]) ).

fof(f544,plain,
    ( ! [X48,X16,X30] : c_Lambda_Osubst(c_Lambda_Olift(X16,X48),X30,X48) = X16
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f543]) ).

fof(f794,plain,
    ( ! [X38,X10,X37] :
        ( hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X10,c_Lambda_OdB_OVar(X37),X38)))
        | ~ hBOOL(hAPP(c_InductTermi_OIT,X10)) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f793]) ).

fof(f1353,plain,
    ( spl0_167
    | ~ spl0_39
    | ~ spl0_92 ),
    inference(avatar_split_clause,[],[f802,f768,f489,f1351]) ).

fof(f1351,plain,
    ( spl0_167
  <=> ! [X2,X0,X1] :
        ( c_List_Oappend(X2,c_List_Olist_ONil(X1),X1) != X0
        | X0 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f489,plain,
    ( spl0_39
  <=> ! [X0,X3] : c_List_Oappend(X0,c_List_Olist_ONil(X3),X3) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f768,plain,
    ( spl0_92
  <=> ! [X4,X0,X5,X3] :
        ( X4 = X5
        | c_List_Oappend(X5,X0,X3) != c_List_Oappend(X4,X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f802,plain,
    ( ! [X2,X0,X1] :
        ( c_List_Oappend(X2,c_List_Olist_ONil(X1),X1) != X0
        | X0 = X2 )
    | ~ spl0_39
    | ~ spl0_92 ),
    inference(superposition,[],[f769,f490]) ).

fof(f490,plain,
    ( ! [X3,X0] : c_List_Oappend(X0,c_List_Olist_ONil(X3),X3) = X0
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f489]) ).

fof(f769,plain,
    ( ! [X3,X0,X4,X5] :
        ( c_List_Oappend(X5,X0,X3) != c_List_Oappend(X4,X0,X3)
        | X4 = X5 )
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f768]) ).

fof(f1335,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f301,f1332]) ).

fof(f1332,plain,
    ( spl0_166
  <=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f301,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    inference(definition_unfolding,[],[f224,f263]) ).

fof(f263,axiom,
    v_i____ = v_n____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).

fof(f224,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_headT_0) ).

fof(f1330,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f265,f1328]) ).

fof(f1328,plain,
    ( spl0_165
  <=> ! [X37,X10,X16,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X10,X16,X37)),c_Lambda_Osubst(X30,X16,X37))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f265,axiom,
    ! [X10,X37,X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(X10,X16,X37)),c_Lambda_Osubst(X30,X16,X37))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).

fof(f1326,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f254,f1324]) ).

fof(f1324,plain,
    ( spl0_164
  <=> ! [X40,X29,X19,X39] :
        ( X19 = X29
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X19),X40,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f254,axiom,
    ! [X40,X39,X29,X19] :
      ( X19 = X29
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X19),X40,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).

fof(f1322,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f253,f1320]) ).

fof(f1320,plain,
    ( spl0_163
  <=> ! [X29,X39,X40,X19] :
        ( X39 = X40
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X19),X40,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f253,axiom,
    ! [X40,X39,X29,X19] :
      ( X39 = X40
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X19),X40,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).

fof(f1318,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f232,f1316]) ).

fof(f1316,plain,
    ( spl0_162
  <=> ! [X44,X50,X36,X16] :
        ( ~ c_Type_Otyping(c_Type_Oshift(X50,c_HOL_Ozero__class_Ozero(tc_nat),X36,tc_Type_Otype),X16,X44)
        | c_Type_Otyping(X50,c_Lambda_OdB_OAbs(X16),hAPP(hAPP(c_Type_Otype_OFun,X36),X44)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f232,axiom,
    ! [X50,X36,X44,X16] :
      ( ~ c_Type_Otyping(c_Type_Oshift(X50,c_HOL_Ozero__class_Ozero(tc_nat),X36,tc_Type_Otype),X16,X44)
      | c_Type_Otyping(X50,c_Lambda_OdB_OAbs(X16),hAPP(hAPP(c_Type_Otype_OFun,X36),X44)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).

fof(f1314,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f180,f1312]) ).

fof(f1312,plain,
    ( spl0_161
  <=> ! [X43,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X43))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X30)),c_Lambda_OdB_OAbs(X43))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f180,axiom,
    ! [X30,X43] :
      ( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X30),X43))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X30)),c_Lambda_OdB_OAbs(X43))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).

fof(f1310,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f155,f1308]) ).

fof(f1308,plain,
    ( spl0_160
  <=> ! [X39,X40,X30,X10] :
        ( X39 = X40
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X40,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30),X39,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f155,axiom,
    ! [X40,X39,X10,X30] :
      ( X39 = X40
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X40,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30),X39,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).

fof(f1306,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f154,f1304]) ).

fof(f1304,plain,
    ( spl0_159
  <=> ! [X40,X10,X30,X39] :
        ( X10 = X30
        | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X40,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30),X39,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f154,axiom,
    ! [X40,X10,X39,X30] :
      ( X10 = X30
      | c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X40,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30),X39,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).

fof(f1302,plain,
    ( spl0_158
    | ~ spl0_38
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f796,f764,f485,f1300]) ).

fof(f1300,plain,
    ( spl0_158
  <=> ! [X2,X0,X1] :
        ( c_List_Oappend(c_List_Olist_ONil(X0),X2,X0) != X1
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f485,plain,
    ( spl0_38
  <=> ! [X5,X3] : c_List_Oappend(c_List_Olist_ONil(X3),X5,X3) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f764,plain,
    ( spl0_91
  <=> ! [X4,X0,X5,X3] :
        ( X4 = X5
        | c_List_Oappend(X0,X5,X3) != c_List_Oappend(X0,X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f796,plain,
    ( ! [X2,X0,X1] :
        ( c_List_Oappend(c_List_Olist_ONil(X0),X2,X0) != X1
        | X1 = X2 )
    | ~ spl0_38
    | ~ spl0_91 ),
    inference(superposition,[],[f765,f486]) ).

fof(f486,plain,
    ( ! [X3,X5] : c_List_Oappend(c_List_Olist_ONil(X3),X5,X3) = X5
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f485]) ).

fof(f765,plain,
    ( ! [X3,X0,X4,X5] :
        ( c_List_Oappend(X0,X5,X3) != c_List_Oappend(X0,X4,X3)
        | X4 = X5 )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f764]) ).

fof(f1298,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f143,f1296]) ).

fof(f1296,plain,
    ( spl0_157
  <=> ! [X15,X37,X36,X2] :
        ( c_Type_Otypings(X15,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X36,X15,X37,X2))
        | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f143,axiom,
    ! [X2,X36,X37,X15] :
      ( c_Type_Otypings(X15,X2,c_Type_Osko__Type__Xvar__app__typesE__1__1(X36,X15,X37,X2))
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X37),X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).

fof(f1294,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f61,f1292]) ).

fof(f1292,plain,
    ( spl0_156
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
        | X20 = X21
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f61,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
      | X20 = X21
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f1290,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f60,f1288]) ).

fof(f1288,plain,
    ( spl0_155
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
        | X20 = X21
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f60,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | X20 = X21
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f1286,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f59,f1284]) ).

fof(f1284,plain,
    ( spl0_154
  <=> ! [X13,X3,X21,X20] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
        | X20 = X21
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f59,axiom,
    ! [X21,X3,X13,X20] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
      | X20 = X21
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X13) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X21),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f1258,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f228,f1256]) ).

fof(f228,axiom,
    ! [X48,X16,X30] : c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,X30),X16),X48) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(X30,X48)),c_Lambda_Olift(X16,X48)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).

fof(f1254,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f187,f1252]) ).

fof(f1252,plain,
    ( spl0_152
  <=> ! [X15,X36,X16,X2] :
        ( c_Type_Otypings(X15,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X36,X15,X16,X2))
        | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f187,axiom,
    ! [X2,X36,X16,X15] :
      ( c_Type_Otypings(X15,X2,c_Type_Osko__Type__Xlist__app__typeE__1__1(X36,X15,X16,X2))
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).

fof(f1250,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f145,f1248]) ).

fof(f1248,plain,
    ( spl0_151
  <=> ! [X15,X36,X16,X2] :
        ( c_Type_Otypings(X15,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X36,X15,X16,X2))
        | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f145,axiom,
    ! [X2,X36,X16,X15] :
      ( c_Type_Otypings(X15,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X36,X15,X16,X2))
      | ~ c_Type_Otyping(X15,c_List_Ofoldl(c_Lambda_OdB_OApp,X16,X2,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).

fof(f1246,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f99,f1244]) ).

fof(f1244,plain,
    ( spl0_150
  <=> ! [X13,X0,X3] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
        | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X0,X13,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X13,X0,X3,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f99,axiom,
    ! [X3,X0,X13] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X3)
      | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X3),X0,X13,X3,X3) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X3),X13,X0,X3,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).

fof(f1242,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f86,f1240]) ).

fof(f1240,plain,
    ( spl0_149
  <=> ! [X18,X10,X3,X8,X1] :
        ( ~ hBOOL(hAPP(hAPP(X10,X8),X18))
        | c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X1,X3),c_List_Olist_OCons(X18,X1,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f86,axiom,
    ! [X3,X10,X18,X8,X1] :
      ( ~ hBOOL(hAPP(hAPP(X10,X8),X18))
      | c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X1,X3),c_List_Olist_OCons(X18,X1,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).

fof(f1238,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f85,f1236]) ).

fof(f1236,plain,
    ( spl0_148
  <=> ! [X3,X10,X0,X8,X5,X1] :
        ( X1 = X8
        | X0 = X5
        | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f85,axiom,
    ! [X3,X10,X0,X1,X8,X5] :
      ( X1 = X8
      | X0 = X5
      | ~ c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X8,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).

fof(f1197,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f216,f1195]) ).

fof(f1195,plain,
    ( spl0_147
  <=> ! [X16,X36,X15,X26] :
        ( ~ c_Type_Otyping(X15,hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26),X36)
        | c_Type_Otyping(X15,X26,c_Type_Osko__Type__Xtyping__elims__2__1(X36,X15,X16,X26)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f216,axiom,
    ! [X36,X26,X16,X15] :
      ( ~ c_Type_Otyping(X15,hAPP(hAPP(c_Lambda_OdB_OApp,X16),X26),X36)
      | c_Type_Otyping(X15,X26,c_Type_Osko__Type__Xtyping__elims__2__1(X36,X15,X16,X26)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).

fof(f1193,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f208,f1191]) ).

fof(f1191,plain,
    ( spl0_146
  <=> ! [X15,X16,X36,X49] :
        ( ~ c_Type_Otyping(X15,X16,X36)
        | c_Type_Otyping(X15,X49,X36)
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X49)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f208,axiom,
    ! [X36,X49,X16,X15] :
      ( ~ c_Type_Otyping(X15,X16,X36)
      | c_Type_Otyping(X15,X49,X36)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X16),X49)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).

fof(f1189,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f206,f1187]) ).

fof(f1187,plain,
    ( spl0_145
  <=> ! [X37,X30,X10] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X10,X37)),c_Lambda_Olift(X30,X37))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f206,axiom,
    ! [X10,X37,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X10),X30))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Olift(X10,X37)),c_Lambda_Olift(X30,X37))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).

fof(f1185,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f192,f1183]) ).

fof(f1183,plain,
    ( spl0_144
  <=> ! [X2,X30,X10] :
        ( X10 = X30
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X2,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f192,axiom,
    ! [X2,X10,X30] :
      ( X10 = X30
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X10,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).

fof(f1181,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f129,f1179]) ).

fof(f1179,plain,
    ( spl0_143
  <=> ! [X10,X0,X5,X3,X1] :
        ( ~ c_ListOrder_Ostep1(X10,X5,X0,X3)
        | c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f129,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( ~ c_ListOrder_Ostep1(X10,X5,X0,X3)
      | c_ListOrder_Ostep1(X10,c_List_Olist_OCons(X1,X5,X3),c_List_Olist_OCons(X1,X0,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).

fof(f1177,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f89,f1175]) ).

fof(f1175,plain,
    ( spl0_142
  <=> ! [X10,X13,X3,X20] :
        ( ~ c_Wellfounded_Oaccp(X10,X13,X3)
        | c_Wellfounded_Oaccp(X10,X20,X3)
        | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X20),X13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f89,axiom,
    ! [X3,X10,X13,X20] :
      ( ~ c_Wellfounded_Oaccp(X10,X13,X3)
      | c_Wellfounded_Oaccp(X10,X20,X3)
      | ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X20),X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).

fof(f1173,plain,
    ( spl0_141
    | ~ spl0_44
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f887,f807,f510,f1171]) ).

fof(f1171,plain,
    ( spl0_141
  <=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f510,plain,
    ( spl0_44
  <=> ! [X50,X1] : c_Type_Otyping(X50,c_Lambda_OdB_OVar(X1),hAPP(X50,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f807,plain,
    ( spl0_99
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f887,plain,
    ( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(X0),X0)
    | ~ spl0_44
    | ~ spl0_99 ),
    inference(superposition,[],[f511,f808]) ).

fof(f808,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f807]) ).

fof(f511,plain,
    ( ! [X50,X1] : c_Type_Otyping(X50,c_Lambda_OdB_OVar(X1),hAPP(X50,X1))
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f510]) ).

fof(f1169,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f31,f1167]) ).

fof(f1167,plain,
    ( spl0_140
  <=> ! [X10,X0,X5,X3,X1] :
        ( ~ c_ListOrder_Ostep1(X10,X5,X0,X3)
        | c_ListOrder_Ostep1(X10,c_List_Oappend(X5,X1,X3),c_List_Oappend(X0,X1,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f31,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( ~ c_ListOrder_Ostep1(X10,X5,X0,X3)
      | c_ListOrder_Ostep1(X10,c_List_Oappend(X5,X1,X3),c_List_Oappend(X0,X1,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).

fof(f1165,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f30,f1163]) ).

fof(f1163,plain,
    ( spl0_139
  <=> ! [X7,X14,X10,X3,X1] :
        ( ~ c_ListOrder_Ostep1(X10,X14,X7,X3)
        | c_ListOrder_Ostep1(X10,c_List_Oappend(X1,X14,X3),c_List_Oappend(X1,X7,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f30,axiom,
    ! [X3,X10,X1,X7,X14] :
      ( ~ c_ListOrder_Ostep1(X10,X14,X7,X3)
      | c_ListOrder_Ostep1(X10,c_List_Oappend(X1,X14,X3),c_List_Oappend(X1,X7,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).

fof(f1124,plain,
    ( spl0_138
    | ~ spl0_44
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f841,f760,f510,f1122]) ).

fof(f1122,plain,
    ( spl0_138
  <=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f760,plain,
    ( spl0_90
  <=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f841,plain,
    ( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
    | ~ spl0_44
    | ~ spl0_90 ),
    inference(superposition,[],[f511,f761]) ).

fof(f761,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f760]) ).

fof(f1081,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f240,f1079]) ).

fof(f1079,plain,
    ( spl0_137
  <=> ! [X16,X30] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30)),X16)),c_Lambda_Osubst(X30,X16,c_HOL_Ozero__class_Ozero(tc_nat)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f240,axiom,
    ! [X16,X30] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30)),X16)),c_Lambda_Osubst(X30,X16,c_HOL_Ozero__class_Ozero(tc_nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).

fof(f1077,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f221,f1075]) ).

fof(f1075,plain,
    ( spl0_136
  <=> ! [X48,X37,X30] :
        ( X37 = X48
        | c_HOL_Oord__class_Oless(X48,X37,tc_nat)
        | c_Lambda_OdB_OVar(X37) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X37),X30,X48) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f221,axiom,
    ! [X48,X37,X30] :
      ( X37 = X48
      | c_HOL_Oord__class_Oless(X48,X37,tc_nat)
      | c_Lambda_OdB_OVar(X37) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X37),X30,X48) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).

fof(f1073,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f172,f1071]) ).

fof(f172,axiom,
    ! [X2,X10,X29,X39] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X10),X39,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).

fof(f1069,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f146,f1067]) ).

fof(f1067,plain,
    ( spl0_134
  <=> ! [X38,X36,X3,X15,X37] :
        ( ~ c_HOL_Oord__class_Oless(X38,X37,tc_nat)
        | hAPP(c_Type_Oshift(X15,X37,X36,X3),X38) = hAPP(X15,X38) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f146,axiom,
    ! [X38,X3,X36,X37,X15] :
      ( ~ c_HOL_Oord__class_Oless(X38,X37,tc_nat)
      | hAPP(c_Type_Oshift(X15,X37,X36,X3),X38) = hAPP(X15,X38) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).

fof(f1065,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f94,f1063]) ).

fof(f1063,plain,
    ( spl0_133
  <=> ! [X1,X8,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f94,axiom,
    ! [X3,X1,X8] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

fof(f1061,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f93,f1059]) ).

fof(f1059,plain,
    ( spl0_132
  <=> ! [X13,X20,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f93,axiom,
    ! [X3,X13,X20] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X20),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f1057,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f71,f1055]) ).

fof(f1055,plain,
    ( spl0_131
  <=> ! [X10,X13,X12,X3,X20] :
        ( ~ hBOOL(hAPP(hAPP(X10,X20),X13))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X12),X13),X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f71,axiom,
    ! [X3,X10,X12,X13,X20] :
      ( ~ hBOOL(hAPP(hAPP(X10,X20),X13))
      | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X12),X13),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).

fof(f1052,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f70,f1050]) ).

fof(f1050,plain,
    ( spl0_130
  <=> ! [X10,X13,X12,X3,X20] :
        ( hBOOL(hAPP(hAPP(X10,X20),X13))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X12),X13),X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f70,axiom,
    ! [X3,X10,X12,X13,X20] :
      ( hBOOL(hAPP(hAPP(X10,X20),X13))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X3,X12),X13),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).

fof(f1048,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f37,f1046]) ).

fof(f1046,plain,
    ( spl0_129
  <=> ! [X3,X4,X6,X1] : c_List_Olist_OCons(X1,c_List_Oappend(X6,X4,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X1,X6,X3),X4,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f37,axiom,
    ! [X3,X1,X6,X4] : c_List_Olist_OCons(X1,c_List_Oappend(X6,X4,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X1,X6,X3),X4,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).

fof(f1044,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f13,f1042]) ).

fof(f1042,plain,
    ( spl0_128
  <=> ! [X9,X0,X5,X3] :
        ( ~ c_List_Olistsp(X9,X0,X3)
        | ~ c_List_Olistsp(X9,X5,X3)
        | c_List_Olistsp(X9,c_List_Oappend(X0,X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f13,axiom,
    ! [X3,X0,X9,X5] :
      ( ~ c_List_Olistsp(X9,X0,X3)
      | ~ c_List_Olistsp(X9,X5,X3)
      | c_List_Olistsp(X9,c_List_Oappend(X0,X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).

fof(f1040,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f3,f1038]) ).

fof(f1038,plain,
    ( spl0_127
  <=> ! [X0,X6,X3,X7] : c_List_Oappend(X0,c_List_Oappend(X6,X7,X3),X3) = c_List_Oappend(c_List_Oappend(X0,X6,X3),X7,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f3,axiom,
    ! [X3,X0,X6,X7] : c_List_Oappend(X0,c_List_Oappend(X6,X7,X3),X3) = c_List_Oappend(c_List_Oappend(X0,X6,X3),X7,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).

fof(f993,plain,
    ( spl0_126
    | ~ spl0_35
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f816,f780,f471,f991]) ).

fof(f991,plain,
    ( spl0_126
  <=> ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_as____ = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f471,plain,
    ( spl0_35
  <=> v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f780,plain,
    ( spl0_95
  <=> ! [X24,X23,X13,X31,X3] :
        ( X24 = X31
        | c_List_Olist_OCons(X23,X24,X3) != c_List_Olist_OCons(X13,X31,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f816,plain,
    ( ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_as____ = X1 )
    | ~ spl0_35
    | ~ spl0_95 ),
    inference(superposition,[],[f781,f473]) ).

fof(f473,plain,
    ( v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f471]) ).

fof(f781,plain,
    ( ! [X31,X3,X24,X23,X13] :
        ( c_List_Olist_OCons(X23,X24,X3) != c_List_Olist_OCons(X13,X31,X3)
        | X24 = X31 )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f780]) ).

fof(f961,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f299,f958]) ).

fof(f958,plain,
    ( spl0_125
  <=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f299,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    inference(definition_unfolding,[],[f219,f263]) ).

fof(f219,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).

fof(f956,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f259,f954]) ).

fof(f954,plain,
    ( spl0_124
  <=> ! [X15,X16,X36,X49] :
        ( ~ c_Type_Otyping(X15,X16,X36)
        | c_Type_Otyping(X15,X49,X36)
        | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X16),X49)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f259,axiom,
    ! [X36,X49,X16,X15] :
      ( ~ c_Type_Otyping(X15,X16,X36)
      | c_Type_Otyping(X15,X49,X36)
      | ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X16),X49)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).

fof(f952,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f256,f950]) ).

fof(f950,plain,
    ( spl0_123
  <=> ! [X15,X37,X44,X36,X16] :
        ( ~ c_Type_Otyping(X15,X16,X36)
        | c_Type_Otyping(c_Type_Oshift(X15,X37,X44,tc_Type_Otype),c_Lambda_Olift(X16,X37),X36) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f256,axiom,
    ! [X36,X37,X44,X16,X15] :
      ( ~ c_Type_Otyping(X15,X16,X36)
      | c_Type_Otyping(c_Type_Oshift(X15,X37,X44,tc_Type_Otype),c_Lambda_Olift(X16,X37),X36) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).

fof(f948,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f252,f946]) ).

fof(f252,axiom,
    ! [X56,X54,X57,X55] :
      ( X54 = X56
      | hAPP(hAPP(c_Type_Otype_OFun,X54),X55) != hAPP(hAPP(c_Type_Otype_OFun,X56),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).

fof(f944,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f251,f942]) ).

fof(f942,plain,
    ( spl0_121
  <=> ! [X54,X57,X55,X56] :
        ( X55 = X57
        | hAPP(hAPP(c_Type_Otype_OFun,X54),X55) != hAPP(hAPP(c_Type_Otype_OFun,X56),X57) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f251,axiom,
    ! [X56,X54,X57,X55] :
      ( X55 = X57
      | hAPP(hAPP(c_Type_Otype_OFun,X54),X55) != hAPP(hAPP(c_Type_Otype_OFun,X56),X57) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).

fof(f940,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f245,f938]) ).

fof(f938,plain,
    ( spl0_120
  <=> ! [X29,X40] :
        ( ~ c_List_Olistsp(c_InductTermi_OIT,X40,tc_Lambda_OdB)
        | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X40,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f245,axiom,
    ! [X40,X29] :
      ( ~ c_List_Olistsp(c_InductTermi_OIT,X40,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X40,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).

fof(f936,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f244,f934]) ).

fof(f934,plain,
    ( spl0_119
  <=> ! [X35,X34,X46,X47] :
        ( X34 = X46
        | hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X47) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f244,axiom,
    ! [X46,X47,X34,X35] :
      ( X34 = X46
      | hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X47) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).

fof(f932,plain,
    ( spl0_118
    | ~ spl0_35
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f813,f776,f471,f930]) ).

fof(f930,plain,
    ( spl0_118
  <=> ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_a____ = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f776,plain,
    ( spl0_94
  <=> ! [X31,X13,X23,X3,X24] :
        ( X13 = X23
        | c_List_Olist_OCons(X23,X24,X3) != c_List_Olist_OCons(X13,X31,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f813,plain,
    ( ! [X0,X1] :
        ( v_rs____ != c_List_Olist_OCons(X0,X1,tc_Lambda_OdB)
        | v_a____ = X0 )
    | ~ spl0_35
    | ~ spl0_94 ),
    inference(superposition,[],[f777,f473]) ).

fof(f777,plain,
    ( ! [X31,X3,X24,X23,X13] :
        ( c_List_Olist_OCons(X23,X24,X3) != c_List_Olist_OCons(X13,X31,X3)
        | X13 = X23 )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f776]) ).

fof(f928,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f243,f926]) ).

fof(f926,plain,
    ( spl0_117
  <=> ! [X34,X46,X35,X47] :
        ( X35 = X47
        | hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X47) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f243,axiom,
    ! [X46,X47,X34,X35] :
      ( X35 = X47
      | hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X47) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).

fof(f924,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f227,f921]) ).

fof(f921,plain,
    ( spl0_116
  <=> c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f227,axiom,
    c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).

fof(f919,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f201,f917]) ).

fof(f917,plain,
    ( spl0_115
  <=> ! [X16,X30] :
        ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X16))
        | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X30)),c_Lambda_OdB_OAbs(X16))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f201,axiom,
    ! [X16,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X30),X16))
      | hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X30)),c_Lambda_OdB_OAbs(X16))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).

fof(f915,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f199,f913]) ).

fof(f913,plain,
    ( spl0_114
  <=> ! [X29,X16,X39,X30] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30)),X16) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X39,tc_Lambda_OdB,tc_Lambda_OdB) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f199,axiom,
    ! [X39,X29,X16,X30] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X30)),X16) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X29),X39,tc_Lambda_OdB,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).

fof(f911,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f183,f909]) ).

fof(f909,plain,
    ( spl0_113
  <=> ! [X8,X3,X25,X1] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_HOL_Oord__class_Oless(X8,X1,X3)
        | ~ c_HOL_Oord__class_Oless(X25,X8,X3)
        | c_HOL_Oord__class_Oless(X25,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f183,axiom,
    ! [X3,X1,X8,X25] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X8,X1,X3)
      | ~ c_HOL_Oord__class_Oless(X25,X8,X3)
      | c_HOL_Oord__class_Oless(X25,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

fof(f907,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f182,f905]) ).

fof(f905,plain,
    ( spl0_112
  <=> ! [X8,X3,X25,X1] :
        ( ~ class_Orderings_Opreorder(X3)
        | ~ c_HOL_Oord__class_Oless(X1,X8,X3)
        | ~ c_HOL_Oord__class_Oless(X8,X25,X3)
        | c_HOL_Oord__class_Oless(X1,X25,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f182,axiom,
    ! [X3,X1,X8,X25] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X1,X8,X3)
      | ~ c_HOL_Oord__class_Oless(X8,X25,X3)
      | c_HOL_Oord__class_Oless(X1,X25,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

fof(f903,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f174,f901]) ).

fof(f901,plain,
    ( spl0_111
  <=> ! [X10,X8,X3,X1] :
        ( ~ hBOOL(hAPP(hAPP(X10,X1),X8))
        | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X8)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f174,axiom,
    ! [X3,X10,X1,X8] :
      ( ~ hBOOL(hAPP(hAPP(X10,X1),X8))
      | hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X8)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).

fof(f899,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f151,f897]) ).

fof(f897,plain,
    ( spl0_110
  <=> ! [X29,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X3)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X29,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f151,axiom,
    ! [X3,X29] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X29,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

fof(f895,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f150,f893]) ).

fof(f893,plain,
    ( spl0_109
  <=> ! [X29,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X3)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X29,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f150,axiom,
    ! [X3,X29] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

fof(f891,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f134,f889]) ).

fof(f889,plain,
    ( spl0_108
  <=> ! [X10,X13,X3,X20] :
        ( ~ c_Wellfounded_Oaccp(X10,X20,X3)
        | c_Wellfounded_Oaccp(X10,X13,X3)
        | ~ hBOOL(hAPP(hAPP(X10,X13),X20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f134,axiom,
    ! [X3,X10,X13,X20] :
      ( ~ c_Wellfounded_Oaccp(X10,X20,X3)
      | c_Wellfounded_Oaccp(X10,X13,X3)
      | ~ hBOOL(hAPP(hAPP(X10,X13),X20)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).

fof(f886,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f115,f884]) ).

fof(f884,plain,
    ( spl0_107
  <=> ! [X29,X19,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X3)
        | c_HOL_Oord__class_Oless(X19,X29,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X19,X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f115,axiom,
    ! [X3,X29,X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | c_HOL_Oord__class_Oless(X19,X29,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X19,X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

fof(f882,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f114,f880]) ).

fof(f880,plain,
    ( spl0_106
  <=> ! [X29,X19,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X3)
        | ~ c_HOL_Oord__class_Oless(X19,X29,tc_nat)
        | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X19,X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f114,axiom,
    ! [X3,X29,X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(X19,X29,tc_nat)
      | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X19,X3),c_Nat_Osemiring__1__class_Oof__nat(X29,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

fof(f849,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f238,f847]) ).

fof(f847,plain,
    ( spl0_105
  <=> ! [X19,X39,X30] :
        ( c_Lambda_OdB_OVar(X19) = X30
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f238,axiom,
    ! [X39,X19,X30] :
      ( c_Lambda_OdB_OVar(X19) = X30
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).

fof(f845,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f204,f843]) ).

fof(f843,plain,
    ( spl0_104
  <=> ! [X16,X37] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
        | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X16),c_Lambda_OdB_OVar(X37)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f204,axiom,
    ! [X37,X16] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
      | hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X16),c_Lambda_OdB_OVar(X37)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).

fof(f840,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f197,f838]) ).

fof(f838,plain,
    ( spl0_103
  <=> ! [X30,X39,X19] :
        ( c_List_Olist_ONil(tc_Lambda_OdB) = X39
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f197,axiom,
    ! [X39,X19,X30] :
      ( c_List_Olist_ONil(tc_Lambda_OdB) = X39
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).

fof(f836,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f191,f834]) ).

fof(f834,plain,
    ( spl0_102
  <=> ! [X39,X30,X10] :
        ( c_List_Olist_ONil(tc_Lambda_OdB) = X39
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f191,axiom,
    ! [X39,X10,X30] :
      ( c_List_Olist_ONil(tc_Lambda_OdB) = X39
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).

fof(f832,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f189,f830]) ).

fof(f830,plain,
    ( spl0_101
  <=> ! [X39,X30,X10] :
        ( c_Lambda_OdB_OAbs(X10) = X30
        | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f189,axiom,
    ! [X10,X39,X30] :
      ( c_Lambda_OdB_OAbs(X10) = X30
      | c_List_Ofoldl(c_Lambda_OdB_OApp,X30,X39,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).

fof(f828,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f156,f826]) ).

fof(f826,plain,
    ( spl0_100
  <=> ! [X1,X8,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | X1 = X8
        | c_HOL_Oord__class_Oless(X8,X1,X3)
        | c_HOL_Oord__class_Oless(X1,X8,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f156,axiom,
    ! [X3,X1,X8] :
      ( ~ class_Orderings_Olinorder(X3)
      | X1 = X8
      | c_HOL_Oord__class_Oless(X8,X1,X3)
      | c_HOL_Oord__class_Oless(X1,X8,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

fof(f809,plain,
    ( spl0_99
    | ~ spl0_13
    | ~ spl0_82 ),
    inference(avatar_split_clause,[],[f732,f690,f372,f807]) ).

fof(f372,plain,
    ( spl0_13
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f690,plain,
    ( spl0_82
  <=> ! [X13,X3] :
        ( ~ class_OrderedGroup_Omonoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X13) = X13 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f732,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0
    | ~ spl0_13
    | ~ spl0_82 ),
    inference(resolution,[],[f691,f374]) ).

fof(f374,plain,
    ( class_OrderedGroup_Omonoid__add(tc_nat)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f372]) ).

fof(f691,plain,
    ( ! [X3,X13] :
        ( ~ class_OrderedGroup_Omonoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X13) = X13 )
    | ~ spl0_82 ),
    inference(avatar_component_clause,[],[f690]) ).

fof(f795,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f250,f793]) ).

fof(f250,axiom,
    ! [X38,X10,X37] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X10))
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X10,c_Lambda_OdB_OVar(X37),X38))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).

fof(f791,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f249,f789]) ).

fof(f789,plain,
    ( spl0_97
  <=> ! [X38,X37,X26] :
        ( ~ c_HOL_Oord__class_Oless(X38,X37,tc_nat)
        | c_Lambda_OdB_OVar(X38) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X38),X26,X37) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f249,axiom,
    ! [X38,X37,X26] :
      ( ~ c_HOL_Oord__class_Oless(X38,X37,tc_nat)
      | c_Lambda_OdB_OVar(X38) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X38),X26,X37) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).

fof(f787,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f214,f784]) ).

fof(f214,axiom,
    v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).

fof(f782,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f127,f780]) ).

fof(f127,axiom,
    ! [X31,X3,X24,X23,X13] :
      ( X24 = X31
      | c_List_Olist_OCons(X23,X24,X3) != c_List_Olist_OCons(X13,X31,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).

fof(f778,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f126,f776]) ).

fof(f126,axiom,
    ! [X31,X3,X24,X23,X13] :
      ( X13 = X23
      | c_List_Olist_OCons(X23,X24,X3) != c_List_Olist_OCons(X13,X31,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).

fof(f774,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f96,f772]) ).

fof(f772,plain,
    ( spl0_93
  <=> ! [X29,X19,X3] :
        ( ~ class_Nat_Osemiring__char__0(X3)
        | X19 = X29
        | c_Nat_Osemiring__1__class_Oof__nat(X19,X3) != c_Nat_Osemiring__1__class_Oof__nat(X29,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f96,axiom,
    ! [X3,X29,X19] :
      ( ~ class_Nat_Osemiring__char__0(X3)
      | X19 = X29
      | c_Nat_Osemiring__1__class_Oof__nat(X19,X3) != c_Nat_Osemiring__1__class_Oof__nat(X29,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

fof(f770,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f27,f768]) ).

fof(f27,axiom,
    ! [X3,X0,X4,X5] :
      ( X4 = X5
      | c_List_Oappend(X5,X0,X3) != c_List_Oappend(X4,X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).

fof(f766,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f26,f764]) ).

fof(f26,axiom,
    ! [X3,X0,X4,X5] :
      ( X4 = X5
      | c_List_Oappend(X0,X5,X3) != c_List_Oappend(X0,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).

fof(f762,plain,
    ( spl0_90
    | ~ spl0_8
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f730,f682,f347,f760]) ).

fof(f347,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f682,plain,
    ( spl0_80
  <=> ! [X13,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_HOL_Ozero__class_Ozero(X3)) = X13 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f730,plain,
    ( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
    | ~ spl0_8
    | ~ spl0_80 ),
    inference(resolution,[],[f683,f349]) ).

fof(f349,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f683,plain,
    ( ! [X3,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_HOL_Ozero__class_Ozero(X3)) = X13 )
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f682]) ).

fof(f721,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f207,f719]) ).

fof(f719,plain,
    ( spl0_89
  <=> ! [X48,X37] :
        ( ~ c_HOL_Oord__class_Oless(X37,X48,tc_nat)
        | c_Lambda_OdB_OVar(X37) = c_Lambda_Olift(c_Lambda_OdB_OVar(X37),X48) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f207,axiom,
    ! [X48,X37] :
      ( ~ c_HOL_Oord__class_Oless(X37,X48,tc_nat)
      | c_Lambda_OdB_OVar(X37) = c_Lambda_Olift(c_Lambda_OdB_OVar(X37),X48) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).

fof(f717,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f161,f715]) ).

fof(f715,plain,
    ( spl0_88
  <=> ! [X29,X19] :
        ( X19 = X29
        | c_HOL_Oord__class_Oless(X19,X29,tc_nat)
        | c_HOL_Oord__class_Oless(X29,X19,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f161,axiom,
    ! [X29,X19] :
      ( X19 = X29
      | c_HOL_Oord__class_Oless(X19,X29,tc_nat)
      | c_HOL_Oord__class_Oless(X29,X19,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

fof(f713,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f91,f711]) ).

fof(f711,plain,
    ( spl0_87
  <=> ! [X10] :
        ( hBOOL(hAPP(c_InductTermi_OIT,X10))
        | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X10,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f91,axiom,
    ! [X10] :
      ( hBOOL(hAPP(c_InductTermi_OIT,X10))
      | ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X10,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).

fof(f709,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f90,f707]) ).

fof(f707,plain,
    ( spl0_86
  <=> ! [X16] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
        | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X16,tc_Lambda_OdB) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f90,axiom,
    ! [X16] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
      | c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X16,tc_Lambda_OdB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).

fof(f705,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f51,f703]) ).

fof(f703,plain,
    ( spl0_85
  <=> ! [X1,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f51,axiom,
    ! [X3,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

fof(f701,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f50,f699]) ).

fof(f699,plain,
    ( spl0_84
  <=> ! [X13,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X13) = X13 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f50,axiom,
    ! [X3,X13] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X13) = X13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f697,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f48,f695]) ).

fof(f695,plain,
    ( spl0_83
  <=> ! [X13,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_HOL_Ozero__class_Ozero(X3)) = X13 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f48,axiom,
    ! [X3,X13] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_HOL_Ozero__class_Ozero(X3)) = X13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f692,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f47,f690]) ).

fof(f47,axiom,
    ! [X3,X13] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X13) = X13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f688,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f46,f686]) ).

fof(f686,plain,
    ( spl0_81
  <=> ! [X13,X3] :
        ( ~ class_OrderedGroup_Omonoid__add(X3)
        | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_HOL_Ozero__class_Ozero(X3)) = X13 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f46,axiom,
    ! [X3,X13] :
      ( ~ class_OrderedGroup_Omonoid__add(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_HOL_Ozero__class_Ozero(X3)) = X13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f684,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f45,f682]) ).

fof(f45,axiom,
    ! [X3,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
      | hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X13),c_HOL_Ozero__class_Ozero(X3)) = X13 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f680,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f29,f678]) ).

fof(f678,plain,
    ( spl0_79
  <=> ! [X9,X0,X5,X3] :
        ( c_List_Olistsp(X9,X0,X3)
        | ~ c_List_Olistsp(X9,c_List_Oappend(X0,X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f29,axiom,
    ! [X3,X0,X9,X5] :
      ( c_List_Olistsp(X9,X0,X3)
      | ~ c_List_Olistsp(X9,c_List_Oappend(X0,X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).

fof(f676,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f28,f674]) ).

fof(f674,plain,
    ( spl0_78
  <=> ! [X5,X0,X9,X3] :
        ( c_List_Olistsp(X9,X5,X3)
        | ~ c_List_Olistsp(X9,c_List_Oappend(X0,X5,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f28,axiom,
    ! [X3,X0,X9,X5] :
      ( c_List_Olistsp(X9,X5,X3)
      | ~ c_List_Olistsp(X9,c_List_Oappend(X0,X5,X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).

fof(f672,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f17,f670]) ).

fof(f670,plain,
    ( spl0_77
  <=> ! [X5,X0,X3] :
        ( c_List_Olist_ONil(X3) = X5
        | c_List_Oappend(X0,X5,X3) != c_List_Olist_ONil(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f17,axiom,
    ! [X3,X0,X5] :
      ( c_List_Olist_ONil(X3) = X5
      | c_List_Oappend(X0,X5,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).

fof(f668,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f16,f666]) ).

fof(f666,plain,
    ( spl0_76
  <=> ! [X5,X0,X3] :
        ( c_List_Olist_ONil(X3) = X0
        | c_List_Oappend(X0,X5,X3) != c_List_Olist_ONil(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f16,axiom,
    ! [X3,X0,X5] :
      ( c_List_Olist_ONil(X3) = X0
      | c_List_Oappend(X0,X5,X3) != c_List_Olist_ONil(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).

fof(f662,plain,
    ( spl0_75
    | ~ spl0_44
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f618,f596,f510,f660]) ).

fof(f660,plain,
    ( spl0_75
  <=> ! [X2,X0,X1,X3] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f596,plain,
    ( spl0_64
  <=> ! [X36,X1,X3,X15] : hAPP(c_Type_Oshift(X15,X1,X36,X3),X1) = X36 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f618,plain,
    ( ! [X2,X3,X0,X1] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2)
    | ~ spl0_44
    | ~ spl0_64 ),
    inference(superposition,[],[f511,f597]) ).

fof(f597,plain,
    ( ! [X3,X36,X1,X15] : hAPP(c_Type_Oshift(X15,X1,X36,X3),X1) = X36
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f596]) ).

fof(f651,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f294,f649]) ).

fof(f649,plain,
    ( spl0_74
  <=> ! [X3,X62,X63] :
        ( X62 = X63
        | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X62),X63)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f294,axiom,
    ! [X3,X62,X63] :
      ( X62 = X63
      | ~ hBOOL(hAPP(hAPP(c_fequal(X3),X62),X63)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f647,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f264,f645]) ).

fof(f645,plain,
    ( spl0_73
  <=> ! [X36,X37,X15] :
        ( ~ c_Type_Otyping(X15,c_Lambda_OdB_OVar(X37),X36)
        | hAPP(X15,X37) = X36 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f264,axiom,
    ! [X36,X37,X15] :
      ( ~ c_Type_Otyping(X15,c_Lambda_OdB_OVar(X37),X36)
      | hAPP(X15,X37) = X36 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).

fof(f643,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f236,f641]) ).

fof(f641,plain,
    ( spl0_72
  <=> ! [X16,X37] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X16,X37))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f236,axiom,
    ! [X37,X16] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X16))
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X16,X37))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).

fof(f639,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f140,f637]) ).

fof(f637,plain,
    ( spl0_71
  <=> ! [X13,X20,X3] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_HOL_Oord__class_Oless(X20,X13,X3)
        | ~ c_HOL_Oord__class_Oless(X13,X20,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f140,axiom,
    ! [X3,X13,X20] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X20,X13,X3)
      | ~ c_HOL_Oord__class_Oless(X13,X20,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f635,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f137,f633]) ).

fof(f633,plain,
    ( spl0_70
  <=> ! [X1,X8,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | ~ c_HOL_Oord__class_Oless(X8,X1,X3)
        | ~ c_HOL_Oord__class_Oless(X1,X8,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f137,axiom,
    ! [X3,X1,X8] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X8,X1,X3)
      | ~ c_HOL_Oord__class_Oless(X1,X8,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f630,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f136,f628]) ).

fof(f628,plain,
    ( spl0_69
  <=> ! [X1,X8,X3] :
        ( ~ class_Orderings_Opreorder(X3)
        | ~ c_HOL_Oord__class_Oless(X1,X8,X3)
        | ~ c_HOL_Oord__class_Oless(X8,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f136,axiom,
    ! [X3,X1,X8] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X1,X8,X3)
      | ~ c_HOL_Oord__class_Oless(X8,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

fof(f626,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f12,f624]) ).

fof(f624,plain,
    ( spl0_68
  <=> ! [X5,X0,X3] :
        ( c_List_Olist_ONil(X3) = X5
        | c_List_Oappend(X0,X5,X3) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f12,axiom,
    ! [X3,X0,X5] :
      ( c_List_Olist_ONil(X3) = X5
      | c_List_Oappend(X0,X5,X3) != X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).

fof(f622,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f9,f620]) ).

fof(f620,plain,
    ( spl0_67
  <=> ! [X5,X0,X3] :
        ( c_List_Olist_ONil(X3) = X0
        | c_List_Oappend(X0,X5,X3) != X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f9,axiom,
    ! [X3,X0,X5] :
      ( c_List_Olist_ONil(X3) = X0
      | c_List_Oappend(X0,X5,X3) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).

fof(f609,plain,
    ( spl0_66
    | ~ spl0_12
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f604,f568,f367,f606]) ).

fof(f606,plain,
    ( spl0_66
  <=> 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_66])]) ).

fof(f367,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f568,plain,
    ( spl0_57
  <=> ! [X3] :
        ( ~ class_Ring__and__Field_Osemiring__1(X3)
        | c_HOL_Ozero__class_Ozero(X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f604,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_12
    | ~ spl0_57 ),
    inference(resolution,[],[f569,f369]) ).

fof(f369,plain,
    ( class_Ring__and__Field_Osemiring__1(tc_nat)
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f367]) ).

fof(f569,plain,
    ( ! [X3] :
        ( ~ class_Ring__and__Field_Osemiring__1(X3)
        | c_HOL_Ozero__class_Ozero(X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f568]) ).

fof(f603,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f303,f600]) ).

fof(f600,plain,
    ( spl0_65
  <=> c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_T____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f303,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),v_T____),
    inference(forward_demodulation,[],[f300,f214]) ).

fof(f300,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    inference(definition_unfolding,[],[f225,f263]) ).

fof(f225,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_varT_0) ).

fof(f598,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f233,f596]) ).

fof(f233,axiom,
    ! [X3,X36,X1,X15] : hAPP(c_Type_Oshift(X15,X1,X36,X3),X1) = X36,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).

fof(f594,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f200,f592]) ).

fof(f592,plain,
    ( spl0_63
  <=> ! [X3,X10] : c_Transitive__Closure_Ortranclp(X10,X3) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X10,X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f200,axiom,
    ! [X3,X10] : c_Transitive__Closure_Ortranclp(X10,X3) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X10,X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).

fof(f590,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f194,f588]) ).

fof(f588,plain,
    ( spl0_62
  <=> ! [X10] :
        ( ~ hBOOL(hAPP(c_InductTermi_OIT,X10))
        | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f194,axiom,
    ! [X10] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,X10))
      | hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X10))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).

fof(f586,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f148,f584]) ).

fof(f584,plain,
    ( spl0_61
  <=> ! [X29] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X29
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X29,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f148,axiom,
    ! [X29] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X29
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X29,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

fof(f582,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f119,f580]) ).

fof(f580,plain,
    ( spl0_60
  <=> ! [X12,X3,X10] : c_Predicate_Oconversep(c_Predicate_Oconversep(X10,X3,X12),X12,X3) = X10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f119,axiom,
    ! [X3,X10,X12] : c_Predicate_Oconversep(c_Predicate_Oconversep(X10,X3,X12),X12,X3) = X10,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).

fof(f578,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f107,f576]) ).

fof(f107,axiom,
    ! [X3,X11,X12,X13] : c_List_Ofoldl(X11,X13,c_List_Olist_ONil(X12),X3,X12) = X13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).

fof(f574,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f68,f572]) ).

fof(f572,plain,
    ( spl0_58
  <=> ! [X13,X12,X11,X3] : c_List_Ofoldr(X11,c_List_Olist_ONil(X12),X13,X12,X3) = X13 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f68,axiom,
    ! [X3,X11,X12,X13] : c_List_Ofoldr(X11,c_List_Olist_ONil(X12),X13,X12,X3) = X13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).

fof(f570,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f64,f568]) ).

fof(f64,axiom,
    ! [X3] :
      ( ~ class_Ring__and__Field_Osemiring__1(X3)
      | c_HOL_Ozero__class_Ozero(X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

fof(f566,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f54,f564]) ).

fof(f564,plain,
    ( spl0_56
  <=> ! [X19,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X3)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X19,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f54,axiom,
    ! [X3,X19] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X3)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X19,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

fof(f560,plain,
    ( ~ spl0_55
    | ~ spl0_35
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f517,f493,f471,f557]) ).

fof(f557,plain,
    ( spl0_55
  <=> c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f493,plain,
    ( spl0_40
  <=> ! [X18,X1,X3] : c_List_Olist_ONil(X3) != c_List_Olist_OCons(X1,X18,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f517,plain,
    ( c_List_Olist_ONil(tc_Lambda_OdB) != v_rs____
    | ~ spl0_35
    | ~ spl0_40 ),
    inference(superposition,[],[f494,f473]) ).

fof(f494,plain,
    ( ! [X3,X1,X18] : c_List_Olist_ONil(X3) != c_List_Olist_OCons(X1,X18,X3)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f493]) ).

fof(f555,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f297,f552]) ).

fof(f297,plain,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    inference(definition_unfolding,[],[f271,f263]) ).

fof(f271,axiom,
    c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

fof(f550,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f296,f547]) ).

fof(f547,plain,
    ( spl0_53
  <=> c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,v_Ts____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f296,plain,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_n____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    inference(definition_unfolding,[],[f223,f263]) ).

fof(f223,axiom,
    c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argsT_0) ).

fof(f545,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f268,f543]) ).

fof(f268,axiom,
    ! [X48,X16,X30] : c_Lambda_Osubst(c_Lambda_Olift(X16,X48),X30,X48) = X16,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).

fof(f541,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f255,f539]) ).

fof(f539,plain,
    ( spl0_51
  <=> ! [X33,X58] :
        ( X33 = X58
        | c_Lambda_OdB_OVar(X33) != c_Lambda_OdB_OVar(X58) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f255,axiom,
    ! [X58,X33] :
      ( X33 = X58
      | c_Lambda_OdB_OVar(X33) != c_Lambda_OdB_OVar(X58) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).

fof(f537,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f202,f535]) ).

fof(f202,axiom,
    ! [X46,X47,X33] : c_Lambda_OdB_OVar(X33) != hAPP(hAPP(c_Lambda_OdB_OApp,X46),X47),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).

fof(f533,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f177,f531]) ).

fof(f531,plain,
    ( spl0_49
  <=> ! [X1,X3,X10] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f177,axiom,
    ! [X3,X10,X1] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X10,X3),X1),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).

fof(f529,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f171,f527]) ).

fof(f527,plain,
    ( spl0_48
  <=> ! [X32,X42] :
        ( X32 = X42
        | c_Lambda_OdB_OAbs(X32) != c_Lambda_OdB_OAbs(X42) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f171,axiom,
    ! [X42,X32] :
      ( X32 = X42
      | c_Lambda_OdB_OAbs(X32) != c_Lambda_OdB_OAbs(X42) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).

fof(f525,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f142,f523]) ).

fof(f142,axiom,
    ! [X34,X35,X32] : c_Lambda_OdB_OAbs(X32) != hAPP(hAPP(c_Lambda_OdB_OApp,X34),X35),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).

fof(f521,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f109,f519]) ).

fof(f519,plain,
    ( spl0_46
  <=> ! [X3] : c_fequal(X3) = c_Predicate_Oconversep(c_fequal(X3),X3,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f109,axiom,
    ! [X3] : c_fequal(X3) = c_Predicate_Oconversep(c_fequal(X3),X3,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).

fof(f516,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f293,f514]) ).

fof(f514,plain,
    ( spl0_45
  <=> ! [X1,X3] : hBOOL(hAPP(hAPP(c_fequal(X3),X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f293,axiom,
    ! [X3,X1] : hBOOL(hAPP(hAPP(c_fequal(X3),X1),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f512,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f266,f510]) ).

fof(f266,axiom,
    ! [X50,X1] : c_Type_Otyping(X50,c_Lambda_OdB_OVar(X1),hAPP(X50,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).

fof(f508,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f260,f506]) ).

fof(f506,plain,
    ( spl0_43
  <=> ! [X48,X26] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X48),X26,X48) = X26 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f260,axiom,
    ! [X48,X26] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X48),X26,X48) = X26,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).

fof(f504,plain,
    ( ~ spl0_42
    | ~ spl0_29
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f483,f471,f447,f501]) ).

fof(f501,plain,
    ( spl0_42
  <=> v_rs____ = v_as____ ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f447,plain,
    ( spl0_29
  <=> ! [X0,X1,X3] : c_List_Olist_OCons(X1,X0,X3) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f483,plain,
    ( v_rs____ != v_as____
    | ~ spl0_29
    | ~ spl0_35 ),
    inference(superposition,[],[f448,f473]) ).

fof(f448,plain,
    ( ! [X3,X0,X1] : c_List_Olist_OCons(X1,X0,X3) != X0
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f447]) ).

fof(f499,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f247,f497]) ).

fof(f247,axiom,
    ! [X37,X16] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X37)),X16)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).

fof(f495,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f58,f493]) ).

fof(f58,axiom,
    ! [X3,X1,X18] : c_List_Olist_ONil(X3) != c_List_Olist_OCons(X1,X18,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).

fof(f491,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f25,f489]) ).

fof(f25,axiom,
    ! [X3,X0] : c_List_Oappend(X0,c_List_Olist_ONil(X3),X3) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).

fof(f487,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f22,f485]) ).

fof(f22,axiom,
    ! [X3,X5] : c_List_Oappend(c_List_Olist_ONil(X3),X5,X3) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).

fof(f482,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f274,f480]) ).

fof(f480,plain,
    ( spl0_37
  <=> ! [X61,X60] :
        ( ~ class_Orderings_Oorder(X61)
        | class_Orderings_Oorder(tc_fun(X60,X61)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f274,axiom,
    ! [X60,X61] :
      ( ~ class_Orderings_Oorder(X61)
      | class_Orderings_Oorder(tc_fun(X60,X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f478,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f273,f476]) ).

fof(f476,plain,
    ( spl0_36
  <=> ! [X61,X60] :
        ( ~ class_Orderings_Opreorder(X61)
        | class_Orderings_Opreorder(tc_fun(X60,X61)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f273,axiom,
    ! [X60,X61] :
      ( ~ class_Orderings_Opreorder(X61)
      | class_Orderings_Opreorder(tc_fun(X60,X61)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f474,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f195,f471]) ).

fof(f195,axiom,
    v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_0) ).

fof(f469,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f167,f467]) ).

fof(f467,plain,
    ( spl0_34
  <=> ! [X1,X3] :
        ( ~ class_Orderings_Oorder(X3)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f167,axiom,
    ! [X3,X1] :
      ( ~ class_Orderings_Oorder(X3)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f465,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f166,f463]) ).

fof(f463,plain,
    ( spl0_33
  <=> ! [X1,X3] :
        ( ~ class_Orderings_Olinorder(X3)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f166,axiom,
    ! [X3,X1] :
      ( ~ class_Orderings_Olinorder(X3)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f461,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f165,f459]) ).

fof(f459,plain,
    ( spl0_32
  <=> ! [X1,X3] :
        ( ~ class_Orderings_Opreorder(X3)
        | ~ c_HOL_Oord__class_Oless(X1,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f165,axiom,
    ! [X3,X1] :
      ( ~ class_Orderings_Opreorder(X3)
      | ~ c_HOL_Oord__class_Oless(X1,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f457,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f101,f455]) ).

fof(f455,plain,
    ( spl0_31
  <=> ! [X0,X3,X10] : ~ c_ListOrder_Ostep1(X10,X0,c_List_Olist_ONil(X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f101,axiom,
    ! [X3,X10,X0] : ~ c_ListOrder_Ostep1(X10,X0,c_List_Olist_ONil(X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).

fof(f453,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f100,f451]) ).

fof(f451,plain,
    ( spl0_30
  <=> ! [X0,X3,X10] : ~ c_ListOrder_Ostep1(X10,c_List_Olist_ONil(X3),X0,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f100,axiom,
    ! [X3,X10,X0] : ~ c_ListOrder_Ostep1(X10,c_List_Olist_ONil(X3),X0,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).

fof(f449,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f52,f447]) ).

fof(f52,axiom,
    ! [X3,X0,X1] : c_List_Olist_OCons(X1,X0,X3) != X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).

fof(f445,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f231,f443]) ).

fof(f443,plain,
    ( spl0_28
  <=> ! [X29] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X29))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f231,axiom,
    ! [X29] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X29))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).

fof(f441,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f185,f439]) ).

fof(f439,plain,
    ( spl0_27
  <=> ! [X19] : ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f185,axiom,
    ! [X19] : ~ c_HOL_Oord__class_Oless(X19,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

fof(f437,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f175,f435]) ).

fof(f435,plain,
    ( spl0_26
  <=> ! [X32,X33] : c_Lambda_OdB_OAbs(X32) != c_Lambda_OdB_OVar(X33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f175,axiom,
    ! [X32,X33] : c_Lambda_OdB_OAbs(X32) != c_Lambda_OdB_OVar(X33),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).

fof(f433,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f87,f431]) ).

fof(f431,plain,
    ( spl0_25
  <=> ! [X9,X3] : c_List_Olistsp(X9,c_List_Olist_ONil(X3),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f87,axiom,
    ! [X3,X9] : c_List_Olistsp(X9,c_List_Olist_ONil(X3),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).

fof(f429,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f270,f426]) ).

fof(f270,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

fof(f424,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f267,f421]) ).

fof(f421,plain,
    ( spl0_23
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f267,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).

fof(f419,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f179,f416]) ).

fof(f416,plain,
    ( spl0_22
  <=> c_Type_Otyping(v_ea______,v_ua______,v_T____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f179,axiom,
    c_Type_Otyping(v_ea______,v_ua______,v_T____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).

fof(f414,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f169,f412]) ).

fof(f412,plain,
    ( spl0_21
  <=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f169,axiom,
    ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f410,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f84,f407]) ).

fof(f407,plain,
    ( spl0_20
  <=> hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f84,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).

fof(f405,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f292,f402]) ).

fof(f402,plain,
    ( spl0_19
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f292,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f400,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f291,f397]) ).

fof(f397,plain,
    ( spl0_18
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f291,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f395,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f290,f392]) ).

fof(f392,plain,
    ( spl0_17
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f290,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f390,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f289,f387]) ).

fof(f387,plain,
    ( spl0_16
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f289,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f385,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f288,f382]) ).

fof(f382,plain,
    ( spl0_15
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f288,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f380,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f287,f377]) ).

fof(f377,plain,
    ( spl0_14
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f287,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

fof(f375,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f286,f372]) ).

fof(f286,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f370,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f285,f367]) ).

fof(f285,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f365,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f284,f362]) ).

fof(f362,plain,
    ( spl0_11
  <=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f284,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).

fof(f360,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f283,f357]) ).

fof(f357,plain,
    ( spl0_10
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f283,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f355,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f282,f352]) ).

fof(f352,plain,
    ( spl0_9
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f282,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f350,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f281,f347]) ).

fof(f281,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(f345,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f280,f342]) ).

fof(f342,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f280,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f340,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f279,f337]) ).

fof(f337,plain,
    ( spl0_6
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f279,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f335,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f278,f332]) ).

fof(f332,plain,
    ( spl0_5
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f278,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f330,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f277,f327]) ).

fof(f327,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f277,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f325,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f276,f322]) ).

fof(f322,plain,
    ( spl0_3
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f276,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(f320,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f275,f317]) ).

fof(f317,plain,
    ( spl0_2
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f275,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f315,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f295,f312]) ).

fof(f295,plain,
    ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_n____),v_T_H_H____),
    inference(definition_unfolding,[],[f272,f263]) ).

fof(f272,axiom,
    ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.07  % Problem    : LCL817-1 : TPTP v8.1.2. Released v4.1.0.
% 0.01/0.08  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.27  % Computer : n006.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit   : 300
% 0.07/0.27  % WCLimit    : 300
% 0.07/0.27  % DateTime   : Mon Apr 29 22:59:05 EDT 2024
% 0.07/0.27  % CPUTime    : 
% 0.07/0.27  % (32751)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.28  % (32754)WARNING: value z3 for option sas not known
% 0.07/0.28  % (32753)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.28  % (32752)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.28  % (32754)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)
% 0.07/0.28  % (32755)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.28  % (32756)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)
% 0.07/0.28  % (32757)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)
% 0.07/0.28  % (32758)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)
% 0.11/0.31  TRYING [1]
% 0.11/0.32  TRYING [2]
% 0.11/0.33  TRYING [1]
% 0.11/0.33  % (32756)First to succeed.
% 0.11/0.34  TRYING [2]
% 0.11/0.34  % (32757)Also succeeded, but the first one will report.
% 0.11/0.34  % (32756)Refutation found. Thanks to Tanya!
% 0.11/0.34  % SZS status Unsatisfiable for theBenchmark
% 0.11/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35  % (32756)------------------------------
% 0.11/0.35  % (32756)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.35  % (32756)Termination reason: Refutation
% 0.11/0.35  
% 0.11/0.35  % (32756)Memory used [KB]: 2344
% 0.11/0.35  % (32756)Time elapsed: 0.059 s
% 0.11/0.35  % (32756)Instructions burned: 170 (million)
% 0.11/0.35  % (32756)------------------------------
% 0.11/0.35  % (32756)------------------------------
% 0.11/0.35  % (32751)Success in time 0.076 s
%------------------------------------------------------------------------------