TSTP Solution File: SWC254+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC254+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.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 16:15:20 EDT 2024

% Result   : Theorem 0.17s 0.38s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  175
% Syntax   : Number of formulae    :  998 (  55 unt;   0 def)
%            Number of atoms       : 4187 (1027 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives : 4975 (1786   ~;2049   |; 765   &)
%                                         (  83 <=>; 292  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   47 (  45 usr;   7 prp; 0-4 aty)
%            Number of functors    :   58 (  58 usr;   7 con; 0-2 aty)
%            Number of variables   : 2035 (1696   !; 339   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1131,plain,
    $false,
    inference(avatar_sat_refutation,[],[f682,f742,f802,f805,f898,f1125,f1130]) ).

fof(f1130,plain,
    spl73_2,
    inference(avatar_contradiction_clause,[],[f1129]) ).

fof(f1129,plain,
    ( $false
    | spl73_2 ),
    inference(global_subsumption,[],[f390,f398,f397,f420,f422,f423,f432,f648,f433,f434,f435,f436,f437,f440,f438,f646,f442,f441,f450,f458,f462,f461,f460,f473,f476,f491,f625,f502,f645,f513,f628,f525,f629,f537,f630,f549,f631,f560,f632,f633,f634,f635,f574,f636,f577,f576,f575,f580,f581,f582,f583,f584,f585,f638,f589,f588,f639,f593,f592,f591,f640,f596,f595,f643,f599,f598,f601,f603,f602,f604,f605,f606,f607,f608,f609,f610,f611,f612,f391,f392,f393,f394,f399,f400,f401,f402,f403,f404,f405,f406,f407,f613,f614,f395,f396,f615,f620,f622,f650,f651,f652,f493,f504,f516,f528,f540,f551,f562,f408,f409,f410,f411,f463,f464,f465,f466,f467,f468,f487,f488,f489,f490,f497,f498,f499,f500,f501,f508,f509,f510,f511,f512,f520,f521,f522,f523,f524,f532,f533,f534,f535,f536,f544,f545,f546,f547,f548,f555,f556,f557,f558,f559,f644,f649,f653,f412,f413,f414,f415,f416,f417,f418,f484,f494,f505,f517,f529,f541,f542,f552,f553,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f386,f387,f388,f451,f459,f469,f685,f710,f711,f686,f687,f470,f713,f738,f739,f481,f714,f715,f492,f503,f514,f515,f526,f527,f538,f539,f550,f561,f384,f385,f447,f455,f471,f746,f747,f472,f474,f475,f748,f749,f477,f479,f750,f751,f563,f565,f567,f569,f767,f768,f579,f769,f770,f570,f571,f647,f389,f419,f421,f690,f691,f692,f693,f694,f695,f696,f697,f698,f699,f424,f700,f701,f702,f703,f704,f814,f705,f815,f706,f816,f707,f817,f708,f818,f709,f819,f718,f425,f822,f719,f720,f721,f722,f723,f724,f725,f726,f727,f728,f729,f427,f730,f731,f732,f828,f733,f829,f734,f830,f735,f831,f736,f832,f737,f833,f428,f429,f431,f444,f445,f448,f452,f453,f456,f848,f849,f850,f478,f882,f852,f854,f855,f888,f860,f861,f862,f863,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f857,f480,f931,f901,f903,f904,f909,f910,f911,f912,f913,f914,f915,f916,f917,f918,f919,f920,f921,f922,f923,f924,f925,f926,f927,f928,f929,f930,f482,f572,f942,f943,f944,f945,f946,f973,f974,f951,f952,f953,f954,f955,f956,f957,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f947,f975,f976,f978,f979,f980,f989,f990,f991,f992,f993,f994,f995,f996,f948,f999,f1000,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1014,f1015,f1016,f1017,f1018,f573,f1021,f1022,f1023,f1024,f1025,f1052,f1053,f1030,f1031,f1032,f1033,f1034,f1035,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1019,f1020,f1026,f1056,f1057,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1078,f1079,f1077,f1081,f1082,f1027,f1084,f1085,f1087,f1088,f1089,f1090,f1091,f1092,f1093,f1094,f1095,f1096,f1097,f1098,f1099,f1100,f1101,f1102,f1103,f1104,f1106,f1107,f1105,f1109,f1110,f587,f981,f982,f983,f984,f985,f986,f987,f988,f624,f1120,f1126,f905,f1127,f856,f680]) ).

fof(f680,plain,
    ( ~ sP1(sK22,sK22,sK23,sK23)
    | spl73_2 ),
    inference(avatar_component_clause,[],[f679]) ).

fof(f679,plain,
    ( spl73_2
  <=> sP1(sK22,sK22,sK23,sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_2])]) ).

fof(f856,plain,
    ( nil = sK22
    | hd(sK22) = sK28(sK22) ),
    inference(resolution,[],[f478,f391]) ).

fof(f1127,plain,
    ( hd(sK22) = sK28(sK22)
    | nil = sK22 ),
    inference(forward_demodulation,[],[f884,f396]) ).

fof(f884,plain,
    ( nil = sK22
    | hd(sK24) = sK28(sK24) ),
    inference(forward_demodulation,[],[f858,f396]) ).

fof(f858,plain,
    ( nil = sK24
    | hd(sK24) = sK28(sK24) ),
    inference(resolution,[],[f478,f393]) ).

fof(f905,plain,
    ( nil = sK22
    | tl(sK22) = sK29(sK22) ),
    inference(resolution,[],[f480,f391]) ).

fof(f1126,plain,
    ( tl(sK22) = sK29(sK22)
    | nil = sK22 ),
    inference(forward_demodulation,[],[f934,f396]) ).

fof(f934,plain,
    ( nil = sK22
    | tl(sK24) = sK29(sK24) ),
    inference(forward_demodulation,[],[f907,f396]) ).

fof(f907,plain,
    ( nil = sK24
    | tl(sK24) = sK29(sK24) ),
    inference(resolution,[],[f480,f393]) ).

fof(f1120,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | cons(X0,nil) = cons(sK30(cons(X0,nil)),nil) ),
    inference(duplicate_literal_removal,[],[f1118]) ).

fof(f1118,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | cons(X0,nil) = cons(sK30(cons(X0,nil)),nil)
      | ~ ssList(cons(X0,nil)) ),
    inference(resolution,[],[f624,f482]) ).

fof(f624,plain,
    ! [X1] :
      ( singletonP(cons(X1,nil))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,nil)) ),
    inference(equality_resolution,[],[f483]) ).

fof(f483,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f294]) ).

fof(f294,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK30(X0),nil) = X0
            & ssItem(sK30(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f292,f293]) ).

fof(f293,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK30(X0),nil) = X0
        & ssItem(sK30(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f292,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f291]) ).

fof(f291,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f988,plain,
    ! [X0] :
      ( sP12(X0)
      | sK22 = tl(cons(sK46(X0),sK22)) ),
    inference(resolution,[],[f947,f521]) ).

fof(f987,plain,
    ! [X0] :
      ( sP12(X0)
      | sK22 = tl(cons(sK45(X0),sK22)) ),
    inference(resolution,[],[f947,f520]) ).

fof(f986,plain,
    ! [X0] :
      ( sP10(X0)
      | sK22 = tl(cons(sK41(X0),sK22)) ),
    inference(resolution,[],[f947,f509]) ).

fof(f985,plain,
    ! [X0] :
      ( sP10(X0)
      | sK22 = tl(cons(sK40(X0),sK22)) ),
    inference(resolution,[],[f947,f508]) ).

fof(f984,plain,
    ! [X0] :
      ( sP8(X0)
      | sK22 = tl(cons(sK36(X0),sK22)) ),
    inference(resolution,[],[f947,f498]) ).

fof(f983,plain,
    ! [X0] :
      ( sP8(X0)
      | sK22 = tl(cons(sK35(X0),sK22)) ),
    inference(resolution,[],[f947,f497]) ).

fof(f982,plain,
    ! [X0] :
      ( sP6(X0)
      | sK22 = tl(cons(sK32(X0),sK22)) ),
    inference(resolution,[],[f947,f488]) ).

fof(f981,plain,
    ! [X0] :
      ( sP6(X0)
      | sK22 = tl(cons(sK31(X0),sK22)) ),
    inference(resolution,[],[f947,f487]) ).

fof(f587,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f365]) ).

fof(f365,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f1110,plain,
    ! [X0] :
      ( leq(X0,sK72)
      | nil = cons(sK72,sK23)
      | ~ sP2(cons(sK72,sK23),X0) ),
    inference(superposition,[],[f448,f1105]) ).

fof(f1109,plain,
    ! [X0] :
      ( lt(X0,sK72)
      | nil = cons(sK72,sK23)
      | ~ sP4(cons(sK72,sK23),X0) ),
    inference(superposition,[],[f456,f1105]) ).

fof(f1105,plain,
    sK72 = hd(cons(sK72,sK23)),
    inference(resolution,[],[f1027,f614]) ).

fof(f1107,plain,
    ! [X0] :
      ( leq(X0,sK71)
      | nil = cons(sK71,sK23)
      | ~ sP2(cons(sK71,sK23),X0) ),
    inference(superposition,[],[f448,f1104]) ).

fof(f1106,plain,
    ! [X0] :
      ( lt(X0,sK71)
      | nil = cons(sK71,sK23)
      | ~ sP4(cons(sK71,sK23),X0) ),
    inference(superposition,[],[f456,f1104]) ).

fof(f1104,plain,
    sK71 = hd(cons(sK71,sK23)),
    inference(resolution,[],[f1027,f613]) ).

fof(f1103,plain,
    ! [X0] :
      ( sK61(X0) = hd(cons(sK61(X0),sK23))
      | sP18(X0) ),
    inference(resolution,[],[f1027,f556]) ).

fof(f1102,plain,
    ! [X0] :
      ( sK60(X0) = hd(cons(sK60(X0),sK23))
      | sP18(X0) ),
    inference(resolution,[],[f1027,f555]) ).

fof(f1101,plain,
    ! [X0] :
      ( sK56(X0) = hd(cons(sK56(X0),sK23))
      | sP16(X0) ),
    inference(resolution,[],[f1027,f545]) ).

fof(f1100,plain,
    ! [X0] :
      ( sK55(X0) = hd(cons(sK55(X0),sK23))
      | sP16(X0) ),
    inference(resolution,[],[f1027,f544]) ).

fof(f1099,plain,
    ! [X0] :
      ( sK51(X0) = hd(cons(sK51(X0),sK23))
      | sP14(X0) ),
    inference(resolution,[],[f1027,f533]) ).

fof(f1098,plain,
    ! [X0] :
      ( sK50(X0) = hd(cons(sK50(X0),sK23))
      | sP14(X0) ),
    inference(resolution,[],[f1027,f532]) ).

fof(f1097,plain,
    ! [X0] :
      ( sK46(X0) = hd(cons(sK46(X0),sK23))
      | sP12(X0) ),
    inference(resolution,[],[f1027,f521]) ).

fof(f1096,plain,
    ! [X0] :
      ( sK45(X0) = hd(cons(sK45(X0),sK23))
      | sP12(X0) ),
    inference(resolution,[],[f1027,f520]) ).

fof(f1095,plain,
    ! [X0] :
      ( sK41(X0) = hd(cons(sK41(X0),sK23))
      | sP10(X0) ),
    inference(resolution,[],[f1027,f509]) ).

fof(f1094,plain,
    ! [X0] :
      ( sK40(X0) = hd(cons(sK40(X0),sK23))
      | sP10(X0) ),
    inference(resolution,[],[f1027,f508]) ).

fof(f1093,plain,
    ! [X0] :
      ( sK36(X0) = hd(cons(sK36(X0),sK23))
      | sP8(X0) ),
    inference(resolution,[],[f1027,f498]) ).

fof(f1092,plain,
    ! [X0] :
      ( sK35(X0) = hd(cons(sK35(X0),sK23))
      | sP8(X0) ),
    inference(resolution,[],[f1027,f497]) ).

fof(f1091,plain,
    ! [X0] :
      ( sK32(X0) = hd(cons(sK32(X0),sK23))
      | sP6(X0) ),
    inference(resolution,[],[f1027,f488]) ).

fof(f1090,plain,
    ! [X0] :
      ( sK31(X0) = hd(cons(sK31(X0),sK23))
      | sP6(X0) ),
    inference(resolution,[],[f1027,f487]) ).

fof(f1089,plain,
    ! [X0] :
      ( sK30(X0) = hd(cons(sK30(X0),sK23))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f1027,f481]) ).

fof(f1088,plain,
    ! [X0] :
      ( sK28(X0) = hd(cons(sK28(X0),sK23))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f1027,f477]) ).

fof(f1087,plain,
    ! [X0] :
      ( sK27(X0) = hd(cons(sK27(X0),sK23))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f1027,f472]) ).

fof(f1085,plain,
    ! [X0,X1] :
      ( sK20(X0,X1) = hd(cons(sK20(X0,X1),sK23))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f1027,f387]) ).

fof(f1084,plain,
    ! [X0] :
      ( hd(X0) = hd(cons(hd(X0),sK23))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f1027,f474]) ).

fof(f1027,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK23)) = X0 ),
    inference(resolution,[],[f573,f392]) ).

fof(f1082,plain,
    ! [X0] :
      ( leq(X0,sK72)
      | nil = cons(sK72,sK22)
      | ~ sP2(cons(sK72,sK22),X0) ),
    inference(superposition,[],[f448,f1077]) ).

fof(f1081,plain,
    ! [X0] :
      ( lt(X0,sK72)
      | nil = cons(sK72,sK22)
      | ~ sP4(cons(sK72,sK22),X0) ),
    inference(superposition,[],[f456,f1077]) ).

fof(f1077,plain,
    sK72 = hd(cons(sK72,sK22)),
    inference(resolution,[],[f1026,f614]) ).

fof(f1079,plain,
    ! [X0] :
      ( leq(X0,sK71)
      | nil = cons(sK71,sK22)
      | ~ sP2(cons(sK71,sK22),X0) ),
    inference(superposition,[],[f448,f1076]) ).

fof(f1078,plain,
    ! [X0] :
      ( lt(X0,sK71)
      | nil = cons(sK71,sK22)
      | ~ sP4(cons(sK71,sK22),X0) ),
    inference(superposition,[],[f456,f1076]) ).

fof(f1076,plain,
    sK71 = hd(cons(sK71,sK22)),
    inference(resolution,[],[f1026,f613]) ).

fof(f1075,plain,
    ! [X0] :
      ( sK61(X0) = hd(cons(sK61(X0),sK22))
      | sP18(X0) ),
    inference(resolution,[],[f1026,f556]) ).

fof(f1074,plain,
    ! [X0] :
      ( sK60(X0) = hd(cons(sK60(X0),sK22))
      | sP18(X0) ),
    inference(resolution,[],[f1026,f555]) ).

fof(f1073,plain,
    ! [X0] :
      ( sK56(X0) = hd(cons(sK56(X0),sK22))
      | sP16(X0) ),
    inference(resolution,[],[f1026,f545]) ).

fof(f1072,plain,
    ! [X0] :
      ( sK55(X0) = hd(cons(sK55(X0),sK22))
      | sP16(X0) ),
    inference(resolution,[],[f1026,f544]) ).

fof(f1071,plain,
    ! [X0] :
      ( sK51(X0) = hd(cons(sK51(X0),sK22))
      | sP14(X0) ),
    inference(resolution,[],[f1026,f533]) ).

fof(f1070,plain,
    ! [X0] :
      ( sK50(X0) = hd(cons(sK50(X0),sK22))
      | sP14(X0) ),
    inference(resolution,[],[f1026,f532]) ).

fof(f1069,plain,
    ! [X0] :
      ( sK46(X0) = hd(cons(sK46(X0),sK22))
      | sP12(X0) ),
    inference(resolution,[],[f1026,f521]) ).

fof(f1068,plain,
    ! [X0] :
      ( sK45(X0) = hd(cons(sK45(X0),sK22))
      | sP12(X0) ),
    inference(resolution,[],[f1026,f520]) ).

fof(f1067,plain,
    ! [X0] :
      ( sK41(X0) = hd(cons(sK41(X0),sK22))
      | sP10(X0) ),
    inference(resolution,[],[f1026,f509]) ).

fof(f1066,plain,
    ! [X0] :
      ( sK40(X0) = hd(cons(sK40(X0),sK22))
      | sP10(X0) ),
    inference(resolution,[],[f1026,f508]) ).

fof(f1065,plain,
    ! [X0] :
      ( sK36(X0) = hd(cons(sK36(X0),sK22))
      | sP8(X0) ),
    inference(resolution,[],[f1026,f498]) ).

fof(f1064,plain,
    ! [X0] :
      ( sK35(X0) = hd(cons(sK35(X0),sK22))
      | sP8(X0) ),
    inference(resolution,[],[f1026,f497]) ).

fof(f1063,plain,
    ! [X0] :
      ( sK32(X0) = hd(cons(sK32(X0),sK22))
      | sP6(X0) ),
    inference(resolution,[],[f1026,f488]) ).

fof(f1062,plain,
    ! [X0] :
      ( sK31(X0) = hd(cons(sK31(X0),sK22))
      | sP6(X0) ),
    inference(resolution,[],[f1026,f487]) ).

fof(f1061,plain,
    ! [X0] :
      ( sK30(X0) = hd(cons(sK30(X0),sK22))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f1026,f481]) ).

fof(f1060,plain,
    ! [X0] :
      ( sK28(X0) = hd(cons(sK28(X0),sK22))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f1026,f477]) ).

fof(f1059,plain,
    ! [X0] :
      ( sK27(X0) = hd(cons(sK27(X0),sK22))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f1026,f472]) ).

fof(f1057,plain,
    ! [X0,X1] :
      ( sK20(X0,X1) = hd(cons(sK20(X0,X1),sK22))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f1026,f387]) ).

fof(f1056,plain,
    ! [X0] :
      ( hd(X0) = hd(cons(hd(X0),sK22))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f1026,f474]) ).

fof(f1026,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK22)) = X0 ),
    inference(resolution,[],[f573,f391]) ).

fof(f1020,plain,
    sK23 = tl(cons(sK72,sK23)),
    inference(resolution,[],[f948,f614]) ).

fof(f1019,plain,
    sK23 = tl(cons(sK71,sK23)),
    inference(resolution,[],[f948,f613]) ).

fof(f1051,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK64(X1))) = X0
      | sP18(X1) ),
    inference(resolution,[],[f573,f559]) ).

fof(f1050,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK63(X1))) = X0
      | sP18(X1) ),
    inference(resolution,[],[f573,f558]) ).

fof(f1049,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK62(X1))) = X0
      | sP18(X1) ),
    inference(resolution,[],[f573,f557]) ).

fof(f1048,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK59(X1))) = X0
      | sP16(X1) ),
    inference(resolution,[],[f573,f548]) ).

fof(f1047,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK58(X1))) = X0
      | sP16(X1) ),
    inference(resolution,[],[f573,f547]) ).

fof(f1046,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK57(X1))) = X0
      | sP16(X1) ),
    inference(resolution,[],[f573,f546]) ).

fof(f1045,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK54(X1))) = X0
      | sP14(X1) ),
    inference(resolution,[],[f573,f536]) ).

fof(f1044,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK53(X1))) = X0
      | sP14(X1) ),
    inference(resolution,[],[f573,f535]) ).

fof(f1043,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK52(X1))) = X0
      | sP14(X1) ),
    inference(resolution,[],[f573,f534]) ).

fof(f1042,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK49(X1))) = X0
      | sP12(X1) ),
    inference(resolution,[],[f573,f524]) ).

fof(f1041,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK48(X1))) = X0
      | sP12(X1) ),
    inference(resolution,[],[f573,f523]) ).

fof(f1040,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK47(X1))) = X0
      | sP12(X1) ),
    inference(resolution,[],[f573,f522]) ).

fof(f1039,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK44(X1))) = X0
      | sP10(X1) ),
    inference(resolution,[],[f573,f512]) ).

fof(f1038,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK43(X1))) = X0
      | sP10(X1) ),
    inference(resolution,[],[f573,f511]) ).

fof(f1037,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK42(X1))) = X0
      | sP10(X1) ),
    inference(resolution,[],[f573,f510]) ).

fof(f1036,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK39(X1))) = X0
      | sP8(X1) ),
    inference(resolution,[],[f573,f501]) ).

fof(f1035,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK38(X1))) = X0
      | sP8(X1) ),
    inference(resolution,[],[f573,f500]) ).

fof(f1034,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK37(X1))) = X0
      | sP8(X1) ),
    inference(resolution,[],[f573,f499]) ).

fof(f1033,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK34(X1))) = X0
      | sP6(X1) ),
    inference(resolution,[],[f573,f490]) ).

fof(f1032,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK33(X1))) = X0
      | sP6(X1) ),
    inference(resolution,[],[f573,f489]) ).

fof(f1031,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK29(X1))) = X0
      | nil = X1
      | ~ ssList(X1) ),
    inference(resolution,[],[f573,f479]) ).

fof(f1030,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK26(X1))) = X0
      | nil = X1
      | ~ ssList(X1) ),
    inference(resolution,[],[f573,f471]) ).

fof(f1053,plain,
    ! [X0] :
      ( hd(cons(X0,sK23)) = X0
      | ~ ssItem(X0) ),
    inference(forward_demodulation,[],[f1029,f395]) ).

fof(f1029,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK25)) = X0 ),
    inference(resolution,[],[f573,f394]) ).

fof(f1052,plain,
    ! [X0] :
      ( hd(cons(X0,sK22)) = X0
      | ~ ssItem(X0) ),
    inference(forward_demodulation,[],[f1028,f396]) ).

fof(f1028,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK24)) = X0 ),
    inference(resolution,[],[f573,f393]) ).

fof(f1025,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,sK21(X1,X2))) = X0
      | ~ sP0(X1,X2) ),
    inference(resolution,[],[f573,f388]) ).

fof(f1024,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,tl(X1))) = X0
      | nil = X1
      | ~ ssList(X1) ),
    inference(resolution,[],[f573,f475]) ).

fof(f1023,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | hd(cons(X0,nil)) = X0 ),
    inference(resolution,[],[f573,f407]) ).

fof(f1022,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,app(X1,X2))) = X0
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(resolution,[],[f573,f579]) ).

fof(f1021,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | hd(cons(X0,cons(X1,X2))) = X0
      | ~ ssItem(X1)
      | ~ ssList(X2) ),
    inference(resolution,[],[f573,f569]) ).

fof(f573,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | hd(cons(X1,X0)) = X1 ),
    inference(cnf_transformation,[],[f182]) ).

fof(f182,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(cons(X1,X0)) = X1
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f1018,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK61(X0),sK23))
      | sP18(X0) ),
    inference(resolution,[],[f948,f556]) ).

fof(f1017,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK60(X0),sK23))
      | sP18(X0) ),
    inference(resolution,[],[f948,f555]) ).

fof(f1016,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK56(X0),sK23))
      | sP16(X0) ),
    inference(resolution,[],[f948,f545]) ).

fof(f1015,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK55(X0),sK23))
      | sP16(X0) ),
    inference(resolution,[],[f948,f544]) ).

fof(f1014,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK51(X0),sK23))
      | sP14(X0) ),
    inference(resolution,[],[f948,f533]) ).

fof(f1013,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK50(X0),sK23))
      | sP14(X0) ),
    inference(resolution,[],[f948,f532]) ).

fof(f1012,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK46(X0),sK23))
      | sP12(X0) ),
    inference(resolution,[],[f948,f521]) ).

fof(f1011,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK45(X0),sK23))
      | sP12(X0) ),
    inference(resolution,[],[f948,f520]) ).

fof(f1010,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK41(X0),sK23))
      | sP10(X0) ),
    inference(resolution,[],[f948,f509]) ).

fof(f1009,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK40(X0),sK23))
      | sP10(X0) ),
    inference(resolution,[],[f948,f508]) ).

fof(f1008,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK36(X0),sK23))
      | sP8(X0) ),
    inference(resolution,[],[f948,f498]) ).

fof(f1007,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK35(X0),sK23))
      | sP8(X0) ),
    inference(resolution,[],[f948,f497]) ).

fof(f1006,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK32(X0),sK23))
      | sP6(X0) ),
    inference(resolution,[],[f948,f488]) ).

fof(f1005,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK31(X0),sK23))
      | sP6(X0) ),
    inference(resolution,[],[f948,f487]) ).

fof(f1004,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK30(X0),sK23))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f948,f481]) ).

fof(f1003,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK28(X0),sK23))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f948,f477]) ).

fof(f1002,plain,
    ! [X0] :
      ( sK23 = tl(cons(sK27(X0),sK23))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f948,f472]) ).

fof(f1000,plain,
    ! [X0,X1] :
      ( sK23 = tl(cons(sK20(X0,X1),sK23))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f948,f387]) ).

fof(f999,plain,
    ! [X0] :
      ( sK23 = tl(cons(hd(X0),sK23))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f948,f474]) ).

fof(f948,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | sK23 = tl(cons(X0,sK23)) ),
    inference(resolution,[],[f572,f392]) ).

fof(f996,plain,
    sK22 = tl(cons(sK72,sK22)),
    inference(resolution,[],[f947,f614]) ).

fof(f995,plain,
    sK22 = tl(cons(sK71,sK22)),
    inference(resolution,[],[f947,f613]) ).

fof(f994,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK61(X0),sK22))
      | sP18(X0) ),
    inference(resolution,[],[f947,f556]) ).

fof(f993,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK60(X0),sK22))
      | sP18(X0) ),
    inference(resolution,[],[f947,f555]) ).

fof(f992,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK56(X0),sK22))
      | sP16(X0) ),
    inference(resolution,[],[f947,f545]) ).

fof(f991,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK55(X0),sK22))
      | sP16(X0) ),
    inference(resolution,[],[f947,f544]) ).

fof(f990,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK51(X0),sK22))
      | sP14(X0) ),
    inference(resolution,[],[f947,f533]) ).

fof(f989,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK50(X0),sK22))
      | sP14(X0) ),
    inference(resolution,[],[f947,f532]) ).

fof(f980,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK30(X0),sK22))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f947,f481]) ).

fof(f979,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK28(X0),sK22))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f947,f477]) ).

fof(f978,plain,
    ! [X0] :
      ( sK22 = tl(cons(sK27(X0),sK22))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f947,f472]) ).

fof(f976,plain,
    ! [X0,X1] :
      ( sK22 = tl(cons(sK20(X0,X1),sK22))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f947,f387]) ).

fof(f975,plain,
    ! [X0] :
      ( sK22 = tl(cons(hd(X0),sK22))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f947,f474]) ).

fof(f947,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | sK22 = tl(cons(X0,sK22)) ),
    inference(resolution,[],[f572,f391]) ).

fof(f972,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK64(X1) = tl(cons(X0,sK64(X1)))
      | sP18(X1) ),
    inference(resolution,[],[f572,f559]) ).

fof(f971,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK63(X1) = tl(cons(X0,sK63(X1)))
      | sP18(X1) ),
    inference(resolution,[],[f572,f558]) ).

fof(f970,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK62(X1) = tl(cons(X0,sK62(X1)))
      | sP18(X1) ),
    inference(resolution,[],[f572,f557]) ).

fof(f969,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK59(X1) = tl(cons(X0,sK59(X1)))
      | sP16(X1) ),
    inference(resolution,[],[f572,f548]) ).

fof(f968,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK58(X1) = tl(cons(X0,sK58(X1)))
      | sP16(X1) ),
    inference(resolution,[],[f572,f547]) ).

fof(f967,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK57(X1) = tl(cons(X0,sK57(X1)))
      | sP16(X1) ),
    inference(resolution,[],[f572,f546]) ).

fof(f966,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK54(X1) = tl(cons(X0,sK54(X1)))
      | sP14(X1) ),
    inference(resolution,[],[f572,f536]) ).

fof(f965,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK53(X1) = tl(cons(X0,sK53(X1)))
      | sP14(X1) ),
    inference(resolution,[],[f572,f535]) ).

fof(f964,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK52(X1) = tl(cons(X0,sK52(X1)))
      | sP14(X1) ),
    inference(resolution,[],[f572,f534]) ).

fof(f963,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK49(X1) = tl(cons(X0,sK49(X1)))
      | sP12(X1) ),
    inference(resolution,[],[f572,f524]) ).

fof(f962,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK48(X1) = tl(cons(X0,sK48(X1)))
      | sP12(X1) ),
    inference(resolution,[],[f572,f523]) ).

fof(f961,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK47(X1) = tl(cons(X0,sK47(X1)))
      | sP12(X1) ),
    inference(resolution,[],[f572,f522]) ).

fof(f960,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK44(X1) = tl(cons(X0,sK44(X1)))
      | sP10(X1) ),
    inference(resolution,[],[f572,f512]) ).

fof(f959,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK43(X1) = tl(cons(X0,sK43(X1)))
      | sP10(X1) ),
    inference(resolution,[],[f572,f511]) ).

fof(f958,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK42(X1) = tl(cons(X0,sK42(X1)))
      | sP10(X1) ),
    inference(resolution,[],[f572,f510]) ).

fof(f957,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK39(X1) = tl(cons(X0,sK39(X1)))
      | sP8(X1) ),
    inference(resolution,[],[f572,f501]) ).

fof(f956,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK38(X1) = tl(cons(X0,sK38(X1)))
      | sP8(X1) ),
    inference(resolution,[],[f572,f500]) ).

fof(f955,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK37(X1) = tl(cons(X0,sK37(X1)))
      | sP8(X1) ),
    inference(resolution,[],[f572,f499]) ).

fof(f954,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK34(X1) = tl(cons(X0,sK34(X1)))
      | sP6(X1) ),
    inference(resolution,[],[f572,f490]) ).

fof(f953,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK33(X1) = tl(cons(X0,sK33(X1)))
      | sP6(X1) ),
    inference(resolution,[],[f572,f489]) ).

fof(f952,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK29(X1) = tl(cons(X0,sK29(X1)))
      | nil = X1
      | ~ ssList(X1) ),
    inference(resolution,[],[f572,f479]) ).

fof(f951,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | sK26(X1) = tl(cons(X0,sK26(X1)))
      | nil = X1
      | ~ ssList(X1) ),
    inference(resolution,[],[f572,f471]) ).

fof(f974,plain,
    ! [X0] :
      ( sK23 = tl(cons(X0,sK23))
      | ~ ssItem(X0) ),
    inference(forward_demodulation,[],[f950,f395]) ).

fof(f950,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | sK25 = tl(cons(X0,sK25)) ),
    inference(resolution,[],[f572,f394]) ).

fof(f973,plain,
    ! [X0] :
      ( sK22 = tl(cons(X0,sK22))
      | ~ ssItem(X0) ),
    inference(forward_demodulation,[],[f949,f396]) ).

fof(f949,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | sK24 = tl(cons(X0,sK24)) ),
    inference(resolution,[],[f572,f393]) ).

fof(f946,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | sK21(X1,X2) = tl(cons(X0,sK21(X1,X2)))
      | ~ sP0(X1,X2) ),
    inference(resolution,[],[f572,f388]) ).

fof(f945,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | tl(X1) = tl(cons(X0,tl(X1)))
      | nil = X1
      | ~ ssList(X1) ),
    inference(resolution,[],[f572,f475]) ).

fof(f944,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | nil = tl(cons(X0,nil)) ),
    inference(resolution,[],[f572,f407]) ).

fof(f943,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | app(X1,X2) = tl(cons(X0,app(X1,X2)))
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(resolution,[],[f572,f579]) ).

fof(f942,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | cons(X1,X2) = tl(cons(X0,cons(X1,X2)))
      | ~ ssItem(X1)
      | ~ ssList(X2) ),
    inference(resolution,[],[f572,f569]) ).

fof(f572,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | tl(cons(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(cons(X1,X0)) = X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => tl(cons(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

fof(f482,plain,
    ! [X0] :
      ( ~ singletonP(X0)
      | cons(sK30(X0),nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f294]) ).

fof(f930,plain,
    ! [X0] :
      ( nil = sK64(X0)
      | tl(sK64(X0)) = sK29(sK64(X0))
      | sP18(X0) ),
    inference(resolution,[],[f480,f559]) ).

fof(f929,plain,
    ! [X0] :
      ( nil = sK63(X0)
      | tl(sK63(X0)) = sK29(sK63(X0))
      | sP18(X0) ),
    inference(resolution,[],[f480,f558]) ).

fof(f928,plain,
    ! [X0] :
      ( nil = sK62(X0)
      | tl(sK62(X0)) = sK29(sK62(X0))
      | sP18(X0) ),
    inference(resolution,[],[f480,f557]) ).

fof(f927,plain,
    ! [X0] :
      ( nil = sK59(X0)
      | tl(sK59(X0)) = sK29(sK59(X0))
      | sP16(X0) ),
    inference(resolution,[],[f480,f548]) ).

fof(f926,plain,
    ! [X0] :
      ( nil = sK58(X0)
      | tl(sK58(X0)) = sK29(sK58(X0))
      | sP16(X0) ),
    inference(resolution,[],[f480,f547]) ).

fof(f925,plain,
    ! [X0] :
      ( nil = sK57(X0)
      | tl(sK57(X0)) = sK29(sK57(X0))
      | sP16(X0) ),
    inference(resolution,[],[f480,f546]) ).

fof(f924,plain,
    ! [X0] :
      ( nil = sK54(X0)
      | tl(sK54(X0)) = sK29(sK54(X0))
      | sP14(X0) ),
    inference(resolution,[],[f480,f536]) ).

fof(f923,plain,
    ! [X0] :
      ( nil = sK53(X0)
      | tl(sK53(X0)) = sK29(sK53(X0))
      | sP14(X0) ),
    inference(resolution,[],[f480,f535]) ).

fof(f922,plain,
    ! [X0] :
      ( nil = sK52(X0)
      | tl(sK52(X0)) = sK29(sK52(X0))
      | sP14(X0) ),
    inference(resolution,[],[f480,f534]) ).

fof(f921,plain,
    ! [X0] :
      ( nil = sK49(X0)
      | tl(sK49(X0)) = sK29(sK49(X0))
      | sP12(X0) ),
    inference(resolution,[],[f480,f524]) ).

fof(f920,plain,
    ! [X0] :
      ( nil = sK48(X0)
      | tl(sK48(X0)) = sK29(sK48(X0))
      | sP12(X0) ),
    inference(resolution,[],[f480,f523]) ).

fof(f919,plain,
    ! [X0] :
      ( nil = sK47(X0)
      | tl(sK47(X0)) = sK29(sK47(X0))
      | sP12(X0) ),
    inference(resolution,[],[f480,f522]) ).

fof(f918,plain,
    ! [X0] :
      ( nil = sK44(X0)
      | tl(sK44(X0)) = sK29(sK44(X0))
      | sP10(X0) ),
    inference(resolution,[],[f480,f512]) ).

fof(f917,plain,
    ! [X0] :
      ( nil = sK43(X0)
      | tl(sK43(X0)) = sK29(sK43(X0))
      | sP10(X0) ),
    inference(resolution,[],[f480,f511]) ).

fof(f916,plain,
    ! [X0] :
      ( nil = sK42(X0)
      | tl(sK42(X0)) = sK29(sK42(X0))
      | sP10(X0) ),
    inference(resolution,[],[f480,f510]) ).

fof(f915,plain,
    ! [X0] :
      ( nil = sK39(X0)
      | tl(sK39(X0)) = sK29(sK39(X0))
      | sP8(X0) ),
    inference(resolution,[],[f480,f501]) ).

fof(f914,plain,
    ! [X0] :
      ( nil = sK38(X0)
      | tl(sK38(X0)) = sK29(sK38(X0))
      | sP8(X0) ),
    inference(resolution,[],[f480,f500]) ).

fof(f913,plain,
    ! [X0] :
      ( nil = sK37(X0)
      | tl(sK37(X0)) = sK29(sK37(X0))
      | sP8(X0) ),
    inference(resolution,[],[f480,f499]) ).

fof(f912,plain,
    ! [X0] :
      ( nil = sK34(X0)
      | tl(sK34(X0)) = sK29(sK34(X0))
      | sP6(X0) ),
    inference(resolution,[],[f480,f490]) ).

fof(f911,plain,
    ! [X0] :
      ( nil = sK33(X0)
      | tl(sK33(X0)) = sK29(sK33(X0))
      | sP6(X0) ),
    inference(resolution,[],[f480,f489]) ).

fof(f910,plain,
    ! [X0] :
      ( nil = sK29(X0)
      | tl(sK29(X0)) = sK29(sK29(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f480,f479]) ).

fof(f909,plain,
    ! [X0] :
      ( nil = sK26(X0)
      | tl(sK26(X0)) = sK29(sK26(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f480,f471]) ).

fof(f904,plain,
    ! [X0,X1] :
      ( nil = sK21(X0,X1)
      | tl(sK21(X0,X1)) = sK29(sK21(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f480,f388]) ).

fof(f903,plain,
    ! [X0] :
      ( nil = tl(X0)
      | tl(tl(X0)) = sK29(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f480,f475]) ).

fof(f901,plain,
    ! [X0,X1] :
      ( nil = app(X0,X1)
      | tl(app(X0,X1)) = sK29(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(resolution,[],[f480,f579]) ).

fof(f931,plain,
    ! [X0,X1] :
      ( tl(cons(X0,X1)) = sK29(cons(X0,X1))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(subsumption_resolution,[],[f900,f570]) ).

fof(f900,plain,
    ! [X0,X1] :
      ( nil = cons(X0,X1)
      | tl(cons(X0,X1)) = sK29(cons(X0,X1))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(resolution,[],[f480,f569]) ).

fof(f480,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | tl(X0) = sK29(X0) ),
    inference(cnf_transformation,[],[f290]) ).

fof(f290,plain,
    ! [X0] :
      ( ( tl(X0) = sK29(X0)
        & ssList(sK29(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f159,f289]) ).

fof(f289,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK29(X0)
        & ssList(sK29(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f158]) ).

fof(f158,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).

fof(f857,plain,
    ( nil = sK23
    | hd(sK23) = sK28(sK23) ),
    inference(resolution,[],[f478,f392]) ).

fof(f881,plain,
    ! [X0] :
      ( nil = sK64(X0)
      | hd(sK64(X0)) = sK28(sK64(X0))
      | sP18(X0) ),
    inference(resolution,[],[f478,f559]) ).

fof(f880,plain,
    ! [X0] :
      ( nil = sK63(X0)
      | hd(sK63(X0)) = sK28(sK63(X0))
      | sP18(X0) ),
    inference(resolution,[],[f478,f558]) ).

fof(f879,plain,
    ! [X0] :
      ( nil = sK62(X0)
      | hd(sK62(X0)) = sK28(sK62(X0))
      | sP18(X0) ),
    inference(resolution,[],[f478,f557]) ).

fof(f878,plain,
    ! [X0] :
      ( nil = sK59(X0)
      | hd(sK59(X0)) = sK28(sK59(X0))
      | sP16(X0) ),
    inference(resolution,[],[f478,f548]) ).

fof(f877,plain,
    ! [X0] :
      ( nil = sK58(X0)
      | hd(sK58(X0)) = sK28(sK58(X0))
      | sP16(X0) ),
    inference(resolution,[],[f478,f547]) ).

fof(f876,plain,
    ! [X0] :
      ( nil = sK57(X0)
      | hd(sK57(X0)) = sK28(sK57(X0))
      | sP16(X0) ),
    inference(resolution,[],[f478,f546]) ).

fof(f875,plain,
    ! [X0] :
      ( nil = sK54(X0)
      | hd(sK54(X0)) = sK28(sK54(X0))
      | sP14(X0) ),
    inference(resolution,[],[f478,f536]) ).

fof(f874,plain,
    ! [X0] :
      ( nil = sK53(X0)
      | hd(sK53(X0)) = sK28(sK53(X0))
      | sP14(X0) ),
    inference(resolution,[],[f478,f535]) ).

fof(f873,plain,
    ! [X0] :
      ( nil = sK52(X0)
      | hd(sK52(X0)) = sK28(sK52(X0))
      | sP14(X0) ),
    inference(resolution,[],[f478,f534]) ).

fof(f872,plain,
    ! [X0] :
      ( nil = sK49(X0)
      | hd(sK49(X0)) = sK28(sK49(X0))
      | sP12(X0) ),
    inference(resolution,[],[f478,f524]) ).

fof(f871,plain,
    ! [X0] :
      ( nil = sK48(X0)
      | hd(sK48(X0)) = sK28(sK48(X0))
      | sP12(X0) ),
    inference(resolution,[],[f478,f523]) ).

fof(f870,plain,
    ! [X0] :
      ( nil = sK47(X0)
      | hd(sK47(X0)) = sK28(sK47(X0))
      | sP12(X0) ),
    inference(resolution,[],[f478,f522]) ).

fof(f869,plain,
    ! [X0] :
      ( nil = sK44(X0)
      | hd(sK44(X0)) = sK28(sK44(X0))
      | sP10(X0) ),
    inference(resolution,[],[f478,f512]) ).

fof(f868,plain,
    ! [X0] :
      ( nil = sK43(X0)
      | hd(sK43(X0)) = sK28(sK43(X0))
      | sP10(X0) ),
    inference(resolution,[],[f478,f511]) ).

fof(f867,plain,
    ! [X0] :
      ( nil = sK42(X0)
      | hd(sK42(X0)) = sK28(sK42(X0))
      | sP10(X0) ),
    inference(resolution,[],[f478,f510]) ).

fof(f866,plain,
    ! [X0] :
      ( nil = sK39(X0)
      | hd(sK39(X0)) = sK28(sK39(X0))
      | sP8(X0) ),
    inference(resolution,[],[f478,f501]) ).

fof(f865,plain,
    ! [X0] :
      ( nil = sK38(X0)
      | hd(sK38(X0)) = sK28(sK38(X0))
      | sP8(X0) ),
    inference(resolution,[],[f478,f500]) ).

fof(f864,plain,
    ! [X0] :
      ( nil = sK37(X0)
      | hd(sK37(X0)) = sK28(sK37(X0))
      | sP8(X0) ),
    inference(resolution,[],[f478,f499]) ).

fof(f863,plain,
    ! [X0] :
      ( nil = sK34(X0)
      | hd(sK34(X0)) = sK28(sK34(X0))
      | sP6(X0) ),
    inference(resolution,[],[f478,f490]) ).

fof(f862,plain,
    ! [X0] :
      ( nil = sK33(X0)
      | hd(sK33(X0)) = sK28(sK33(X0))
      | sP6(X0) ),
    inference(resolution,[],[f478,f489]) ).

fof(f861,plain,
    ! [X0] :
      ( nil = sK29(X0)
      | hd(sK29(X0)) = sK28(sK29(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f478,f479]) ).

fof(f860,plain,
    ! [X0] :
      ( nil = sK26(X0)
      | hd(sK26(X0)) = sK28(sK26(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f478,f471]) ).

fof(f888,plain,
    ( hd(sK23) = sK28(sK23)
    | nil = sK23 ),
    inference(forward_demodulation,[],[f887,f395]) ).

fof(f887,plain,
    ( nil = sK23
    | hd(sK25) = sK28(sK25) ),
    inference(forward_demodulation,[],[f859,f395]) ).

fof(f859,plain,
    ( nil = sK25
    | hd(sK25) = sK28(sK25) ),
    inference(resolution,[],[f478,f394]) ).

fof(f855,plain,
    ! [X0,X1] :
      ( nil = sK21(X0,X1)
      | hd(sK21(X0,X1)) = sK28(sK21(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f478,f388]) ).

fof(f854,plain,
    ! [X0] :
      ( nil = tl(X0)
      | hd(tl(X0)) = sK28(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f478,f475]) ).

fof(f852,plain,
    ! [X0,X1] :
      ( nil = app(X0,X1)
      | hd(app(X0,X1)) = sK28(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(resolution,[],[f478,f579]) ).

fof(f882,plain,
    ! [X0,X1] :
      ( hd(cons(X0,X1)) = sK28(cons(X0,X1))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(subsumption_resolution,[],[f851,f570]) ).

fof(f851,plain,
    ! [X0,X1] :
      ( nil = cons(X0,X1)
      | hd(cons(X0,X1)) = sK28(cons(X0,X1))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(resolution,[],[f478,f569]) ).

fof(f478,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | hd(X0) = sK28(X0) ),
    inference(cnf_transformation,[],[f288]) ).

fof(f288,plain,
    ! [X0] :
      ( ( hd(X0) = sK28(X0)
        & ssItem(sK28(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f157,f287]) ).

fof(f287,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK28(X0)
        & ssItem(sK28(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).

fof(f850,plain,
    ! [X0,X1] :
      ( nil = X0
      | ~ sP4(X0,X1)
      | ~ lt(hd(X0),X1)
      | ~ ssItem(X1)
      | ~ ssItem(hd(X0)) ),
    inference(resolution,[],[f456,f421]) ).

fof(f849,plain,
    ! [X0,X1] :
      ( nil = X0
      | ~ sP4(X0,X1)
      | leq(X1,hd(X0))
      | ~ ssItem(hd(X0))
      | ~ ssItem(X1) ),
    inference(resolution,[],[f456,f431]) ).

fof(f848,plain,
    ! [X0] :
      ( nil = X0
      | ~ sP4(X0,hd(X0))
      | ~ ssItem(hd(X0)) ),
    inference(resolution,[],[f456,f409]) ).

fof(f456,plain,
    ! [X0,X1] :
      ( lt(X1,hd(X0))
      | nil = X0
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f281]) ).

fof(f281,plain,
    ! [X0,X1] :
      ( ( sP4(X0,X1)
        | ( ( ~ lt(X1,hd(X0))
            | ~ strictorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( lt(X1,hd(X0))
          & strictorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP4(X0,X1) ) ),
    inference(rectify,[],[f280]) ).

fof(f280,plain,
    ! [X1,X0] :
      ( ( sP4(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP4(X1,X0) ) ),
    inference(flattening,[],[f279]) ).

fof(f279,plain,
    ! [X1,X0] :
      ( ( sP4(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP4(X1,X0) ) ),
    inference(nnf_transformation,[],[f229]) ).

fof(f229,plain,
    ! [X1,X0] :
      ( sP4(X1,X0)
    <=> ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f453,plain,
    ! [X0,X1] :
      ( strictorderedP(cons(X0,X1))
      | ~ sP4(X1,X0)
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f278,plain,
    ! [X0,X1] :
      ( ( ( strictorderedP(cons(X0,X1))
          | ~ sP4(X1,X0) )
        & ( sP4(X1,X0)
          | ~ strictorderedP(cons(X0,X1)) ) )
      | ~ sP5(X0,X1) ),
    inference(nnf_transformation,[],[f230]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( ( strictorderedP(cons(X0,X1))
      <=> sP4(X1,X0) )
      | ~ sP5(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f452,plain,
    ! [X0,X1] :
      ( ~ strictorderedP(cons(X0,X1))
      | sP4(X1,X0)
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f278]) ).

fof(f448,plain,
    ! [X0,X1] :
      ( leq(X1,hd(X0))
      | nil = X0
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f277]) ).

fof(f277,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ( ( ~ leq(X1,hd(X0))
            | ~ totalorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( leq(X1,hd(X0))
          & totalorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f276]) ).

fof(f276,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(flattening,[],[f275]) ).

fof(f275,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(nnf_transformation,[],[f226]) ).

fof(f226,plain,
    ! [X1,X0] :
      ( sP2(X1,X0)
    <=> ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f445,plain,
    ! [X0,X1] :
      ( totalorderedP(cons(X0,X1))
      | ~ sP2(X1,X0)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f274]) ).

fof(f274,plain,
    ! [X0,X1] :
      ( ( ( totalorderedP(cons(X0,X1))
          | ~ sP2(X1,X0) )
        & ( sP2(X1,X0)
          | ~ totalorderedP(cons(X0,X1)) ) )
      | ~ sP3(X0,X1) ),
    inference(nnf_transformation,[],[f227]) ).

fof(f227,plain,
    ! [X0,X1] :
      ( ( totalorderedP(cons(X0,X1))
      <=> sP2(X1,X0) )
      | ~ sP3(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f444,plain,
    ! [X0,X1] :
      ( ~ totalorderedP(cons(X0,X1))
      | sP2(X1,X0)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f274]) ).

fof(f431,plain,
    ! [X0,X1] :
      ( ~ lt(X0,X1)
      | leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f269,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f268]) ).

fof(f268,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( lt(X0,X1)
              | ~ leq(X0,X1)
              | X0 = X1 )
            & ( ( leq(X0,X1)
                & X0 != X1 )
              | ~ lt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f124]) ).

fof(f124,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f93,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).

fof(f429,plain,
    ! [X0,X1] :
      ( geq(X0,X1)
      | ~ leq(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f267,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( geq(X0,X1)
              | ~ leq(X1,X0) )
            & ( leq(X1,X0)
              | ~ geq(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( geq(X0,X1)
          <=> leq(X1,X0) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( geq(X0,X1)
          <=> leq(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).

fof(f428,plain,
    ! [X0,X1] :
      ( ~ geq(X0,X1)
      | leq(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f833,plain,
    ! [X0] :
      ( sK64(X0) = app(nil,sK64(X0))
      | strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f737,f664]) ).

fof(f737,plain,
    ! [X0] :
      ( sP18(X0)
      | sK64(X0) = app(nil,sK64(X0)) ),
    inference(resolution,[],[f470,f559]) ).

fof(f832,plain,
    ! [X0] :
      ( sK63(X0) = app(nil,sK63(X0))
      | strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f736,f664]) ).

fof(f736,plain,
    ! [X0] :
      ( sP18(X0)
      | sK63(X0) = app(nil,sK63(X0)) ),
    inference(resolution,[],[f470,f558]) ).

fof(f831,plain,
    ! [X0] :
      ( sK62(X0) = app(nil,sK62(X0))
      | strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f735,f664]) ).

fof(f735,plain,
    ! [X0] :
      ( sP18(X0)
      | sK62(X0) = app(nil,sK62(X0)) ),
    inference(resolution,[],[f470,f557]) ).

fof(f830,plain,
    ! [X0] :
      ( sK59(X0) = app(nil,sK59(X0))
      | totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f734,f662]) ).

fof(f734,plain,
    ! [X0] :
      ( sP16(X0)
      | sK59(X0) = app(nil,sK59(X0)) ),
    inference(resolution,[],[f470,f548]) ).

fof(f829,plain,
    ! [X0] :
      ( sK58(X0) = app(nil,sK58(X0))
      | totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f733,f662]) ).

fof(f733,plain,
    ! [X0] :
      ( sP16(X0)
      | sK58(X0) = app(nil,sK58(X0)) ),
    inference(resolution,[],[f470,f547]) ).

fof(f828,plain,
    ! [X0] :
      ( sK57(X0) = app(nil,sK57(X0))
      | totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f732,f662]) ).

fof(f732,plain,
    ! [X0] :
      ( sP16(X0)
      | sK57(X0) = app(nil,sK57(X0)) ),
    inference(resolution,[],[f470,f546]) ).

fof(f731,plain,
    ! [X0] :
      ( sP14(X0)
      | sK54(X0) = app(nil,sK54(X0)) ),
    inference(resolution,[],[f470,f536]) ).

fof(f730,plain,
    ! [X0] :
      ( sP14(X0)
      | sK53(X0) = app(nil,sK53(X0)) ),
    inference(resolution,[],[f470,f535]) ).

fof(f427,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f266]) ).

fof(f266,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

fof(f729,plain,
    ! [X0] :
      ( sP14(X0)
      | sK52(X0) = app(nil,sK52(X0)) ),
    inference(resolution,[],[f470,f534]) ).

fof(f728,plain,
    ! [X0] :
      ( sP12(X0)
      | sK49(X0) = app(nil,sK49(X0)) ),
    inference(resolution,[],[f470,f524]) ).

fof(f727,plain,
    ! [X0] :
      ( sP12(X0)
      | sK48(X0) = app(nil,sK48(X0)) ),
    inference(resolution,[],[f470,f523]) ).

fof(f726,plain,
    ! [X0] :
      ( sP12(X0)
      | sK47(X0) = app(nil,sK47(X0)) ),
    inference(resolution,[],[f470,f522]) ).

fof(f725,plain,
    ! [X0] :
      ( sP10(X0)
      | sK44(X0) = app(nil,sK44(X0)) ),
    inference(resolution,[],[f470,f512]) ).

fof(f724,plain,
    ! [X0] :
      ( sP10(X0)
      | sK43(X0) = app(nil,sK43(X0)) ),
    inference(resolution,[],[f470,f511]) ).

fof(f723,plain,
    ! [X0] :
      ( sP10(X0)
      | sK42(X0) = app(nil,sK42(X0)) ),
    inference(resolution,[],[f470,f510]) ).

fof(f722,plain,
    ! [X0] :
      ( sP8(X0)
      | sK39(X0) = app(nil,sK39(X0)) ),
    inference(resolution,[],[f470,f501]) ).

fof(f721,plain,
    ! [X0] :
      ( sP8(X0)
      | sK38(X0) = app(nil,sK38(X0)) ),
    inference(resolution,[],[f470,f500]) ).

fof(f720,plain,
    ! [X0] :
      ( sP8(X0)
      | sK37(X0) = app(nil,sK37(X0)) ),
    inference(resolution,[],[f470,f499]) ).

fof(f719,plain,
    ! [X0] :
      ( sP6(X0)
      | sK34(X0) = app(nil,sK34(X0)) ),
    inference(resolution,[],[f470,f490]) ).

fof(f822,plain,
    ! [X0,X1] :
      ( ~ lt(X0,X1)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ gt(X0,X1) ),
    inference(duplicate_literal_removal,[],[f821]) ).

fof(f821,plain,
    ! [X0,X1] :
      ( ~ lt(X0,X1)
      | ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ gt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(resolution,[],[f425,f419]) ).

fof(f425,plain,
    ! [X0,X1] :
      ( gt(X0,X1)
      | ~ lt(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f265]) ).

fof(f265,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( gt(X0,X1)
              | ~ lt(X1,X0) )
            & ( lt(X1,X0)
              | ~ gt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( gt(X0,X1)
          <=> lt(X1,X0) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( gt(X0,X1)
          <=> lt(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).

fof(f718,plain,
    ! [X0] :
      ( sP6(X0)
      | sK33(X0) = app(nil,sK33(X0)) ),
    inference(resolution,[],[f470,f489]) ).

fof(f819,plain,
    ! [X0] :
      ( sK64(X0) = app(sK64(X0),nil)
      | strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f709,f664]) ).

fof(f709,plain,
    ! [X0] :
      ( sP18(X0)
      | sK64(X0) = app(sK64(X0),nil) ),
    inference(resolution,[],[f469,f559]) ).

fof(f818,plain,
    ! [X0] :
      ( sK63(X0) = app(sK63(X0),nil)
      | strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f708,f664]) ).

fof(f708,plain,
    ! [X0] :
      ( sP18(X0)
      | sK63(X0) = app(sK63(X0),nil) ),
    inference(resolution,[],[f469,f558]) ).

fof(f817,plain,
    ! [X0] :
      ( sK62(X0) = app(sK62(X0),nil)
      | strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f707,f664]) ).

fof(f707,plain,
    ! [X0] :
      ( sP18(X0)
      | sK62(X0) = app(sK62(X0),nil) ),
    inference(resolution,[],[f469,f557]) ).

fof(f816,plain,
    ! [X0] :
      ( sK59(X0) = app(sK59(X0),nil)
      | totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f706,f662]) ).

fof(f706,plain,
    ! [X0] :
      ( sP16(X0)
      | sK59(X0) = app(sK59(X0),nil) ),
    inference(resolution,[],[f469,f548]) ).

fof(f815,plain,
    ! [X0] :
      ( sK58(X0) = app(sK58(X0),nil)
      | totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f705,f662]) ).

fof(f705,plain,
    ! [X0] :
      ( sP16(X0)
      | sK58(X0) = app(sK58(X0),nil) ),
    inference(resolution,[],[f469,f547]) ).

fof(f814,plain,
    ! [X0] :
      ( sK57(X0) = app(sK57(X0),nil)
      | totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f704,f662]) ).

fof(f704,plain,
    ! [X0] :
      ( sP16(X0)
      | sK57(X0) = app(sK57(X0),nil) ),
    inference(resolution,[],[f469,f546]) ).

fof(f703,plain,
    ! [X0] :
      ( sP14(X0)
      | sK54(X0) = app(sK54(X0),nil) ),
    inference(resolution,[],[f469,f536]) ).

fof(f702,plain,
    ! [X0] :
      ( sP14(X0)
      | sK53(X0) = app(sK53(X0),nil) ),
    inference(resolution,[],[f469,f535]) ).

fof(f701,plain,
    ! [X0] :
      ( sP14(X0)
      | sK52(X0) = app(sK52(X0),nil) ),
    inference(resolution,[],[f469,f534]) ).

fof(f700,plain,
    ! [X0] :
      ( sP12(X0)
      | sK49(X0) = app(sK49(X0),nil) ),
    inference(resolution,[],[f469,f524]) ).

fof(f424,plain,
    ! [X0,X1] :
      ( ~ gt(X0,X1)
      | lt(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f265]) ).

fof(f699,plain,
    ! [X0] :
      ( sP12(X0)
      | sK48(X0) = app(sK48(X0),nil) ),
    inference(resolution,[],[f469,f523]) ).

fof(f698,plain,
    ! [X0] :
      ( sP12(X0)
      | sK47(X0) = app(sK47(X0),nil) ),
    inference(resolution,[],[f469,f522]) ).

fof(f697,plain,
    ! [X0] :
      ( sP10(X0)
      | sK44(X0) = app(sK44(X0),nil) ),
    inference(resolution,[],[f469,f512]) ).

fof(f696,plain,
    ! [X0] :
      ( sP10(X0)
      | sK43(X0) = app(sK43(X0),nil) ),
    inference(resolution,[],[f469,f511]) ).

fof(f695,plain,
    ! [X0] :
      ( sP10(X0)
      | sK42(X0) = app(sK42(X0),nil) ),
    inference(resolution,[],[f469,f510]) ).

fof(f694,plain,
    ! [X0] :
      ( sP8(X0)
      | sK39(X0) = app(sK39(X0),nil) ),
    inference(resolution,[],[f469,f501]) ).

fof(f693,plain,
    ! [X0] :
      ( sP8(X0)
      | sK38(X0) = app(sK38(X0),nil) ),
    inference(resolution,[],[f469,f500]) ).

fof(f692,plain,
    ! [X0] :
      ( sP8(X0)
      | sK37(X0) = app(sK37(X0),nil) ),
    inference(resolution,[],[f469,f499]) ).

fof(f691,plain,
    ! [X0] :
      ( sP6(X0)
      | sK34(X0) = app(sK34(X0),nil) ),
    inference(resolution,[],[f469,f490]) ).

fof(f690,plain,
    ! [X0] :
      ( sP6(X0)
      | sK33(X0) = app(sK33(X0),nil) ),
    inference(resolution,[],[f469,f489]) ).

fof(f421,plain,
    ! [X0,X1] :
      ( ~ lt(X1,X0)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
           => ~ lt(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).

fof(f419,plain,
    ! [X0,X1] :
      ( ~ gt(X1,X0)
      | ~ gt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ gt(X1,X0)
          | ~ gt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ gt(X1,X0)
          | ~ gt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f94]) ).

fof(f94,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( gt(X0,X1)
           => ~ gt(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).

fof(f389,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | cons(sK20(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f259]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( ( app(sK21(X0,X1),cons(sK20(X0,X1),nil)) = X0
        & cons(sK20(X0,X1),nil) = X1
        & ssList(sK21(X0,X1))
        & ssItem(sK20(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f256,f258,f257]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( app(X3,cons(X2,nil)) = X0
              & cons(X2,nil) = X1
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( app(X3,cons(sK20(X0,X1),nil)) = X0
            & cons(sK20(X0,X1),nil) = X1
            & ssList(X3) )
        & ssItem(sK20(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X3,cons(sK20(X0,X1),nil)) = X0
          & cons(sK20(X0,X1),nil) = X1
          & ssList(X3) )
     => ( app(sK21(X0,X1),cons(sK20(X0,X1),nil)) = X0
        & cons(sK20(X0,X1),nil) = X1
        & ssList(sK21(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( app(X3,cons(X2,nil)) = X0
              & cons(X2,nil) = X1
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f255]) ).

fof(f255,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X5,cons(X4,nil)) = X3
              & cons(X4,nil) = X2
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    inference(nnf_transformation,[],[f223]) ).

fof(f223,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X5,cons(X4,nil)) = X3
              & cons(X4,nil) = X2
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f647,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f618]) ).

fof(f618,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f439]) ).

fof(f439,plain,
    ! [X2,X0,X1] :
      ( memberP(cons(X1,X2),X0)
      | X0 != X1
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f271,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f270]) ).

fof(f270,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f135]) ).

fof(f135,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

fof(f571,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

fof(f570,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f770,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | app(X1,X0) = app(app(X1,X0),nil) ),
    inference(resolution,[],[f579,f469]) ).

fof(f769,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | app(X1,X0) = app(nil,app(X1,X0)) ),
    inference(resolution,[],[f579,f470]) ).

fof(f579,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f768,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | cons(X0,X1) = app(cons(X0,X1),nil) ),
    inference(resolution,[],[f569,f469]) ).

fof(f767,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | cons(X0,X1) = app(nil,cons(X0,X1)) ),
    inference(resolution,[],[f569,f470]) ).

fof(f569,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f567,plain,
    ! [X0] :
      ( ~ frontsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f359]) ).

fof(f359,plain,
    ! [X0] :
      ( ( ( frontsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ frontsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ( frontsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( frontsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

fof(f565,plain,
    ! [X0] :
      ( ~ rearsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f358]) ).

fof(f358,plain,
    ! [X0] :
      ( ( ( rearsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ rearsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0] :
      ( ( rearsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( rearsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

fof(f563,plain,
    ! [X0] :
      ( ~ segmentP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f357]) ).

fof(f357,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f751,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | sK29(X0) = app(sK29(X0),nil) ),
    inference(resolution,[],[f479,f469]) ).

fof(f750,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | sK29(X0) = app(nil,sK29(X0)) ),
    inference(resolution,[],[f479,f470]) ).

fof(f479,plain,
    ! [X0] :
      ( ssList(sK29(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f290]) ).

fof(f477,plain,
    ! [X0] :
      ( ssItem(sK28(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f288]) ).

fof(f749,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | tl(X0) = app(tl(X0),nil) ),
    inference(resolution,[],[f475,f469]) ).

fof(f748,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | tl(X0) = app(nil,tl(X0)) ),
    inference(resolution,[],[f475,f470]) ).

fof(f475,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

fof(f474,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f472,plain,
    ! [X0] :
      ( ssItem(sK27(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f286]) ).

fof(f286,plain,
    ! [X0] :
      ( ( cons(sK27(X0),sK26(X0)) = X0
        & ssItem(sK27(X0))
        & ssList(sK26(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f149,f285,f284]) ).

fof(f284,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
     => ( ? [X2] :
            ( cons(X2,sK26(X0)) = X0
            & ssItem(X2) )
        & ssList(sK26(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f285,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK26(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK27(X0),sK26(X0)) = X0
        & ssItem(sK27(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f149,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ? [X1] :
            ( ? [X2] :
                ( cons(X2,X1) = X0
                & ssItem(X2) )
            & ssList(X1) )
        | nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

fof(f747,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | sK26(X0) = app(sK26(X0),nil) ),
    inference(resolution,[],[f471,f469]) ).

fof(f746,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | sK26(X0) = app(nil,sK26(X0)) ),
    inference(resolution,[],[f471,f470]) ).

fof(f471,plain,
    ! [X0] :
      ( ssList(sK26(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f286]) ).

fof(f455,plain,
    ! [X0,X1] :
      ( ~ sP4(X0,X1)
      | nil = X0
      | strictorderedP(X0) ),
    inference(cnf_transformation,[],[f281]) ).

fof(f447,plain,
    ! [X0,X1] :
      ( ~ sP2(X0,X1)
      | nil = X0
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f277]) ).

fof(f385,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X0,X1,X2,X3)
      | sP0(X2,X1) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ! [X0,X1,X2,X3] :
      ( ( ~ singletonP(X0)
        & sP0(X2,X1)
        & neq(X3,nil) )
      | ~ sP1(X0,X1,X2,X3) ),
    inference(rectify,[],[f253]) ).

fof(f253,plain,
    ! [X0,X2,X3,X1] :
      ( ( ~ singletonP(X0)
        & sP0(X3,X2)
        & neq(X1,nil) )
      | ~ sP1(X0,X2,X3,X1) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f224,plain,
    ! [X0,X2,X3,X1] :
      ( ( ~ singletonP(X0)
        & sP0(X3,X2)
        & neq(X1,nil) )
      | ~ sP1(X0,X2,X3,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f384,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X0,X1,X2,X3)
      | neq(X3,nil) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f561,plain,
    ! [X0] :
      ( ~ lt(sK60(X0),sK61(X0))
      | sP18(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f356,plain,
    ! [X0] :
      ( ( sP18(X0)
        | ( ~ lt(sK60(X0),sK61(X0))
          & app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),sK64(X0))) = X0
          & ssList(sK64(X0))
          & ssList(sK63(X0))
          & ssList(sK62(X0))
          & ssItem(sK61(X0))
          & ssItem(sK60(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP18(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61,sK62,sK63,sK64])],[f350,f355,f354,f353,f352,f351]) ).

fof(f351,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ lt(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ lt(sK60(X0),X2)
                        & app(app(X3,cons(sK60(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK60(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f352,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(sK60(X0),X2)
                      & app(app(X3,cons(sK60(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK60(X0),sK61(X0))
                    & app(app(X3,cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK61(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f353,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK60(X0),sK61(X0))
                  & app(app(X3,cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK60(X0),sK61(X0))
                & app(app(sK62(X0),cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK62(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f354,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK60(X0),sK61(X0))
              & app(app(sK62(X0),cons(sK60(X0),X4)),cons(sK61(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK60(X0),sK61(X0))
            & app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK63(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f355,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK60(X0),sK61(X0))
          & app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK60(X0),sK61(X0))
        & app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),sK64(X0))) = X0
        & ssList(sK64(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ! [X0] :
      ( ( sP18(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP18(X0) ) ),
    inference(rectify,[],[f349]) ).

fof(f349,plain,
    ! [X0] :
      ( ( sP18(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP18(X0) ) ),
    inference(nnf_transformation,[],[f250]) ).

fof(f250,plain,
    ! [X0] :
      ( sP18(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( lt(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).

fof(f550,plain,
    ! [X0] :
      ( ~ leq(sK55(X0),sK56(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f347,plain,
    ! [X0] :
      ( ( sP16(X0)
        | ( ~ leq(sK55(X0),sK56(X0))
          & app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0
          & ssList(sK59(X0))
          & ssList(sK58(X0))
          & ssList(sK57(X0))
          & ssItem(sK56(X0))
          & ssItem(sK55(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP16(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58,sK59])],[f341,f346,f345,f344,f343,f342]) ).

fof(f342,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ leq(sK55(X0),X2)
                        & app(app(X3,cons(sK55(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK55(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f343,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ leq(sK55(X0),X2)
                      & app(app(X3,cons(sK55(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ leq(sK55(X0),sK56(X0))
                    & app(app(X3,cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK56(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ leq(sK55(X0),sK56(X0))
                  & app(app(X3,cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ leq(sK55(X0),sK56(X0))
                & app(app(sK57(X0),cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK57(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ leq(sK55(X0),sK56(X0))
              & app(app(sK57(X0),cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ leq(sK55(X0),sK56(X0))
            & app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK58(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ leq(sK55(X0),sK56(X0))
          & app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ leq(sK55(X0),sK56(X0))
        & app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0
        & ssList(sK59(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f341,plain,
    ! [X0] :
      ( ( sP16(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP16(X0) ) ),
    inference(rectify,[],[f340]) ).

fof(f340,plain,
    ! [X0] :
      ( ( sP16(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP16(X0) ) ),
    inference(nnf_transformation,[],[f247]) ).

fof(f247,plain,
    ! [X0] :
      ( sP16(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( leq(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

fof(f539,plain,
    ! [X0] :
      ( leq(sK51(X0),sK50(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f338,plain,
    ! [X0] :
      ( ( sP14(X0)
        | ( leq(sK51(X0),sK50(X0))
          & leq(sK50(X0),sK51(X0))
          & app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0
          & ssList(sK54(X0))
          & ssList(sK53(X0))
          & ssList(sK52(X0))
          & ssItem(sK51(X0))
          & ssItem(sK50(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ~ leq(X7,X6)
                            | ~ leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP14(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52,sK53,sK54])],[f332,f337,f336,f335,f334,f333]) ).

fof(f333,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( leq(X2,X1)
                          & leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( leq(X2,sK50(X0))
                        & leq(sK50(X0),X2)
                        & app(app(X3,cons(sK50(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK50(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( leq(X2,sK50(X0))
                      & leq(sK50(X0),X2)
                      & app(app(X3,cons(sK50(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( leq(sK51(X0),sK50(X0))
                    & leq(sK50(X0),sK51(X0))
                    & app(app(X3,cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f335,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( leq(sK51(X0),sK50(X0))
                  & leq(sK50(X0),sK51(X0))
                  & app(app(X3,cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( leq(sK51(X0),sK50(X0))
                & leq(sK50(X0),sK51(X0))
                & app(app(sK52(X0),cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( leq(sK51(X0),sK50(X0))
              & leq(sK50(X0),sK51(X0))
              & app(app(sK52(X0),cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( leq(sK51(X0),sK50(X0))
            & leq(sK50(X0),sK51(X0))
            & app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK53(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f337,plain,
    ! [X0] :
      ( ? [X5] :
          ( leq(sK51(X0),sK50(X0))
          & leq(sK50(X0),sK51(X0))
          & app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),X5)) = X0
          & ssList(X5) )
     => ( leq(sK51(X0),sK50(X0))
        & leq(sK50(X0),sK51(X0))
        & app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0
        & ssList(sK54(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f332,plain,
    ! [X0] :
      ( ( sP14(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( leq(X2,X1)
                            & leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( ~ leq(X7,X6)
                            | ~ leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP14(X0) ) ),
    inference(rectify,[],[f331]) ).

fof(f331,plain,
    ! [X0] :
      ( ( sP14(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( leq(X2,X1)
                            & leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ leq(X2,X1)
                            | ~ leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP14(X0) ) ),
    inference(nnf_transformation,[],[f244]) ).

fof(f244,plain,
    ! [X0] :
      ( sP14(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( ~ leq(X2,X1)
                          | ~ leq(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

fof(f538,plain,
    ! [X0] :
      ( leq(sK50(X0),sK51(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f527,plain,
    ! [X0] :
      ( ~ lt(sK46(X0),sK45(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f329,plain,
    ! [X0] :
      ( ( sP12(X0)
        | ( ~ lt(sK46(X0),sK45(X0))
          & ~ lt(sK45(X0),sK46(X0))
          & app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0
          & ssList(sK49(X0))
          & ssList(sK48(X0))
          & ssList(sK47(X0))
          & ssItem(sK46(X0))
          & ssItem(sK45(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X7,X6)
                            | lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP12(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46,sK47,sK48,sK49])],[f323,f328,f327,f326,f325,f324]) ).

fof(f324,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ lt(X2,X1)
                          & ~ lt(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ lt(X2,sK45(X0))
                        & ~ lt(sK45(X0),X2)
                        & app(app(X3,cons(sK45(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK45(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f325,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(X2,sK45(X0))
                      & ~ lt(sK45(X0),X2)
                      & app(app(X3,cons(sK45(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK46(X0),sK45(X0))
                    & ~ lt(sK45(X0),sK46(X0))
                    & app(app(X3,cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK46(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f326,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK46(X0),sK45(X0))
                  & ~ lt(sK45(X0),sK46(X0))
                  & app(app(X3,cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK46(X0),sK45(X0))
                & ~ lt(sK45(X0),sK46(X0))
                & app(app(sK47(X0),cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK47(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f327,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK46(X0),sK45(X0))
              & ~ lt(sK45(X0),sK46(X0))
              & app(app(sK47(X0),cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK46(X0),sK45(X0))
            & ~ lt(sK45(X0),sK46(X0))
            & app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK48(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f328,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK46(X0),sK45(X0))
          & ~ lt(sK45(X0),sK46(X0))
          & app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK46(X0),sK45(X0))
        & ~ lt(sK45(X0),sK46(X0))
        & app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0
        & ssList(sK49(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f323,plain,
    ! [X0] :
      ( ( sP12(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X2,X1)
                            & ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( lt(X7,X6)
                            | lt(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP12(X0) ) ),
    inference(rectify,[],[f322]) ).

fof(f322,plain,
    ! [X0] :
      ( ( sP12(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ lt(X2,X1)
                            & ~ lt(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X2,X1)
                            | lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP12(X0) ) ),
    inference(nnf_transformation,[],[f241]) ).

fof(f241,plain,
    ! [X0] :
      ( sP12(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( lt(X2,X1)
                          | lt(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

fof(f526,plain,
    ! [X0] :
      ( ~ lt(sK45(X0),sK46(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f515,plain,
    ! [X0] :
      ( ~ leq(sK41(X0),sK40(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f320,plain,
    ! [X0] :
      ( ( sP10(X0)
        | ( ~ leq(sK41(X0),sK40(X0))
          & ~ leq(sK40(X0),sK41(X0))
          & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
          & ssList(sK44(X0))
          & ssList(sK43(X0))
          & ssList(sK42(X0))
          & ssItem(sK41(X0))
          & ssItem(sK40(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X7,X6)
                            | leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP10(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43,sK44])],[f314,f319,f318,f317,f316,f315]) ).

fof(f315,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ leq(X2,X1)
                          & ~ leq(X1,X2)
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ~ leq(X2,sK40(X0))
                        & ~ leq(sK40(X0),X2)
                        & app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK40(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f316,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ leq(X2,sK40(X0))
                      & ~ leq(sK40(X0),X2)
                      & app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ leq(sK41(X0),sK40(X0))
                    & ~ leq(sK40(X0),sK41(X0))
                    & app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK41(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f317,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ leq(sK41(X0),sK40(X0))
                  & ~ leq(sK40(X0),sK41(X0))
                  & app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ leq(sK41(X0),sK40(X0))
                & ~ leq(sK40(X0),sK41(X0))
                & app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK42(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f318,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ leq(sK41(X0),sK40(X0))
              & ~ leq(sK40(X0),sK41(X0))
              & app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ leq(sK41(X0),sK40(X0))
            & ~ leq(sK40(X0),sK41(X0))
            & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK43(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f319,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ leq(sK41(X0),sK40(X0))
          & ~ leq(sK40(X0),sK41(X0))
          & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ leq(sK41(X0),sK40(X0))
        & ~ leq(sK40(X0),sK41(X0))
        & app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
        & ssList(sK44(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f314,plain,
    ! [X0] :
      ( ( sP10(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X2,X1)
                            & ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( leq(X7,X6)
                            | leq(X6,X7)
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP10(X0) ) ),
    inference(rectify,[],[f313]) ).

fof(f313,plain,
    ! [X0] :
      ( ( sP10(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ~ leq(X2,X1)
                            & ~ leq(X1,X2)
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X2,X1)
                            | leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP10(X0) ) ),
    inference(nnf_transformation,[],[f238]) ).

fof(f238,plain,
    ! [X0] :
      ( sP10(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( leq(X2,X1)
                          | leq(X1,X2)
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

fof(f514,plain,
    ! [X0] :
      ( ~ leq(sK40(X0),sK41(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f503,plain,
    ! [X0] :
      ( sP8(X0)
      | sK35(X0) = sK36(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f311,plain,
    ! [X0] :
      ( ( sP8(X0)
        | ( sK35(X0) = sK36(X0)
          & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
          & ssList(sK39(X0))
          & ssList(sK38(X0))
          & ssList(sK37(X0))
          & ssItem(sK36(X0))
          & ssItem(sK35(X0)) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( X6 != X7
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP8(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37,sK38,sK39])],[f305,f310,f309,f308,f307,f306]) ).

fof(f306,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( X1 = X2
                          & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                          & ssList(X5) )
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( sK35(X0) = X2
                        & app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK35(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f307,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( sK35(X0) = X2
                      & app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( sK35(X0) = sK36(X0)
                    & app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK36(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f308,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sK35(X0) = sK36(X0)
                  & app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( sK35(X0) = sK36(X0)
                & app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK37(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f309,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( sK35(X0) = sK36(X0)
              & app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( sK35(X0) = sK36(X0)
            & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK38(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f310,plain,
    ! [X0] :
      ( ? [X5] :
          ( sK35(X0) = sK36(X0)
          & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
          & ssList(X5) )
     => ( sK35(X0) = sK36(X0)
        & app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
        & ssList(sK39(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f305,plain,
    ! [X0] :
      ( ( sP8(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( X1 = X2
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ! [X10] :
                            ( X6 != X7
                            | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                            | ~ ssList(X10) )
                        | ~ ssList(X9) )
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | ~ ssItem(X6) )
        | ~ sP8(X0) ) ),
    inference(rectify,[],[f304]) ).

fof(f304,plain,
    ! [X0] :
      ( ( sP8(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( X1 = X2
                            & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                            & ssList(X5) )
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP8(X0) ) ),
    inference(nnf_transformation,[],[f235]) ).

fof(f235,plain,
    ! [X0] :
      ( sP8(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ! [X5] :
                          ( X1 != X2
                          | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                          | ~ ssList(X5) )
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f492,plain,
    ! [X0] :
      ( sK31(X0) != sK32(X0)
      | sP6(X0) ),
    inference(cnf_transformation,[],[f302]) ).

fof(f302,plain,
    ! [X0] :
      ( ( sP6(X0)
        | ( sK31(X0) != sK32(X0)
          & app(sK33(X0),cons(sK31(X0),cons(sK32(X0),sK34(X0)))) = X0
          & ssList(sK34(X0))
          & ssList(sK33(X0))
          & ssItem(sK32(X0))
          & ssItem(sK31(X0)) ) )
      & ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( X5 = X6
                        | app(X7,cons(X5,cons(X6,X8))) != X0
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            | ~ ssItem(X5) )
        | ~ sP6(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34])],[f297,f301,f300,f299,f298]) ).

fof(f298,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( X1 != X2
                      & app(X3,cons(X1,cons(X2,X4))) = X0
                      & ssList(X4) )
                  & ssList(X3) )
              & ssItem(X2) )
          & ssItem(X1) )
     => ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( sK31(X0) != X2
                    & app(X3,cons(sK31(X0),cons(X2,X4))) = X0
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK31(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f299,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( sK31(X0) != X2
                  & app(X3,cons(sK31(X0),cons(X2,X4))) = X0
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( sK31(X0) != sK32(X0)
                & app(X3,cons(sK31(X0),cons(sK32(X0),X4))) = X0
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK32(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f300,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( sK31(X0) != sK32(X0)
              & app(X3,cons(sK31(X0),cons(sK32(X0),X4))) = X0
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( sK31(X0) != sK32(X0)
            & app(sK33(X0),cons(sK31(X0),cons(sK32(X0),X4))) = X0
            & ssList(X4) )
        & ssList(sK33(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f301,plain,
    ! [X0] :
      ( ? [X4] :
          ( sK31(X0) != sK32(X0)
          & app(sK33(X0),cons(sK31(X0),cons(sK32(X0),X4))) = X0
          & ssList(X4) )
     => ( sK31(X0) != sK32(X0)
        & app(sK33(X0),cons(sK31(X0),cons(sK32(X0),sK34(X0)))) = X0
        & ssList(sK34(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f297,plain,
    ! [X0] :
      ( ( sP6(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( X1 != X2
                        & app(X3,cons(X1,cons(X2,X4))) = X0
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( X5 = X6
                        | app(X7,cons(X5,cons(X6,X8))) != X0
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            | ~ ssItem(X5) )
        | ~ sP6(X0) ) ),
    inference(rectify,[],[f296]) ).

fof(f296,plain,
    ! [X0] :
      ( ( sP6(X0)
        | ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( X1 != X2
                        & app(X3,cons(X1,cons(X2,X4))) = X0
                        & ssList(X4) )
                    & ssList(X3) )
                & ssItem(X2) )
            & ssItem(X1) ) )
      & ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( X1 = X2
                        | app(X3,cons(X1,cons(X2,X4))) != X0
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) )
        | ~ sP6(X0) ) ),
    inference(nnf_transformation,[],[f232]) ).

fof(f232,plain,
    ! [X0] :
      ( sP6(X0)
    <=> ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( X1 = X2
                      | app(X3,cons(X1,cons(X2,X4))) != X0
                      | ~ ssList(X4) )
                  | ~ ssList(X3) )
              | ~ ssItem(X2) )
          | ~ ssItem(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f715,plain,
    sK23 = app(nil,sK23),
    inference(resolution,[],[f470,f392]) ).

fof(f714,plain,
    sK22 = app(nil,sK22),
    inference(resolution,[],[f470,f391]) ).

fof(f481,plain,
    ! [X0] :
      ( ssItem(sK30(X0))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f294]) ).

fof(f739,plain,
    sK23 = app(nil,sK23),
    inference(forward_demodulation,[],[f717,f395]) ).

fof(f717,plain,
    sK25 = app(nil,sK25),
    inference(resolution,[],[f470,f394]) ).

fof(f738,plain,
    sK22 = app(nil,sK22),
    inference(forward_demodulation,[],[f716,f396]) ).

fof(f716,plain,
    sK24 = app(nil,sK24),
    inference(resolution,[],[f470,f393]) ).

fof(f713,plain,
    ! [X0,X1] :
      ( sK21(X0,X1) = app(nil,sK21(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f470,f388]) ).

fof(f470,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f687,plain,
    sK23 = app(sK23,nil),
    inference(resolution,[],[f469,f392]) ).

fof(f686,plain,
    sK22 = app(sK22,nil),
    inference(resolution,[],[f469,f391]) ).

fof(f711,plain,
    sK23 = app(sK23,nil),
    inference(forward_demodulation,[],[f689,f395]) ).

fof(f689,plain,
    sK25 = app(sK25,nil),
    inference(resolution,[],[f469,f394]) ).

fof(f710,plain,
    sK22 = app(sK22,nil),
    inference(forward_demodulation,[],[f688,f396]) ).

fof(f688,plain,
    sK24 = app(sK24,nil),
    inference(resolution,[],[f469,f393]) ).

fof(f685,plain,
    ! [X0,X1] :
      ( sK21(X0,X1) = app(sK21(X0,X1),nil)
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f469,f388]) ).

fof(f469,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

fof(f459,plain,
    ! [X0,X1] :
      ( sP5(X0,X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f231]) ).

fof(f231,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP5(X0,X1)
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(definition_folding,[],[f138,f230,f229]) ).

fof(f138,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( strictorderedP(cons(X0,X1))
          <=> ( ( lt(X0,hd(X1))
                & strictorderedP(X1)
                & nil != X1 )
              | nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( strictorderedP(cons(X0,X1))
          <=> ( ( lt(X0,hd(X1))
                & strictorderedP(X1)
                & nil != X1 )
              | nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).

fof(f451,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f228]) ).

fof(f228,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP3(X0,X1)
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(definition_folding,[],[f137,f227,f226]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( totalorderedP(cons(X0,X1))
          <=> ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( totalorderedP(cons(X0,X1))
          <=> ( ( leq(X0,hd(X1))
                & totalorderedP(X1)
                & nil != X1 )
              | nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).

fof(f388,plain,
    ! [X0,X1] :
      ( ssList(sK21(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f387,plain,
    ! [X0,X1] :
      ( ssItem(sK20(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f386,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X0,X1,X2,X3)
      | ~ singletonP(X0) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f666,plain,
    ( sP1(sK22,sK22,sK23,sK23)
    | neq(sK23,nil) ),
    inference(forward_demodulation,[],[f665,f396]) ).

fof(f665,plain,
    ( sP1(sK22,sK24,sK23,sK23)
    | neq(sK23,nil) ),
    inference(forward_demodulation,[],[f397,f395]) ).

fof(f673,plain,
    ( sP1(sK22,sK22,sK23,sK23)
    | ~ neq(sK23,nil) ),
    inference(forward_demodulation,[],[f672,f396]) ).

fof(f672,plain,
    ( sP1(sK22,sK24,sK23,sK23)
    | ~ neq(sK23,nil) ),
    inference(forward_demodulation,[],[f671,f395]) ).

fof(f671,plain,
    ( ~ neq(sK23,nil)
    | sP1(sK22,sK24,sK25,sK23) ),
    inference(forward_demodulation,[],[f398,f395]) ).

fof(f664,plain,
    ! [X0] :
      ( ~ sP18(X0)
      | strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f553,f562]) ).

fof(f663,plain,
    ! [X0] :
      ( sP18(X0)
      | ~ strictorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f552,f562]) ).

fof(f662,plain,
    ! [X0] :
      ( ~ sP16(X0)
      | totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f542,f551]) ).

fof(f661,plain,
    ! [X0] :
      ( sP16(X0)
      | ~ totalorderedP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f541,f551]) ).

fof(f660,plain,
    ! [X0] :
      ( sP14(X0)
      | ~ cyclefreeP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f529,f540]) ).

fof(f659,plain,
    ! [X0] :
      ( sP12(X0)
      | ~ strictorderP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f517,f528]) ).

fof(f658,plain,
    ! [X0] :
      ( sP10(X0)
      | ~ totalorderP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f505,f516]) ).

fof(f657,plain,
    ! [X0] :
      ( sP8(X0)
      | ~ duplicatefreeP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f494,f504]) ).

fof(f656,plain,
    ! [X0] :
      ( sP6(X0)
      | ~ equalelemsP(X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f484,f493]) ).

fof(f553,plain,
    ! [X0] :
      ( ~ sP19(X0)
      | ~ sP18(X0)
      | strictorderedP(X0) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f348,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ~ sP18(X0) )
        & ( sP18(X0)
          | ~ strictorderedP(X0) ) )
      | ~ sP19(X0) ),
    inference(nnf_transformation,[],[f251]) ).

fof(f251,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> sP18(X0) )
      | ~ sP19(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).

fof(f552,plain,
    ! [X0] :
      ( ~ sP19(X0)
      | ~ strictorderedP(X0)
      | sP18(X0) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f542,plain,
    ! [X0] :
      ( ~ sP17(X0)
      | ~ sP16(X0)
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f339,plain,
    ! [X0] :
      ( ( ( totalorderedP(X0)
          | ~ sP16(X0) )
        & ( sP16(X0)
          | ~ totalorderedP(X0) ) )
      | ~ sP17(X0) ),
    inference(nnf_transformation,[],[f248]) ).

fof(f248,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> sP16(X0) )
      | ~ sP17(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).

fof(f541,plain,
    ! [X0] :
      ( ~ sP17(X0)
      | ~ totalorderedP(X0)
      | sP16(X0) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f529,plain,
    ! [X0] :
      ( ~ sP15(X0)
      | ~ cyclefreeP(X0)
      | sP14(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f330,plain,
    ! [X0] :
      ( ( ( cyclefreeP(X0)
          | ~ sP14(X0) )
        & ( sP14(X0)
          | ~ cyclefreeP(X0) ) )
      | ~ sP15(X0) ),
    inference(nnf_transformation,[],[f245]) ).

fof(f245,plain,
    ! [X0] :
      ( ( cyclefreeP(X0)
      <=> sP14(X0) )
      | ~ sP15(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

fof(f517,plain,
    ! [X0] :
      ( ~ sP13(X0)
      | ~ strictorderP(X0)
      | sP12(X0) ),
    inference(cnf_transformation,[],[f321]) ).

fof(f321,plain,
    ! [X0] :
      ( ( ( strictorderP(X0)
          | ~ sP12(X0) )
        & ( sP12(X0)
          | ~ strictorderP(X0) ) )
      | ~ sP13(X0) ),
    inference(nnf_transformation,[],[f242]) ).

fof(f242,plain,
    ! [X0] :
      ( ( strictorderP(X0)
      <=> sP12(X0) )
      | ~ sP13(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

fof(f505,plain,
    ! [X0] :
      ( ~ sP11(X0)
      | ~ totalorderP(X0)
      | sP10(X0) ),
    inference(cnf_transformation,[],[f312]) ).

fof(f312,plain,
    ! [X0] :
      ( ( ( totalorderP(X0)
          | ~ sP10(X0) )
        & ( sP10(X0)
          | ~ totalorderP(X0) ) )
      | ~ sP11(X0) ),
    inference(nnf_transformation,[],[f239]) ).

fof(f239,plain,
    ! [X0] :
      ( ( totalorderP(X0)
      <=> sP10(X0) )
      | ~ sP11(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

fof(f494,plain,
    ! [X0] :
      ( ~ sP9(X0)
      | ~ duplicatefreeP(X0)
      | sP8(X0) ),
    inference(cnf_transformation,[],[f303]) ).

fof(f303,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ~ sP8(X0) )
        & ( sP8(X0)
          | ~ duplicatefreeP(X0) ) )
      | ~ sP9(X0) ),
    inference(nnf_transformation,[],[f236]) ).

fof(f236,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> sP8(X0) )
      | ~ sP9(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f484,plain,
    ! [X0] :
      ( ~ sP7(X0)
      | ~ equalelemsP(X0)
      | sP6(X0) ),
    inference(cnf_transformation,[],[f295]) ).

fof(f295,plain,
    ! [X0] :
      ( ( ( equalelemsP(X0)
          | ~ sP6(X0) )
        & ( sP6(X0)
          | ~ equalelemsP(X0) ) )
      | ~ sP7(X0) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f233,plain,
    ! [X0] :
      ( ( equalelemsP(X0)
      <=> sP6(X0) )
      | ~ sP7(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f418,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).

fof(f417,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).

fof(f416,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f63]) ).

fof(f63,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).

fof(f415,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).

fof(f414,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,axiom,
    ! [X0] :
      ( ssItem(X0)
     => cyclefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).

fof(f413,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,axiom,
    ! [X0] :
      ( ssItem(X0)
     => duplicatefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).

fof(f412,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,axiom,
    ! [X0] :
      ( ssItem(X0)
     => equalelemsP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).

fof(f653,plain,
    nil = app(nil,nil),
    inference(global_subsumption,[],[f386,f385,f384,f390,f389,f388,f387,f398,f397,f396,f395,f394,f393,f392,f391,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f425,f424,f427,f649,f429,f428,f432,f431,f648,f433,f434,f435,f436,f437,f440,f647,f438,f646,f442,f441,f445,f444,f450,f620,f448,f447,f451,f453,f452,f458,f622,f456,f455,f459,f462,f461,f460,f463,f464,f465,f466,f467,f468,f469,f470,f473,f472,f471,f474,f475,f476,f478,f477,f480,f479,f624,f482,f481,f484,f492,f491,f490,f489,f488,f487,f625,f493,f494,f503,f502,f501,f500,f499,f498,f497,f645,f504,f505,f515,f514,f513,f512,f511,f510,f509,f508,f628,f516,f517,f527,f526,f525,f524,f523,f522,f521,f520,f629,f528,f529,f539,f538,f537,f536,f535,f534,f533,f532,f630,f540,f542,f541,f550,f549,f548,f547,f546,f545,f544,f631,f551,f553,f552,f561,f560,f559,f558,f557,f556,f555,f632,f562,f633,f650,f563,f634,f651,f565,f635,f652,f567,f569,f570,f571,f572,f573,f574,f636,f577,f576,f575,f579,f580,f581,f582,f583,f584,f585,f587,f644,f638,f589,f588,f639,f593,f592,f591,f640,f596,f595,f643]) ).

fof(f649,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f616]) ).

fof(f616,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f426]) ).

fof(f426,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f266]) ).

fof(f644,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f637]) ).

fof(f637,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f586]) ).

fof(f586,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f365]) ).

fof(f559,plain,
    ! [X0] :
      ( ssList(sK64(X0))
      | sP18(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f558,plain,
    ! [X0] :
      ( ssList(sK63(X0))
      | sP18(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f557,plain,
    ! [X0] :
      ( ssList(sK62(X0))
      | sP18(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f556,plain,
    ! [X0] :
      ( ssItem(sK61(X0))
      | sP18(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f555,plain,
    ! [X0] :
      ( ssItem(sK60(X0))
      | sP18(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f548,plain,
    ! [X0] :
      ( ssList(sK59(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f547,plain,
    ! [X0] :
      ( ssList(sK58(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f546,plain,
    ! [X0] :
      ( ssList(sK57(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f545,plain,
    ! [X0] :
      ( ssItem(sK56(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f544,plain,
    ! [X0] :
      ( ssItem(sK55(X0))
      | sP16(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f536,plain,
    ! [X0] :
      ( ssList(sK54(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f535,plain,
    ! [X0] :
      ( ssList(sK53(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f534,plain,
    ! [X0] :
      ( ssList(sK52(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f533,plain,
    ! [X0] :
      ( ssItem(sK51(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f532,plain,
    ! [X0] :
      ( ssItem(sK50(X0))
      | sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f524,plain,
    ! [X0] :
      ( ssList(sK49(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f523,plain,
    ! [X0] :
      ( ssList(sK48(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f522,plain,
    ! [X0] :
      ( ssList(sK47(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f521,plain,
    ! [X0] :
      ( ssItem(sK46(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f520,plain,
    ! [X0] :
      ( ssItem(sK45(X0))
      | sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f512,plain,
    ! [X0] :
      ( ssList(sK44(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f511,plain,
    ! [X0] :
      ( ssList(sK43(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f510,plain,
    ! [X0] :
      ( ssList(sK42(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f509,plain,
    ! [X0] :
      ( ssItem(sK41(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f508,plain,
    ! [X0] :
      ( ssItem(sK40(X0))
      | sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f501,plain,
    ! [X0] :
      ( ssList(sK39(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f500,plain,
    ! [X0] :
      ( ssList(sK38(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f499,plain,
    ! [X0] :
      ( ssList(sK37(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f498,plain,
    ! [X0] :
      ( ssItem(sK36(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f497,plain,
    ! [X0] :
      ( ssItem(sK35(X0))
      | sP8(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f490,plain,
    ! [X0] :
      ( ssList(sK34(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f302]) ).

fof(f489,plain,
    ! [X0] :
      ( ssList(sK33(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f302]) ).

fof(f488,plain,
    ! [X0] :
      ( ssItem(sK32(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f302]) ).

fof(f487,plain,
    ! [X0] :
      ( ssItem(sK31(X0))
      | sP6(X0) ),
    inference(cnf_transformation,[],[f302]) ).

fof(f468,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,axiom,
    ! [X0] :
      ( ssList(X0)
     => rearsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).

fof(f467,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).

fof(f466,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).

fof(f465,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0] :
      ( frontsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).

fof(f464,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,axiom,
    ! [X0] :
      ( ssList(X0)
     => rearsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).

fof(f463,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).

fof(f411,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0] :
      ( ssItem(X0)
     => leq(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).

fof(f410,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f89]) ).

fof(f89,axiom,
    ! [X0] :
      ( ssItem(X0)
     => geq(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).

fof(f409,plain,
    ! [X0] :
      ( ~ lt(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ lt(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f90]) ).

fof(f90,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ lt(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).

fof(f408,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f562,plain,
    ! [X0] :
      ( sP19(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f252]) ).

fof(f252,plain,
    ! [X0] :
      ( sP19(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f174,f251,f250]) ).

fof(f174,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f173]) ).

fof(f173,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => lt(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).

fof(f551,plain,
    ! [X0] :
      ( sP17(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f249,plain,
    ! [X0] :
      ( sP17(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f172,f248,f247]) ).

fof(f172,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f171]) ).

fof(f171,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( totalorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => leq(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).

fof(f540,plain,
    ! [X0] :
      ( sP15(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f246]) ).

fof(f246,plain,
    ! [X0] :
      ( sP15(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f170,f245,f244]) ).

fof(f170,plain,
    ! [X0] :
      ( ( cyclefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ leq(X2,X1)
                            | ~ leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f169]) ).

fof(f169,plain,
    ! [X0] :
      ( ( cyclefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( ~ leq(X2,X1)
                            | ~ leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( cyclefreeP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => ~ ( leq(X2,X1)
                                  & leq(X1,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).

fof(f528,plain,
    ! [X0] :
      ( sP13(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f243]) ).

fof(f243,plain,
    ! [X0] :
      ( sP13(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f168,f242,f241]) ).

fof(f168,plain,
    ! [X0] :
      ( ( strictorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X2,X1)
                            | lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f167]) ).

fof(f167,plain,
    ! [X0] :
      ( ( strictorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X2,X1)
                            | lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => ( lt(X2,X1)
                                | lt(X1,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).

fof(f516,plain,
    ! [X0] :
      ( sP11(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f240]) ).

fof(f240,plain,
    ! [X0] :
      ( sP11(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f166,f239,f238]) ).

fof(f166,plain,
    ! [X0] :
      ( ( totalorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X2,X1)
                            | leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f165]) ).

fof(f165,plain,
    ! [X0] :
      ( ( totalorderP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X2,X1)
                            | leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( totalorderP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => ( leq(X2,X1)
                                | leq(X1,X2) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).

fof(f504,plain,
    ! [X0] :
      ( sP9(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f237]) ).

fof(f237,plain,
    ! [X0] :
      ( sP9(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f164,f236,f235]) ).

fof(f164,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f163]) ).

fof(f163,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( X1 != X2
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( duplicatefreeP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => X1 != X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).

fof(f493,plain,
    ! [X0] :
      ( sP7(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f234]) ).

fof(f234,plain,
    ! [X0] :
      ( sP7(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f162,f233,f232]) ).

fof(f162,plain,
    ! [X0] :
      ( ( equalelemsP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( X1 = X2
                        | app(X3,cons(X1,cons(X2,X4))) != X0
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f161]) ).

fof(f161,plain,
    ! [X0] :
      ( ( equalelemsP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( X1 = X2
                        | app(X3,cons(X1,cons(X2,X4))) != X0
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( equalelemsP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ( app(X3,cons(X1,cons(X2,X4))) = X0
                         => X1 = X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).

fof(f652,plain,
    frontsegP(nil,nil),
    inference(global_subsumption,[],[f386,f385,f384,f390,f389,f388,f387,f398,f397,f396,f395,f394,f393,f392,f391,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f425,f424,f427,f649,f429,f428,f432,f431,f648,f433,f434,f435,f436,f437,f440,f647,f438,f646,f442,f441,f445,f444,f450,f620,f448,f447,f451,f453,f452,f458,f622,f456,f455,f459,f462,f461,f460,f463,f464,f465,f466,f467,f468,f469,f470,f473,f472,f471,f474,f475,f476,f478,f477,f480,f479,f624,f482,f481,f484,f492,f491,f490,f489,f488,f487,f625,f493,f494,f503,f502,f501,f500,f499,f498,f497,f645,f504,f505,f515,f514,f513,f512,f511,f510,f509,f508,f628,f516,f517,f527,f526,f525,f524,f523,f522,f521,f520,f629,f528,f529,f539,f538,f537,f536,f535,f534,f533,f532,f630,f540,f542,f541,f550,f549,f548,f547,f546,f545,f544,f631,f551,f553,f552,f561,f560,f559,f558,f557,f556,f555,f632,f562,f633,f650,f563,f634,f651,f565,f635]) ).

fof(f651,plain,
    rearsegP(nil,nil),
    inference(global_subsumption,[],[f386,f385,f384,f390,f389,f388,f387,f398,f397,f396,f395,f394,f393,f392,f391,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f425,f424,f427,f649,f429,f428,f432,f431,f648,f433,f434,f435,f436,f437,f440,f647,f438,f646,f442,f441,f445,f444,f450,f620,f448,f447,f451,f453,f452,f458,f622,f456,f455,f459,f462,f461,f460,f463,f464,f465,f466,f467,f468,f469,f470,f473,f472,f471,f474,f475,f476,f478,f477,f480,f479,f624,f482,f481,f484,f492,f491,f490,f489,f488,f487,f625,f493,f494,f503,f502,f501,f500,f499,f498,f497,f645,f504,f505,f515,f514,f513,f512,f511,f510,f509,f508,f628,f516,f517,f527,f526,f525,f524,f523,f522,f521,f520,f629,f528,f529,f539,f538,f537,f536,f535,f534,f533,f532,f630,f540,f542,f541,f550,f549,f548,f547,f546,f545,f544,f631,f551,f553,f552,f561,f560,f559,f558,f557,f556,f555,f632,f562,f633,f650,f563,f634]) ).

fof(f650,plain,
    segmentP(nil,nil),
    inference(global_subsumption,[],[f386,f385,f384,f390,f389,f388,f387,f398,f397,f396,f395,f394,f393,f392,f391,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f425,f424,f427,f649,f429,f428,f432,f431,f648,f433,f434,f435,f436,f437,f440,f647,f438,f646,f442,f441,f445,f444,f450,f620,f448,f447,f451,f453,f452,f458,f622,f456,f455,f459,f462,f461,f460,f463,f464,f465,f466,f467,f468,f469,f470,f473,f472,f471,f474,f475,f476,f478,f477,f480,f479,f624,f482,f481,f484,f492,f491,f490,f489,f488,f487,f625,f493,f494,f503,f502,f501,f500,f499,f498,f497,f645,f504,f505,f515,f514,f513,f512,f511,f510,f509,f508,f628,f516,f517,f527,f526,f525,f524,f523,f522,f521,f520,f629,f528,f529,f539,f538,f537,f536,f535,f534,f533,f532,f630,f540,f542,f541,f550,f549,f548,f547,f546,f545,f544,f631,f551,f553,f552,f561,f560,f559,f558,f557,f556,f555,f632,f562,f633]) ).

fof(f622,plain,
    ! [X1] : sP4(nil,X1),
    inference(equality_resolution,[],[f457]) ).

fof(f457,plain,
    ! [X0,X1] :
      ( sP4(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f281]) ).

fof(f620,plain,
    ! [X1] : sP2(nil,X1),
    inference(equality_resolution,[],[f449]) ).

fof(f449,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f277]) ).

fof(f615,plain,
    sK71 != sK72,
    inference(cnf_transformation,[],[f383]) ).

fof(f383,plain,
    ( sK71 != sK72
    & ssItem(sK72)
    & ssItem(sK71) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72])],[f2,f382,f381]) ).

fof(f381,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( X0 != X1
            & ssItem(X1) )
        & ssItem(X0) )
   => ( ? [X1] :
          ( sK71 != X1
          & ssItem(X1) )
      & ssItem(sK71) ) ),
    introduced(choice_axiom,[]) ).

fof(f382,plain,
    ( ? [X1] :
        ( sK71 != X1
        & ssItem(X1) )
   => ( sK71 != sK72
      & ssItem(sK72) ) ),
    introduced(choice_axiom,[]) ).

fof(f2,axiom,
    ? [X0] :
      ( ? [X1] :
          ( X0 != X1
          & ssItem(X1) )
      & ssItem(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

fof(f396,plain,
    sK22 = sK24,
    inference(cnf_transformation,[],[f264]) ).

fof(f264,plain,
    ( ( ( ~ neq(sK25,nil)
        & neq(sK23,nil) )
      | sP1(sK22,sK24,sK25,sK23) )
    & sK22 = sK24
    & sK23 = sK25
    & ssList(sK25)
    & ssList(sK24)
    & ssList(sK23)
    & ssList(sK22) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25])],[f225,f263,f262,f261,f260]) ).

fof(f260,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | sP1(X0,X2,X3,X1) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP1(sK22,X2,X3,X1) )
                  & sK22 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f261,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | sP1(sK22,X2,X3,X1) )
                & sK22 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK23,nil) )
                | sP1(sK22,X2,X3,sK23) )
              & sK22 = X2
              & sK23 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f262,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK23,nil) )
              | sP1(sK22,X2,X3,sK23) )
            & sK22 = X2
            & sK23 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK23,nil) )
            | sP1(sK22,sK24,X3,sK23) )
          & sK22 = sK24
          & sK23 = X3
          & ssList(X3) )
      & ssList(sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f263,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK23,nil) )
          | sP1(sK22,sK24,X3,sK23) )
        & sK22 = sK24
        & sK23 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK25,nil)
          & neq(sK23,nil) )
        | sP1(sK22,sK24,sK25,sK23) )
      & sK22 = sK24
      & sK23 = sK25
      & ssList(sK25) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP1(X0,X2,X3,X1) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f99,f224,f223]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ~ singletonP(X0)
                      & ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X3
                              & cons(X4,nil) = X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ~ singletonP(X0)
                      & ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X3
                              & cons(X4,nil) = X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( singletonP(X0)
                          | ! [X4] :
                              ( ssItem(X4)
                             => ! [X5] :
                                  ( ssList(X5)
                                 => ( app(X5,cons(X4,nil)) != X3
                                    | cons(X4,nil) != X2 ) ) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( singletonP(X0)
                        | ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ( app(X5,cons(X4,nil)) != X3
                                  | cons(X4,nil) != X2 ) ) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f395,plain,
    sK23 = sK25,
    inference(cnf_transformation,[],[f264]) ).

fof(f614,plain,
    ssItem(sK72),
    inference(cnf_transformation,[],[f383]) ).

fof(f613,plain,
    ssItem(sK71),
    inference(cnf_transformation,[],[f383]) ).

fof(f407,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f406,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).

fof(f405,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).

fof(f404,plain,
    totalorderP(nil),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    totalorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).

fof(f403,plain,
    strictorderP(nil),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    strictorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).

fof(f402,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).

fof(f401,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

fof(f400,plain,
    equalelemsP(nil),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,axiom,
    equalelemsP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).

fof(f399,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f394,plain,
    ssList(sK25),
    inference(cnf_transformation,[],[f264]) ).

fof(f393,plain,
    ssList(sK24),
    inference(cnf_transformation,[],[f264]) ).

fof(f392,plain,
    ssList(sK23),
    inference(cnf_transformation,[],[f264]) ).

fof(f391,plain,
    ssList(sK22),
    inference(cnf_transformation,[],[f264]) ).

fof(f612,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(app(app(X2,X0),X3),X1)
      | ~ segmentP(X0,X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f222]) ).

fof(f222,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f221,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( segmentP(X0,X1)
                   => segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).

fof(f611,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X2)
      | ~ frontsegP(X1,X2)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f220]) ).

fof(f220,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( frontsegP(X0,X2)
              | ~ frontsegP(X1,X2)
              | ~ frontsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f219]) ).

fof(f219,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( frontsegP(X0,X2)
              | ~ frontsegP(X1,X2)
              | ~ frontsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( frontsegP(X1,X2)
                  & frontsegP(X0,X1) )
               => frontsegP(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).

fof(f610,plain,
    ! [X2,X0,X1] :
      ( rearsegP(X0,X2)
      | ~ rearsegP(X1,X2)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f218]) ).

fof(f218,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(X0,X2)
              | ~ rearsegP(X1,X2)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f217]) ).

fof(f217,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(X0,X2)
              | ~ rearsegP(X1,X2)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( rearsegP(X1,X2)
                  & rearsegP(X0,X1) )
               => rearsegP(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).

fof(f609,plain,
    ! [X2,X0,X1] :
      ( segmentP(X0,X2)
      | ~ segmentP(X1,X2)
      | ~ segmentP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f216,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( segmentP(X0,X2)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f215]) ).

fof(f215,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( segmentP(X0,X2)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( segmentP(X1,X2)
                  & segmentP(X0,X1) )
               => segmentP(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).

fof(f608,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | app(X1,X2) != app(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f214]) ).

fof(f214,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X1,X2) != app(X1,X0)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f213]) ).

fof(f213,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X1,X2) != app(X1,X0)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f80]) ).

fof(f80,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( app(X1,X2) = app(X1,X0)
               => X0 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).

fof(f607,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | app(X2,X1) != app(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f212]) ).

fof(f212,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X2,X1) != app(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f211]) ).

fof(f211,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X2,X1) != app(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f79]) ).

fof(f79,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( app(X2,X1) = app(X0,X1)
               => X0 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).

fof(f606,plain,
    ! [X2,X0,X1] :
      ( frontsegP(app(X0,X2),X1)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f210]) ).

fof(f210,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( frontsegP(app(X0,X2),X1)
              | ~ frontsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f209]) ).

fof(f209,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( frontsegP(app(X0,X2),X1)
              | ~ frontsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( frontsegP(X0,X1)
               => frontsegP(app(X0,X2),X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).

fof(f605,plain,
    ! [X2,X0,X1] :
      ( rearsegP(app(X2,X0),X1)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f208]) ).

fof(f208,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(app(X2,X0),X1)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f207]) ).

fof(f207,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(app(X2,X0),X1)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( rearsegP(X0,X1)
               => rearsegP(app(X2,X0),X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).

fof(f604,plain,
    ! [X2,X0,X1] :
      ( app(app(X0,X1),X2) = app(X0,app(X1,X2))
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f206]) ).

fof(f206,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( app(app(X0,X1),X2) = app(X0,app(X1,X2))
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f82,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).

fof(f602,plain,
    ! [X2,X3,X0,X1] :
      ( X2 = X3
      | cons(X2,X0) != cons(X3,X1)
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f205,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( X0 = X1
                    & X2 = X3 )
                  | cons(X2,X0) != cons(X3,X1)
                  | ~ ssItem(X3) )
              | ~ ssItem(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f204]) ).

fof(f204,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( X0 = X1
                    & X2 = X3 )
                  | cons(X2,X0) != cons(X3,X1)
                  | ~ ssItem(X3) )
              | ~ ssItem(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ! [X3] :
                  ( ssItem(X3)
                 => ( cons(X2,X0) = cons(X3,X1)
                   => ( X0 = X1
                      & X2 = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).

fof(f603,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | cons(X2,X0) != cons(X3,X1)
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f601,plain,
    ! [X2,X0,X1] :
      ( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f203]) ).

fof(f203,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
              | ~ ssItem(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssItem(X2)
             => cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).

fof(f598,plain,
    ! [X0,X1] :
      ( nil = X1
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f380]) ).

fof(f380,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f379]) ).

fof(f379,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f202]) ).

fof(f202,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).

fof(f599,plain,
    ! [X0,X1] :
      ( nil = X0
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f380]) ).

fof(f643,plain,
    ( nil = app(nil,nil)
    | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f642]) ).

fof(f642,plain,
    ( nil = app(nil,nil)
    | ~ ssList(nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f641]) ).

fof(f641,plain,
    ! [X1] :
      ( nil = app(nil,X1)
      | nil != X1
      | ~ ssList(X1)
      | ~ ssList(nil) ),
    inference(equality_resolution,[],[f600]) ).

fof(f600,plain,
    ! [X0,X1] :
      ( nil = app(X0,X1)
      | nil != X0
      | nil != X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f380]) ).

fof(f595,plain,
    ! [X0,X1] :
      ( ssList(sK70(X0,X1))
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f378]) ).

fof(f378,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK70(X0,X1)) = X0
                & ssList(sK70(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f376,f377]) ).

fof(f377,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK70(X0,X1)) = X0
        & ssList(sK70(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f376,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X1,X3) = X0
                  & ssList(X3) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f375]) ).

fof(f375,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f201]) ).

fof(f201,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

fof(f596,plain,
    ! [X0,X1] :
      ( app(X1,sK70(X0,X1)) = X0
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f378]) ).

fof(f640,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f597]) ).

fof(f597,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f378]) ).

fof(f591,plain,
    ! [X0,X1] :
      ( ssList(sK68(X0,X1))
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f374]) ).

fof(f374,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK68(X0,X1),X1),sK69(X0,X1)) = X0
                & ssList(sK69(X0,X1))
                & ssList(sK68(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69])],[f371,f373,f372]) ).

fof(f372,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK68(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK68(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f373,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK68(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK68(X0,X1),X1),sK69(X0,X1)) = X0
        & ssList(sK69(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f371,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f370]) ).

fof(f370,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f200]) ).

fof(f200,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

fof(f592,plain,
    ! [X0,X1] :
      ( ssList(sK69(X0,X1))
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f374]) ).

fof(f593,plain,
    ! [X0,X1] :
      ( app(app(sK68(X0,X1),X1),sK69(X0,X1)) = X0
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f374]) ).

fof(f639,plain,
    ! [X2,X3,X1] :
      ( segmentP(app(app(X2,X1),X3),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(app(X2,X1),X3)) ),
    inference(equality_resolution,[],[f594]) ).

fof(f594,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(X0,X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f374]) ).

fof(f588,plain,
    ! [X0,X1] :
      ( ssList(sK67(X0,X1))
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f369]) ).

fof(f369,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(sK67(X0,X1),X1) = X0
                & ssList(sK67(X0,X1)) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f367,f368]) ).

fof(f368,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X3,X1) = X0
          & ssList(X3) )
     => ( app(sK67(X0,X1),X1) = X0
        & ssList(sK67(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f367,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X3,X1) = X0
                  & ssList(X3) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f366]) ).

fof(f366,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X2,X1) = X0
                  & ssList(X2) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

fof(f589,plain,
    ! [X0,X1] :
      ( app(sK67(X0,X1),X1) = X0
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f369]) ).

fof(f638,plain,
    ! [X2,X1] :
      ( rearsegP(app(X2,X1),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X2,X1)) ),
    inference(equality_resolution,[],[f590]) ).

fof(f590,plain,
    ! [X2,X0,X1] :
      ( rearsegP(X0,X1)
      | app(X2,X1) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f369]) ).

fof(f585,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ frontsegP(X1,X0)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f197]) ).

fof(f197,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f196]) ).

fof(f196,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( frontsegP(X1,X0)
              & frontsegP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).

fof(f584,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ segmentP(X1,X0)
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f195]) ).

fof(f195,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ segmentP(X1,X0)
          | ~ segmentP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f194]) ).

fof(f194,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ segmentP(X1,X0)
          | ~ segmentP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( segmentP(X1,X0)
              & segmentP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).

fof(f583,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ rearsegP(X1,X0)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f193]) ).

fof(f193,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ rearsegP(X1,X0)
          | ~ rearsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f192]) ).

fof(f192,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ rearsegP(X1,X0)
          | ~ rearsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( rearsegP(X1,X0)
              & rearsegP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).

fof(f582,plain,
    ! [X0,X1] :
      ( X0 = X1
      | tl(X0) != tl(X1)
      | hd(X0) != hd(X1)
      | nil = X0
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f191,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | tl(X0) != tl(X1)
          | hd(X0) != hd(X1)
          | nil = X0
          | nil = X1
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f190]) ).

fof(f190,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | tl(X0) != tl(X1)
          | hd(X0) != hd(X1)
          | nil = X0
          | nil = X1
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f77]) ).

fof(f77,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( tl(X0) = tl(X1)
              & hd(X0) = hd(X1)
              & nil != X0
              & nil != X1 )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77) ).

fof(f581,plain,
    ! [X0,X1] :
      ( tl(app(X0,X1)) = app(tl(X0),X1)
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f189,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(app(X0,X1)) = app(tl(X0),X1)
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f188]) ).

fof(f188,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(app(X0,X1)) = app(tl(X0),X1)
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f86]) ).

fof(f86,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil != X0
           => tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).

fof(f580,plain,
    ! [X0,X1] :
      ( hd(X0) = hd(app(X0,X1))
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f187]) ).

fof(f187,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f186]) ).

fof(f186,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f85,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil != X0
           => hd(X0) = hd(app(X0,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).

fof(f575,plain,
    ! [X0,X1] :
      ( ssList(sK65(X0,X1))
      | ~ memberP(X0,X1)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f364]) ).

fof(f364,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(sK65(X0,X1),cons(X1,sK66(X0,X1))) = X0
                & ssList(sK66(X0,X1))
                & ssList(sK65(X0,X1)) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK65,sK66])],[f361,f363,f362]) ).

fof(f362,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X4,cons(X1,X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(sK65(X0,X1),cons(X1,X5)) = X0
            & ssList(X5) )
        & ssList(sK65(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f363,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(sK65(X0,X1),cons(X1,X5)) = X0
          & ssList(X5) )
     => ( app(sK65(X0,X1),cons(X1,sK66(X0,X1))) = X0
        & ssList(sK66(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f361,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(X4,cons(X1,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f360]) ).

fof(f360,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(X2,cons(X1,X3)) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(f576,plain,
    ! [X0,X1] :
      ( ssList(sK66(X0,X1))
      | ~ memberP(X0,X1)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f364]) ).

fof(f577,plain,
    ! [X0,X1] :
      ( app(sK65(X0,X1),cons(X1,sK66(X0,X1))) = X0
      | ~ memberP(X0,X1)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f364]) ).

fof(f636,plain,
    ! [X2,X3,X1] :
      ( memberP(app(X2,cons(X1,X3)),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(app(X2,cons(X1,X3))) ),
    inference(equality_resolution,[],[f578]) ).

fof(f578,plain,
    ! [X2,X3,X0,X1] :
      ( memberP(X0,X1)
      | app(X2,cons(X1,X3)) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f364]) ).

fof(f574,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f635,plain,
    ( frontsegP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f568]) ).

fof(f568,plain,
    ! [X0] :
      ( frontsegP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f359]) ).

fof(f634,plain,
    ( rearsegP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f566]) ).

fof(f566,plain,
    ! [X0] :
      ( rearsegP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f358]) ).

fof(f633,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f564]) ).

fof(f564,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f357]) ).

fof(f632,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP18(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f554]) ).

fof(f554,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( lt(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP18(X0) ),
    inference(cnf_transformation,[],[f356]) ).

fof(f560,plain,
    ! [X0] :
      ( sP18(X0)
      | app(app(sK62(X0),cons(sK60(X0),sK63(X0))),cons(sK61(X0),sK64(X0))) = X0 ),
    inference(cnf_transformation,[],[f356]) ).

fof(f631,plain,
    ! [X10,X8,X6,X9,X7] :
      ( leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f543]) ).

fof(f543,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( leq(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP16(X0) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f549,plain,
    ! [X0] :
      ( sP16(X0)
      | app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0 ),
    inference(cnf_transformation,[],[f347]) ).

fof(f630,plain,
    ! [X10,X8,X6,X9,X7] :
      ( ~ leq(X7,X6)
      | ~ leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f531]) ).

fof(f531,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( ~ leq(X7,X6)
      | ~ leq(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP14(X0) ),
    inference(cnf_transformation,[],[f338]) ).

fof(f537,plain,
    ! [X0] :
      ( sP14(X0)
      | app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0 ),
    inference(cnf_transformation,[],[f338]) ).

fof(f629,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(X7,X6)
      | lt(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f519]) ).

fof(f519,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( lt(X7,X6)
      | lt(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP12(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f525,plain,
    ! [X0] :
      ( sP12(X0)
      | app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0 ),
    inference(cnf_transformation,[],[f329]) ).

fof(f628,plain,
    ! [X10,X8,X6,X9,X7] :
      ( leq(X7,X6)
      | leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f507]) ).

fof(f507,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( leq(X7,X6)
      | leq(X6,X7)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP10(X0) ),
    inference(cnf_transformation,[],[f320]) ).

fof(f513,plain,
    ! [X0] :
      ( sP10(X0)
      | app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0 ),
    inference(cnf_transformation,[],[f320]) ).

fof(f645,plain,
    ! [X10,X8,X9,X7] :
      ( ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ sP8(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
    inference(duplicate_literal_removal,[],[f627]) ).

fof(f627,plain,
    ! [X10,X8,X9,X7] :
      ( ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X7)
      | ~ sP8(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f626]) ).

fof(f626,plain,
    ! [X10,X0,X8,X9,X7] :
      ( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X7)
      | ~ sP8(X0) ),
    inference(equality_resolution,[],[f496]) ).

fof(f496,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( X6 != X7
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f311]) ).

fof(f502,plain,
    ! [X0] :
      ( sP8(X0)
      | app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0 ),
    inference(cnf_transformation,[],[f311]) ).

fof(f625,plain,
    ! [X8,X6,X7,X5] :
      ( X5 = X6
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6)
      | ~ ssItem(X5)
      | ~ sP6(app(X7,cons(X5,cons(X6,X8)))) ),
    inference(equality_resolution,[],[f486]) ).

fof(f486,plain,
    ! [X0,X8,X6,X7,X5] :
      ( X5 = X6
      | app(X7,cons(X5,cons(X6,X8))) != X0
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6)
      | ~ ssItem(X5)
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f302]) ).

fof(f491,plain,
    ! [X0] :
      ( sP6(X0)
      | app(sK33(X0),cons(sK31(X0),cons(sK32(X0),sK34(X0)))) = X0 ),
    inference(cnf_transformation,[],[f302]) ).

fof(f476,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f155,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).

fof(f473,plain,
    ! [X0] :
      ( cons(sK27(X0),sK26(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f286]) ).

fof(f460,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | memberP(X1,X0)
      | ~ memberP(app(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f283]) ).

fof(f283,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f282]) ).

fof(f282,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & ~ memberP(X1,X0) ) )
                & ( memberP(X2,X0)
                  | memberP(X1,X0)
                  | ~ memberP(app(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f139]) ).

fof(f139,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(app(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | memberP(X1,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).

fof(f461,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f283]) ).

fof(f462,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f283]) ).

fof(f458,plain,
    ! [X0,X1] :
      ( sP4(X0,X1)
      | ~ lt(X1,hd(X0))
      | ~ strictorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f281]) ).

fof(f450,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | ~ leq(X1,hd(X0))
      | ~ totalorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f277]) ).

fof(f441,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ frontsegP(cons(X0,X2),cons(X1,X3))
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f273,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                      | ~ frontsegP(X2,X3)
                      | X0 != X1 )
                    & ( ( frontsegP(X2,X3)
                        & X0 = X1 )
                      | ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f272]) ).

fof(f272,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                      | ~ frontsegP(X2,X3)
                      | X0 != X1 )
                    & ( ( frontsegP(X2,X3)
                        & X0 = X1 )
                      | ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( frontsegP(cons(X0,X2),cons(X1,X3))
                  <=> ( frontsegP(X2,X3)
                      & X0 = X1 ) )
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( frontsegP(cons(X0,X2),cons(X1,X3))
                  <=> ( frontsegP(X2,X3)
                      & X0 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).

fof(f442,plain,
    ! [X2,X3,X0,X1] :
      ( frontsegP(X2,X3)
      | ~ frontsegP(cons(X0,X2),cons(X1,X3))
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f646,plain,
    ! [X2,X3,X1] :
      ( frontsegP(cons(X1,X2),cons(X1,X3))
      | ~ frontsegP(X2,X3)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f619]) ).

fof(f619,plain,
    ! [X2,X3,X1] :
      ( frontsegP(cons(X1,X2),cons(X1,X3))
      | ~ frontsegP(X2,X3)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f443]) ).

fof(f443,plain,
    ! [X2,X3,X0,X1] :
      ( frontsegP(cons(X0,X2),cons(X1,X3))
      | ~ frontsegP(X2,X3)
      | X0 != X1
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f438,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | X0 = X1
      | ~ memberP(cons(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f440,plain,
    ! [X2,X0,X1] :
      ( memberP(cons(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f437,plain,
    ! [X2,X0,X1] :
      ( lt(X0,X2)
      | ~ lt(X1,X2)
      | ~ lt(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ lt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ lt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( lt(X1,X2)
                  & lt(X0,X1) )
               => lt(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).

fof(f436,plain,
    ! [X2,X0,X1] :
      ( lt(X0,X2)
      | ~ lt(X1,X2)
      | ~ leq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f131]) ).

fof(f131,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f91]) ).

fof(f91,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( lt(X1,X2)
                  & leq(X0,X1) )
               => lt(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).

fof(f435,plain,
    ! [X2,X0,X1] :
      ( leq(X0,X2)
      | ~ leq(X1,X2)
      | ~ leq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( leq(X0,X2)
              | ~ leq(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f129]) ).

fof(f129,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( leq(X0,X2)
              | ~ leq(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( leq(X1,X2)
                  & leq(X0,X1) )
               => leq(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

fof(f434,plain,
    ! [X2,X0,X1] :
      ( geq(X0,X2)
      | ~ geq(X1,X2)
      | ~ geq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( geq(X0,X2)
              | ~ geq(X1,X2)
              | ~ geq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( geq(X0,X2)
              | ~ geq(X1,X2)
              | ~ geq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f88]) ).

fof(f88,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( geq(X1,X2)
                  & geq(X0,X1) )
               => geq(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).

fof(f433,plain,
    ! [X2,X0,X1] :
      ( gt(X0,X2)
      | ~ gt(X1,X2)
      | ~ gt(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( gt(X0,X2)
              | ~ gt(X1,X2)
              | ~ gt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f125]) ).

fof(f125,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( gt(X0,X2)
              | ~ gt(X1,X2)
              | ~ gt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f95]) ).

fof(f95,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssItem(X2)
             => ( ( gt(X1,X2)
                  & gt(X0,X1) )
               => gt(X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).

fof(f648,plain,
    ! [X1] :
      ( ~ lt(X1,X1)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f617]) ).

fof(f617,plain,
    ! [X1] :
      ( ~ lt(X1,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f430]) ).

fof(f430,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f432,plain,
    ! [X0,X1] :
      ( lt(X0,X1)
      | ~ leq(X0,X1)
      | X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f423,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ leq(X1,X0)
      | ~ leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ leq(X1,X0)
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ leq(X1,X0)
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( ( leq(X1,X0)
              & leq(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).

fof(f422,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ geq(X1,X0)
      | ~ geq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ geq(X1,X0)
          | ~ geq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f117]) ).

fof(f117,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ geq(X1,X0)
          | ~ geq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f87,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( ( geq(X1,X0)
              & geq(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).

fof(f420,plain,
    ! [X0,X1] :
      ( lt(X0,X1)
      | X0 = X1
      | ~ leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ! [X1] :
          ( lt(X0,X1)
          | X0 = X1
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ! [X1] :
          ( lt(X0,X1)
          | X0 = X1
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f92]) ).

fof(f92,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( leq(X0,X1)
           => ( lt(X0,X1)
              | X0 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).

fof(f397,plain,
    ( neq(sK23,nil)
    | sP1(sK22,sK24,sK25,sK23) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f398,plain,
    ( ~ neq(sK25,nil)
    | sP1(sK22,sK24,sK25,sK23) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f390,plain,
    ! [X0,X1] :
      ( app(sK21(X0,X1),cons(sK20(X0,X1),nil)) = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f1125,plain,
    ( ~ spl73_2
    | ~ spl73_3 ),
    inference(avatar_contradiction_clause,[],[f1124]) ).

fof(f1124,plain,
    ( $false
    | ~ spl73_2
    | ~ spl73_3 ),
    inference(subsumption_resolution,[],[f1123,f391]) ).

fof(f1123,plain,
    ( ~ ssList(sK22)
    | ~ spl73_2
    | ~ spl73_3 ),
    inference(forward_demodulation,[],[f1122,f777]) ).

fof(f777,plain,
    ( sK22 = cons(sK20(sK23,sK22),nil)
    | ~ spl73_2 ),
    inference(resolution,[],[f389,f743]) ).

fof(f743,plain,
    ( sP0(sK23,sK22)
    | ~ spl73_2 ),
    inference(resolution,[],[f385,f681]) ).

fof(f681,plain,
    ( sP1(sK22,sK22,sK23,sK23)
    | ~ spl73_2 ),
    inference(avatar_component_clause,[],[f679]) ).

fof(f1122,plain,
    ( ~ ssList(cons(sK20(sK23,sK22),nil))
    | ~ spl73_2
    | ~ spl73_3 ),
    inference(subsumption_resolution,[],[f1121,f796]) ).

fof(f796,plain,
    ( ssItem(sK20(sK23,sK22))
    | ~ spl73_3 ),
    inference(avatar_component_clause,[],[f795]) ).

fof(f795,plain,
    ( spl73_3
  <=> ssItem(sK20(sK23,sK22)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_3])]) ).

fof(f1121,plain,
    ( ~ ssItem(sK20(sK23,sK22))
    | ~ ssList(cons(sK20(sK23,sK22),nil))
    | ~ spl73_2 ),
    inference(subsumption_resolution,[],[f1119,f683]) ).

fof(f683,plain,
    ( ~ singletonP(sK22)
    | ~ spl73_2 ),
    inference(resolution,[],[f386,f681]) ).

fof(f1119,plain,
    ( singletonP(sK22)
    | ~ ssItem(sK20(sK23,sK22))
    | ~ ssList(cons(sK20(sK23,sK22),nil))
    | ~ spl73_2 ),
    inference(superposition,[],[f624,f777]) ).

fof(f898,plain,
    ( spl73_5
    | spl73_6 ),
    inference(avatar_split_clause,[],[f857,f895,f891]) ).

fof(f891,plain,
    ( spl73_5
  <=> hd(sK23) = sK28(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_5])]) ).

fof(f895,plain,
    ( spl73_6
  <=> nil = sK23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_6])]) ).

fof(f805,plain,
    ( ~ spl73_2
    | spl73_3 ),
    inference(avatar_contradiction_clause,[],[f804]) ).

fof(f804,plain,
    ( $false
    | ~ spl73_2
    | spl73_3 ),
    inference(subsumption_resolution,[],[f803,f743]) ).

fof(f803,plain,
    ( ~ sP0(sK23,sK22)
    | spl73_3 ),
    inference(resolution,[],[f797,f387]) ).

fof(f797,plain,
    ( ~ ssItem(sK20(sK23,sK22))
    | spl73_3 ),
    inference(avatar_component_clause,[],[f795]) ).

fof(f802,plain,
    ( ~ spl73_3
    | spl73_4
    | ~ spl73_2 ),
    inference(avatar_split_clause,[],[f778,f679,f799,f795]) ).

fof(f799,plain,
    ( spl73_4
  <=> equalelemsP(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_4])]) ).

fof(f778,plain,
    ( equalelemsP(sK22)
    | ~ ssItem(sK20(sK23,sK22))
    | ~ spl73_2 ),
    inference(superposition,[],[f412,f777]) ).

fof(f742,plain,
    ( spl73_1
    | ~ spl73_2 ),
    inference(avatar_contradiction_clause,[],[f741]) ).

fof(f741,plain,
    ( $false
    | spl73_1
    | ~ spl73_2 ),
    inference(subsumption_resolution,[],[f740,f676]) ).

fof(f676,plain,
    ( ~ neq(sK23,nil)
    | spl73_1 ),
    inference(avatar_component_clause,[],[f675]) ).

fof(f675,plain,
    ( spl73_1
  <=> neq(sK23,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl73_1])]) ).

fof(f740,plain,
    ( neq(sK23,nil)
    | ~ spl73_2 ),
    inference(resolution,[],[f384,f681]) ).

fof(f682,plain,
    ( spl73_1
    | spl73_2 ),
    inference(avatar_split_clause,[],[f666,f679,f675]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : SWC254+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n028.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Apr 30 04:31:14 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.17/0.32  % (30324)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.33  % (30327)WARNING: value z3 for option sas not known
% 0.17/0.34  % (30327)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)
% 0.17/0.34  % (30325)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.34  % (30330)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)
% 0.17/0.34  % (30331)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)
% 0.17/0.34  % (30328)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.34  % (30329)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)
% 0.17/0.34  % (30326)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.35  TRYING [1]
% 0.17/0.35  TRYING [1]
% 0.17/0.35  TRYING [2]
% 0.17/0.36  TRYING [2]
% 0.17/0.36  % (30327)First to succeed.
% 0.17/0.37  TRYING [3]
% 0.17/0.37  TRYING [3]
% 0.17/0.37  TRYING [1]
% 0.17/0.37  TRYING [2]
% 0.17/0.37  % (30330)Also succeeded, but the first one will report.
% 0.17/0.38  % (30327)Refutation found. Thanks to Tanya!
% 0.17/0.38  % SZS status Theorem for theBenchmark
% 0.17/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.38  % (30327)------------------------------
% 0.17/0.38  % (30327)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.38  % (30327)Termination reason: Refutation
% 0.17/0.38  
% 0.17/0.38  % (30327)Memory used [KB]: 1609
% 0.17/0.38  % (30327)Time elapsed: 0.039 s
% 0.17/0.38  % (30327)Instructions burned: 90 (million)
% 0.17/0.38  % (30327)------------------------------
% 0.17/0.38  % (30327)------------------------------
% 0.17/0.38  % (30324)Success in time 0.059 s
%------------------------------------------------------------------------------