TSTP Solution File: SWC339+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC339+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.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 May 21 05:13:18 EDT 2024

% Result   : Theorem 1.19s 0.53s
% Output   : Refutation 1.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  477
% Syntax   : Number of formulae    : 1392 ( 249 unt;   0 def)
%            Number of atoms       : 5617 ( 935 equ)
%            Maximal formula atoms :   56 (   4 avg)
%            Number of connectives : 6892 (2667   ~;2696   |; 844   &)
%                                         ( 387 <=>; 298  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  349 ( 347 usr; 311 prp; 0-2 aty)
%            Number of functors    :   58 (  58 usr;   9 con; 0-2 aty)
%            Number of variables   : 2174 (1805   !; 369   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3851,plain,
    $false,
    inference(avatar_sat_refutation,[],[f650,f655,f660,f665,f670,f675,f684,f689,f694,f699,f704,f709,f714,f719,f724,f729,f734,f739,f744,f749,f753,f757,f761,f765,f769,f773,f777,f781,f785,f810,f829,f833,f837,f841,f845,f849,f853,f858,f862,f866,f870,f874,f878,f882,f886,f890,f894,f898,f903,f907,f911,f915,f919,f923,f927,f931,f935,f939,f943,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f988,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1034,f1039,f1079,f1126,f1173,f1198,f1202,f1206,f1210,f1214,f1219,f1223,f1227,f1231,f1235,f1239,f1243,f1247,f1251,f1255,f1259,f1264,f1268,f1272,f1276,f1280,f1284,f1288,f1293,f1298,f1302,f1306,f1311,f1315,f1319,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1433,f1437,f1441,f1445,f1449,f1453,f1457,f1461,f1465,f1469,f1474,f1478,f1482,f1486,f1490,f1515,f1559,f1563,f1567,f1572,f1576,f1580,f1584,f1588,f1592,f1596,f1600,f1605,f1609,f1613,f1617,f1621,f1625,f1629,f1633,f1637,f1641,f1645,f1650,f1654,f1658,f1662,f1666,f1677,f1757,f1827,f1831,f1835,f1839,f1843,f1848,f1852,f1934,f1938,f1942,f1947,f1951,f1955,f1959,f2044,f2049,f2053,f2057,f2061,f2065,f2069,f2073,f2077,f2081,f2093,f2156,f2160,f2164,f2170,f2174,f2178,f2182,f2186,f2252,f2256,f2260,f2264,f2268,f2272,f2276,f2282,f2286,f2321,f2325,f2329,f2333,f2384,f2390,f2394,f2398,f2483,f2487,f2491,f2497,f2501,f2505,f2509,f2513,f2517,f2521,f2525,f2529,f2533,f2539,f2579,f2583,f2587,f2606,f2610,f2614,f2622,f2626,f2630,f2674,f2683,f2688,f2693,f2698,f2703,f2708,f2713,f2718,f2867,f2962,f2967,f2972,f2977,f2992,f2997,f3003,f3016,f3044,f3094,f3101,f3121,f3122,f3162,f3191,f3197,f3201,f3206,f3210,f3214,f3218,f3223,f3227,f3231,f3235,f3241,f3255,f3305,f3315,f3320,f3518,f3524,f3529,f3535,f3541,f3547,f3553,f3559,f3565,f3605,f3645,f3650,f3690,f3697,f3737,f3743,f3783,f3789,f3794,f3833,f3838,f3843,f3848,f3850]) ).

fof(f3850,plain,
    ( ~ spl71_2
    | ~ spl71_1
    | ~ spl71_3
    | ~ spl71_4
    | spl71_6
    | ~ spl71_9
    | ~ spl71_242 ),
    inference(avatar_split_clause,[],[f2599,f2585,f686,f672,f662,f657,f647,f652]) ).

fof(f652,plain,
    ( spl71_2
  <=> ssList(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_2])]) ).

fof(f647,plain,
    ( spl71_1
  <=> ssList(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_1])]) ).

fof(f657,plain,
    ( spl71_3
  <=> ssList(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_3])]) ).

fof(f662,plain,
    ( spl71_4
  <=> ssList(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_4])]) ).

fof(f672,plain,
    ( spl71_6
  <=> segmentP(sK21,sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_6])]) ).

fof(f686,plain,
    ( spl71_9
  <=> sK21 = app(app(sK22,sK20),sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_9])]) ).

fof(f2585,plain,
    ( spl71_242
  <=> ! [X2,X1,X3] :
        ( segmentP(app(app(X2,X1),X3),X1)
        | ~ ssList(X3)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(app(app(X2,X1),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_242])]) ).

fof(f2599,plain,
    ( segmentP(sK21,sK20)
    | ~ ssList(sK23)
    | ~ ssList(sK22)
    | ~ ssList(sK20)
    | ~ ssList(sK21)
    | ~ spl71_9
    | ~ spl71_242 ),
    inference(superposition,[],[f2586,f688]) ).

fof(f688,plain,
    ( sK21 = app(app(sK22,sK20),sK23)
    | ~ spl71_9 ),
    inference(avatar_component_clause,[],[f686]) ).

fof(f2586,plain,
    ( ! [X2,X3,X1] :
        ( segmentP(app(app(X2,X1),X3),X1)
        | ~ ssList(X3)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(app(app(X2,X1),X3)) )
    | ~ spl71_242 ),
    inference(avatar_component_clause,[],[f2585]) ).

fof(f3848,plain,
    ( spl71_310
    | ~ spl71_4
    | ~ spl71_194 ),
    inference(avatar_split_clause,[],[f2106,f2059,f662,f3846]) ).

fof(f3846,plain,
    ( spl71_310
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK23) = app(cons(X0,nil),sK23) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_310])]) ).

fof(f2059,plain,
    ( spl71_194
  <=> ! [X0,X1] :
        ( cons(X1,X0) = app(cons(X1,nil),X0)
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_194])]) ).

fof(f2106,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK23) = app(cons(X0,nil),sK23) )
    | ~ spl71_4
    | ~ spl71_194 ),
    inference(resolution,[],[f2060,f664]) ).

fof(f664,plain,
    ( ssList(sK23)
    | ~ spl71_4 ),
    inference(avatar_component_clause,[],[f662]) ).

fof(f2060,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssItem(X1)
        | cons(X1,X0) = app(cons(X1,nil),X0) )
    | ~ spl71_194 ),
    inference(avatar_component_clause,[],[f2059]) ).

fof(f3843,plain,
    ( spl71_309
    | ~ spl71_3
    | ~ spl71_194 ),
    inference(avatar_split_clause,[],[f2105,f2059,f657,f3841]) ).

fof(f3841,plain,
    ( spl71_309
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK22) = app(cons(X0,nil),sK22) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_309])]) ).

fof(f2105,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK22) = app(cons(X0,nil),sK22) )
    | ~ spl71_3
    | ~ spl71_194 ),
    inference(resolution,[],[f2060,f659]) ).

fof(f659,plain,
    ( ssList(sK22)
    | ~ spl71_3 ),
    inference(avatar_component_clause,[],[f657]) ).

fof(f3838,plain,
    ( spl71_308
    | ~ spl71_2
    | ~ spl71_194 ),
    inference(avatar_split_clause,[],[f2104,f2059,f652,f3836]) ).

fof(f3836,plain,
    ( spl71_308
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK21) = app(cons(X0,nil),sK21) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_308])]) ).

fof(f2104,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK21) = app(cons(X0,nil),sK21) )
    | ~ spl71_2
    | ~ spl71_194 ),
    inference(resolution,[],[f2060,f654]) ).

fof(f654,plain,
    ( ssList(sK21)
    | ~ spl71_2 ),
    inference(avatar_component_clause,[],[f652]) ).

fof(f3833,plain,
    ( spl71_307
    | ~ spl71_1
    | ~ spl71_194 ),
    inference(avatar_split_clause,[],[f2103,f2059,f647,f3831]) ).

fof(f3831,plain,
    ( spl71_307
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK20) = app(cons(X0,nil),sK20) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_307])]) ).

fof(f2103,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | cons(X0,sK20) = app(cons(X0,nil),sK20) )
    | ~ spl71_1
    | ~ spl71_194 ),
    inference(resolution,[],[f2060,f649]) ).

fof(f649,plain,
    ( ssList(sK20)
    | ~ spl71_1 ),
    inference(avatar_component_clause,[],[f647]) ).

fof(f3794,plain,
    ( spl71_306
    | ~ spl71_13
    | ~ spl71_271 ),
    inference(avatar_split_clause,[],[f3261,f3091,f706,f3791]) ).

fof(f3791,plain,
    ( spl71_306
  <=> cyclefreeP(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_306])]) ).

fof(f706,plain,
    ( spl71_13
  <=> cyclefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_13])]) ).

fof(f3091,plain,
    ( spl71_271
  <=> nil = sK23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_271])]) ).

fof(f3261,plain,
    ( cyclefreeP(sK23)
    | ~ spl71_13
    | ~ spl71_271 ),
    inference(superposition,[],[f708,f3093]) ).

fof(f3093,plain,
    ( nil = sK23
    | ~ spl71_271 ),
    inference(avatar_component_clause,[],[f3091]) ).

fof(f708,plain,
    ( cyclefreeP(nil)
    | ~ spl71_13 ),
    inference(avatar_component_clause,[],[f706]) ).

fof(f3789,plain,
    ( spl71_305
    | ~ spl71_276
    | ~ spl71_304 ),
    inference(avatar_split_clause,[],[f3784,f3780,f3194,f3786]) ).

fof(f3786,plain,
    ( spl71_305
  <=> sK22 = cons(sK26(sK22),sK27(sK22)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_305])]) ).

fof(f3194,plain,
    ( spl71_276
  <=> tl(sK22) = sK27(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_276])]) ).

fof(f3780,plain,
    ( spl71_304
  <=> sK22 = cons(sK26(sK22),tl(sK22)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_304])]) ).

fof(f3784,plain,
    ( sK22 = cons(sK26(sK22),sK27(sK22))
    | ~ spl71_276
    | ~ spl71_304 ),
    inference(forward_demodulation,[],[f3782,f3195]) ).

fof(f3195,plain,
    ( tl(sK22) = sK27(sK22)
    | ~ spl71_276 ),
    inference(avatar_component_clause,[],[f3194]) ).

fof(f3782,plain,
    ( sK22 = cons(sK26(sK22),tl(sK22))
    | ~ spl71_304 ),
    inference(avatar_component_clause,[],[f3780]) ).

fof(f3783,plain,
    ( spl71_269
    | spl71_304
    | ~ spl71_3
    | ~ spl71_187
    | ~ spl71_268 ),
    inference(avatar_split_clause,[],[f3256,f3037,f1949,f657,f3780,f3041]) ).

fof(f3041,plain,
    ( spl71_269
  <=> nil = sK22 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_269])]) ).

fof(f1949,plain,
    ( spl71_187
  <=> ! [X0] :
        ( cons(hd(X0),tl(X0)) = X0
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_187])]) ).

fof(f3037,plain,
    ( spl71_268
  <=> hd(sK22) = sK26(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_268])]) ).

fof(f3256,plain,
    ( sK22 = cons(sK26(sK22),tl(sK22))
    | nil = sK22
    | ~ spl71_3
    | ~ spl71_187
    | ~ spl71_268 ),
    inference(forward_demodulation,[],[f2007,f3039]) ).

fof(f3039,plain,
    ( hd(sK22) = sK26(sK22)
    | ~ spl71_268 ),
    inference(avatar_component_clause,[],[f3037]) ).

fof(f2007,plain,
    ( nil = sK22
    | sK22 = cons(hd(sK22),tl(sK22))
    | ~ spl71_3
    | ~ spl71_187 ),
    inference(resolution,[],[f1950,f659]) ).

fof(f1950,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(hd(X0),tl(X0)) = X0 )
    | ~ spl71_187 ),
    inference(avatar_component_clause,[],[f1949]) ).

fof(f3743,plain,
    ( spl71_303
    | ~ spl71_286
    | ~ spl71_302 ),
    inference(avatar_split_clause,[],[f3738,f3734,f3238,f3740]) ).

fof(f3740,plain,
    ( spl71_303
  <=> sK20 = cons(sK26(sK20),sK27(sK20)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_303])]) ).

fof(f3238,plain,
    ( spl71_286
  <=> tl(sK20) = sK27(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_286])]) ).

fof(f3734,plain,
    ( spl71_302
  <=> sK20 = cons(sK26(sK20),tl(sK20)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_302])]) ).

fof(f3738,plain,
    ( sK20 = cons(sK26(sK20),sK27(sK20))
    | ~ spl71_286
    | ~ spl71_302 ),
    inference(forward_demodulation,[],[f3736,f3240]) ).

fof(f3240,plain,
    ( tl(sK20) = sK27(sK20)
    | ~ spl71_286 ),
    inference(avatar_component_clause,[],[f3238]) ).

fof(f3736,plain,
    ( sK20 = cons(sK26(sK20),tl(sK20))
    | ~ spl71_302 ),
    inference(avatar_component_clause,[],[f3734]) ).

fof(f3737,plain,
    ( spl71_8
    | spl71_302
    | ~ spl71_1
    | ~ spl71_187
    | ~ spl71_259 ),
    inference(avatar_split_clause,[],[f3248,f2864,f1949,f647,f3734,f681]) ).

fof(f681,plain,
    ( spl71_8
  <=> nil = sK20 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_8])]) ).

fof(f2864,plain,
    ( spl71_259
  <=> hd(sK20) = sK26(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_259])]) ).

fof(f3248,plain,
    ( sK20 = cons(sK26(sK20),tl(sK20))
    | nil = sK20
    | ~ spl71_1
    | ~ spl71_187
    | ~ spl71_259 ),
    inference(forward_demodulation,[],[f2005,f2866]) ).

fof(f2866,plain,
    ( hd(sK20) = sK26(sK20)
    | ~ spl71_259 ),
    inference(avatar_component_clause,[],[f2864]) ).

fof(f2005,plain,
    ( nil = sK20
    | sK20 = cons(hd(sK20),tl(sK20))
    | ~ spl71_1
    | ~ spl71_187 ),
    inference(resolution,[],[f1950,f649]) ).

fof(f3697,plain,
    ( spl71_301
    | ~ spl71_266
    | ~ spl71_273
    | ~ spl71_300 ),
    inference(avatar_split_clause,[],[f3692,f3687,f3118,f3000,f3694]) ).

fof(f3694,plain,
    ( spl71_301
  <=> sK21 = cons(sK26(sK21),sK27(sK21)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_301])]) ).

fof(f3000,plain,
    ( spl71_266
  <=> hd(sK21) = sK26(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_266])]) ).

fof(f3118,plain,
    ( spl71_273
  <=> tl(sK21) = sK27(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_273])]) ).

fof(f3687,plain,
    ( spl71_300
  <=> sK21 = cons(hd(sK21),tl(sK21)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_300])]) ).

fof(f3692,plain,
    ( sK21 = cons(sK26(sK21),sK27(sK21))
    | ~ spl71_266
    | ~ spl71_273
    | ~ spl71_300 ),
    inference(forward_demodulation,[],[f3691,f3002]) ).

fof(f3002,plain,
    ( hd(sK21) = sK26(sK21)
    | ~ spl71_266 ),
    inference(avatar_component_clause,[],[f3000]) ).

fof(f3691,plain,
    ( sK21 = cons(hd(sK21),sK27(sK21))
    | ~ spl71_273
    | ~ spl71_300 ),
    inference(forward_demodulation,[],[f3689,f3120]) ).

fof(f3120,plain,
    ( tl(sK21) = sK27(sK21)
    | ~ spl71_273 ),
    inference(avatar_component_clause,[],[f3118]) ).

fof(f3689,plain,
    ( sK21 = cons(hd(sK21),tl(sK21))
    | ~ spl71_300 ),
    inference(avatar_component_clause,[],[f3687]) ).

fof(f3690,plain,
    ( spl71_300
    | spl71_264
    | ~ spl71_2
    | ~ spl71_187 ),
    inference(avatar_split_clause,[],[f2006,f1949,f652,f2989,f3687]) ).

fof(f2989,plain,
    ( spl71_264
  <=> nil = sK21 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_264])]) ).

fof(f2006,plain,
    ( nil = sK21
    | sK21 = cons(hd(sK21),tl(sK21))
    | ~ spl71_2
    | ~ spl71_187 ),
    inference(resolution,[],[f1950,f654]) ).

fof(f3650,plain,
    ( spl71_299
    | spl71_269
    | ~ spl71_3
    | ~ spl71_185 ),
    inference(avatar_split_clause,[],[f1971,f1940,f657,f3041,f3647]) ).

fof(f3647,plain,
    ( spl71_299
  <=> sK22 = cons(sK25(sK22),sK24(sK22)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_299])]) ).

fof(f1940,plain,
    ( spl71_185
  <=> ! [X0] :
        ( cons(sK25(X0),sK24(X0)) = X0
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_185])]) ).

fof(f1971,plain,
    ( nil = sK22
    | sK22 = cons(sK25(sK22),sK24(sK22))
    | ~ spl71_3
    | ~ spl71_185 ),
    inference(resolution,[],[f1941,f659]) ).

fof(f1941,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | cons(sK25(X0),sK24(X0)) = X0 )
    | ~ spl71_185 ),
    inference(avatar_component_clause,[],[f1940]) ).

fof(f3645,plain,
    ( spl71_298
    | ~ spl71_12
    | ~ spl71_271 ),
    inference(avatar_split_clause,[],[f3260,f3091,f701,f3642]) ).

fof(f3642,plain,
    ( spl71_298
  <=> duplicatefreeP(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_298])]) ).

fof(f701,plain,
    ( spl71_12
  <=> duplicatefreeP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_12])]) ).

fof(f3260,plain,
    ( duplicatefreeP(sK23)
    | ~ spl71_12
    | ~ spl71_271 ),
    inference(superposition,[],[f703,f3093]) ).

fof(f703,plain,
    ( duplicatefreeP(nil)
    | ~ spl71_12 ),
    inference(avatar_component_clause,[],[f701]) ).

fof(f3605,plain,
    ( spl71_297
    | spl71_264
    | ~ spl71_2
    | ~ spl71_185 ),
    inference(avatar_split_clause,[],[f1970,f1940,f652,f2989,f3602]) ).

fof(f3602,plain,
    ( spl71_297
  <=> sK21 = cons(sK25(sK21),sK24(sK21)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_297])]) ).

fof(f1970,plain,
    ( nil = sK21
    | sK21 = cons(sK25(sK21),sK24(sK21))
    | ~ spl71_2
    | ~ spl71_185 ),
    inference(resolution,[],[f1941,f654]) ).

fof(f3565,plain,
    ( spl71_296
    | spl71_8
    | ~ spl71_1
    | ~ spl71_185 ),
    inference(avatar_split_clause,[],[f1969,f1940,f647,f681,f3562]) ).

fof(f3562,plain,
    ( spl71_296
  <=> sK20 = cons(sK25(sK20),sK24(sK20)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_296])]) ).

fof(f1969,plain,
    ( nil = sK20
    | sK20 = cons(sK25(sK20),sK24(sK20))
    | ~ spl71_1
    | ~ spl71_185 ),
    inference(resolution,[],[f1941,f649]) ).

fof(f3559,plain,
    ( spl71_295
    | ~ spl71_18
    | ~ spl71_30 ),
    inference(avatar_split_clause,[],[f821,f783,f731,f3556]) ).

fof(f3556,plain,
    ( spl71_295
  <=> sP17(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_295])]) ).

fof(f731,plain,
    ( spl71_18
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_18])]) ).

fof(f783,plain,
    ( spl71_30
  <=> ! [X0] :
        ( sP17(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_30])]) ).

fof(f821,plain,
    ( sP17(nil)
    | ~ spl71_18
    | ~ spl71_30 ),
    inference(resolution,[],[f784,f733]) ).

fof(f733,plain,
    ( ssList(nil)
    | ~ spl71_18 ),
    inference(avatar_component_clause,[],[f731]) ).

fof(f784,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sP17(X0) )
    | ~ spl71_30 ),
    inference(avatar_component_clause,[],[f783]) ).

fof(f3553,plain,
    ( spl71_294
    | ~ spl71_18
    | ~ spl71_29 ),
    inference(avatar_split_clause,[],[f816,f779,f731,f3550]) ).

fof(f3550,plain,
    ( spl71_294
  <=> sP15(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_294])]) ).

fof(f779,plain,
    ( spl71_29
  <=> ! [X0] :
        ( sP15(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_29])]) ).

fof(f816,plain,
    ( sP15(nil)
    | ~ spl71_18
    | ~ spl71_29 ),
    inference(resolution,[],[f780,f733]) ).

fof(f780,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sP15(X0) )
    | ~ spl71_29 ),
    inference(avatar_component_clause,[],[f779]) ).

fof(f3547,plain,
    ( spl71_293
    | ~ spl71_18
    | ~ spl71_28 ),
    inference(avatar_split_clause,[],[f811,f775,f731,f3544]) ).

fof(f3544,plain,
    ( spl71_293
  <=> sP13(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_293])]) ).

fof(f775,plain,
    ( spl71_28
  <=> ! [X0] :
        ( sP13(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_28])]) ).

fof(f811,plain,
    ( sP13(nil)
    | ~ spl71_18
    | ~ spl71_28 ),
    inference(resolution,[],[f776,f733]) ).

fof(f776,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sP13(X0) )
    | ~ spl71_28 ),
    inference(avatar_component_clause,[],[f775]) ).

fof(f3541,plain,
    ( spl71_292
    | ~ spl71_18
    | ~ spl71_27 ),
    inference(avatar_split_clause,[],[f801,f771,f731,f3538]) ).

fof(f3538,plain,
    ( spl71_292
  <=> sP11(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_292])]) ).

fof(f771,plain,
    ( spl71_27
  <=> ! [X0] :
        ( sP11(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_27])]) ).

fof(f801,plain,
    ( sP11(nil)
    | ~ spl71_18
    | ~ spl71_27 ),
    inference(resolution,[],[f772,f733]) ).

fof(f772,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sP11(X0) )
    | ~ spl71_27 ),
    inference(avatar_component_clause,[],[f771]) ).

fof(f3535,plain,
    ( spl71_291
    | ~ spl71_18
    | ~ spl71_26 ),
    inference(avatar_split_clause,[],[f796,f767,f731,f3532]) ).

fof(f3532,plain,
    ( spl71_291
  <=> sP9(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_291])]) ).

fof(f767,plain,
    ( spl71_26
  <=> ! [X0] :
        ( sP9(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_26])]) ).

fof(f796,plain,
    ( sP9(nil)
    | ~ spl71_18
    | ~ spl71_26 ),
    inference(resolution,[],[f768,f733]) ).

fof(f768,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sP9(X0) )
    | ~ spl71_26 ),
    inference(avatar_component_clause,[],[f767]) ).

fof(f3529,plain,
    ( spl71_290
    | ~ spl71_18
    | ~ spl71_25 ),
    inference(avatar_split_clause,[],[f791,f763,f731,f3526]) ).

fof(f3526,plain,
    ( spl71_290
  <=> sP7(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_290])]) ).

fof(f763,plain,
    ( spl71_25
  <=> ! [X0] :
        ( sP7(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_25])]) ).

fof(f791,plain,
    ( sP7(nil)
    | ~ spl71_18
    | ~ spl71_25 ),
    inference(resolution,[],[f764,f733]) ).

fof(f764,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sP7(X0) )
    | ~ spl71_25 ),
    inference(avatar_component_clause,[],[f763]) ).

fof(f3524,plain,
    ( spl71_289
    | ~ spl71_11
    | ~ spl71_271 ),
    inference(avatar_split_clause,[],[f3259,f3091,f696,f3521]) ).

fof(f3521,plain,
    ( spl71_289
  <=> equalelemsP(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_289])]) ).

fof(f696,plain,
    ( spl71_11
  <=> equalelemsP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_11])]) ).

fof(f3259,plain,
    ( equalelemsP(sK23)
    | ~ spl71_11
    | ~ spl71_271 ),
    inference(superposition,[],[f698,f3093]) ).

fof(f698,plain,
    ( equalelemsP(nil)
    | ~ spl71_11 ),
    inference(avatar_component_clause,[],[f696]) ).

fof(f3518,plain,
    ( spl71_288
    | ~ spl71_18
    | ~ spl71_24 ),
    inference(avatar_split_clause,[],[f786,f759,f731,f3515]) ).

fof(f3515,plain,
    ( spl71_288
  <=> sP5(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_288])]) ).

fof(f759,plain,
    ( spl71_24
  <=> ! [X0] :
        ( sP5(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_24])]) ).

fof(f786,plain,
    ( sP5(nil)
    | ~ spl71_18
    | ~ spl71_24 ),
    inference(resolution,[],[f760,f733]) ).

fof(f760,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | sP5(X0) )
    | ~ spl71_24 ),
    inference(avatar_component_clause,[],[f759]) ).

fof(f3320,plain,
    ( ~ spl71_287
    | spl71_10
    | ~ spl71_271 ),
    inference(avatar_split_clause,[],[f3258,f3091,f691,f3317]) ).

fof(f3317,plain,
    ( spl71_287
  <=> singletonP(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_287])]) ).

fof(f691,plain,
    ( spl71_10
  <=> singletonP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_10])]) ).

fof(f3258,plain,
    ( ~ singletonP(sK23)
    | spl71_10
    | ~ spl71_271 ),
    inference(superposition,[],[f693,f3093]) ).

fof(f693,plain,
    ( ~ singletonP(nil)
    | spl71_10 ),
    inference(avatar_component_clause,[],[f691]) ).

fof(f3315,plain,
    ( spl71_276
    | spl71_269
    | ~ spl71_3
    | ~ spl71_167 ),
    inference(avatar_split_clause,[],[f1729,f1639,f657,f3041,f3194]) ).

fof(f1639,plain,
    ( spl71_167
  <=> ! [X0] :
        ( tl(X0) = sK27(X0)
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_167])]) ).

fof(f1729,plain,
    ( nil = sK22
    | tl(sK22) = sK27(sK22)
    | ~ spl71_3
    | ~ spl71_167 ),
    inference(resolution,[],[f1640,f659]) ).

fof(f1640,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | tl(X0) = sK27(X0) )
    | ~ spl71_167 ),
    inference(avatar_component_clause,[],[f1639]) ).

fof(f3305,plain,
    ( spl71_286
    | spl71_8
    | ~ spl71_1
    | ~ spl71_167 ),
    inference(avatar_split_clause,[],[f1727,f1639,f647,f681,f3238]) ).

fof(f1727,plain,
    ( nil = sK20
    | tl(sK20) = sK27(sK20)
    | ~ spl71_1
    | ~ spl71_167 ),
    inference(resolution,[],[f1640,f649]) ).

fof(f3255,plain,
    ( spl71_269
    | ~ spl71_271
    | ~ spl71_272 ),
    inference(avatar_split_clause,[],[f3252,f3098,f3091,f3041]) ).

fof(f3098,plain,
    ( spl71_272
  <=> sK22 = sK23 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_272])]) ).

fof(f3252,plain,
    ( nil = sK22
    | ~ spl71_271
    | ~ spl71_272 ),
    inference(forward_demodulation,[],[f3093,f3100]) ).

fof(f3100,plain,
    ( sK22 = sK23
    | ~ spl71_272 ),
    inference(avatar_component_clause,[],[f3098]) ).

fof(f3241,plain,
    ( spl71_286
    | spl71_274
    | ~ spl71_1
    | ~ spl71_167
    | ~ spl71_269 ),
    inference(avatar_split_clause,[],[f3126,f3041,f1639,f647,f3159,f3238]) ).

fof(f3159,plain,
    ( spl71_274
  <=> sK20 = sK22 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_274])]) ).

fof(f3126,plain,
    ( sK20 = sK22
    | tl(sK20) = sK27(sK20)
    | ~ spl71_1
    | ~ spl71_167
    | ~ spl71_269 ),
    inference(forward_demodulation,[],[f1727,f3043]) ).

fof(f3043,plain,
    ( nil = sK22
    | ~ spl71_269 ),
    inference(avatar_component_clause,[],[f3041]) ).

fof(f3235,plain,
    ( spl71_285
    | ~ spl71_4
    | ~ spl71_171 ),
    inference(avatar_split_clause,[],[f1795,f1656,f662,f3233]) ).

fof(f3233,plain,
    ( spl71_285
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK23)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_285])]) ).

fof(f1656,plain,
    ( spl71_171
  <=> ! [X0,X1] :
        ( hd(cons(X1,X0)) = X1
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_171])]) ).

fof(f1795,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK23)) = X0 )
    | ~ spl71_4
    | ~ spl71_171 ),
    inference(resolution,[],[f1657,f664]) ).

fof(f1657,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssItem(X1)
        | hd(cons(X1,X0)) = X1 )
    | ~ spl71_171 ),
    inference(avatar_component_clause,[],[f1656]) ).

fof(f3231,plain,
    ( spl71_284
    | ~ spl71_3
    | ~ spl71_171 ),
    inference(avatar_split_clause,[],[f1794,f1656,f657,f3229]) ).

fof(f3229,plain,
    ( spl71_284
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK22)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_284])]) ).

fof(f1794,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK22)) = X0 )
    | ~ spl71_3
    | ~ spl71_171 ),
    inference(resolution,[],[f1657,f659]) ).

fof(f3227,plain,
    ( spl71_283
    | ~ spl71_2
    | ~ spl71_171 ),
    inference(avatar_split_clause,[],[f1793,f1656,f652,f3225]) ).

fof(f3225,plain,
    ( spl71_283
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK21)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_283])]) ).

fof(f1793,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK21)) = X0 )
    | ~ spl71_2
    | ~ spl71_171 ),
    inference(resolution,[],[f1657,f654]) ).

fof(f3223,plain,
    ( spl71_282
    | ~ spl71_1
    | ~ spl71_171 ),
    inference(avatar_split_clause,[],[f1792,f1656,f647,f3221]) ).

fof(f3221,plain,
    ( spl71_282
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK20)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_282])]) ).

fof(f1792,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | hd(cons(X0,sK20)) = X0 )
    | ~ spl71_1
    | ~ spl71_171 ),
    inference(resolution,[],[f1657,f649]) ).

fof(f3218,plain,
    ( spl71_281
    | ~ spl71_4
    | ~ spl71_170 ),
    inference(avatar_split_clause,[],[f1765,f1652,f662,f3216]) ).

fof(f3216,plain,
    ( spl71_281
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | sK23 = tl(cons(X0,sK23)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_281])]) ).

fof(f1652,plain,
    ( spl71_170
  <=> ! [X0,X1] :
        ( tl(cons(X1,X0)) = X0
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_170])]) ).

fof(f1765,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | sK23 = tl(cons(X0,sK23)) )
    | ~ spl71_4
    | ~ spl71_170 ),
    inference(resolution,[],[f1653,f664]) ).

fof(f1653,plain,
    ( ! [X0,X1] :
        ( ~ ssList(X0)
        | ~ ssItem(X1)
        | tl(cons(X1,X0)) = X0 )
    | ~ spl71_170 ),
    inference(avatar_component_clause,[],[f1652]) ).

fof(f3214,plain,
    ( spl71_280
    | ~ spl71_3
    | ~ spl71_170 ),
    inference(avatar_split_clause,[],[f1764,f1652,f657,f3212]) ).

fof(f3212,plain,
    ( spl71_280
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | sK22 = tl(cons(X0,sK22)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_280])]) ).

fof(f1764,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | sK22 = tl(cons(X0,sK22)) )
    | ~ spl71_3
    | ~ spl71_170 ),
    inference(resolution,[],[f1653,f659]) ).

fof(f3210,plain,
    ( spl71_279
    | ~ spl71_2
    | ~ spl71_170 ),
    inference(avatar_split_clause,[],[f1763,f1652,f652,f3208]) ).

fof(f3208,plain,
    ( spl71_279
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | sK21 = tl(cons(X0,sK21)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_279])]) ).

fof(f1763,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | sK21 = tl(cons(X0,sK21)) )
    | ~ spl71_2
    | ~ spl71_170 ),
    inference(resolution,[],[f1653,f654]) ).

fof(f3206,plain,
    ( ~ spl71_278
    | spl71_10
    | ~ spl71_269 ),
    inference(avatar_split_clause,[],[f3045,f3041,f691,f3203]) ).

fof(f3203,plain,
    ( spl71_278
  <=> singletonP(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_278])]) ).

fof(f3045,plain,
    ( ~ singletonP(sK22)
    | spl71_10
    | ~ spl71_269 ),
    inference(superposition,[],[f693,f3043]) ).

fof(f3201,plain,
    ( spl71_277
    | ~ spl71_1
    | ~ spl71_170 ),
    inference(avatar_split_clause,[],[f1762,f1652,f647,f3199]) ).

fof(f3199,plain,
    ( spl71_277
  <=> ! [X0] :
        ( ~ ssItem(X0)
        | sK20 = tl(cons(X0,sK20)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_277])]) ).

fof(f1762,plain,
    ( ! [X0] :
        ( ~ ssItem(X0)
        | sK20 = tl(cons(X0,sK20)) )
    | ~ spl71_1
    | ~ spl71_170 ),
    inference(resolution,[],[f1653,f649]) ).

fof(f3197,plain,
    ( ~ spl71_276
    | ~ spl71_272
    | spl71_275 ),
    inference(avatar_split_clause,[],[f3192,f3188,f3098,f3194]) ).

fof(f3188,plain,
    ( spl71_275
  <=> tl(sK23) = sK27(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_275])]) ).

fof(f3192,plain,
    ( tl(sK22) != sK27(sK22)
    | ~ spl71_272
    | spl71_275 ),
    inference(forward_demodulation,[],[f3189,f3100]) ).

fof(f3189,plain,
    ( tl(sK23) != sK27(sK23)
    | spl71_275 ),
    inference(avatar_component_clause,[],[f3188]) ).

fof(f3191,plain,
    ( spl71_275
    | spl71_271
    | ~ spl71_4
    | ~ spl71_167 ),
    inference(avatar_split_clause,[],[f1730,f1639,f662,f3091,f3188]) ).

fof(f1730,plain,
    ( nil = sK23
    | tl(sK23) = sK27(sK23)
    | ~ spl71_4
    | ~ spl71_167 ),
    inference(resolution,[],[f1640,f664]) ).

fof(f3162,plain,
    ( ~ spl71_274
    | spl71_8
    | ~ spl71_269 ),
    inference(avatar_split_clause,[],[f3125,f3041,f681,f3159]) ).

fof(f3125,plain,
    ( sK20 != sK22
    | spl71_8
    | ~ spl71_269 ),
    inference(forward_demodulation,[],[f683,f3043]) ).

fof(f683,plain,
    ( nil != sK20
    | spl71_8 ),
    inference(avatar_component_clause,[],[f681]) ).

fof(f3122,plain,
    ( ~ spl71_2
    | ~ spl71_40
    | spl71_265 ),
    inference(avatar_split_clause,[],[f2998,f2994,f860,f652]) ).

fof(f860,plain,
    ( spl71_40
  <=> ! [X0] :
        ( segmentP(X0,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_40])]) ).

fof(f2994,plain,
    ( spl71_265
  <=> segmentP(sK21,sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_265])]) ).

fof(f2998,plain,
    ( ~ ssList(sK21)
    | ~ spl71_40
    | spl71_265 ),
    inference(resolution,[],[f2996,f861]) ).

fof(f861,plain,
    ( ! [X0] :
        ( segmentP(X0,X0)
        | ~ ssList(X0) )
    | ~ spl71_40 ),
    inference(avatar_component_clause,[],[f860]) ).

fof(f2996,plain,
    ( ~ segmentP(sK21,sK21)
    | spl71_265 ),
    inference(avatar_component_clause,[],[f2994]) ).

fof(f3121,plain,
    ( spl71_273
    | spl71_264
    | ~ spl71_2
    | ~ spl71_167 ),
    inference(avatar_split_clause,[],[f1728,f1639,f652,f2989,f3118]) ).

fof(f1728,plain,
    ( nil = sK21
    | tl(sK21) = sK27(sK21)
    | ~ spl71_2
    | ~ spl71_167 ),
    inference(resolution,[],[f1640,f654]) ).

fof(f3101,plain,
    ( spl71_272
    | ~ spl71_269
    | ~ spl71_271 ),
    inference(avatar_split_clause,[],[f3095,f3091,f3041,f3098]) ).

fof(f3095,plain,
    ( sK22 = sK23
    | ~ spl71_269
    | ~ spl71_271 ),
    inference(forward_demodulation,[],[f3093,f3043]) ).

fof(f3094,plain,
    ( spl71_270
    | spl71_271
    | ~ spl71_4
    | ~ spl71_166 ),
    inference(avatar_split_clause,[],[f1700,f1635,f662,f3091,f3087]) ).

fof(f3087,plain,
    ( spl71_270
  <=> hd(sK23) = sK26(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_270])]) ).

fof(f1635,plain,
    ( spl71_166
  <=> ! [X0] :
        ( hd(X0) = sK26(X0)
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_166])]) ).

fof(f1700,plain,
    ( nil = sK23
    | hd(sK23) = sK26(sK23)
    | ~ spl71_4
    | ~ spl71_166 ),
    inference(resolution,[],[f1636,f664]) ).

fof(f1636,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | nil = X0
        | hd(X0) = sK26(X0) )
    | ~ spl71_166 ),
    inference(avatar_component_clause,[],[f1635]) ).

fof(f3044,plain,
    ( spl71_268
    | spl71_269
    | ~ spl71_3
    | ~ spl71_166 ),
    inference(avatar_split_clause,[],[f1699,f1635,f657,f3041,f3037]) ).

fof(f1699,plain,
    ( nil = sK22
    | hd(sK22) = sK26(sK22)
    | ~ spl71_3
    | ~ spl71_166 ),
    inference(resolution,[],[f1636,f659]) ).

fof(f3016,plain,
    ( spl71_267
    | ~ spl71_7
    | ~ spl71_9 ),
    inference(avatar_split_clause,[],[f2871,f686,f677,f3013]) ).

fof(f3013,plain,
    ( spl71_267
  <=> sK21 = app(app(sK22,sK21),sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_267])]) ).

fof(f677,plain,
    ( spl71_7
  <=> sK20 = sK21 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_7])]) ).

fof(f2871,plain,
    ( sK21 = app(app(sK22,sK21),sK23)
    | ~ spl71_7
    | ~ spl71_9 ),
    inference(superposition,[],[f688,f679]) ).

fof(f679,plain,
    ( sK20 = sK21
    | ~ spl71_7 ),
    inference(avatar_component_clause,[],[f677]) ).

fof(f3003,plain,
    ( spl71_266
    | ~ spl71_7
    | ~ spl71_259 ),
    inference(avatar_split_clause,[],[f2986,f2864,f677,f3000]) ).

fof(f2986,plain,
    ( hd(sK21) = sK26(sK21)
    | ~ spl71_7
    | ~ spl71_259 ),
    inference(forward_demodulation,[],[f2866,f679]) ).

fof(f2997,plain,
    ( ~ spl71_265
    | spl71_6
    | ~ spl71_7 ),
    inference(avatar_split_clause,[],[f2870,f677,f672,f2994]) ).

fof(f2870,plain,
    ( ~ segmentP(sK21,sK21)
    | spl71_6
    | ~ spl71_7 ),
    inference(superposition,[],[f674,f679]) ).

fof(f674,plain,
    ( ~ segmentP(sK21,sK20)
    | spl71_6 ),
    inference(avatar_component_clause,[],[f672]) ).

fof(f2992,plain,
    ( ~ spl71_264
    | ~ spl71_7
    | spl71_8 ),
    inference(avatar_split_clause,[],[f2987,f681,f677,f2989]) ).

fof(f2987,plain,
    ( nil != sK21
    | ~ spl71_7
    | spl71_8 ),
    inference(forward_demodulation,[],[f683,f679]) ).

fof(f2977,plain,
    ( spl71_263
    | ~ spl71_7
    | ~ spl71_8
    | ~ spl71_12 ),
    inference(avatar_split_clause,[],[f2920,f701,f681,f677,f2974]) ).

fof(f2974,plain,
    ( spl71_263
  <=> duplicatefreeP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_263])]) ).

fof(f2920,plain,
    ( duplicatefreeP(sK21)
    | ~ spl71_7
    | ~ spl71_8
    | ~ spl71_12 ),
    inference(forward_demodulation,[],[f2884,f679]) ).

fof(f2884,plain,
    ( duplicatefreeP(sK20)
    | ~ spl71_8
    | ~ spl71_12 ),
    inference(superposition,[],[f703,f682]) ).

fof(f682,plain,
    ( nil = sK20
    | ~ spl71_8 ),
    inference(avatar_component_clause,[],[f681]) ).

fof(f2972,plain,
    ( spl71_262
    | ~ spl71_7
    | ~ spl71_8
    | ~ spl71_11 ),
    inference(avatar_split_clause,[],[f2919,f696,f681,f677,f2969]) ).

fof(f2969,plain,
    ( spl71_262
  <=> equalelemsP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_262])]) ).

fof(f2919,plain,
    ( equalelemsP(sK21)
    | ~ spl71_7
    | ~ spl71_8
    | ~ spl71_11 ),
    inference(forward_demodulation,[],[f2883,f679]) ).

fof(f2883,plain,
    ( equalelemsP(sK20)
    | ~ spl71_8
    | ~ spl71_11 ),
    inference(superposition,[],[f698,f682]) ).

fof(f2967,plain,
    ( ~ spl71_261
    | ~ spl71_7
    | ~ spl71_8
    | spl71_10 ),
    inference(avatar_split_clause,[],[f2918,f691,f681,f677,f2964]) ).

fof(f2964,plain,
    ( spl71_261
  <=> singletonP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_261])]) ).

fof(f2918,plain,
    ( ~ singletonP(sK21)
    | ~ spl71_7
    | ~ spl71_8
    | spl71_10 ),
    inference(forward_demodulation,[],[f2882,f679]) ).

fof(f2882,plain,
    ( ~ singletonP(sK20)
    | ~ spl71_8
    | spl71_10 ),
    inference(superposition,[],[f693,f682]) ).

fof(f2962,plain,
    ( spl71_260
    | ~ spl71_5
    | ~ spl71_7 ),
    inference(avatar_split_clause,[],[f2869,f677,f667,f2959]) ).

fof(f2959,plain,
    ( spl71_260
  <=> totalorderedP(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_260])]) ).

fof(f667,plain,
    ( spl71_5
  <=> totalorderedP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_5])]) ).

fof(f2869,plain,
    ( totalorderedP(sK21)
    | ~ spl71_5
    | ~ spl71_7 ),
    inference(superposition,[],[f669,f679]) ).

fof(f669,plain,
    ( totalorderedP(sK20)
    | ~ spl71_5 ),
    inference(avatar_component_clause,[],[f667]) ).

fof(f2867,plain,
    ( spl71_259
    | spl71_8
    | ~ spl71_1
    | ~ spl71_166 ),
    inference(avatar_split_clause,[],[f1697,f1635,f647,f681,f2864]) ).

fof(f1697,plain,
    ( nil = sK20
    | hd(sK20) = sK26(sK20)
    | ~ spl71_1
    | ~ spl71_166 ),
    inference(resolution,[],[f1636,f649]) ).

fof(f2718,plain,
    ( spl71_258
    | ~ spl71_4
    | ~ spl71_118 ),
    inference(avatar_split_clause,[],[f1406,f1325,f662,f2715]) ).

fof(f2715,plain,
    ( spl71_258
  <=> sK23 = app(nil,sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_258])]) ).

fof(f1325,plain,
    ( spl71_118
  <=> ! [X0] :
        ( app(nil,X0) = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_118])]) ).

fof(f1406,plain,
    ( sK23 = app(nil,sK23)
    | ~ spl71_4
    | ~ spl71_118 ),
    inference(resolution,[],[f1326,f664]) ).

fof(f1326,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(nil,X0) = X0 )
    | ~ spl71_118 ),
    inference(avatar_component_clause,[],[f1325]) ).

fof(f2713,plain,
    ( spl71_257
    | ~ spl71_3
    | ~ spl71_118 ),
    inference(avatar_split_clause,[],[f1405,f1325,f657,f2710]) ).

fof(f2710,plain,
    ( spl71_257
  <=> sK22 = app(nil,sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_257])]) ).

fof(f1405,plain,
    ( sK22 = app(nil,sK22)
    | ~ spl71_3
    | ~ spl71_118 ),
    inference(resolution,[],[f1326,f659]) ).

fof(f2708,plain,
    ( spl71_256
    | ~ spl71_2
    | ~ spl71_118 ),
    inference(avatar_split_clause,[],[f1404,f1325,f652,f2705]) ).

fof(f2705,plain,
    ( spl71_256
  <=> sK21 = app(nil,sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_256])]) ).

fof(f1404,plain,
    ( sK21 = app(nil,sK21)
    | ~ spl71_2
    | ~ spl71_118 ),
    inference(resolution,[],[f1326,f654]) ).

fof(f2703,plain,
    ( spl71_255
    | ~ spl71_1
    | ~ spl71_118 ),
    inference(avatar_split_clause,[],[f1403,f1325,f647,f2700]) ).

fof(f2700,plain,
    ( spl71_255
  <=> sK20 = app(nil,sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_255])]) ).

fof(f1403,plain,
    ( sK20 = app(nil,sK20)
    | ~ spl71_1
    | ~ spl71_118 ),
    inference(resolution,[],[f1326,f649]) ).

fof(f2698,plain,
    ( spl71_254
    | ~ spl71_4
    | ~ spl71_117 ),
    inference(avatar_split_clause,[],[f1381,f1321,f662,f2695]) ).

fof(f2695,plain,
    ( spl71_254
  <=> sK23 = app(sK23,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_254])]) ).

fof(f1321,plain,
    ( spl71_117
  <=> ! [X0] :
        ( app(X0,nil) = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_117])]) ).

fof(f1381,plain,
    ( sK23 = app(sK23,nil)
    | ~ spl71_4
    | ~ spl71_117 ),
    inference(resolution,[],[f1322,f664]) ).

fof(f1322,plain,
    ( ! [X0] :
        ( ~ ssList(X0)
        | app(X0,nil) = X0 )
    | ~ spl71_117 ),
    inference(avatar_component_clause,[],[f1321]) ).

fof(f2693,plain,
    ( spl71_253
    | ~ spl71_3
    | ~ spl71_117 ),
    inference(avatar_split_clause,[],[f1380,f1321,f657,f2690]) ).

fof(f2690,plain,
    ( spl71_253
  <=> sK22 = app(sK22,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_253])]) ).

fof(f1380,plain,
    ( sK22 = app(sK22,nil)
    | ~ spl71_3
    | ~ spl71_117 ),
    inference(resolution,[],[f1322,f659]) ).

fof(f2688,plain,
    ( spl71_252
    | ~ spl71_2
    | ~ spl71_117 ),
    inference(avatar_split_clause,[],[f1379,f1321,f652,f2685]) ).

fof(f2685,plain,
    ( spl71_252
  <=> sK21 = app(sK21,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_252])]) ).

fof(f1379,plain,
    ( sK21 = app(sK21,nil)
    | ~ spl71_2
    | ~ spl71_117 ),
    inference(resolution,[],[f1322,f654]) ).

fof(f2683,plain,
    ( spl71_250
    | ~ spl71_251
    | ~ spl71_31
    | ~ spl71_96 ),
    inference(avatar_split_clause,[],[f1427,f1233,f807,f2680,f2676]) ).

fof(f2676,plain,
    ( spl71_250
  <=> equalelemsP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_250])]) ).

fof(f2680,plain,
    ( spl71_251
  <=> sP4(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_251])]) ).

fof(f807,plain,
    ( spl71_31
  <=> sP5(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_31])]) ).

fof(f1233,plain,
    ( spl71_96
  <=> ! [X0] :
        ( equalelemsP(X0)
        | ~ sP4(X0)
        | ~ sP5(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_96])]) ).

fof(f1427,plain,
    ( ~ sP4(sK20)
    | equalelemsP(sK20)
    | ~ spl71_31
    | ~ spl71_96 ),
    inference(resolution,[],[f809,f1234]) ).

fof(f1234,plain,
    ( ! [X0] :
        ( ~ sP5(X0)
        | ~ sP4(X0)
        | equalelemsP(X0) )
    | ~ spl71_96 ),
    inference(avatar_component_clause,[],[f1233]) ).

fof(f809,plain,
    ( sP5(sK20)
    | ~ spl71_31 ),
    inference(avatar_component_clause,[],[f807]) ).

fof(f2674,plain,
    ( spl71_249
    | ~ spl71_1
    | ~ spl71_117 ),
    inference(avatar_split_clause,[],[f1378,f1321,f647,f2671]) ).

fof(f2671,plain,
    ( spl71_249
  <=> sK20 = app(sK20,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_249])]) ).

fof(f1378,plain,
    ( sK20 = app(sK20,nil)
    | ~ spl71_1
    | ~ spl71_117 ),
    inference(resolution,[],[f1322,f649]) ).

fof(f2630,plain,
    spl71_248,
    inference(avatar_split_clause,[],[f625,f2628]) ).

fof(f2628,plain,
    ( spl71_248
  <=> ! [X10,X9,X7,X6,X8] :
        ( ~ leq(X7,X6)
        | ~ leq(X6,X7)
        | ~ ssList(X10)
        | ~ ssList(X9)
        | ~ ssList(X8)
        | ~ ssItem(X7)
        | ~ ssItem(X6)
        | ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_248])]) ).

fof(f625,plain,
    ! [X10,X8,X6,X9,X7] :
      ( ~ leq(X7,X6)
      | ~ leq(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,[],[f523]) ).

fof(f523,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)
      | ~ sP12(X0) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f331,plain,
    ! [X0] :
      ( ( sP12(X0)
        | ( leq(sK49(X0),sK48(X0))
          & leq(sK48(X0),sK49(X0))
          & app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
          & ssList(sK52(X0))
          & ssList(sK51(X0))
          & ssList(sK50(X0))
          & ssItem(sK49(X0))
          & ssItem(sK48(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) )
        | ~ sP12(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51,sK52])],[f325,f330,f329,f328,f327,f326]) ).

fof(f326,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,sK48(X0))
                        & leq(sK48(X0),X2)
                        & app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK48(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f327,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( leq(X2,sK48(X0))
                      & leq(sK48(X0),X2)
                      & app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( leq(sK49(X0),sK48(X0))
                    & leq(sK48(X0),sK49(X0))
                    & app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK49(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f328,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( leq(sK49(X0),sK48(X0))
                  & leq(sK48(X0),sK49(X0))
                  & app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( leq(sK49(X0),sK48(X0))
                & leq(sK48(X0),sK49(X0))
                & app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK50(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f329,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( leq(sK49(X0),sK48(X0))
              & leq(sK48(X0),sK49(X0))
              & app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( leq(sK49(X0),sK48(X0))
            & leq(sK48(X0),sK49(X0))
            & app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f330,plain,
    ! [X0] :
      ( ? [X5] :
          ( leq(sK49(X0),sK48(X0))
          & leq(sK48(X0),sK49(X0))
          & app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
          & ssList(X5) )
     => ( leq(sK49(X0),sK48(X0))
        & leq(sK48(X0),sK49(X0))
        & app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f325,plain,
    ! [X0] :
      ( ( sP12(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) )
        | ~ sP12(X0) ) ),
    inference(rectify,[],[f324]) ).

fof(f324,plain,
    ! [X0] :
      ( ( sP12(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) )
        | ~ sP12(X0) ) ),
    inference(nnf_transformation,[],[f242]) ).

fof(f242,plain,
    ! [X0] :
      ( sP12(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,[sP12])]) ).

fof(f2626,plain,
    spl71_247,
    inference(avatar_split_clause,[],[f624,f2624]) ).

fof(f2624,plain,
    ( spl71_247
  <=> ! [X10,X9,X7,X6,X8] :
        ( lt(X7,X6)
        | lt(X6,X7)
        | ~ ssList(X10)
        | ~ ssList(X9)
        | ~ ssList(X8)
        | ~ ssItem(X7)
        | ~ ssItem(X6)
        | ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_247])]) ).

fof(f624,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(X7,X6)
      | lt(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,[],[f511]) ).

fof(f511,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)
      | ~ sP10(X0) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f322,plain,
    ! [X0] :
      ( ( sP10(X0)
        | ( ~ lt(sK44(X0),sK43(X0))
          & ~ lt(sK43(X0),sK44(X0))
          & app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
          & ssList(sK47(X0))
          & ssList(sK46(X0))
          & ssList(sK45(X0))
          & ssItem(sK44(X0))
          & ssItem(sK43(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) )
        | ~ sP10(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45,sK46,sK47])],[f316,f321,f320,f319,f318,f317]) ).

fof(f317,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,sK43(X0))
                        & ~ lt(sK43(X0),X2)
                        & app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK43(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f318,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(X2,sK43(X0))
                      & ~ lt(sK43(X0),X2)
                      & app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK44(X0),sK43(X0))
                    & ~ lt(sK43(X0),sK44(X0))
                    & app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK44(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f319,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK44(X0),sK43(X0))
                  & ~ lt(sK43(X0),sK44(X0))
                  & app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK44(X0),sK43(X0))
                & ~ lt(sK43(X0),sK44(X0))
                & app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK45(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f320,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK44(X0),sK43(X0))
              & ~ lt(sK43(X0),sK44(X0))
              & app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK44(X0),sK43(X0))
            & ~ lt(sK43(X0),sK44(X0))
            & app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK46(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f321,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK44(X0),sK43(X0))
          & ~ lt(sK43(X0),sK44(X0))
          & app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK44(X0),sK43(X0))
        & ~ lt(sK43(X0),sK44(X0))
        & app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
        & ssList(sK47(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f316,plain,
    ! [X0] :
      ( ( sP10(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) )
        | ~ sP10(X0) ) ),
    inference(rectify,[],[f315]) ).

fof(f315,plain,
    ! [X0] :
      ( ( sP10(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) )
        | ~ sP10(X0) ) ),
    inference(nnf_transformation,[],[f239]) ).

fof(f239,plain,
    ! [X0] :
      ( sP10(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,[sP10])]) ).

fof(f2622,plain,
    spl71_246,
    inference(avatar_split_clause,[],[f623,f2620]) ).

fof(f2620,plain,
    ( spl71_246
  <=> ! [X10,X9,X7,X6,X8] :
        ( leq(X7,X6)
        | leq(X6,X7)
        | ~ ssList(X10)
        | ~ ssList(X9)
        | ~ ssList(X8)
        | ~ ssItem(X7)
        | ~ ssItem(X6)
        | ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_246])]) ).

fof(f623,plain,
    ! [X10,X8,X6,X9,X7] :
      ( leq(X7,X6)
      | leq(X6,X7)
      | ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X6)
      | ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f499]) ).

fof(f499,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)
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f313,plain,
    ! [X0] :
      ( ( sP8(X0)
        | ( ~ leq(sK39(X0),sK38(X0))
          & ~ leq(sK38(X0),sK39(X0))
          & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
          & ssList(sK42(X0))
          & ssList(sK41(X0))
          & ssList(sK40(X0))
          & ssItem(sK39(X0))
          & ssItem(sK38(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) )
        | ~ sP8(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40,sK41,sK42])],[f307,f312,f311,f310,f309,f308]) ).

fof(f308,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,sK38(X0))
                        & ~ leq(sK38(X0),X2)
                        & app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK38(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f309,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ leq(X2,sK38(X0))
                      & ~ leq(sK38(X0),X2)
                      & app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ leq(sK39(X0),sK38(X0))
                    & ~ leq(sK38(X0),sK39(X0))
                    & app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK39(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f310,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ leq(sK39(X0),sK38(X0))
                  & ~ leq(sK38(X0),sK39(X0))
                  & app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ leq(sK39(X0),sK38(X0))
                & ~ leq(sK38(X0),sK39(X0))
                & app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK40(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f311,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ leq(sK39(X0),sK38(X0))
              & ~ leq(sK38(X0),sK39(X0))
              & app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ leq(sK39(X0),sK38(X0))
            & ~ leq(sK38(X0),sK39(X0))
            & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK41(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f312,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ leq(sK39(X0),sK38(X0))
          & ~ leq(sK38(X0),sK39(X0))
          & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ leq(sK39(X0),sK38(X0))
        & ~ leq(sK38(X0),sK39(X0))
        & app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
        & ssList(sK42(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f307,plain,
    ! [X0] :
      ( ( sP8(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) )
        | ~ sP8(X0) ) ),
    inference(rectify,[],[f306]) ).

fof(f306,plain,
    ! [X0] :
      ( ( sP8(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) )
        | ~ sP8(X0) ) ),
    inference(nnf_transformation,[],[f236]) ).

fof(f236,plain,
    ! [X0] :
      ( sP8(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,[sP8])]) ).

fof(f2614,plain,
    spl71_245,
    inference(avatar_split_clause,[],[f627,f2612]) ).

fof(f2612,plain,
    ( spl71_245
  <=> ! [X10,X9,X7,X6,X8] :
        ( leq(X6,X7)
        | ~ ssList(X10)
        | ~ ssList(X9)
        | ~ ssList(X8)
        | ~ ssItem(X7)
        | ~ ssItem(X6)
        | ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_245])]) ).

fof(f627,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,[],[f546]) ).

fof(f546,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,[],[f349]) ).

fof(f349,plain,
    ! [X0] :
      ( ( sP16(X0)
        | ( ~ leq(sK58(X0),sK59(X0))
          & app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
          & ssList(sK62(X0))
          & ssList(sK61(X0))
          & ssList(sK60(X0))
          & ssItem(sK59(X0))
          & ssItem(sK58(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,[sK58,sK59,sK60,sK61,sK62])],[f343,f348,f347,f346,f345,f344]) ).

fof(f344,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(sK58(X0),X2)
                        & app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK58(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ leq(sK58(X0),X2)
                      & app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ leq(sK58(X0),sK59(X0))
                    & app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK59(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ leq(sK58(X0),sK59(X0))
                  & app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ leq(sK58(X0),sK59(X0))
                & app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK60(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ leq(sK58(X0),sK59(X0))
              & app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ leq(sK58(X0),sK59(X0))
            & app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK61(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ leq(sK58(X0),sK59(X0))
          & app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ leq(sK58(X0),sK59(X0))
        & app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
        & ssList(sK62(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f343,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,[],[f342]) ).

fof(f342,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,[],[f248]) ).

fof(f248,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(f2610,plain,
    spl71_244,
    inference(avatar_split_clause,[],[f626,f2608]) ).

fof(f2608,plain,
    ( spl71_244
  <=> ! [X10,X9,X7,X6,X8] :
        ( lt(X6,X7)
        | ~ ssList(X10)
        | ~ ssList(X9)
        | ~ ssList(X8)
        | ~ ssItem(X7)
        | ~ ssItem(X6)
        | ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_244])]) ).

fof(f626,plain,
    ! [X10,X8,X6,X9,X7] :
      ( lt(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,[],[f535]) ).

fof(f535,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)
      | ~ sP14(X0) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f340,plain,
    ! [X0] :
      ( ( sP14(X0)
        | ( ~ lt(sK53(X0),sK54(X0))
          & app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
          & ssList(sK57(X0))
          & ssList(sK56(X0))
          & ssList(sK55(X0))
          & ssItem(sK54(X0))
          & ssItem(sK53(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) )
        | ~ sP14(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f334,f339,f338,f337,f336,f335]) ).

fof(f335,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(sK53(X0),X2)
                        & app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK53(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ~ lt(sK53(X0),X2)
                      & app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ~ lt(sK53(X0),sK54(X0))
                    & app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK54(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f337,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ~ lt(sK53(X0),sK54(X0))
                  & app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( ~ lt(sK53(X0),sK54(X0))
                & app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK55(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f338,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( ~ lt(sK53(X0),sK54(X0))
              & app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( ~ lt(sK53(X0),sK54(X0))
            & app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK56(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f339,plain,
    ! [X0] :
      ( ? [X5] :
          ( ~ lt(sK53(X0),sK54(X0))
          & app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
          & ssList(X5) )
     => ( ~ lt(sK53(X0),sK54(X0))
        & app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
        & ssList(sK57(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ! [X0] :
      ( ( sP14(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) )
        | ~ sP14(X0) ) ),
    inference(rectify,[],[f333]) ).

fof(f333,plain,
    ! [X0] :
      ( ( sP14(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) )
        | ~ sP14(X0) ) ),
    inference(nnf_transformation,[],[f245]) ).

fof(f245,plain,
    ! [X0] :
      ( sP14(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,[sP14])]) ).

fof(f2606,plain,
    spl71_243,
    inference(avatar_split_clause,[],[f574,f2604]) ).

fof(f2604,plain,
    ( spl71_243
  <=> ! [X0,X1] :
        ( X0 = X1
        | tl(X0) != tl(X1)
        | hd(X0) != hd(X1)
        | nil = X0
        | nil = X1
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_243])]) ).

fof(f574,plain,
    ! [X0,X1] :
      ( X0 = X1
      | tl(X0) != tl(X1)
      | hd(X0) != hd(X1)
      | nil = X0
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f192]) ).

fof(f192,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | tl(X0) != tl(X1)
          | hd(X0) != hd(X1)
          | nil = X0
          | nil = X1
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[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(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/sandbox/benchmark/theBenchmark.p',ax77) ).

fof(f2587,plain,
    spl71_242,
    inference(avatar_split_clause,[],[f635,f2585]) ).

fof(f635,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,[],[f589]) ).

fof(f589,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,[],[f371]) ).

fof(f371,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
                & ssList(sK68(X0,X1))
                & ssList(sK67(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f368,f370,f369]) ).

fof(f369,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK67(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK67(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f370,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK67(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
        & ssList(sK68(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f368,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,[],[f367]) ).

fof(f367,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,[],[f202]) ).

fof(f202,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/sandbox/benchmark/theBenchmark.p',ax7) ).

fof(f2583,plain,
    spl71_241,
    inference(avatar_split_clause,[],[f631,f2581]) ).

fof(f2581,plain,
    ( spl71_241
  <=> ! [X2,X1,X3] :
        ( memberP(app(X2,cons(X1,X3)),X1)
        | ~ ssList(X3)
        | ~ ssList(X2)
        | ~ ssItem(X1)
        | ~ ssList(app(X2,cons(X1,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_241])]) ).

fof(f631,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,[],[f570]) ).

fof(f570,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,[],[f357]) ).

fof(f357,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
                & ssList(sK64(X0,X1))
                & ssList(sK63(X0,X1)) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f354,f356,f355]) ).

fof(f355,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X4,cons(X1,X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(sK63(X0,X1),cons(X1,X5)) = X0
            & ssList(X5) )
        & ssList(sK63(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f356,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(sK63(X0,X1),cons(X1,X5)) = X0
          & ssList(X5) )
     => ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
        & ssList(sK64(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f354,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,[],[f353]) ).

fof(f353,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,[],[f185]) ).

fof(f185,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/sandbox/benchmark/theBenchmark.p',ax3) ).

fof(f2579,plain,
    spl71_240,
    inference(avatar_split_clause,[],[f620,f2577]) ).

fof(f2577,plain,
    ( spl71_240
  <=> ! [X5,X7,X6,X8] :
        ( X5 = X6
        | ~ ssList(X8)
        | ~ ssList(X7)
        | ~ ssItem(X6)
        | ~ ssItem(X5)
        | ~ sP4(app(X7,cons(X5,cons(X6,X8)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_240])]) ).

fof(f620,plain,
    ! [X8,X6,X7,X5] :
      ( X5 = X6
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6)
      | ~ ssItem(X5)
      | ~ sP4(app(X7,cons(X5,cons(X6,X8)))) ),
    inference(equality_resolution,[],[f478]) ).

fof(f478,plain,
    ! [X0,X8,X6,X7,X5] :
      ( X5 = X6
      | app(X7,cons(X5,cons(X6,X8))) != X0
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6)
      | ~ ssItem(X5)
      | ~ sP4(X0) ),
    inference(cnf_transformation,[],[f295]) ).

fof(f295,plain,
    ! [X0] :
      ( ( sP4(X0)
        | ( sK29(X0) != sK30(X0)
          & app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
          & ssList(sK32(X0))
          & ssList(sK31(X0))
          & ssItem(sK30(X0))
          & ssItem(sK29(X0)) ) )
      & ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( X5 = X6
                        | app(X7,cons(X5,cons(X6,X8))) != X0
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            | ~ ssItem(X5) )
        | ~ sP4(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f290,f294,f293,f292,f291]) ).

fof(f291,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] :
                    ( sK29(X0) != X2
                    & app(X3,cons(sK29(X0),cons(X2,X4))) = X0
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK29(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f292,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( sK29(X0) != X2
                  & app(X3,cons(sK29(X0),cons(X2,X4))) = X0
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( sK29(X0) != sK30(X0)
                & app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK30(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f293,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( sK29(X0) != sK30(X0)
              & app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( sK29(X0) != sK30(X0)
            & app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
            & ssList(X4) )
        & ssList(sK31(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f294,plain,
    ! [X0] :
      ( ? [X4] :
          ( sK29(X0) != sK30(X0)
          & app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
          & ssList(X4) )
     => ( sK29(X0) != sK30(X0)
        & app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
        & ssList(sK32(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f290,plain,
    ! [X0] :
      ( ( sP4(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) )
        | ~ sP4(X0) ) ),
    inference(rectify,[],[f289]) ).

fof(f289,plain,
    ! [X0] :
      ( ( sP4(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) )
        | ~ sP4(X0) ) ),
    inference(nnf_transformation,[],[f230]) ).

fof(f230,plain,
    ! [X0] :
      ( sP4(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,[sP4])]) ).

fof(f2539,plain,
    spl71_239,
    inference(avatar_split_clause,[],[f640,f2537]) ).

fof(f2537,plain,
    ( spl71_239
  <=> ! [X10,X7,X9,X8] :
        ( ~ ssList(X10)
        | ~ ssList(X9)
        | ~ ssList(X8)
        | ~ ssItem(X7)
        | ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_239])]) ).

fof(f640,plain,
    ! [X10,X8,X9,X7] :
      ( ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
    inference(duplicate_literal_removal,[],[f622]) ).

fof(f622,plain,
    ! [X10,X8,X9,X7] :
      ( ~ ssList(X10)
      | ~ ssList(X9)
      | ~ ssList(X8)
      | ~ ssItem(X7)
      | ~ ssItem(X7)
      | ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
    inference(equality_resolution,[],[f621]) ).

fof(f621,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)
      | ~ sP6(X0) ),
    inference(equality_resolution,[],[f488]) ).

fof(f488,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)
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f304,plain,
    ! [X0] :
      ( ( sP6(X0)
        | ( sK33(X0) = sK34(X0)
          & app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
          & ssList(sK37(X0))
          & ssList(sK36(X0))
          & ssList(sK35(X0))
          & ssItem(sK34(X0))
          & ssItem(sK33(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) )
        | ~ sP6(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36,sK37])],[f298,f303,f302,f301,f300,f299]) ).

fof(f299,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] :
                        ( sK33(X0) = X2
                        & app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
                        & ssList(X5) )
                    & ssList(X4) )
                & ssList(X3) )
            & ssItem(X2) )
        & ssItem(sK33(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f300,plain,
    ! [X0] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( sK33(X0) = X2
                      & app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( sK33(X0) = sK34(X0)
                    & app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
                    & ssList(X5) )
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK34(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f301,plain,
    ! [X0] :
      ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( sK33(X0) = sK34(X0)
                  & app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
                  & ssList(X5) )
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ? [X5] :
                ( sK33(X0) = sK34(X0)
                & app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
                & ssList(X5) )
            & ssList(X4) )
        & ssList(sK35(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f302,plain,
    ! [X0] :
      ( ? [X4] :
          ( ? [X5] :
              ( sK33(X0) = sK34(X0)
              & app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( sK33(X0) = sK34(X0)
            & app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
            & ssList(X5) )
        & ssList(sK36(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f303,plain,
    ! [X0] :
      ( ? [X5] :
          ( sK33(X0) = sK34(X0)
          & app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
          & ssList(X5) )
     => ( sK33(X0) = sK34(X0)
        & app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
        & ssList(sK37(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f298,plain,
    ! [X0] :
      ( ( sP6(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) )
        | ~ sP6(X0) ) ),
    inference(rectify,[],[f297]) ).

fof(f297,plain,
    ! [X0] :
      ( ( sP6(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) )
        | ~ sP6(X0) ) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f233,plain,
    ! [X0] :
      ( sP6(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,[sP6])]) ).

fof(f2533,plain,
    spl71_238,
    inference(avatar_split_clause,[],[f604,f2531]) ).

fof(f2531,plain,
    ( spl71_238
  <=> ! [X0,X3,X2,X1] :
        ( segmentP(app(app(X2,X0),X3),X1)
        | ~ segmentP(X0,X1)
        | ~ ssList(X3)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_238])]) ).

fof(f604,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,[],[f223]) ).

fof(f223,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,[],[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(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/sandbox/benchmark/theBenchmark.p',ax56) ).

fof(f2529,plain,
    spl71_237,
    inference(avatar_split_clause,[],[f595,f2527]) ).

fof(f2527,plain,
    ( spl71_237
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | cons(X2,X0) != cons(X3,X1)
        | ~ ssItem(X3)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_237])]) ).

fof(f595,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | cons(X2,X0) != cons(X3,X1)
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f206]) ).

fof(f206,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,[],[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(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/sandbox/benchmark/theBenchmark.p',ax19) ).

fof(f2525,plain,
    spl71_236,
    inference(avatar_split_clause,[],[f594,f2523]) ).

fof(f2523,plain,
    ( spl71_236
  <=> ! [X0,X3,X2,X1] :
        ( X2 = X3
        | cons(X2,X0) != cons(X3,X1)
        | ~ ssItem(X3)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_236])]) ).

fof(f594,plain,
    ! [X2,X3,X0,X1] :
      ( X2 = X3
      | cons(X2,X0) != cons(X3,X1)
      | ~ ssItem(X3)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f206]) ).

fof(f2521,plain,
    spl71_235,
    inference(avatar_split_clause,[],[f588,f2519]) ).

fof(f2519,plain,
    ( spl71_235
  <=> ! [X0,X1] :
        ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
        | ~ segmentP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_235])]) ).

fof(f588,plain,
    ! [X0,X1] :
      ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f371]) ).

fof(f2517,plain,
    spl71_234,
    inference(avatar_split_clause,[],[f569,f2515]) ).

fof(f2515,plain,
    ( spl71_234
  <=> ! [X0,X1] :
        ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
        | ~ memberP(X0,X1)
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_234])]) ).

fof(f569,plain,
    ! [X0,X1] :
      ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
      | ~ memberP(X0,X1)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f357]) ).

fof(f2513,plain,
    spl71_233,
    inference(avatar_split_clause,[],[f552,f2511]) ).

fof(f2511,plain,
    ( spl71_233
  <=> ! [X0] :
        ( sP16(X0)
        | app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_233])]) ).

fof(f552,plain,
    ! [X0] :
      ( sP16(X0)
      | app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f2509,plain,
    spl71_232,
    inference(avatar_split_clause,[],[f541,f2507]) ).

fof(f2507,plain,
    ( spl71_232
  <=> ! [X0] :
        ( sP14(X0)
        | app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_232])]) ).

fof(f541,plain,
    ! [X0] :
      ( sP14(X0)
      | app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ),
    inference(cnf_transformation,[],[f340]) ).

fof(f2505,plain,
    spl71_231,
    inference(avatar_split_clause,[],[f529,f2503]) ).

fof(f2503,plain,
    ( spl71_231
  <=> ! [X0] :
        ( sP12(X0)
        | app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_231])]) ).

fof(f529,plain,
    ! [X0] :
      ( sP12(X0)
      | app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ),
    inference(cnf_transformation,[],[f331]) ).

fof(f2501,plain,
    spl71_230,
    inference(avatar_split_clause,[],[f517,f2499]) ).

fof(f2499,plain,
    ( spl71_230
  <=> ! [X0] :
        ( sP10(X0)
        | app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_230])]) ).

fof(f517,plain,
    ! [X0] :
      ( sP10(X0)
      | app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ),
    inference(cnf_transformation,[],[f322]) ).

fof(f2497,plain,
    spl71_229,
    inference(avatar_split_clause,[],[f505,f2495]) ).

fof(f2495,plain,
    ( spl71_229
  <=> ! [X0] :
        ( sP8(X0)
        | app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_229])]) ).

fof(f505,plain,
    ! [X0] :
      ( sP8(X0)
      | app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ),
    inference(cnf_transformation,[],[f313]) ).

fof(f2491,plain,
    spl71_228,
    inference(avatar_split_clause,[],[f494,f2489]) ).

fof(f2489,plain,
    ( spl71_228
  <=> ! [X0] :
        ( sP6(X0)
        | app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_228])]) ).

fof(f494,plain,
    ! [X0] :
      ( sP6(X0)
      | app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ),
    inference(cnf_transformation,[],[f304]) ).

fof(f2487,plain,
    spl71_227,
    inference(avatar_split_clause,[],[f434,f2485]) ).

fof(f2485,plain,
    ( spl71_227
  <=> ! [X0,X3,X2,X1] :
        ( frontsegP(X2,X3)
        | ~ frontsegP(cons(X0,X2),cons(X1,X3))
        | ~ ssList(X3)
        | ~ ssList(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_227])]) ).

fof(f434,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,[],[f266]) ).

fof(f266,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,[],[f265]) ).

fof(f265,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,[],[f137]) ).

fof(f137,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/sandbox/benchmark/theBenchmark.p',ax44) ).

fof(f2483,plain,
    spl71_226,
    inference(avatar_split_clause,[],[f433,f2481]) ).

fof(f2481,plain,
    ( spl71_226
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | ~ frontsegP(cons(X0,X2),cons(X1,X3))
        | ~ ssList(X3)
        | ~ ssList(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_226])]) ).

fof(f433,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,[],[f266]) ).

fof(f2398,plain,
    spl71_225,
    inference(avatar_split_clause,[],[f596,f2396]) ).

fof(f2396,plain,
    ( spl71_225
  <=> ! [X2,X0,X1] :
        ( app(app(X0,X1),X2) = app(X0,app(X1,X2))
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_225])]) ).

fof(f596,plain,
    ! [X2,X0,X1] :
      ( app(app(X0,X1),X2) = app(X0,app(X1,X2))
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f207]) ).

fof(f207,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/sandbox/benchmark/theBenchmark.p',ax82) ).

fof(f2394,plain,
    spl71_224,
    inference(avatar_split_clause,[],[f593,f2392]) ).

fof(f2392,plain,
    ( spl71_224
  <=> ! [X2,X0,X1] :
        ( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
        | ~ ssItem(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_224])]) ).

fof(f593,plain,
    ! [X2,X0,X1] :
      ( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
      | ~ ssItem(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f204]) ).

fof(f204,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/sandbox/benchmark/theBenchmark.p',ax27) ).

fof(f2390,plain,
    spl71_223,
    inference(avatar_split_clause,[],[f452,f2388]) ).

fof(f2388,plain,
    ( spl71_223
  <=> ! [X2,X0,X1] :
        ( memberP(X2,X0)
        | memberP(X1,X0)
        | ~ memberP(app(X1,X2),X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_223])]) ).

fof(f452,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | memberP(X1,X0)
      | ~ memberP(app(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f276,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,[],[f275]) ).

fof(f275,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,[],[f140]) ).

fof(f140,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/sandbox/benchmark/theBenchmark.p',ax36) ).

fof(f2384,plain,
    spl71_222,
    inference(avatar_split_clause,[],[f430,f2382]) ).

fof(f2382,plain,
    ( spl71_222
  <=> ! [X2,X0,X1] :
        ( memberP(X2,X0)
        | X0 = X1
        | ~ memberP(cons(X1,X2),X0)
        | ~ ssList(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_222])]) ).

fof(f430,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | X0 = X1
      | ~ memberP(cons(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f264,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,[],[f263]) ).

fof(f263,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,[],[f136]) ).

fof(f136,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/sandbox/benchmark/theBenchmark.p',ax37) ).

fof(f2333,plain,
    spl71_221,
    inference(avatar_split_clause,[],[f641,f2331]) ).

fof(f2331,plain,
    ( spl71_221
  <=> ! [X2,X1,X3] :
        ( frontsegP(cons(X1,X2),cons(X1,X3))
        | ~ frontsegP(X2,X3)
        | ~ ssList(X3)
        | ~ ssList(X2)
        | ~ ssItem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_221])]) ).

fof(f641,plain,
    ! [X2,X3,X1] :
      ( frontsegP(cons(X1,X2),cons(X1,X3))
      | ~ frontsegP(X2,X3)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f614]) ).

fof(f614,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,[],[f435]) ).

fof(f435,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,[],[f266]) ).

fof(f2329,plain,
    spl71_220,
    inference(avatar_split_clause,[],[f600,f2327]) ).

fof(f2327,plain,
    ( spl71_220
  <=> ! [X2,X0,X1] :
        ( X0 = X2
        | app(X1,X2) != app(X1,X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_220])]) ).

fof(f600,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | app(X1,X2) != app(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f215]) ).

fof(f215,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X1,X2) != app(X1,X0)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f214]) ).

fof(f214,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/sandbox/benchmark/theBenchmark.p',ax80) ).

fof(f2325,plain,
    spl71_219,
    inference(avatar_split_clause,[],[f599,f2323]) ).

fof(f2323,plain,
    ( spl71_219
  <=> ! [X2,X0,X1] :
        ( X0 = X2
        | app(X2,X1) != app(X0,X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_219])]) ).

fof(f599,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | app(X2,X1) != app(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f213]) ).

fof(f213,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X2,X1) != app(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f212]) ).

fof(f212,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/sandbox/benchmark/theBenchmark.p',ax79) ).

fof(f2321,plain,
    spl71_218,
    inference(avatar_split_clause,[],[f573,f2319]) ).

fof(f2319,plain,
    ( spl71_218
  <=> ! [X0,X1] :
        ( tl(app(X0,X1)) = app(tl(X0),X1)
        | nil = X0
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_218])]) ).

fof(f573,plain,
    ! [X0,X1] :
      ( tl(app(X0,X1)) = app(tl(X0),X1)
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f190]) ).

fof(f190,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(app(X0,X1)) = app(tl(X0),X1)
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f189]) ).

fof(f189,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/sandbox/benchmark/theBenchmark.p',ax86) ).

fof(f2286,plain,
    spl71_217,
    inference(avatar_split_clause,[],[f603,f2284]) ).

fof(f2284,plain,
    ( spl71_217
  <=> ! [X2,X0,X1] :
        ( segmentP(X0,X2)
        | ~ segmentP(X1,X2)
        | ~ segmentP(X0,X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_217])]) ).

fof(f603,plain,
    ! [X2,X0,X1] :
      ( segmentP(X0,X2)
      | ~ segmentP(X1,X2)
      | ~ segmentP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f221]) ).

fof(f221,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( segmentP(X0,X2)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f220]) ).

fof(f220,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/sandbox/benchmark/theBenchmark.p',ax53) ).

fof(f2282,plain,
    spl71_216,
    inference(avatar_split_clause,[],[f602,f2280]) ).

fof(f2280,plain,
    ( spl71_216
  <=> ! [X2,X0,X1] :
        ( frontsegP(X0,X2)
        | ~ frontsegP(X1,X2)
        | ~ frontsegP(X0,X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_216])]) ).

fof(f602,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X2)
      | ~ frontsegP(X1,X2)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f219]) ).

fof(f219,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( frontsegP(X0,X2)
              | ~ frontsegP(X1,X2)
              | ~ frontsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f218]) ).

fof(f218,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/sandbox/benchmark/theBenchmark.p',ax40) ).

fof(f2276,plain,
    spl71_215,
    inference(avatar_split_clause,[],[f601,f2274]) ).

fof(f2274,plain,
    ( spl71_215
  <=> ! [X2,X0,X1] :
        ( rearsegP(X0,X2)
        | ~ rearsegP(X1,X2)
        | ~ rearsegP(X0,X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_215])]) ).

fof(f601,plain,
    ! [X2,X0,X1] :
      ( rearsegP(X0,X2)
      | ~ rearsegP(X1,X2)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f217]) ).

fof(f217,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(X0,X2)
              | ~ rearsegP(X1,X2)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f216]) ).

fof(f216,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/sandbox/benchmark/theBenchmark.p',ax47) ).

fof(f2272,plain,
    spl71_214,
    inference(avatar_split_clause,[],[f483,f2270]) ).

fof(f2270,plain,
    ( spl71_214
  <=> ! [X0] :
        ( sP4(X0)
        | app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_214])]) ).

fof(f483,plain,
    ! [X0] :
      ( sP4(X0)
      | app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ),
    inference(cnf_transformation,[],[f295]) ).

fof(f2268,plain,
    spl71_213,
    inference(avatar_split_clause,[],[f429,f2266]) ).

fof(f2266,plain,
    ( spl71_213
  <=> ! [X2,X0,X1] :
        ( lt(X0,X2)
        | ~ lt(X1,X2)
        | ~ lt(X0,X1)
        | ~ ssItem(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_213])]) ).

fof(f429,plain,
    ! [X2,X0,X1] :
      ( lt(X0,X2)
      | ~ lt(X1,X2)
      | ~ lt(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ lt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f134]) ).

fof(f134,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/sandbox/benchmark/theBenchmark.p',ax34) ).

fof(f2264,plain,
    spl71_212,
    inference(avatar_split_clause,[],[f428,f2262]) ).

fof(f2262,plain,
    ( spl71_212
  <=> ! [X2,X0,X1] :
        ( lt(X0,X2)
        | ~ lt(X1,X2)
        | ~ leq(X0,X1)
        | ~ ssItem(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_212])]) ).

fof(f428,plain,
    ! [X2,X0,X1] :
      ( lt(X0,X2)
      | ~ lt(X1,X2)
      | ~ leq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( lt(X0,X2)
              | ~ lt(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f132]) ).

fof(f132,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/sandbox/benchmark/theBenchmark.p',ax91) ).

fof(f2260,plain,
    spl71_211,
    inference(avatar_split_clause,[],[f427,f2258]) ).

fof(f2258,plain,
    ( spl71_211
  <=> ! [X2,X0,X1] :
        ( leq(X0,X2)
        | ~ leq(X1,X2)
        | ~ leq(X0,X1)
        | ~ ssItem(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_211])]) ).

fof(f427,plain,
    ! [X2,X0,X1] :
      ( leq(X0,X2)
      | ~ leq(X1,X2)
      | ~ leq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f131,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( leq(X0,X2)
              | ~ leq(X1,X2)
              | ~ leq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f130]) ).

fof(f130,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/sandbox/benchmark/theBenchmark.p',ax30) ).

fof(f2256,plain,
    spl71_210,
    inference(avatar_split_clause,[],[f426,f2254]) ).

fof(f2254,plain,
    ( spl71_210
  <=> ! [X2,X0,X1] :
        ( geq(X0,X2)
        | ~ geq(X1,X2)
        | ~ geq(X0,X1)
        | ~ ssItem(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_210])]) ).

fof(f426,plain,
    ! [X2,X0,X1] :
      ( geq(X0,X2)
      | ~ geq(X1,X2)
      | ~ geq(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( geq(X0,X2)
              | ~ geq(X1,X2)
              | ~ geq(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f128]) ).

fof(f128,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/sandbox/benchmark/theBenchmark.p',ax88) ).

fof(f2252,plain,
    spl71_209,
    inference(avatar_split_clause,[],[f425,f2250]) ).

fof(f2250,plain,
    ( spl71_209
  <=> ! [X2,X0,X1] :
        ( gt(X0,X2)
        | ~ gt(X1,X2)
        | ~ gt(X0,X1)
        | ~ ssItem(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_209])]) ).

fof(f425,plain,
    ! [X2,X0,X1] :
      ( gt(X0,X2)
      | ~ gt(X1,X2)
      | ~ gt(X0,X1)
      | ~ ssItem(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( gt(X0,X2)
              | ~ gt(X1,X2)
              | ~ gt(X0,X1)
              | ~ ssItem(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f126]) ).

fof(f126,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/sandbox/benchmark/theBenchmark.p',ax95) ).

fof(f2186,plain,
    spl71_208,
    inference(avatar_split_clause,[],[f598,f2184]) ).

fof(f2184,plain,
    ( spl71_208
  <=> ! [X2,X0,X1] :
        ( frontsegP(app(X0,X2),X1)
        | ~ frontsegP(X0,X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_208])]) ).

fof(f598,plain,
    ! [X2,X0,X1] :
      ( frontsegP(app(X0,X2),X1)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f211]) ).

fof(f211,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( frontsegP(app(X0,X2),X1)
              | ~ frontsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f210]) ).

fof(f210,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/sandbox/benchmark/theBenchmark.p',ax43) ).

fof(f2182,plain,
    spl71_207,
    inference(avatar_split_clause,[],[f597,f2180]) ).

fof(f2180,plain,
    ( spl71_207
  <=> ! [X2,X0,X1] :
        ( rearsegP(app(X2,X0),X1)
        | ~ rearsegP(X0,X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_207])]) ).

fof(f597,plain,
    ! [X2,X0,X1] :
      ( rearsegP(app(X2,X0),X1)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f209]) ).

fof(f209,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( rearsegP(app(X2,X0),X1)
              | ~ rearsegP(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f208]) ).

fof(f208,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/sandbox/benchmark/theBenchmark.p',ax50) ).

fof(f2178,plain,
    spl71_206,
    inference(avatar_split_clause,[],[f584,f2176]) ).

fof(f2176,plain,
    ( spl71_206
  <=> ! [X0,X1] :
        ( app(X1,sK66(X0,X1)) = X0
        | ~ frontsegP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_206])]) ).

fof(f584,plain,
    ! [X0,X1] :
      ( app(X1,sK66(X0,X1)) = X0
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f366]) ).

fof(f366,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK66(X0,X1)) = X0
                & ssList(sK66(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f364,f365]) ).

fof(f365,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK66(X0,X1)) = X0
        & ssList(sK66(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f364,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,[],[f363]) ).

fof(f363,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/sandbox/benchmark/theBenchmark.p',ax5) ).

fof(f2174,plain,
    spl71_205,
    inference(avatar_split_clause,[],[f581,f2172]) ).

fof(f2172,plain,
    ( spl71_205
  <=> ! [X0,X1] :
        ( app(sK65(X0,X1),X1) = X0
        | ~ rearsegP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_205])]) ).

fof(f581,plain,
    ! [X0,X1] :
      ( app(sK65(X0,X1),X1) = X0
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f362]) ).

fof(f362,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(sK65(X0,X1),X1) = X0
                & ssList(sK65(X0,X1)) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f360,f361]) ).

fof(f361,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X3,X1) = X0
          & ssList(X3) )
     => ( app(sK65(X0,X1),X1) = X0
        & ssList(sK65(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f360,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,[],[f359]) ).

fof(f359,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,[],[f200]) ).

fof(f200,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/sandbox/benchmark/theBenchmark.p',ax6) ).

fof(f2170,plain,
    spl71_204,
    inference(avatar_split_clause,[],[f572,f2168]) ).

fof(f2168,plain,
    ( spl71_204
  <=> ! [X0,X1] :
        ( hd(X0) = hd(app(X0,X1))
        | nil = X0
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_204])]) ).

fof(f572,plain,
    ! [X0,X1] :
      ( hd(X0) = hd(app(X0,X1))
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f188]) ).

fof(f188,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f187]) ).

fof(f187,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/sandbox/benchmark/theBenchmark.p',ax85) ).

fof(f2164,plain,
    spl71_203,
    inference(avatar_split_clause,[],[f454,f2162]) ).

fof(f2162,plain,
    ( spl71_203
  <=> ! [X2,X0,X1] :
        ( memberP(app(X1,X2),X0)
        | ~ memberP(X2,X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_203])]) ).

fof(f454,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f2160,plain,
    spl71_202,
    inference(avatar_split_clause,[],[f453,f2158]) ).

fof(f2158,plain,
    ( spl71_202
  <=> ! [X2,X0,X1] :
        ( memberP(app(X1,X2),X0)
        | ~ memberP(X1,X0)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_202])]) ).

fof(f453,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X1,X0)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f276]) ).

fof(f2156,plain,
    spl71_201,
    inference(avatar_split_clause,[],[f432,f2154]) ).

fof(f2154,plain,
    ( spl71_201
  <=> ! [X2,X0,X1] :
        ( memberP(cons(X1,X2),X0)
        | ~ memberP(X2,X0)
        | ~ ssList(X2)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_201])]) ).

fof(f432,plain,
    ! [X2,X0,X1] :
      ( memberP(cons(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f2093,plain,
    ( spl71_200
    | ~ spl71_4
    | ~ spl71_30 ),
    inference(avatar_split_clause,[],[f825,f783,f662,f2090]) ).

fof(f2090,plain,
    ( spl71_200
  <=> sP17(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_200])]) ).

fof(f825,plain,
    ( sP17(sK23)
    | ~ spl71_4
    | ~ spl71_30 ),
    inference(resolution,[],[f784,f664]) ).

fof(f2081,plain,
    spl71_199,
    inference(avatar_split_clause,[],[f634,f2079]) ).

fof(f2079,plain,
    ( spl71_199
  <=> ! [X2,X1] :
        ( frontsegP(app(X1,X2),X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(app(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_199])]) ).

fof(f634,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f585]) ).

fof(f585,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f366]) ).

fof(f2077,plain,
    spl71_198,
    inference(avatar_split_clause,[],[f633,f2075]) ).

fof(f2075,plain,
    ( spl71_198
  <=> ! [X2,X1] :
        ( rearsegP(app(X2,X1),X1)
        | ~ ssList(X2)
        | ~ ssList(X1)
        | ~ ssList(app(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_198])]) ).

fof(f633,plain,
    ! [X2,X1] :
      ( rearsegP(app(X2,X1),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X2,X1)) ),
    inference(equality_resolution,[],[f582]) ).

fof(f582,plain,
    ! [X2,X0,X1] :
      ( rearsegP(X0,X1)
      | app(X2,X1) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f362]) ).

fof(f2073,plain,
    spl71_197,
    inference(avatar_split_clause,[],[f577,f2071]) ).

fof(f2071,plain,
    ( spl71_197
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ segmentP(X1,X0)
        | ~ segmentP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_197])]) ).

fof(f577,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ segmentP(X1,X0)
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ segmentP(X1,X0)
          | ~ segmentP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f197]) ).

fof(f197,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/sandbox/benchmark/theBenchmark.p',ax54) ).

fof(f2069,plain,
    spl71_196,
    inference(avatar_split_clause,[],[f576,f2067]) ).

fof(f2067,plain,
    ( spl71_196
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ frontsegP(X1,X0)
        | ~ frontsegP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_196])]) ).

fof(f576,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ frontsegP(X1,X0)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f196]) ).

fof(f196,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f195]) ).

fof(f195,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/sandbox/benchmark/theBenchmark.p',ax41) ).

fof(f2065,plain,
    spl71_195,
    inference(avatar_split_clause,[],[f575,f2063]) ).

fof(f2063,plain,
    ( spl71_195
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ rearsegP(X1,X0)
        | ~ rearsegP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_195])]) ).

fof(f575,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ rearsegP(X1,X0)
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f194,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ rearsegP(X1,X0)
          | ~ rearsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f193]) ).

fof(f193,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/sandbox/benchmark/theBenchmark.p',ax48) ).

fof(f2061,plain,
    spl71_194,
    inference(avatar_split_clause,[],[f566,f2059]) ).

fof(f566,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f184,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/sandbox/benchmark/theBenchmark.p',ax81) ).

fof(f2057,plain,
    spl71_193,
    inference(avatar_split_clause,[],[f415,f2055]) ).

fof(f2055,plain,
    ( spl71_193
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ leq(X1,X0)
        | ~ leq(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_193])]) ).

fof(f415,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ leq(X1,X0)
      | ~ leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ leq(X1,X0)
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f120]) ).

fof(f120,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/sandbox/benchmark/theBenchmark.p',ax29) ).

fof(f2053,plain,
    spl71_192,
    inference(avatar_split_clause,[],[f414,f2051]) ).

fof(f2051,plain,
    ( spl71_192
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ geq(X1,X0)
        | ~ geq(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_192])]) ).

fof(f414,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ geq(X1,X0)
      | ~ geq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ geq(X1,X0)
          | ~ geq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f118]) ).

fof(f118,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/sandbox/benchmark/theBenchmark.p',ax87) ).

fof(f2049,plain,
    ( spl71_191
    | ~ spl71_3
    | ~ spl71_30 ),
    inference(avatar_split_clause,[],[f824,f783,f657,f2046]) ).

fof(f2046,plain,
    ( spl71_191
  <=> sP17(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_191])]) ).

fof(f824,plain,
    ( sP17(sK22)
    | ~ spl71_3
    | ~ spl71_30 ),
    inference(resolution,[],[f784,f659]) ).

fof(f2044,plain,
    spl71_190,
    inference(avatar_split_clause,[],[f412,f2042]) ).

fof(f2042,plain,
    ( spl71_190
  <=> ! [X0,X1] :
        ( lt(X0,X1)
        | X0 = X1
        | ~ leq(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_190])]) ).

fof(f412,plain,
    ! [X0,X1] :
      ( lt(X0,X1)
      | X0 = X1
      | ~ leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( ! [X1] :
          ( lt(X0,X1)
          | X0 = X1
          | ~ leq(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f114]) ).

fof(f114,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/sandbox/benchmark/theBenchmark.p',ax92) ).

fof(f1959,plain,
    spl71_189,
    inference(avatar_split_clause,[],[f591,f1957]) ).

fof(f1957,plain,
    ( spl71_189
  <=> ! [X0,X1] :
        ( nil = X0
        | nil != app(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_189])]) ).

fof(f591,plain,
    ! [X0,X1] :
      ( nil = X0
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f373]) ).

fof(f373,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,[],[f372]) ).

fof(f372,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,[],[f203]) ).

fof(f203,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/sandbox/benchmark/theBenchmark.p',ax83) ).

fof(f1955,plain,
    spl71_188,
    inference(avatar_split_clause,[],[f590,f1953]) ).

fof(f1953,plain,
    ( spl71_188
  <=> ! [X0,X1] :
        ( nil = X1
        | nil != app(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_188])]) ).

fof(f590,plain,
    ! [X0,X1] :
      ( nil = X1
      | nil != app(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f373]) ).

fof(f1951,plain,
    spl71_187,
    inference(avatar_split_clause,[],[f468,f1949]) ).

fof(f468,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f155]) ).

fof(f155,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/sandbox/benchmark/theBenchmark.p',ax78) ).

fof(f1947,plain,
    ( spl71_186
    | ~ spl71_2
    | ~ spl71_30 ),
    inference(avatar_split_clause,[],[f823,f783,f652,f1944]) ).

fof(f1944,plain,
    ( spl71_186
  <=> sP17(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_186])]) ).

fof(f823,plain,
    ( sP17(sK21)
    | ~ spl71_2
    | ~ spl71_30 ),
    inference(resolution,[],[f784,f654]) ).

fof(f1942,plain,
    spl71_185,
    inference(avatar_split_clause,[],[f465,f1940]) ).

fof(f465,plain,
    ! [X0] :
      ( cons(sK25(X0),sK24(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f279]) ).

fof(f279,plain,
    ! [X0] :
      ( ( cons(sK25(X0),sK24(X0)) = X0
        & ssItem(sK25(X0))
        & ssList(sK24(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f150,f278,f277]) ).

fof(f277,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
     => ( ? [X2] :
            ( cons(X2,sK24(X0)) = X0
            & ssItem(X2) )
        & ssList(sK24(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f278,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK24(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK25(X0),sK24(X0)) = X0
        & ssItem(sK25(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f150,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f149]) ).

fof(f149,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/sandbox/benchmark/theBenchmark.p',ax20) ).

fof(f1938,plain,
    spl71_184,
    inference(avatar_split_clause,[],[f450,f1936]) ).

fof(f1936,plain,
    ( spl71_184
  <=> ! [X0,X1] :
        ( sP2(X0,X1)
        | ~ leq(X1,hd(X0))
        | ~ totalorderedP(X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_184])]) ).

fof(f450,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | ~ leq(X1,hd(X0))
      | ~ totalorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f274]) ).

fof(f274,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,[],[f273]) ).

fof(f273,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,[],[f272]) ).

fof(f272,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,[],[f227]) ).

fof(f227,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(f1934,plain,
    spl71_183,
    inference(avatar_split_clause,[],[f442,f1932]) ).

fof(f1932,plain,
    ( spl71_183
  <=> ! [X0,X1] :
        ( sP0(X0,X1)
        | ~ lt(X1,hd(X0))
        | ~ strictorderedP(X0)
        | nil = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_183])]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | ~ lt(X1,hd(X0))
      | ~ strictorderedP(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f270]) ).

fof(f270,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ lt(X1,hd(X0))
            | ~ strictorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( lt(X1,hd(X0))
          & strictorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f269]) ).

fof(f269,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(flattening,[],[f268]) ).

fof(f268,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f224,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f1852,plain,
    spl71_182,
    inference(avatar_split_clause,[],[f587,f1850]) ).

fof(f1850,plain,
    ( spl71_182
  <=> ! [X0,X1] :
        ( ssList(sK68(X0,X1))
        | ~ segmentP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_182])]) ).

fof(f587,plain,
    ! [X0,X1] :
      ( ssList(sK68(X0,X1))
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f371]) ).

fof(f1848,plain,
    ( spl71_181
    | ~ spl71_1
    | ~ spl71_30 ),
    inference(avatar_split_clause,[],[f822,f783,f647,f1845]) ).

fof(f1845,plain,
    ( spl71_181
  <=> sP17(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_181])]) ).

fof(f822,plain,
    ( sP17(sK20)
    | ~ spl71_1
    | ~ spl71_30 ),
    inference(resolution,[],[f784,f649]) ).

fof(f1843,plain,
    spl71_180,
    inference(avatar_split_clause,[],[f586,f1841]) ).

fof(f1841,plain,
    ( spl71_180
  <=> ! [X0,X1] :
        ( ssList(sK67(X0,X1))
        | ~ segmentP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_180])]) ).

fof(f586,plain,
    ! [X0,X1] :
      ( ssList(sK67(X0,X1))
      | ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f371]) ).

fof(f1839,plain,
    spl71_179,
    inference(avatar_split_clause,[],[f583,f1837]) ).

fof(f1837,plain,
    ( spl71_179
  <=> ! [X0,X1] :
        ( ssList(sK66(X0,X1))
        | ~ frontsegP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_179])]) ).

fof(f583,plain,
    ! [X0,X1] :
      ( ssList(sK66(X0,X1))
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f366]) ).

fof(f1835,plain,
    spl71_178,
    inference(avatar_split_clause,[],[f580,f1833]) ).

fof(f1833,plain,
    ( spl71_178
  <=> ! [X0,X1] :
        ( ssList(sK65(X0,X1))
        | ~ rearsegP(X0,X1)
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_178])]) ).

fof(f580,plain,
    ! [X0,X1] :
      ( ssList(sK65(X0,X1))
      | ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f362]) ).

fof(f1831,plain,
    spl71_177,
    inference(avatar_split_clause,[],[f568,f1829]) ).

fof(f1829,plain,
    ( spl71_177
  <=> ! [X0,X1] :
        ( ssList(sK64(X0,X1))
        | ~ memberP(X0,X1)
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_177])]) ).

fof(f568,plain,
    ! [X0,X1] :
      ( ssList(sK64(X0,X1))
      | ~ memberP(X0,X1)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f357]) ).

fof(f1827,plain,
    spl71_176,
    inference(avatar_split_clause,[],[f567,f1825]) ).

fof(f1825,plain,
    ( spl71_176
  <=> ! [X0,X1] :
        ( ssList(sK63(X0,X1))
        | ~ memberP(X0,X1)
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_176])]) ).

fof(f567,plain,
    ! [X0,X1] :
      ( ssList(sK63(X0,X1))
      | ~ memberP(X0,X1)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f357]) ).

fof(f1757,plain,
    ( spl71_175
    | ~ spl71_4
    | ~ spl71_29 ),
    inference(avatar_split_clause,[],[f820,f779,f662,f1754]) ).

fof(f1754,plain,
    ( spl71_175
  <=> sP15(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_175])]) ).

fof(f820,plain,
    ( sP15(sK23)
    | ~ spl71_4
    | ~ spl71_29 ),
    inference(resolution,[],[f780,f664]) ).

fof(f1677,plain,
    ( spl71_174
    | ~ spl71_3
    | ~ spl71_29 ),
    inference(avatar_split_clause,[],[f819,f779,f657,f1674]) ).

fof(f1674,plain,
    ( spl71_174
  <=> sP15(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_174])]) ).

fof(f819,plain,
    ( sP15(sK22)
    | ~ spl71_3
    | ~ spl71_29 ),
    inference(resolution,[],[f780,f659]) ).

fof(f1666,plain,
    spl71_173,
    inference(avatar_split_clause,[],[f619,f1664]) ).

fof(f1664,plain,
    ( spl71_173
  <=> ! [X1] :
        ( singletonP(cons(X1,nil))
        | ~ ssItem(X1)
        | ~ ssList(cons(X1,nil)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_173])]) ).

fof(f619,plain,
    ! [X1] :
      ( singletonP(cons(X1,nil))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,nil)) ),
    inference(equality_resolution,[],[f475]) ).

fof(f475,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f287]) ).

fof(f287,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK28(X0),nil) = X0
            & ssItem(sK28(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f285,f286]) ).

fof(f286,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK28(X0),nil) = X0
        & ssItem(sK28(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f285,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f284]) ).

fof(f284,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,[],[f161]) ).

fof(f161,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/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f1662,plain,
    spl71_172,
    inference(avatar_split_clause,[],[f579,f1660]) ).

fof(f1660,plain,
    ( spl71_172
  <=> ! [X0,X1] :
        ( neq(X0,X1)
        | X0 = X1
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_172])]) ).

fof(f579,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f358]) ).

fof(f358,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f199]) ).

fof(f199,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/sandbox/benchmark/theBenchmark.p',ax15) ).

fof(f1658,plain,
    spl71_171,
    inference(avatar_split_clause,[],[f565,f1656]) ).

fof(f565,plain,
    ! [X0,X1] :
      ( hd(cons(X1,X0)) = X1
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,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/sandbox/benchmark/theBenchmark.p',ax23) ).

fof(f1654,plain,
    spl71_170,
    inference(avatar_split_clause,[],[f564,f1652]) ).

fof(f564,plain,
    ! [X0,X1] :
      ( tl(cons(X1,X0)) = X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f182]) ).

fof(f182,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/sandbox/benchmark/theBenchmark.p',ax25) ).

fof(f1650,plain,
    ( spl71_169
    | ~ spl71_2
    | ~ spl71_29 ),
    inference(avatar_split_clause,[],[f818,f779,f652,f1647]) ).

fof(f1647,plain,
    ( spl71_169
  <=> sP15(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_169])]) ).

fof(f818,plain,
    ( sP15(sK21)
    | ~ spl71_2
    | ~ spl71_29 ),
    inference(resolution,[],[f780,f654]) ).

fof(f1645,plain,
    spl71_168,
    inference(avatar_split_clause,[],[f474,f1643]) ).

fof(f1643,plain,
    ( spl71_168
  <=> ! [X0] :
        ( cons(sK28(X0),nil) = X0
        | ~ singletonP(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_168])]) ).

fof(f474,plain,
    ! [X0] :
      ( cons(sK28(X0),nil) = X0
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f287]) ).

fof(f1641,plain,
    spl71_167,
    inference(avatar_split_clause,[],[f472,f1639]) ).

fof(f472,plain,
    ! [X0] :
      ( tl(X0) = sK27(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f283]) ).

fof(f283,plain,
    ! [X0] :
      ( ( tl(X0) = sK27(X0)
        & ssList(sK27(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f160,f282]) ).

fof(f282,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK27(X0)
        & ssList(sK27(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f159]) ).

fof(f159,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/sandbox/benchmark/theBenchmark.p',ax76) ).

fof(f1637,plain,
    spl71_166,
    inference(avatar_split_clause,[],[f470,f1635]) ).

fof(f470,plain,
    ! [X0] :
      ( hd(X0) = sK26(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f281]) ).

fof(f281,plain,
    ! [X0] :
      ( ( hd(X0) = sK26(X0)
        & ssItem(sK26(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f158,f280]) ).

fof(f280,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK26(X0)
        & ssItem(sK26(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f157]) ).

fof(f157,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/sandbox/benchmark/theBenchmark.p',ax75) ).

fof(f1633,plain,
    spl71_165,
    inference(avatar_split_clause,[],[f448,f1631]) ).

fof(f1631,plain,
    ( spl71_165
  <=> ! [X0,X1] :
        ( leq(X1,hd(X0))
        | nil = X0
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_165])]) ).

fof(f448,plain,
    ! [X0,X1] :
      ( leq(X1,hd(X0))
      | nil = X0
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f274]) ).

fof(f1629,plain,
    spl71_164,
    inference(avatar_split_clause,[],[f445,f1627]) ).

fof(f1627,plain,
    ( spl71_164
  <=> ! [X0,X1] :
        ( totalorderedP(cons(X0,X1))
        | ~ sP2(X1,X0)
        | ~ sP3(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_164])]) ).

fof(f445,plain,
    ! [X0,X1] :
      ( totalorderedP(cons(X0,X1))
      | ~ sP2(X1,X0)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ( ( totalorderedP(cons(X0,X1))
          | ~ sP2(X1,X0) )
        & ( sP2(X1,X0)
          | ~ totalorderedP(cons(X0,X1)) ) )
      | ~ sP3(X0,X1) ),
    inference(nnf_transformation,[],[f228]) ).

fof(f228,plain,
    ! [X0,X1] :
      ( ( totalorderedP(cons(X0,X1))
      <=> sP2(X1,X0) )
      | ~ sP3(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f1625,plain,
    spl71_163,
    inference(avatar_split_clause,[],[f444,f1623]) ).

fof(f1623,plain,
    ( spl71_163
  <=> ! [X0,X1] :
        ( sP2(X1,X0)
        | ~ totalorderedP(cons(X0,X1))
        | ~ sP3(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_163])]) ).

fof(f444,plain,
    ! [X0,X1] :
      ( sP2(X1,X0)
      | ~ totalorderedP(cons(X0,X1))
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f271]) ).

fof(f1621,plain,
    spl71_162,
    inference(avatar_split_clause,[],[f440,f1619]) ).

fof(f1619,plain,
    ( spl71_162
  <=> ! [X0,X1] :
        ( lt(X1,hd(X0))
        | nil = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_162])]) ).

fof(f440,plain,
    ! [X0,X1] :
      ( lt(X1,hd(X0))
      | nil = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f270]) ).

fof(f1617,plain,
    spl71_161,
    inference(avatar_split_clause,[],[f437,f1615]) ).

fof(f1615,plain,
    ( spl71_161
  <=> ! [X0,X1] :
        ( strictorderedP(cons(X0,X1))
        | ~ sP0(X1,X0)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_161])]) ).

fof(f437,plain,
    ! [X0,X1] :
      ( strictorderedP(cons(X0,X1))
      | ~ sP0(X1,X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f267,plain,
    ! [X0,X1] :
      ( ( ( strictorderedP(cons(X0,X1))
          | ~ sP0(X1,X0) )
        & ( sP0(X1,X0)
          | ~ strictorderedP(cons(X0,X1)) ) )
      | ~ sP1(X0,X1) ),
    inference(nnf_transformation,[],[f225]) ).

fof(f225,plain,
    ! [X0,X1] :
      ( ( strictorderedP(cons(X0,X1))
      <=> sP0(X1,X0) )
      | ~ sP1(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f1613,plain,
    spl71_160,
    inference(avatar_split_clause,[],[f436,f1611]) ).

fof(f1611,plain,
    ( spl71_160
  <=> ! [X0,X1] :
        ( sP0(X1,X0)
        | ~ strictorderedP(cons(X0,X1))
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_160])]) ).

fof(f436,plain,
    ! [X0,X1] :
      ( sP0(X1,X0)
      | ~ strictorderedP(cons(X0,X1))
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f267]) ).

fof(f1609,plain,
    spl71_159,
    inference(avatar_split_clause,[],[f423,f1607]) ).

fof(f1607,plain,
    ( spl71_159
  <=> ! [X0,X1] :
        ( leq(X0,X1)
        | ~ lt(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_159])]) ).

fof(f423,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f262]) ).

fof(f262,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,[],[f261]) ).

fof(f261,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,[],[f125]) ).

fof(f125,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/sandbox/benchmark/theBenchmark.p',ax93) ).

fof(f1605,plain,
    ( spl71_158
    | ~ spl71_1
    | ~ spl71_29 ),
    inference(avatar_split_clause,[],[f817,f779,f647,f1602]) ).

fof(f1602,plain,
    ( spl71_158
  <=> sP15(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_158])]) ).

fof(f817,plain,
    ( sP15(sK20)
    | ~ spl71_1
    | ~ spl71_29 ),
    inference(resolution,[],[f780,f649]) ).

fof(f1600,plain,
    spl71_157,
    inference(avatar_split_clause,[],[f421,f1598]) ).

fof(f1598,plain,
    ( spl71_157
  <=> ! [X0,X1] :
        ( geq(X0,X1)
        | ~ leq(X1,X0)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_157])]) ).

fof(f421,plain,
    ! [X0,X1] :
      ( geq(X0,X1)
      | ~ leq(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f260]) ).

fof(f260,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( geq(X0,X1)
              | ~ leq(X1,X0) )
            & ( leq(X1,X0)
              | ~ geq(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f124]) ).

fof(f124,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/sandbox/benchmark/theBenchmark.p',ax32) ).

fof(f1596,plain,
    spl71_156,
    inference(avatar_split_clause,[],[f420,f1594]) ).

fof(f1594,plain,
    ( spl71_156
  <=> ! [X0,X1] :
        ( leq(X1,X0)
        | ~ geq(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_156])]) ).

fof(f420,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | ~ geq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f260]) ).

fof(f1592,plain,
    spl71_155,
    inference(avatar_split_clause,[],[f419,f1590]) ).

fof(f1590,plain,
    ( spl71_155
  <=> ! [X0,X1] :
        ( gt(X0,X1)
        | ~ lt(X1,X0)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_155])]) ).

fof(f419,plain,
    ! [X0,X1] :
      ( gt(X0,X1)
      | ~ lt(X1,X0)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f259,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( gt(X0,X1)
              | ~ lt(X1,X0) )
            & ( lt(X1,X0)
              | ~ gt(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f123]) ).

fof(f123,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/sandbox/benchmark/theBenchmark.p',ax35) ).

fof(f1588,plain,
    spl71_154,
    inference(avatar_split_clause,[],[f418,f1586]) ).

fof(f1586,plain,
    ( spl71_154
  <=> ! [X0,X1] :
        ( lt(X1,X0)
        | ~ gt(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_154])]) ).

fof(f418,plain,
    ! [X0,X1] :
      ( lt(X1,X0)
      | ~ gt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f1584,plain,
    spl71_153,
    inference(avatar_split_clause,[],[f417,f1582]) ).

fof(f1582,plain,
    ( spl71_153
  <=> ! [X0,X1] :
        ( neq(X0,X1)
        | X0 = X1
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_153])]) ).

fof(f417,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f258]) ).

fof(f258,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/sandbox/benchmark/theBenchmark.p',ax1) ).

fof(f1580,plain,
    spl71_152,
    inference(avatar_split_clause,[],[f413,f1578]) ).

fof(f1578,plain,
    ( spl71_152
  <=> ! [X0,X1] :
        ( ~ lt(X1,X0)
        | ~ lt(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_152])]) ).

fof(f413,plain,
    ! [X0,X1] :
      ( ~ lt(X1,X0)
      | ~ lt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ lt(X1,X0)
          | ~ lt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f116]) ).

fof(f116,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/sandbox/benchmark/theBenchmark.p',ax33) ).

fof(f1576,plain,
    spl71_151,
    inference(avatar_split_clause,[],[f411,f1574]) ).

fof(f1574,plain,
    ( spl71_151
  <=> ! [X0,X1] :
        ( ~ gt(X1,X0)
        | ~ gt(X0,X1)
        | ~ ssItem(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_151])]) ).

fof(f411,plain,
    ! [X0,X1] :
      ( ~ gt(X1,X0)
      | ~ gt(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ gt(X1,X0)
          | ~ gt(X0,X1)
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f112]) ).

fof(f112,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/sandbox/benchmark/theBenchmark.p',ax94) ).

fof(f1572,plain,
    ( spl71_150
    | ~ spl71_4
    | ~ spl71_28 ),
    inference(avatar_split_clause,[],[f815,f775,f662,f1569]) ).

fof(f1569,plain,
    ( spl71_150
  <=> sP13(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_150])]) ).

fof(f815,plain,
    ( sP13(sK23)
    | ~ spl71_4
    | ~ spl71_28 ),
    inference(resolution,[],[f776,f664]) ).

fof(f1567,plain,
    spl71_149,
    inference(avatar_split_clause,[],[f642,f1565]) ).

fof(f1565,plain,
    ( spl71_149
  <=> ! [X2,X1] :
        ( memberP(cons(X1,X2),X1)
        | ~ ssList(X2)
        | ~ ssItem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_149])]) ).

fof(f642,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f613]) ).

fof(f613,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f431]) ).

fof(f431,plain,
    ! [X2,X0,X1] :
      ( memberP(cons(X1,X2),X0)
      | X0 != X1
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f1563,plain,
    spl71_148,
    inference(avatar_split_clause,[],[f563,f1561]) ).

fof(f1561,plain,
    ( spl71_148
  <=> ! [X0,X1] :
        ( cons(X1,X0) != X0
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_148])]) ).

fof(f563,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,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/sandbox/benchmark/theBenchmark.p',ax18) ).

fof(f1559,plain,
    spl71_147,
    inference(avatar_split_clause,[],[f562,f1557]) ).

fof(f1557,plain,
    ( spl71_147
  <=> ! [X0,X1] :
        ( nil != cons(X1,X0)
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_147])]) ).

fof(f562,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,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/sandbox/benchmark/theBenchmark.p',ax21) ).

fof(f1515,plain,
    ( spl71_146
    | ~ spl71_3
    | ~ spl71_28 ),
    inference(avatar_split_clause,[],[f814,f775,f657,f1512]) ).

fof(f1512,plain,
    ( spl71_146
  <=> sP13(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_146])]) ).

fof(f814,plain,
    ( sP13(sK22)
    | ~ spl71_3
    | ~ spl71_28 ),
    inference(resolution,[],[f776,f659]) ).

fof(f1490,plain,
    spl71_145,
    inference(avatar_split_clause,[],[f571,f1488]) ).

fof(f1488,plain,
    ( spl71_145
  <=> ! [X0,X1] :
        ( ssList(app(X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_145])]) ).

fof(f571,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f186]) ).

fof(f186,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/sandbox/benchmark/theBenchmark.p',ax26) ).

fof(f1486,plain,
    spl71_144,
    inference(avatar_split_clause,[],[f561,f1484]) ).

fof(f1484,plain,
    ( spl71_144
  <=> ! [X0,X1] :
        ( ssList(cons(X1,X0))
        | ~ ssItem(X1)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_144])]) ).

fof(f561,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,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/sandbox/benchmark/theBenchmark.p',ax16) ).

fof(f1482,plain,
    spl71_143,
    inference(avatar_split_clause,[],[f559,f1480]) ).

fof(f1480,plain,
    ( spl71_143
  <=> ! [X0] :
        ( nil = X0
        | ~ segmentP(nil,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_143])]) ).

fof(f559,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f352]) ).

fof(f352,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f178]) ).

fof(f178,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/sandbox/benchmark/theBenchmark.p',ax58) ).

fof(f1478,plain,
    spl71_142,
    inference(avatar_split_clause,[],[f557,f1476]) ).

fof(f1476,plain,
    ( spl71_142
  <=> ! [X0] :
        ( nil = X0
        | ~ frontsegP(nil,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_142])]) ).

fof(f557,plain,
    ! [X0] :
      ( nil = X0
      | ~ frontsegP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f351]) ).

fof(f351,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/sandbox/benchmark/theBenchmark.p',ax46) ).

fof(f1474,plain,
    ( spl71_141
    | ~ spl71_2
    | ~ spl71_28 ),
    inference(avatar_split_clause,[],[f813,f775,f652,f1471]) ).

fof(f1471,plain,
    ( spl71_141
  <=> sP13(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_141])]) ).

fof(f813,plain,
    ( sP13(sK21)
    | ~ spl71_2
    | ~ spl71_28 ),
    inference(resolution,[],[f776,f654]) ).

fof(f1469,plain,
    spl71_140,
    inference(avatar_split_clause,[],[f555,f1467]) ).

fof(f1467,plain,
    ( spl71_140
  <=> ! [X0] :
        ( nil = X0
        | ~ rearsegP(nil,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_140])]) ).

fof(f555,plain,
    ! [X0] :
      ( nil = X0
      | ~ rearsegP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f350,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/sandbox/benchmark/theBenchmark.p',ax52) ).

fof(f1465,plain,
    spl71_139,
    inference(avatar_split_clause,[],[f471,f1463]) ).

fof(f1463,plain,
    ( spl71_139
  <=> ! [X0] :
        ( ssList(sK27(X0))
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_139])]) ).

fof(f471,plain,
    ! [X0] :
      ( ssList(sK27(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f283]) ).

fof(f1461,plain,
    spl71_138,
    inference(avatar_split_clause,[],[f469,f1459]) ).

fof(f1459,plain,
    ( spl71_138
  <=> ! [X0] :
        ( ssItem(sK26(X0))
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_138])]) ).

fof(f469,plain,
    ! [X0] :
      ( ssItem(sK26(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f281]) ).

fof(f1457,plain,
    spl71_137,
    inference(avatar_split_clause,[],[f467,f1455]) ).

fof(f1455,plain,
    ( spl71_137
  <=> ! [X0] :
        ( ssList(tl(X0))
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_137])]) ).

fof(f467,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f153]) ).

fof(f153,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/sandbox/benchmark/theBenchmark.p',ax24) ).

fof(f1453,plain,
    spl71_136,
    inference(avatar_split_clause,[],[f466,f1451]) ).

fof(f1451,plain,
    ( spl71_136
  <=> ! [X0] :
        ( ssItem(hd(X0))
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_136])]) ).

fof(f466,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f151]) ).

fof(f151,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/sandbox/benchmark/theBenchmark.p',ax22) ).

fof(f1449,plain,
    spl71_135,
    inference(avatar_split_clause,[],[f464,f1447]) ).

fof(f1447,plain,
    ( spl71_135
  <=> ! [X0] :
        ( ssItem(sK25(X0))
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_135])]) ).

fof(f464,plain,
    ! [X0] :
      ( ssItem(sK25(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f279]) ).

fof(f1445,plain,
    spl71_134,
    inference(avatar_split_clause,[],[f463,f1443]) ).

fof(f1443,plain,
    ( spl71_134
  <=> ! [X0] :
        ( ssList(sK24(X0))
        | nil = X0
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_134])]) ).

fof(f463,plain,
    ! [X0] :
      ( ssList(sK24(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f279]) ).

fof(f1441,plain,
    spl71_133,
    inference(avatar_split_clause,[],[f447,f1439]) ).

fof(f1439,plain,
    ( spl71_133
  <=> ! [X0,X1] :
        ( totalorderedP(X0)
        | nil = X0
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_133])]) ).

fof(f447,plain,
    ! [X0,X1] :
      ( totalorderedP(X0)
      | nil = X0
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f274]) ).

fof(f1437,plain,
    spl71_132,
    inference(avatar_split_clause,[],[f439,f1435]) ).

fof(f1435,plain,
    ( spl71_132
  <=> ! [X0,X1] :
        ( strictorderedP(X0)
        | nil = X0
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_132])]) ).

fof(f439,plain,
    ! [X0,X1] :
      ( strictorderedP(X0)
      | nil = X0
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f270]) ).

fof(f1433,plain,
    ( spl71_131
    | ~ spl71_1
    | ~ spl71_28 ),
    inference(avatar_split_clause,[],[f812,f775,f647,f1430]) ).

fof(f1430,plain,
    ( spl71_131
  <=> sP13(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_131])]) ).

fof(f812,plain,
    ( sP13(sK20)
    | ~ spl71_1
    | ~ spl71_28 ),
    inference(resolution,[],[f776,f649]) ).

fof(f1376,plain,
    spl71_130,
    inference(avatar_split_clause,[],[f553,f1374]) ).

fof(f1374,plain,
    ( spl71_130
  <=> ! [X0] :
        ( sP16(X0)
        | ~ leq(sK58(X0),sK59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_130])]) ).

fof(f553,plain,
    ! [X0] :
      ( sP16(X0)
      | ~ leq(sK58(X0),sK59(X0)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f1372,plain,
    spl71_129,
    inference(avatar_split_clause,[],[f542,f1370]) ).

fof(f1370,plain,
    ( spl71_129
  <=> ! [X0] :
        ( sP14(X0)
        | ~ lt(sK53(X0),sK54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_129])]) ).

fof(f542,plain,
    ! [X0] :
      ( sP14(X0)
      | ~ lt(sK53(X0),sK54(X0)) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f1368,plain,
    spl71_128,
    inference(avatar_split_clause,[],[f531,f1366]) ).

fof(f1366,plain,
    ( spl71_128
  <=> ! [X0] :
        ( sP12(X0)
        | leq(sK49(X0),sK48(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_128])]) ).

fof(f531,plain,
    ! [X0] :
      ( sP12(X0)
      | leq(sK49(X0),sK48(X0)) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f1364,plain,
    spl71_127,
    inference(avatar_split_clause,[],[f530,f1362]) ).

fof(f1362,plain,
    ( spl71_127
  <=> ! [X0] :
        ( sP12(X0)
        | leq(sK48(X0),sK49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_127])]) ).

fof(f530,plain,
    ! [X0] :
      ( sP12(X0)
      | leq(sK48(X0),sK49(X0)) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f1360,plain,
    spl71_126,
    inference(avatar_split_clause,[],[f519,f1358]) ).

fof(f1358,plain,
    ( spl71_126
  <=> ! [X0] :
        ( sP10(X0)
        | ~ lt(sK44(X0),sK43(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_126])]) ).

fof(f519,plain,
    ! [X0] :
      ( sP10(X0)
      | ~ lt(sK44(X0),sK43(X0)) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f1356,plain,
    spl71_125,
    inference(avatar_split_clause,[],[f518,f1354]) ).

fof(f1354,plain,
    ( spl71_125
  <=> ! [X0] :
        ( sP10(X0)
        | ~ lt(sK43(X0),sK44(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_125])]) ).

fof(f518,plain,
    ! [X0] :
      ( sP10(X0)
      | ~ lt(sK43(X0),sK44(X0)) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f1352,plain,
    ( spl71_124
    | ~ spl71_4
    | ~ spl71_27 ),
    inference(avatar_split_clause,[],[f805,f771,f662,f1349]) ).

fof(f1349,plain,
    ( spl71_124
  <=> sP11(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_124])]) ).

fof(f805,plain,
    ( sP11(sK23)
    | ~ spl71_4
    | ~ spl71_27 ),
    inference(resolution,[],[f772,f664]) ).

fof(f1347,plain,
    spl71_123,
    inference(avatar_split_clause,[],[f507,f1345]) ).

fof(f1345,plain,
    ( spl71_123
  <=> ! [X0] :
        ( sP8(X0)
        | ~ leq(sK39(X0),sK38(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_123])]) ).

fof(f507,plain,
    ! [X0] :
      ( sP8(X0)
      | ~ leq(sK39(X0),sK38(X0)) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f1343,plain,
    spl71_122,
    inference(avatar_split_clause,[],[f506,f1341]) ).

fof(f1341,plain,
    ( spl71_122
  <=> ! [X0] :
        ( sP8(X0)
        | ~ leq(sK38(X0),sK39(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_122])]) ).

fof(f506,plain,
    ! [X0] :
      ( sP8(X0)
      | ~ leq(sK38(X0),sK39(X0)) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f1339,plain,
    spl71_121,
    inference(avatar_split_clause,[],[f495,f1337]) ).

fof(f1337,plain,
    ( spl71_121
  <=> ! [X0] :
        ( sP6(X0)
        | sK33(X0) = sK34(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_121])]) ).

fof(f495,plain,
    ! [X0] :
      ( sP6(X0)
      | sK33(X0) = sK34(X0) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f1335,plain,
    spl71_120,
    inference(avatar_split_clause,[],[f484,f1333]) ).

fof(f1333,plain,
    ( spl71_120
  <=> ! [X0] :
        ( sP4(X0)
        | sK29(X0) != sK30(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_120])]) ).

fof(f484,plain,
    ! [X0] :
      ( sP4(X0)
      | sK29(X0) != sK30(X0) ),
    inference(cnf_transformation,[],[f295]) ).

fof(f1331,plain,
    spl71_119,
    inference(avatar_split_clause,[],[f473,f1329]) ).

fof(f1329,plain,
    ( spl71_119
  <=> ! [X0] :
        ( ssItem(sK28(X0))
        | ~ singletonP(X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_119])]) ).

fof(f473,plain,
    ! [X0] :
      ( ssItem(sK28(X0))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f287]) ).

fof(f1327,plain,
    spl71_118,
    inference(avatar_split_clause,[],[f462,f1325]) ).

fof(f462,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,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/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f1323,plain,
    spl71_117,
    inference(avatar_split_clause,[],[f461,f1321]) ).

fof(f461,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,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/sandbox/benchmark/theBenchmark.p',ax84) ).

fof(f1319,plain,
    spl71_116,
    inference(avatar_split_clause,[],[f451,f1317]) ).

fof(f1317,plain,
    ( spl71_116
  <=> ! [X0,X1] :
        ( sP3(X0,X1)
        | ~ ssList(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_116])]) ).

fof(f451,plain,
    ! [X0,X1] :
      ( sP3(X0,X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f229]) ).

fof(f229,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP3(X0,X1)
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(definition_folding,[],[f139,f228,f227]) ).

fof(f139,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/sandbox/benchmark/theBenchmark.p',ax67) ).

fof(f1315,plain,
    spl71_115,
    inference(avatar_split_clause,[],[f443,f1313]) ).

fof(f1313,plain,
    ( spl71_115
  <=> ! [X0,X1] :
        ( sP1(X0,X1)
        | ~ ssList(X1)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_115])]) ).

fof(f443,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f226]) ).

fof(f226,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP1(X0,X1)
          | ~ ssList(X1) )
      | ~ ssItem(X0) ),
    inference(definition_folding,[],[f138,f225,f224]) ).

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/sandbox/benchmark/theBenchmark.p',ax70) ).

fof(f1311,plain,
    ( spl71_114
    | ~ spl71_3
    | ~ spl71_27 ),
    inference(avatar_split_clause,[],[f804,f771,f657,f1308]) ).

fof(f1308,plain,
    ( spl71_114
  <=> sP11(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_114])]) ).

fof(f804,plain,
    ( sP11(sK22)
    | ~ spl71_3
    | ~ spl71_27 ),
    inference(resolution,[],[f772,f659]) ).

fof(f1306,plain,
    spl71_113,
    inference(avatar_split_clause,[],[f388,f1304]) ).

fof(f1304,plain,
    ( spl71_113
  <=> ! [X9,X7,X6,X8] :
        ( ~ leq(X8,X6)
        | app(X9,cons(X8,nil)) != sK20
        | ~ ssList(X9)
        | ~ ssItem(X8)
        | app(cons(X6,nil),X7) != sK23
        | ~ ssList(X7)
        | ~ ssItem(X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_113])]) ).

fof(f388,plain,
    ! [X8,X6,X9,X7] :
      ( ~ leq(X8,X6)
      | app(X9,cons(X8,nil)) != sK20
      | ~ ssList(X9)
      | ~ ssItem(X8)
      | app(cons(X6,nil),X7) != sK23
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f257,plain,
    ( ( ~ totalorderedP(sK18)
      | ~ segmentP(sK19,sK18) )
    & ( nil != sK20
      | nil = sK21 )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( ~ leq(X8,X6)
                    | app(X9,cons(X8,nil)) != sK20
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            | app(cons(X6,nil),X7) != sK23
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & ! [X10] :
        ( ! [X11] :
            ( ! [X12] :
                ( ! [X13] :
                    ( ~ leq(X10,X12)
                    | app(cons(X12,nil),X13) != sK20
                    | ~ ssList(X13) )
                | ~ ssItem(X12) )
            | app(X11,cons(X10,nil)) != sK22
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & totalorderedP(sK20)
    & sK21 = app(app(sK22,sK20),sK23)
    & ssList(sK23)
    & ssList(sK22)
    & sK18 = sK20
    & sK19 = sK21
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23])],[f100,f256,f255,f254,f253,f252,f251]) ).

fof(f251,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ totalorderedP(X0)
                      | ~ segmentP(X1,X0) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ? [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ! [X8] :
                                        ( ! [X9] :
                                            ( ~ leq(X8,X6)
                                            | app(X9,cons(X8,nil)) != X2
                                            | ~ ssList(X9) )
                                        | ~ ssItem(X8) )
                                    | app(cons(X6,nil),X7) != X5
                                    | ~ ssList(X7) )
                                | ~ ssItem(X6) )
                            & ! [X10] :
                                ( ! [X11] :
                                    ( ! [X12] :
                                        ( ! [X13] :
                                            ( ~ leq(X10,X12)
                                            | app(cons(X12,nil),X13) != X2
                                            | ~ ssList(X13) )
                                        | ~ ssItem(X12) )
                                    | app(X11,cons(X10,nil)) != X4
                                    | ~ ssList(X11) )
                                | ~ ssItem(X10) )
                            & totalorderedP(X2)
                            & app(app(X4,X2),X5) = X3
                            & ssList(X5) )
                        & ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ totalorderedP(sK18)
                    | ~ segmentP(X1,sK18) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ leq(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ leq(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & totalorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & sK18 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ totalorderedP(sK18)
                  | ~ segmentP(X1,sK18) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ? [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ! [X9] :
                                        ( ~ leq(X8,X6)
                                        | app(X9,cons(X8,nil)) != X2
                                        | ~ ssList(X9) )
                                    | ~ ssItem(X8) )
                                | app(cons(X6,nil),X7) != X5
                                | ~ ssList(X7) )
                            | ~ ssItem(X6) )
                        & ! [X10] :
                            ( ! [X11] :
                                ( ! [X12] :
                                    ( ! [X13] :
                                        ( ~ leq(X10,X12)
                                        | app(cons(X12,nil),X13) != X2
                                        | ~ ssList(X13) )
                                    | ~ ssItem(X12) )
                                | app(X11,cons(X10,nil)) != X4
                                | ~ ssList(X11) )
                            | ~ ssItem(X10) )
                        & totalorderedP(X2)
                        & app(app(X4,X2),X5) = X3
                        & ssList(X5) )
                    & ssList(X4) )
                & sK18 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ totalorderedP(sK18)
                | ~ segmentP(sK19,sK18) )
              & ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ! [X9] :
                                      ( ~ leq(X8,X6)
                                      | app(X9,cons(X8,nil)) != X2
                                      | ~ ssList(X9) )
                                  | ~ ssItem(X8) )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & ! [X10] :
                          ( ! [X11] :
                              ( ! [X12] :
                                  ( ! [X13] :
                                      ( ~ leq(X10,X12)
                                      | app(cons(X12,nil),X13) != X2
                                      | ~ ssList(X13) )
                                  | ~ ssItem(X12) )
                              | app(X11,cons(X10,nil)) != X4
                              | ~ ssList(X11) )
                          | ~ ssItem(X10) )
                      & totalorderedP(X2)
                      & app(app(X4,X2),X5) = X3
                      & ssList(X5) )
                  & ssList(X4) )
              & sK18 = X2
              & sK19 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ totalorderedP(sK18)
              | ~ segmentP(sK19,sK18) )
            & ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ? [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ! [X9] :
                                    ( ~ leq(X8,X6)
                                    | app(X9,cons(X8,nil)) != X2
                                    | ~ ssList(X9) )
                                | ~ ssItem(X8) )
                            | app(cons(X6,nil),X7) != X5
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & ! [X10] :
                        ( ! [X11] :
                            ( ! [X12] :
                                ( ! [X13] :
                                    ( ~ leq(X10,X12)
                                    | app(cons(X12,nil),X13) != X2
                                    | ~ ssList(X13) )
                                | ~ ssItem(X12) )
                            | app(X11,cons(X10,nil)) != X4
                            | ~ ssList(X11) )
                        | ~ ssItem(X10) )
                    & totalorderedP(X2)
                    & app(app(X4,X2),X5) = X3
                    & ssList(X5) )
                & ssList(X4) )
            & sK18 = X2
            & sK19 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ totalorderedP(sK18)
            | ~ segmentP(sK19,sK18) )
          & ( nil != sK20
            | nil = X3 )
          & ? [X4] :
              ( ? [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ! [X9] :
                                  ( ~ leq(X8,X6)
                                  | app(X9,cons(X8,nil)) != sK20
                                  | ~ ssList(X9) )
                              | ~ ssItem(X8) )
                          | app(cons(X6,nil),X7) != X5
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & ! [X10] :
                      ( ! [X11] :
                          ( ! [X12] :
                              ( ! [X13] :
                                  ( ~ leq(X10,X12)
                                  | app(cons(X12,nil),X13) != sK20
                                  | ~ ssList(X13) )
                              | ~ ssItem(X12) )
                          | app(X11,cons(X10,nil)) != X4
                          | ~ ssList(X11) )
                      | ~ ssItem(X10) )
                  & totalorderedP(sK20)
                  & app(app(X4,sK20),X5) = X3
                  & ssList(X5) )
              & ssList(X4) )
          & sK18 = sK20
          & sK19 = X3
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f254,plain,
    ( ? [X3] :
        ( ( ~ totalorderedP(sK18)
          | ~ segmentP(sK19,sK18) )
        & ( nil != sK20
          | nil = X3 )
        & ? [X4] :
            ( ? [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ! [X9] :
                                ( ~ leq(X8,X6)
                                | app(X9,cons(X8,nil)) != sK20
                                | ~ ssList(X9) )
                            | ~ ssItem(X8) )
                        | app(cons(X6,nil),X7) != X5
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & ! [X10] :
                    ( ! [X11] :
                        ( ! [X12] :
                            ( ! [X13] :
                                ( ~ leq(X10,X12)
                                | app(cons(X12,nil),X13) != sK20
                                | ~ ssList(X13) )
                            | ~ ssItem(X12) )
                        | app(X11,cons(X10,nil)) != X4
                        | ~ ssList(X11) )
                    | ~ ssItem(X10) )
                & totalorderedP(sK20)
                & app(app(X4,sK20),X5) = X3
                & ssList(X5) )
            & ssList(X4) )
        & sK18 = sK20
        & sK19 = X3
        & ssList(X3) )
   => ( ( ~ totalorderedP(sK18)
        | ~ segmentP(sK19,sK18) )
      & ( nil != sK20
        | nil = sK21 )
      & ? [X4] :
          ( ? [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ! [X9] :
                              ( ~ leq(X8,X6)
                              | app(X9,cons(X8,nil)) != sK20
                              | ~ ssList(X9) )
                          | ~ ssItem(X8) )
                      | app(cons(X6,nil),X7) != X5
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & ! [X10] :
                  ( ! [X11] :
                      ( ! [X12] :
                          ( ! [X13] :
                              ( ~ leq(X10,X12)
                              | app(cons(X12,nil),X13) != sK20
                              | ~ ssList(X13) )
                          | ~ ssItem(X12) )
                      | app(X11,cons(X10,nil)) != X4
                      | ~ ssList(X11) )
                  | ~ ssItem(X10) )
              & totalorderedP(sK20)
              & app(app(X4,sK20),X5) = sK21
              & ssList(X5) )
          & ssList(X4) )
      & sK18 = sK20
      & sK19 = sK21
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f255,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ! [X9] :
                            ( ~ leq(X8,X6)
                            | app(X9,cons(X8,nil)) != sK20
                            | ~ ssList(X9) )
                        | ~ ssItem(X8) )
                    | app(cons(X6,nil),X7) != X5
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & ! [X10] :
                ( ! [X11] :
                    ( ! [X12] :
                        ( ! [X13] :
                            ( ~ leq(X10,X12)
                            | app(cons(X12,nil),X13) != sK20
                            | ~ ssList(X13) )
                        | ~ ssItem(X12) )
                    | app(X11,cons(X10,nil)) != X4
                    | ~ ssList(X11) )
                | ~ ssItem(X10) )
            & totalorderedP(sK20)
            & app(app(X4,sK20),X5) = sK21
            & ssList(X5) )
        & ssList(X4) )
   => ( ? [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ! [X9] :
                          ( ~ leq(X8,X6)
                          | app(X9,cons(X8,nil)) != sK20
                          | ~ ssList(X9) )
                      | ~ ssItem(X8) )
                  | app(cons(X6,nil),X7) != X5
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & ! [X10] :
              ( ! [X11] :
                  ( ! [X12] :
                      ( ! [X13] :
                          ( ~ leq(X10,X12)
                          | app(cons(X12,nil),X13) != sK20
                          | ~ ssList(X13) )
                      | ~ ssItem(X12) )
                  | app(X11,cons(X10,nil)) != sK22
                  | ~ ssList(X11) )
              | ~ ssItem(X10) )
          & totalorderedP(sK20)
          & sK21 = app(app(sK22,sK20),X5)
          & ssList(X5) )
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f256,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ! [X9] :
                        ( ~ leq(X8,X6)
                        | app(X9,cons(X8,nil)) != sK20
                        | ~ ssList(X9) )
                    | ~ ssItem(X8) )
                | app(cons(X6,nil),X7) != X5
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & ! [X10] :
            ( ! [X11] :
                ( ! [X12] :
                    ( ! [X13] :
                        ( ~ leq(X10,X12)
                        | app(cons(X12,nil),X13) != sK20
                        | ~ ssList(X13) )
                    | ~ ssItem(X12) )
                | app(X11,cons(X10,nil)) != sK22
                | ~ ssList(X11) )
            | ~ ssItem(X10) )
        & totalorderedP(sK20)
        & sK21 = app(app(sK22,sK20),X5)
        & ssList(X5) )
   => ( ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( ! [X9] :
                      ( ~ leq(X8,X6)
                      | app(X9,cons(X8,nil)) != sK20
                      | ~ ssList(X9) )
                  | ~ ssItem(X8) )
              | app(cons(X6,nil),X7) != sK23
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & ! [X10] :
          ( ! [X11] :
              ( ! [X12] :
                  ( ! [X13] :
                      ( ~ leq(X10,X12)
                      | app(cons(X12,nil),X13) != sK20
                      | ~ ssList(X13) )
                  | ~ ssItem(X12) )
              | app(X11,cons(X10,nil)) != sK22
              | ~ ssList(X11) )
          | ~ ssItem(X10) )
      & totalorderedP(sK20)
      & sK21 = app(app(sK22,sK20),sK23)
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ totalorderedP(X0)
                    | ~ segmentP(X1,X0) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ leq(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ leq(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & totalorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ totalorderedP(X0)
                    | ~ segmentP(X1,X0) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ? [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ leq(X8,X6)
                                          | app(X9,cons(X8,nil)) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(cons(X6,nil),X7) != X5
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ leq(X10,X12)
                                          | app(cons(X12,nil),X13) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(X11,cons(X10,nil)) != X4
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & totalorderedP(X2)
                          & app(app(X4,X2),X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( totalorderedP(X0)
                        & segmentP(X1,X0) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( leq(X8,X6)
                                                & app(X9,cons(X8,nil)) = X2
                                                & ssList(X9) )
                                            & ssItem(X8) )
                                        & app(cons(X6,nil),X7) = X5
                                        & ssList(X7) )
                                    & ssItem(X6) )
                                | ? [X10] :
                                    ( ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( leq(X10,X12)
                                                & app(cons(X12,nil),X13) = X2
                                                & ssList(X13) )
                                            & ssItem(X12) )
                                        & app(X11,cons(X10,nil)) = X4
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | ~ totalorderedP(X2)
                                | app(app(X4,X2),X5) != X3 ) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( totalorderedP(X0)
                        & segmentP(X1,X0) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ? [X10] :
                                    ( ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( leq(X12,X10)
                                                & app(X13,cons(X12,nil)) = X2
                                                & ssList(X13) )
                                            & ssItem(X12) )
                                        & app(cons(X10,nil),X11) = X5
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( leq(X6,X8)
                                                & app(cons(X8,nil),X9) = X2
                                                & ssList(X9) )
                                            & ssItem(X8) )
                                        & app(X7,cons(X6,nil)) = X4
                                        & ssList(X7) )
                                    & ssItem(X6) )
                                | ~ totalorderedP(X2)
                                | app(app(X4,X2),X5) != X3 ) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( totalorderedP(X0)
                      & segmentP(X1,X0) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( ? [X10] :
                                  ( ? [X11] :
                                      ( ? [X12] :
                                          ( ? [X13] :
                                              ( leq(X12,X10)
                                              & app(X13,cons(X12,nil)) = X2
                                              & ssList(X13) )
                                          & ssItem(X12) )
                                      & app(cons(X10,nil),X11) = X5
                                      & ssList(X11) )
                                  & ssItem(X10) )
                              | ? [X6] :
                                  ( ? [X7] :
                                      ( ? [X8] :
                                          ( ? [X9] :
                                              ( leq(X6,X8)
                                              & app(cons(X8,nil),X9) = X2
                                              & ssList(X9) )
                                          & ssItem(X8) )
                                      & app(X7,cons(X6,nil)) = X4
                                      & ssList(X7) )
                                  & ssItem(X6) )
                              | ~ totalorderedP(X2)
                              | app(app(X4,X2),X5) != X3 ) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f1302,plain,
    spl71_112,
    inference(avatar_split_clause,[],[f387,f1300]) ).

fof(f1300,plain,
    ( spl71_112
  <=> ! [X10,X11,X13,X12] :
        ( ~ leq(X10,X12)
        | app(cons(X12,nil),X13) != sK20
        | ~ ssList(X13)
        | ~ ssItem(X12)
        | app(X11,cons(X10,nil)) != sK22
        | ~ ssList(X11)
        | ~ ssItem(X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_112])]) ).

fof(f387,plain,
    ! [X10,X11,X12,X13] :
      ( ~ leq(X10,X12)
      | app(cons(X12,nil),X13) != sK20
      | ~ ssList(X13)
      | ~ ssItem(X12)
      | app(X11,cons(X10,nil)) != sK22
      | ~ ssList(X11)
      | ~ ssItem(X10) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f1298,plain,
    ( spl71_111
    | ~ spl71_2
    | ~ spl71_27 ),
    inference(avatar_split_clause,[],[f803,f771,f652,f1295]) ).

fof(f1295,plain,
    ( spl71_111
  <=> sP11(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_111])]) ).

fof(f803,plain,
    ( sP11(sK21)
    | ~ spl71_2
    | ~ spl71_27 ),
    inference(resolution,[],[f772,f654]) ).

fof(f1293,plain,
    ( spl71_110
    | ~ spl71_1
    | ~ spl71_27 ),
    inference(avatar_split_clause,[],[f802,f771,f647,f1290]) ).

fof(f1290,plain,
    ( spl71_110
  <=> sP11(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_110])]) ).

fof(f802,plain,
    ( sP11(sK20)
    | ~ spl71_1
    | ~ spl71_27 ),
    inference(resolution,[],[f772,f649]) ).

fof(f1288,plain,
    spl71_109,
    inference(avatar_split_clause,[],[f545,f1286]) ).

fof(f1286,plain,
    ( spl71_109
  <=> ! [X0] :
        ( totalorderedP(X0)
        | ~ sP16(X0)
        | ~ sP17(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_109])]) ).

fof(f545,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | ~ sP16(X0)
      | ~ sP17(X0) ),
    inference(cnf_transformation,[],[f341]) ).

fof(f341,plain,
    ! [X0] :
      ( ( ( totalorderedP(X0)
          | ~ sP16(X0) )
        & ( sP16(X0)
          | ~ totalorderedP(X0) ) )
      | ~ sP17(X0) ),
    inference(nnf_transformation,[],[f249]) ).

fof(f249,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> sP16(X0) )
      | ~ sP17(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).

fof(f1284,plain,
    spl71_108,
    inference(avatar_split_clause,[],[f544,f1282]) ).

fof(f1282,plain,
    ( spl71_108
  <=> ! [X0] :
        ( sP16(X0)
        | ~ totalorderedP(X0)
        | ~ sP17(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_108])]) ).

fof(f544,plain,
    ! [X0] :
      ( sP16(X0)
      | ~ totalorderedP(X0)
      | ~ sP17(X0) ),
    inference(cnf_transformation,[],[f341]) ).

fof(f1280,plain,
    spl71_107,
    inference(avatar_split_clause,[],[f534,f1278]) ).

fof(f1278,plain,
    ( spl71_107
  <=> ! [X0] :
        ( strictorderedP(X0)
        | ~ sP14(X0)
        | ~ sP15(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_107])]) ).

fof(f534,plain,
    ! [X0] :
      ( strictorderedP(X0)
      | ~ sP14(X0)
      | ~ sP15(X0) ),
    inference(cnf_transformation,[],[f332]) ).

fof(f332,plain,
    ! [X0] :
      ( ( ( strictorderedP(X0)
          | ~ sP14(X0) )
        & ( sP14(X0)
          | ~ strictorderedP(X0) ) )
      | ~ sP15(X0) ),
    inference(nnf_transformation,[],[f246]) ).

fof(f246,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> sP14(X0) )
      | ~ sP15(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

fof(f1276,plain,
    spl71_106,
    inference(avatar_split_clause,[],[f533,f1274]) ).

fof(f1274,plain,
    ( spl71_106
  <=> ! [X0] :
        ( sP14(X0)
        | ~ strictorderedP(X0)
        | ~ sP15(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_106])]) ).

fof(f533,plain,
    ! [X0] :
      ( sP14(X0)
      | ~ strictorderedP(X0)
      | ~ sP15(X0) ),
    inference(cnf_transformation,[],[f332]) ).

fof(f1272,plain,
    spl71_105,
    inference(avatar_split_clause,[],[f522,f1270]) ).

fof(f1270,plain,
    ( spl71_105
  <=> ! [X0] :
        ( cyclefreeP(X0)
        | ~ sP12(X0)
        | ~ sP13(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_105])]) ).

fof(f522,plain,
    ! [X0] :
      ( cyclefreeP(X0)
      | ~ sP12(X0)
      | ~ sP13(X0) ),
    inference(cnf_transformation,[],[f323]) ).

fof(f323,plain,
    ! [X0] :
      ( ( ( cyclefreeP(X0)
          | ~ sP12(X0) )
        & ( sP12(X0)
          | ~ cyclefreeP(X0) ) )
      | ~ sP13(X0) ),
    inference(nnf_transformation,[],[f243]) ).

fof(f243,plain,
    ! [X0] :
      ( ( cyclefreeP(X0)
      <=> sP12(X0) )
      | ~ sP13(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

fof(f1268,plain,
    spl71_104,
    inference(avatar_split_clause,[],[f521,f1266]) ).

fof(f1266,plain,
    ( spl71_104
  <=> ! [X0] :
        ( sP12(X0)
        | ~ cyclefreeP(X0)
        | ~ sP13(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_104])]) ).

fof(f521,plain,
    ! [X0] :
      ( sP12(X0)
      | ~ cyclefreeP(X0)
      | ~ sP13(X0) ),
    inference(cnf_transformation,[],[f323]) ).

fof(f1264,plain,
    ( spl71_103
    | ~ spl71_4
    | ~ spl71_26 ),
    inference(avatar_split_clause,[],[f800,f767,f662,f1261]) ).

fof(f1261,plain,
    ( spl71_103
  <=> sP9(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_103])]) ).

fof(f800,plain,
    ( sP9(sK23)
    | ~ spl71_4
    | ~ spl71_26 ),
    inference(resolution,[],[f768,f664]) ).

fof(f1259,plain,
    spl71_102,
    inference(avatar_split_clause,[],[f510,f1257]) ).

fof(f1257,plain,
    ( spl71_102
  <=> ! [X0] :
        ( strictorderP(X0)
        | ~ sP10(X0)
        | ~ sP11(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_102])]) ).

fof(f510,plain,
    ! [X0] :
      ( strictorderP(X0)
      | ~ sP10(X0)
      | ~ sP11(X0) ),
    inference(cnf_transformation,[],[f314]) ).

fof(f314,plain,
    ! [X0] :
      ( ( ( strictorderP(X0)
          | ~ sP10(X0) )
        & ( sP10(X0)
          | ~ strictorderP(X0) ) )
      | ~ sP11(X0) ),
    inference(nnf_transformation,[],[f240]) ).

fof(f240,plain,
    ! [X0] :
      ( ( strictorderP(X0)
      <=> sP10(X0) )
      | ~ sP11(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

fof(f1255,plain,
    spl71_101,
    inference(avatar_split_clause,[],[f509,f1253]) ).

fof(f1253,plain,
    ( spl71_101
  <=> ! [X0] :
        ( sP10(X0)
        | ~ strictorderP(X0)
        | ~ sP11(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_101])]) ).

fof(f509,plain,
    ! [X0] :
      ( sP10(X0)
      | ~ strictorderP(X0)
      | ~ sP11(X0) ),
    inference(cnf_transformation,[],[f314]) ).

fof(f1251,plain,
    spl71_100,
    inference(avatar_split_clause,[],[f498,f1249]) ).

fof(f1249,plain,
    ( spl71_100
  <=> ! [X0] :
        ( totalorderP(X0)
        | ~ sP8(X0)
        | ~ sP9(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_100])]) ).

fof(f498,plain,
    ! [X0] :
      ( totalorderP(X0)
      | ~ sP8(X0)
      | ~ sP9(X0) ),
    inference(cnf_transformation,[],[f305]) ).

fof(f305,plain,
    ! [X0] :
      ( ( ( totalorderP(X0)
          | ~ sP8(X0) )
        & ( sP8(X0)
          | ~ totalorderP(X0) ) )
      | ~ sP9(X0) ),
    inference(nnf_transformation,[],[f237]) ).

fof(f237,plain,
    ! [X0] :
      ( ( totalorderP(X0)
      <=> sP8(X0) )
      | ~ sP9(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f1247,plain,
    spl71_99,
    inference(avatar_split_clause,[],[f497,f1245]) ).

fof(f1245,plain,
    ( spl71_99
  <=> ! [X0] :
        ( sP8(X0)
        | ~ totalorderP(X0)
        | ~ sP9(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_99])]) ).

fof(f497,plain,
    ! [X0] :
      ( sP8(X0)
      | ~ totalorderP(X0)
      | ~ sP9(X0) ),
    inference(cnf_transformation,[],[f305]) ).

fof(f1243,plain,
    spl71_98,
    inference(avatar_split_clause,[],[f487,f1241]) ).

fof(f1241,plain,
    ( spl71_98
  <=> ! [X0] :
        ( duplicatefreeP(X0)
        | ~ sP6(X0)
        | ~ sP7(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_98])]) ).

fof(f487,plain,
    ! [X0] :
      ( duplicatefreeP(X0)
      | ~ sP6(X0)
      | ~ sP7(X0) ),
    inference(cnf_transformation,[],[f296]) ).

fof(f296,plain,
    ! [X0] :
      ( ( ( duplicatefreeP(X0)
          | ~ sP6(X0) )
        & ( sP6(X0)
          | ~ duplicatefreeP(X0) ) )
      | ~ sP7(X0) ),
    inference(nnf_transformation,[],[f234]) ).

fof(f234,plain,
    ! [X0] :
      ( ( duplicatefreeP(X0)
      <=> sP6(X0) )
      | ~ sP7(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f1239,plain,
    spl71_97,
    inference(avatar_split_clause,[],[f486,f1237]) ).

fof(f1237,plain,
    ( spl71_97
  <=> ! [X0] :
        ( sP6(X0)
        | ~ duplicatefreeP(X0)
        | ~ sP7(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_97])]) ).

fof(f486,plain,
    ! [X0] :
      ( sP6(X0)
      | ~ duplicatefreeP(X0)
      | ~ sP7(X0) ),
    inference(cnf_transformation,[],[f296]) ).

fof(f1235,plain,
    spl71_96,
    inference(avatar_split_clause,[],[f477,f1233]) ).

fof(f477,plain,
    ! [X0] :
      ( equalelemsP(X0)
      | ~ sP4(X0)
      | ~ sP5(X0) ),
    inference(cnf_transformation,[],[f288]) ).

fof(f288,plain,
    ! [X0] :
      ( ( ( equalelemsP(X0)
          | ~ sP4(X0) )
        & ( sP4(X0)
          | ~ equalelemsP(X0) ) )
      | ~ sP5(X0) ),
    inference(nnf_transformation,[],[f231]) ).

fof(f231,plain,
    ! [X0] :
      ( ( equalelemsP(X0)
      <=> sP4(X0) )
      | ~ sP5(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f1231,plain,
    spl71_95,
    inference(avatar_split_clause,[],[f476,f1229]) ).

fof(f1229,plain,
    ( spl71_95
  <=> ! [X0] :
        ( sP4(X0)
        | ~ equalelemsP(X0)
        | ~ sP5(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_95])]) ).

fof(f476,plain,
    ! [X0] :
      ( sP4(X0)
      | ~ equalelemsP(X0)
      | ~ sP5(X0) ),
    inference(cnf_transformation,[],[f288]) ).

fof(f1227,plain,
    spl71_94,
    inference(avatar_split_clause,[],[f410,f1225]) ).

fof(f1225,plain,
    ( spl71_94
  <=> ! [X0] :
        ( totalorderedP(cons(X0,nil))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_94])]) ).

fof(f410,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,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/sandbox/benchmark/theBenchmark.p',ax65) ).

fof(f1223,plain,
    spl71_93,
    inference(avatar_split_clause,[],[f409,f1221]) ).

fof(f1221,plain,
    ( spl71_93
  <=> ! [X0] :
        ( strictorderedP(cons(X0,nil))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_93])]) ).

fof(f409,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,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/sandbox/benchmark/theBenchmark.p',ax68) ).

fof(f1219,plain,
    ( spl71_92
    | ~ spl71_3
    | ~ spl71_26 ),
    inference(avatar_split_clause,[],[f799,f767,f657,f1216]) ).

fof(f1216,plain,
    ( spl71_92
  <=> sP9(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_92])]) ).

fof(f799,plain,
    ( sP9(sK22)
    | ~ spl71_3
    | ~ spl71_26 ),
    inference(resolution,[],[f768,f659]) ).

fof(f1214,plain,
    spl71_91,
    inference(avatar_split_clause,[],[f408,f1212]) ).

fof(f1212,plain,
    ( spl71_91
  <=> ! [X0] :
        ( cyclefreeP(cons(X0,nil))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_91])]) ).

fof(f408,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,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/sandbox/benchmark/theBenchmark.p',ax59) ).

fof(f1210,plain,
    spl71_90,
    inference(avatar_split_clause,[],[f407,f1208]) ).

fof(f1208,plain,
    ( spl71_90
  <=> ! [X0] :
        ( equalelemsP(cons(X0,nil))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_90])]) ).

fof(f407,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,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/sandbox/benchmark/theBenchmark.p',ax73) ).

fof(f1206,plain,
    spl71_89,
    inference(avatar_split_clause,[],[f406,f1204]) ).

fof(f1204,plain,
    ( spl71_89
  <=> ! [X0] :
        ( strictorderP(cons(X0,nil))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_89])]) ).

fof(f406,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,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/sandbox/benchmark/theBenchmark.p',ax63) ).

fof(f1202,plain,
    spl71_88,
    inference(avatar_split_clause,[],[f405,f1200]) ).

fof(f1200,plain,
    ( spl71_88
  <=> ! [X0] :
        ( totalorderP(cons(X0,nil))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_88])]) ).

fof(f405,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,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/sandbox/benchmark/theBenchmark.p',ax61) ).

fof(f1198,plain,
    spl71_87,
    inference(avatar_split_clause,[],[f404,f1196]) ).

fof(f1196,plain,
    ( spl71_87
  <=> ! [X0] :
        ( duplicatefreeP(cons(X0,nil))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_87])]) ).

fof(f404,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/sandbox/benchmark/theBenchmark.p',ax71) ).

fof(f1173,plain,
    ( spl71_86
    | ~ spl71_2
    | ~ spl71_26 ),
    inference(avatar_split_clause,[],[f798,f767,f652,f1170]) ).

fof(f1170,plain,
    ( spl71_86
  <=> sP9(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_86])]) ).

fof(f798,plain,
    ( sP9(sK21)
    | ~ spl71_2
    | ~ spl71_26 ),
    inference(resolution,[],[f768,f654]) ).

fof(f1126,plain,
    ( spl71_85
    | ~ spl71_1
    | ~ spl71_26 ),
    inference(avatar_split_clause,[],[f797,f767,f647,f1123]) ).

fof(f1123,plain,
    ( spl71_85
  <=> sP9(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_85])]) ).

fof(f797,plain,
    ( sP9(sK20)
    | ~ spl71_1
    | ~ spl71_26 ),
    inference(resolution,[],[f768,f649]) ).

fof(f1079,plain,
    ( spl71_84
    | ~ spl71_4
    | ~ spl71_25 ),
    inference(avatar_split_clause,[],[f795,f763,f662,f1076]) ).

fof(f1076,plain,
    ( spl71_84
  <=> sP7(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_84])]) ).

fof(f795,plain,
    ( sP7(sK23)
    | ~ spl71_4
    | ~ spl71_25 ),
    inference(resolution,[],[f764,f664]) ).

fof(f1039,plain,
    ( spl71_83
    | ~ spl71_3
    | ~ spl71_25 ),
    inference(avatar_split_clause,[],[f794,f763,f657,f1036]) ).

fof(f1036,plain,
    ( spl71_83
  <=> sP7(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_83])]) ).

fof(f794,plain,
    ( sP7(sK22)
    | ~ spl71_3
    | ~ spl71_25 ),
    inference(resolution,[],[f764,f659]) ).

fof(f1034,plain,
    ( spl71_82
    | ~ spl71_2
    | ~ spl71_25 ),
    inference(avatar_split_clause,[],[f793,f763,f652,f1031]) ).

fof(f1031,plain,
    ( spl71_82
  <=> sP7(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_82])]) ).

fof(f793,plain,
    ( sP7(sK21)
    | ~ spl71_2
    | ~ spl71_25 ),
    inference(resolution,[],[f764,f654]) ).

fof(f1029,plain,
    spl71_81,
    inference(avatar_split_clause,[],[f644,f1027]) ).

fof(f1027,plain,
    ( spl71_81
  <=> ! [X1] :
        ( ~ neq(X1,X1)
        | ~ ssItem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_81])]) ).

fof(f644,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f611]) ).

fof(f611,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f416]) ).

fof(f416,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f258]) ).

fof(f1025,plain,
    spl71_80,
    inference(avatar_split_clause,[],[f639,f1023]) ).

fof(f1023,plain,
    ( spl71_80
  <=> ! [X1] :
        ( ~ neq(X1,X1)
        | ~ ssList(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_80])]) ).

fof(f639,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f632]) ).

fof(f632,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f578]) ).

fof(f578,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f358]) ).

fof(f1021,plain,
    spl71_79,
    inference(avatar_split_clause,[],[f551,f1019]) ).

fof(f1019,plain,
    ( spl71_79
  <=> ! [X0] :
        ( sP16(X0)
        | ssList(sK62(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_79])]) ).

fof(f551,plain,
    ! [X0] :
      ( sP16(X0)
      | ssList(sK62(X0)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f1017,plain,
    spl71_78,
    inference(avatar_split_clause,[],[f550,f1015]) ).

fof(f1015,plain,
    ( spl71_78
  <=> ! [X0] :
        ( sP16(X0)
        | ssList(sK61(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_78])]) ).

fof(f550,plain,
    ! [X0] :
      ( sP16(X0)
      | ssList(sK61(X0)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f1013,plain,
    spl71_77,
    inference(avatar_split_clause,[],[f549,f1011]) ).

fof(f1011,plain,
    ( spl71_77
  <=> ! [X0] :
        ( sP16(X0)
        | ssList(sK60(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_77])]) ).

fof(f549,plain,
    ! [X0] :
      ( sP16(X0)
      | ssList(sK60(X0)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f1009,plain,
    spl71_76,
    inference(avatar_split_clause,[],[f548,f1007]) ).

fof(f1007,plain,
    ( spl71_76
  <=> ! [X0] :
        ( sP16(X0)
        | ssItem(sK59(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_76])]) ).

fof(f548,plain,
    ! [X0] :
      ( sP16(X0)
      | ssItem(sK59(X0)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f1005,plain,
    spl71_75,
    inference(avatar_split_clause,[],[f547,f1003]) ).

fof(f1003,plain,
    ( spl71_75
  <=> ! [X0] :
        ( sP16(X0)
        | ssItem(sK58(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_75])]) ).

fof(f547,plain,
    ! [X0] :
      ( sP16(X0)
      | ssItem(sK58(X0)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f1001,plain,
    spl71_74,
    inference(avatar_split_clause,[],[f540,f999]) ).

fof(f999,plain,
    ( spl71_74
  <=> ! [X0] :
        ( sP14(X0)
        | ssList(sK57(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_74])]) ).

fof(f540,plain,
    ! [X0] :
      ( sP14(X0)
      | ssList(sK57(X0)) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f997,plain,
    spl71_73,
    inference(avatar_split_clause,[],[f539,f995]) ).

fof(f995,plain,
    ( spl71_73
  <=> ! [X0] :
        ( sP14(X0)
        | ssList(sK56(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_73])]) ).

fof(f539,plain,
    ! [X0] :
      ( sP14(X0)
      | ssList(sK56(X0)) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f993,plain,
    ( spl71_72
    | ~ spl71_1
    | ~ spl71_25 ),
    inference(avatar_split_clause,[],[f792,f763,f647,f990]) ).

fof(f990,plain,
    ( spl71_72
  <=> sP7(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_72])]) ).

fof(f792,plain,
    ( sP7(sK20)
    | ~ spl71_1
    | ~ spl71_25 ),
    inference(resolution,[],[f764,f649]) ).

fof(f988,plain,
    spl71_71,
    inference(avatar_split_clause,[],[f538,f986]) ).

fof(f986,plain,
    ( spl71_71
  <=> ! [X0] :
        ( sP14(X0)
        | ssList(sK55(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_71])]) ).

fof(f538,plain,
    ! [X0] :
      ( sP14(X0)
      | ssList(sK55(X0)) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f984,plain,
    spl71_70,
    inference(avatar_split_clause,[],[f537,f982]) ).

fof(f982,plain,
    ( spl71_70
  <=> ! [X0] :
        ( sP14(X0)
        | ssItem(sK54(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_70])]) ).

fof(f537,plain,
    ! [X0] :
      ( sP14(X0)
      | ssItem(sK54(X0)) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f980,plain,
    spl71_69,
    inference(avatar_split_clause,[],[f536,f978]) ).

fof(f978,plain,
    ( spl71_69
  <=> ! [X0] :
        ( sP14(X0)
        | ssItem(sK53(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_69])]) ).

fof(f536,plain,
    ! [X0] :
      ( sP14(X0)
      | ssItem(sK53(X0)) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f976,plain,
    spl71_68,
    inference(avatar_split_clause,[],[f528,f974]) ).

fof(f974,plain,
    ( spl71_68
  <=> ! [X0] :
        ( sP12(X0)
        | ssList(sK52(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_68])]) ).

fof(f528,plain,
    ! [X0] :
      ( sP12(X0)
      | ssList(sK52(X0)) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f972,plain,
    spl71_67,
    inference(avatar_split_clause,[],[f527,f970]) ).

fof(f970,plain,
    ( spl71_67
  <=> ! [X0] :
        ( sP12(X0)
        | ssList(sK51(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_67])]) ).

fof(f527,plain,
    ! [X0] :
      ( sP12(X0)
      | ssList(sK51(X0)) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f968,plain,
    spl71_66,
    inference(avatar_split_clause,[],[f526,f966]) ).

fof(f966,plain,
    ( spl71_66
  <=> ! [X0] :
        ( sP12(X0)
        | ssList(sK50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_66])]) ).

fof(f526,plain,
    ! [X0] :
      ( sP12(X0)
      | ssList(sK50(X0)) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f964,plain,
    spl71_65,
    inference(avatar_split_clause,[],[f525,f962]) ).

fof(f962,plain,
    ( spl71_65
  <=> ! [X0] :
        ( sP12(X0)
        | ssItem(sK49(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_65])]) ).

fof(f525,plain,
    ! [X0] :
      ( sP12(X0)
      | ssItem(sK49(X0)) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f960,plain,
    spl71_64,
    inference(avatar_split_clause,[],[f524,f958]) ).

fof(f958,plain,
    ( spl71_64
  <=> ! [X0] :
        ( sP12(X0)
        | ssItem(sK48(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_64])]) ).

fof(f524,plain,
    ! [X0] :
      ( sP12(X0)
      | ssItem(sK48(X0)) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f956,plain,
    spl71_63,
    inference(avatar_split_clause,[],[f516,f954]) ).

fof(f954,plain,
    ( spl71_63
  <=> ! [X0] :
        ( sP10(X0)
        | ssList(sK47(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_63])]) ).

fof(f516,plain,
    ! [X0] :
      ( sP10(X0)
      | ssList(sK47(X0)) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f952,plain,
    spl71_62,
    inference(avatar_split_clause,[],[f515,f950]) ).

fof(f950,plain,
    ( spl71_62
  <=> ! [X0] :
        ( sP10(X0)
        | ssList(sK46(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_62])]) ).

fof(f515,plain,
    ! [X0] :
      ( sP10(X0)
      | ssList(sK46(X0)) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f948,plain,
    ( spl71_61
    | ~ spl71_4
    | ~ spl71_24 ),
    inference(avatar_split_clause,[],[f790,f759,f662,f945]) ).

fof(f945,plain,
    ( spl71_61
  <=> sP5(sK23) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_61])]) ).

fof(f790,plain,
    ( sP5(sK23)
    | ~ spl71_4
    | ~ spl71_24 ),
    inference(resolution,[],[f760,f664]) ).

fof(f943,plain,
    spl71_60,
    inference(avatar_split_clause,[],[f514,f941]) ).

fof(f941,plain,
    ( spl71_60
  <=> ! [X0] :
        ( sP10(X0)
        | ssList(sK45(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_60])]) ).

fof(f514,plain,
    ! [X0] :
      ( sP10(X0)
      | ssList(sK45(X0)) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f939,plain,
    spl71_59,
    inference(avatar_split_clause,[],[f513,f937]) ).

fof(f937,plain,
    ( spl71_59
  <=> ! [X0] :
        ( sP10(X0)
        | ssItem(sK44(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_59])]) ).

fof(f513,plain,
    ! [X0] :
      ( sP10(X0)
      | ssItem(sK44(X0)) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f935,plain,
    spl71_58,
    inference(avatar_split_clause,[],[f512,f933]) ).

fof(f933,plain,
    ( spl71_58
  <=> ! [X0] :
        ( sP10(X0)
        | ssItem(sK43(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_58])]) ).

fof(f512,plain,
    ! [X0] :
      ( sP10(X0)
      | ssItem(sK43(X0)) ),
    inference(cnf_transformation,[],[f322]) ).

fof(f931,plain,
    spl71_57,
    inference(avatar_split_clause,[],[f504,f929]) ).

fof(f929,plain,
    ( spl71_57
  <=> ! [X0] :
        ( sP8(X0)
        | ssList(sK42(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_57])]) ).

fof(f504,plain,
    ! [X0] :
      ( sP8(X0)
      | ssList(sK42(X0)) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f927,plain,
    spl71_56,
    inference(avatar_split_clause,[],[f503,f925]) ).

fof(f925,plain,
    ( spl71_56
  <=> ! [X0] :
        ( sP8(X0)
        | ssList(sK41(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_56])]) ).

fof(f503,plain,
    ! [X0] :
      ( sP8(X0)
      | ssList(sK41(X0)) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f923,plain,
    spl71_55,
    inference(avatar_split_clause,[],[f502,f921]) ).

fof(f921,plain,
    ( spl71_55
  <=> ! [X0] :
        ( sP8(X0)
        | ssList(sK40(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_55])]) ).

fof(f502,plain,
    ! [X0] :
      ( sP8(X0)
      | ssList(sK40(X0)) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f919,plain,
    spl71_54,
    inference(avatar_split_clause,[],[f501,f917]) ).

fof(f917,plain,
    ( spl71_54
  <=> ! [X0] :
        ( sP8(X0)
        | ssItem(sK39(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_54])]) ).

fof(f501,plain,
    ! [X0] :
      ( sP8(X0)
      | ssItem(sK39(X0)) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f915,plain,
    spl71_53,
    inference(avatar_split_clause,[],[f500,f913]) ).

fof(f913,plain,
    ( spl71_53
  <=> ! [X0] :
        ( sP8(X0)
        | ssItem(sK38(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_53])]) ).

fof(f500,plain,
    ! [X0] :
      ( sP8(X0)
      | ssItem(sK38(X0)) ),
    inference(cnf_transformation,[],[f313]) ).

fof(f911,plain,
    spl71_52,
    inference(avatar_split_clause,[],[f493,f909]) ).

fof(f909,plain,
    ( spl71_52
  <=> ! [X0] :
        ( sP6(X0)
        | ssList(sK37(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_52])]) ).

fof(f493,plain,
    ! [X0] :
      ( sP6(X0)
      | ssList(sK37(X0)) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f907,plain,
    spl71_51,
    inference(avatar_split_clause,[],[f492,f905]) ).

fof(f905,plain,
    ( spl71_51
  <=> ! [X0] :
        ( sP6(X0)
        | ssList(sK36(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_51])]) ).

fof(f492,plain,
    ! [X0] :
      ( sP6(X0)
      | ssList(sK36(X0)) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f903,plain,
    ( spl71_50
    | ~ spl71_3
    | ~ spl71_24 ),
    inference(avatar_split_clause,[],[f789,f759,f657,f900]) ).

fof(f900,plain,
    ( spl71_50
  <=> sP5(sK22) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_50])]) ).

fof(f789,plain,
    ( sP5(sK22)
    | ~ spl71_3
    | ~ spl71_24 ),
    inference(resolution,[],[f760,f659]) ).

fof(f898,plain,
    spl71_49,
    inference(avatar_split_clause,[],[f491,f896]) ).

fof(f896,plain,
    ( spl71_49
  <=> ! [X0] :
        ( sP6(X0)
        | ssList(sK35(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_49])]) ).

fof(f491,plain,
    ! [X0] :
      ( sP6(X0)
      | ssList(sK35(X0)) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f894,plain,
    spl71_48,
    inference(avatar_split_clause,[],[f490,f892]) ).

fof(f892,plain,
    ( spl71_48
  <=> ! [X0] :
        ( sP6(X0)
        | ssItem(sK34(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_48])]) ).

fof(f490,plain,
    ! [X0] :
      ( sP6(X0)
      | ssItem(sK34(X0)) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f890,plain,
    spl71_47,
    inference(avatar_split_clause,[],[f489,f888]) ).

fof(f888,plain,
    ( spl71_47
  <=> ! [X0] :
        ( sP6(X0)
        | ssItem(sK33(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_47])]) ).

fof(f489,plain,
    ! [X0] :
      ( sP6(X0)
      | ssItem(sK33(X0)) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f886,plain,
    spl71_46,
    inference(avatar_split_clause,[],[f482,f884]) ).

fof(f884,plain,
    ( spl71_46
  <=> ! [X0] :
        ( sP4(X0)
        | ssList(sK32(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_46])]) ).

fof(f482,plain,
    ! [X0] :
      ( sP4(X0)
      | ssList(sK32(X0)) ),
    inference(cnf_transformation,[],[f295]) ).

fof(f882,plain,
    spl71_45,
    inference(avatar_split_clause,[],[f481,f880]) ).

fof(f880,plain,
    ( spl71_45
  <=> ! [X0] :
        ( sP4(X0)
        | ssList(sK31(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_45])]) ).

fof(f481,plain,
    ! [X0] :
      ( sP4(X0)
      | ssList(sK31(X0)) ),
    inference(cnf_transformation,[],[f295]) ).

fof(f878,plain,
    spl71_44,
    inference(avatar_split_clause,[],[f480,f876]) ).

fof(f876,plain,
    ( spl71_44
  <=> ! [X0] :
        ( sP4(X0)
        | ssItem(sK30(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_44])]) ).

fof(f480,plain,
    ! [X0] :
      ( sP4(X0)
      | ssItem(sK30(X0)) ),
    inference(cnf_transformation,[],[f295]) ).

fof(f874,plain,
    spl71_43,
    inference(avatar_split_clause,[],[f479,f872]) ).

fof(f872,plain,
    ( spl71_43
  <=> ! [X0] :
        ( sP4(X0)
        | ssItem(sK29(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_43])]) ).

fof(f479,plain,
    ! [X0] :
      ( sP4(X0)
      | ssItem(sK29(X0)) ),
    inference(cnf_transformation,[],[f295]) ).

fof(f870,plain,
    spl71_42,
    inference(avatar_split_clause,[],[f460,f868]) ).

fof(f868,plain,
    ( spl71_42
  <=> ! [X0] :
        ( rearsegP(X0,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_42])]) ).

fof(f460,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( rearsegP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f49]) ).

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

fof(f866,plain,
    spl71_41,
    inference(avatar_split_clause,[],[f459,f864]) ).

fof(f864,plain,
    ( spl71_41
  <=> ! [X0] :
        ( segmentP(X0,nil)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_41])]) ).

fof(f459,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

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

fof(f862,plain,
    spl71_40,
    inference(avatar_split_clause,[],[f458,f860]) ).

fof(f458,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/sandbox/benchmark/theBenchmark.p',ax55) ).

fof(f858,plain,
    ( spl71_39
    | ~ spl71_2
    | ~ spl71_24 ),
    inference(avatar_split_clause,[],[f788,f759,f652,f855]) ).

fof(f855,plain,
    ( spl71_39
  <=> sP5(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_39])]) ).

fof(f788,plain,
    ( sP5(sK21)
    | ~ spl71_2
    | ~ spl71_24 ),
    inference(resolution,[],[f760,f654]) ).

fof(f853,plain,
    spl71_38,
    inference(avatar_split_clause,[],[f457,f851]) ).

fof(f851,plain,
    ( spl71_38
  <=> ! [X0] :
        ( frontsegP(X0,nil)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_38])]) ).

fof(f457,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/sandbox/benchmark/theBenchmark.p',ax45) ).

fof(f849,plain,
    spl71_37,
    inference(avatar_split_clause,[],[f456,f847]) ).

fof(f847,plain,
    ( spl71_37
  <=> ! [X0] :
        ( frontsegP(X0,X0)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_37])]) ).

fof(f456,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/sandbox/benchmark/theBenchmark.p',ax42) ).

fof(f845,plain,
    spl71_36,
    inference(avatar_split_clause,[],[f455,f843]) ).

fof(f843,plain,
    ( spl71_36
  <=> ! [X0] :
        ( rearsegP(X0,nil)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_36])]) ).

fof(f455,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/sandbox/benchmark/theBenchmark.p',ax51) ).

fof(f841,plain,
    spl71_35,
    inference(avatar_split_clause,[],[f403,f839]) ).

fof(f839,plain,
    ( spl71_35
  <=> ! [X0] :
        ( leq(X0,X0)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_35])]) ).

fof(f403,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( leq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f31]) ).

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

fof(f837,plain,
    spl71_34,
    inference(avatar_split_clause,[],[f402,f835]) ).

fof(f835,plain,
    ( spl71_34
  <=> ! [X0] :
        ( geq(X0,X0)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_34])]) ).

fof(f402,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( geq(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f89]) ).

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

fof(f833,plain,
    spl71_33,
    inference(avatar_split_clause,[],[f401,f831]) ).

fof(f831,plain,
    ( spl71_33
  <=> ! [X0] :
        ( ~ lt(X0,X0)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_33])]) ).

fof(f401,plain,
    ! [X0] :
      ( ~ lt(X0,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ lt(X0,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f90]) ).

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

fof(f829,plain,
    spl71_32,
    inference(avatar_split_clause,[],[f400,f827]) ).

fof(f827,plain,
    ( spl71_32
  <=> ! [X0] :
        ( ~ memberP(nil,X0)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_32])]) ).

fof(f400,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f810,plain,
    ( spl71_31
    | ~ spl71_1
    | ~ spl71_24 ),
    inference(avatar_split_clause,[],[f787,f759,f647,f807]) ).

fof(f787,plain,
    ( sP5(sK20)
    | ~ spl71_1
    | ~ spl71_24 ),
    inference(resolution,[],[f760,f649]) ).

fof(f785,plain,
    spl71_30,
    inference(avatar_split_clause,[],[f554,f783]) ).

fof(f554,plain,
    ! [X0] :
      ( sP17(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f250]) ).

fof(f250,plain,
    ! [X0] :
      ( sP17(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f175,f249,f248]) ).

fof(f175,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,[],[f174]) ).

fof(f174,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/sandbox/benchmark/theBenchmark.p',ax11) ).

fof(f781,plain,
    spl71_29,
    inference(avatar_split_clause,[],[f543,f779]) ).

fof(f543,plain,
    ! [X0] :
      ( sP15(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f247]) ).

fof(f247,plain,
    ! [X0] :
      ( sP15(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f173,f246,f245]) ).

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(flattening,[],[f172]) ).

fof(f172,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/sandbox/benchmark/theBenchmark.p',ax12) ).

fof(f777,plain,
    spl71_28,
    inference(avatar_split_clause,[],[f532,f775]) ).

fof(f532,plain,
    ! [X0] :
      ( sP13(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f244]) ).

fof(f244,plain,
    ! [X0] :
      ( sP13(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f171,f243,f242]) ).

fof(f171,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,[],[f170]) ).

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(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/sandbox/benchmark/theBenchmark.p',ax8) ).

fof(f773,plain,
    spl71_27,
    inference(avatar_split_clause,[],[f520,f771]) ).

fof(f520,plain,
    ! [X0] :
      ( sP11(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f241]) ).

fof(f241,plain,
    ! [X0] :
      ( sP11(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f169,f240,f239]) ).

fof(f169,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,[],[f168]) ).

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(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/sandbox/benchmark/theBenchmark.p',ax10) ).

fof(f769,plain,
    spl71_26,
    inference(avatar_split_clause,[],[f508,f767]) ).

fof(f508,plain,
    ! [X0] :
      ( sP9(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f238]) ).

fof(f238,plain,
    ! [X0] :
      ( sP9(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f167,f237,f236]) ).

fof(f167,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,[],[f166]) ).

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(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/sandbox/benchmark/theBenchmark.p',ax9) ).

fof(f765,plain,
    spl71_25,
    inference(avatar_split_clause,[],[f496,f763]) ).

fof(f496,plain,
    ! [X0] :
      ( sP7(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f235]) ).

fof(f235,plain,
    ! [X0] :
      ( sP7(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f165,f234,f233]) ).

fof(f165,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,[],[f164]) ).

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(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/sandbox/benchmark/theBenchmark.p',ax13) ).

fof(f761,plain,
    spl71_24,
    inference(avatar_split_clause,[],[f485,f759]) ).

fof(f485,plain,
    ! [X0] :
      ( sP5(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f232]) ).

fof(f232,plain,
    ! [X0] :
      ( sP5(X0)
      | ~ ssList(X0) ),
    inference(definition_folding,[],[f163,f231,f230]) ).

fof(f163,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,[],[f162]) ).

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(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/sandbox/benchmark/theBenchmark.p',ax14) ).

fof(f757,plain,
    spl71_23,
    inference(avatar_split_clause,[],[f617,f755]) ).

fof(f755,plain,
    ( spl71_23
  <=> ! [X1] : sP2(nil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_23])]) ).

fof(f617,plain,
    ! [X1] : sP2(nil,X1),
    inference(equality_resolution,[],[f449]) ).

fof(f449,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f274]) ).

fof(f753,plain,
    spl71_22,
    inference(avatar_split_clause,[],[f615,f751]) ).

fof(f751,plain,
    ( spl71_22
  <=> ! [X1] : sP0(nil,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_22])]) ).

fof(f615,plain,
    ! [X1] : sP0(nil,X1),
    inference(equality_resolution,[],[f441]) ).

fof(f441,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f270]) ).

fof(f749,plain,
    ~ spl71_21,
    inference(avatar_split_clause,[],[f607,f746]) ).

fof(f746,plain,
    ( spl71_21
  <=> sK69 = sK70 ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_21])]) ).

fof(f607,plain,
    sK69 != sK70,
    inference(cnf_transformation,[],[f376]) ).

fof(f376,plain,
    ( sK69 != sK70
    & ssItem(sK70)
    & ssItem(sK69) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f2,f375,f374]) ).

fof(f374,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( X0 != X1
            & ssItem(X1) )
        & ssItem(X0) )
   => ( ? [X1] :
          ( sK69 != X1
          & ssItem(X1) )
      & ssItem(sK69) ) ),
    introduced(choice_axiom,[]) ).

fof(f375,plain,
    ( ? [X1] :
        ( sK69 != X1
        & ssItem(X1) )
   => ( sK69 != sK70
      & ssItem(sK70) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f744,plain,
    spl71_20,
    inference(avatar_split_clause,[],[f606,f741]) ).

fof(f741,plain,
    ( spl71_20
  <=> ssItem(sK70) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_20])]) ).

fof(f606,plain,
    ssItem(sK70),
    inference(cnf_transformation,[],[f376]) ).

fof(f739,plain,
    spl71_19,
    inference(avatar_split_clause,[],[f605,f736]) ).

fof(f736,plain,
    ( spl71_19
  <=> ssItem(sK69) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_19])]) ).

fof(f605,plain,
    ssItem(sK69),
    inference(cnf_transformation,[],[f376]) ).

fof(f734,plain,
    spl71_18,
    inference(avatar_split_clause,[],[f399,f731]) ).

fof(f399,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f729,plain,
    spl71_17,
    inference(avatar_split_clause,[],[f398,f726]) ).

fof(f726,plain,
    ( spl71_17
  <=> totalorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_17])]) ).

fof(f398,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

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

fof(f724,plain,
    spl71_16,
    inference(avatar_split_clause,[],[f397,f721]) ).

fof(f721,plain,
    ( spl71_16
  <=> strictorderedP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_16])]) ).

fof(f397,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

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

fof(f719,plain,
    spl71_15,
    inference(avatar_split_clause,[],[f396,f716]) ).

fof(f716,plain,
    ( spl71_15
  <=> totalorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_15])]) ).

fof(f396,plain,
    totalorderP(nil),
    inference(cnf_transformation,[],[f62]) ).

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

fof(f714,plain,
    spl71_14,
    inference(avatar_split_clause,[],[f395,f711]) ).

fof(f711,plain,
    ( spl71_14
  <=> strictorderP(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl71_14])]) ).

fof(f395,plain,
    strictorderP(nil),
    inference(cnf_transformation,[],[f64]) ).

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

fof(f709,plain,
    spl71_13,
    inference(avatar_split_clause,[],[f394,f706]) ).

fof(f394,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

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

fof(f704,plain,
    spl71_12,
    inference(avatar_split_clause,[],[f393,f701]) ).

fof(f393,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

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

fof(f699,plain,
    spl71_11,
    inference(avatar_split_clause,[],[f392,f696]) ).

fof(f392,plain,
    equalelemsP(nil),
    inference(cnf_transformation,[],[f74]) ).

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

fof(f694,plain,
    ~ spl71_10,
    inference(avatar_split_clause,[],[f391,f691]) ).

fof(f391,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

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

fof(f689,plain,
    spl71_9,
    inference(avatar_split_clause,[],[f385,f686]) ).

fof(f385,plain,
    sK21 = app(app(sK22,sK20),sK23),
    inference(cnf_transformation,[],[f257]) ).

fof(f684,plain,
    ( spl71_7
    | ~ spl71_8 ),
    inference(avatar_split_clause,[],[f645,f681,f677]) ).

fof(f645,plain,
    ( nil != sK20
    | sK20 = sK21 ),
    inference(inner_rewriting,[],[f389]) ).

fof(f389,plain,
    ( nil != sK20
    | nil = sK21 ),
    inference(cnf_transformation,[],[f257]) ).

fof(f675,plain,
    ( ~ spl71_6
    | ~ spl71_5 ),
    inference(avatar_split_clause,[],[f608,f667,f672]) ).

fof(f608,plain,
    ( ~ totalorderedP(sK20)
    | ~ segmentP(sK21,sK20) ),
    inference(definition_unfolding,[],[f390,f382,f381,f382]) ).

fof(f381,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f257]) ).

fof(f382,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f257]) ).

fof(f390,plain,
    ( ~ totalorderedP(sK18)
    | ~ segmentP(sK19,sK18) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f670,plain,
    spl71_5,
    inference(avatar_split_clause,[],[f386,f667]) ).

fof(f386,plain,
    totalorderedP(sK20),
    inference(cnf_transformation,[],[f257]) ).

fof(f665,plain,
    spl71_4,
    inference(avatar_split_clause,[],[f384,f662]) ).

fof(f384,plain,
    ssList(sK23),
    inference(cnf_transformation,[],[f257]) ).

fof(f660,plain,
    spl71_3,
    inference(avatar_split_clause,[],[f383,f657]) ).

fof(f383,plain,
    ssList(sK22),
    inference(cnf_transformation,[],[f257]) ).

fof(f655,plain,
    spl71_2,
    inference(avatar_split_clause,[],[f380,f652]) ).

fof(f380,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f257]) ).

fof(f650,plain,
    spl71_1,
    inference(avatar_split_clause,[],[f379,f647]) ).

fof(f379,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f257]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC339+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n026.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 03:04:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (22980)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40  % (22983)WARNING: value z3 for option sas not known
% 0.21/0.40  % (22984)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40  % (22981)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40  % (22982)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40  % (22985)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)
% 0.21/0.40  % (22986)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40  % (22983)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)
% 0.21/0.40  % (22987)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)
% 0.21/0.43  TRYING [1]
% 0.21/0.43  TRYING [1]
% 0.21/0.43  TRYING [2]
% 0.21/0.43  TRYING [2]
% 0.21/0.44  TRYING [3]
% 0.21/0.44  TRYING [3]
% 0.21/0.49  TRYING [4]
% 0.21/0.50  TRYING [1]
% 0.21/0.50  TRYING [2]
% 0.21/0.50  TRYING [4]
% 0.21/0.51  % (22985)First to succeed.
% 0.21/0.51  TRYING [3]
% 1.19/0.53  % (22985)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22980"
% 1.19/0.53  % (22985)Refutation found. Thanks to Tanya!
% 1.19/0.53  % SZS status Theorem for theBenchmark
% 1.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.19/0.54  % (22985)------------------------------
% 1.19/0.54  % (22985)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.19/0.54  % (22985)Termination reason: Refutation
% 1.19/0.54  
% 1.19/0.54  % (22985)Memory used [KB]: 3149
% 1.19/0.54  % (22985)Time elapsed: 0.130 s
% 1.19/0.54  % (22985)Instructions burned: 189 (million)
% 1.19/0.54  % (22980)Success in time 0.155 s
%------------------------------------------------------------------------------