TSTP Solution File: SWC384-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC384-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 10:25:58 EDT 2024
% Result : Unsatisfiable 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 541
% Syntax : Number of formulae : 1319 ( 239 unt; 0 def)
% Number of atoms : 4184 ( 532 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 5241 (2376 ~;2513 |; 0 &)
% ( 352 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 373 ( 371 usr; 353 prp; 0-2 aty)
% Number of functors : 56 ( 56 usr; 10 con; 0-2 aty)
% Number of variables : 1048 (1048 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4468,plain,
$false,
inference(avatar_sat_refutation,[],[f246,f251,f256,f265,f270,f276,f281,f287,f304,f309,f314,f319,f325,f330,f336,f341,f347,f352,f358,f363,f369,f374,f380,f385,f391,f396,f402,f407,f412,f418,f422,f426,f430,f434,f438,f442,f446,f450,f454,f459,f463,f467,f471,f475,f479,f483,f487,f491,f495,f499,f503,f507,f511,f515,f519,f523,f527,f531,f535,f539,f543,f547,f551,f555,f559,f563,f567,f571,f575,f580,f584,f588,f592,f596,f600,f604,f608,f612,f617,f622,f626,f631,f632,f636,f640,f645,f649,f653,f657,f661,f666,f670,f674,f676,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f753,f788,f793,f828,f833,f868,f874,f878,f882,f887,f894,f900,f908,f914,f919,f927,f933,f941,f945,f957,f961,f966,f970,f974,f978,f982,f986,f990,f994,f998,f1003,f1009,f1013,f1020,f1024,f1028,f1032,f1037,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1079,f1083,f1088,f1092,f1106,f1200,f1263,f1276,f1280,f1284,f1288,f1329,f1371,f1375,f1379,f1383,f1387,f1391,f1395,f1400,f1404,f1408,f1412,f1416,f1465,f1494,f1498,f1502,f1506,f1510,f1515,f1519,f1523,f1527,f1605,f1612,f1617,f1626,f1631,f1640,f1644,f1648,f1649,f1654,f1658,f1662,f1666,f1670,f1687,f1723,f1728,f1769,f1773,f1774,f1779,f1840,f1844,f1848,f1852,f1856,f1886,f1890,f2002,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2060,f2087,f2091,f2111,f2115,f2119,f2124,f2128,f2132,f2316,f2322,f2327,f2334,f2341,f2345,f2355,f2359,f2363,f2368,f2382,f2387,f2392,f2393,f2666,f2673,f2676,f2677,f2678,f2679,f2680,f2681,f2685,f2689,f2695,f2699,f2704,f2753,f2803,f2881,f2886,f2894,f2943,f2950,f2955,f3001,f3051,f3058,f3075,f3081,f3086,f3129,f3135,f3137,f3142,f3147,f3165,f3170,f3185,f3189,f3194,f3210,f3215,f3224,f3238,f3260,f3265,f3270,f3444,f3450,f3456,f3461,f3505,f3511,f3515,f3519,f3523,f3603,f3607,f3611,f3615,f3619,f3624,f3628,f3632,f3636,f3640,f3644,f3648,f3652,f3656,f3660,f3664,f3669,f3673,f3677,f3681,f3685,f3689,f3693,f3698,f3702,f3707,f3712,f3763,f3772,f3778,f3785,f3831,f3832,f3836,f3875,f3928,f3938,f3945,f3954,f3960,f3965,f3970,f3974,f3979,f3983,f4173,f4177,f4181,f4185,f4189,f4193,f4198,f4202,f4207,f4212,f4217,f4219,f4302,f4303,f4316,f4318,f4358,f4363,f4365,f4401,f4409,f4414,f4418,f4424,f4425,f4434,f4439,f4463,f4467]) ).
fof(f4467,plain,
( spl0_32
| spl0_4 ),
inference(avatar_split_clause,[],[f198,f258,f415]) ).
fof(f415,plain,
( spl0_32
<=> sk4 = app(app(sk6,sk3),sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f258,plain,
( spl0_4
<=> nil = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f198,axiom,
( nil = sk4
| sk4 = app(app(sk6,sk3),sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f4463,plain,
( spl0_8
| spl0_352
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f4284,f3055,f4436,f278]) ).
fof(f278,plain,
( spl0_8
<=> nil = sk3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f4436,plain,
( spl0_352
<=> sk4 = app(app(sk6,sk3),sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f3055,plain,
( spl0_263
<=> sk6 = sk7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f4284,plain,
( sk4 = app(app(sk6,sk3),sk6)
| nil = sk3
| ~ spl0_263 ),
inference(forward_demodulation,[],[f204,f3057]) ).
fof(f3057,plain,
( sk6 = sk7
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f3055]) ).
fof(f204,axiom,
( nil = sk3
| sk4 = app(app(sk6,sk3),sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f4439,plain,
( ~ spl0_352
| spl0_32
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3231,f3055,f415,f4436]) ).
fof(f3231,plain,
( sk4 != app(app(sk6,sk3),sk6)
| spl0_32
| ~ spl0_263 ),
inference(forward_demodulation,[],[f416,f3057]) ).
fof(f416,plain,
( sk4 != app(app(sk6,sk3),sk7)
| spl0_32 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f4434,plain,
( ~ spl0_278
| spl0_32
| ~ spl0_263
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4415,f4309,f3055,f415,f3235]) ).
fof(f3235,plain,
( spl0_278
<=> sk4 = sk6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f4309,plain,
( spl0_348
<=> sk6 = app(app(sk6,sk3),sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f4415,plain,
( sk4 != sk6
| spl0_32
| ~ spl0_263
| ~ spl0_348 ),
inference(forward_demodulation,[],[f3231,f4311]) ).
fof(f4311,plain,
( sk6 = app(app(sk6,sk3),sk6)
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f4309]) ).
fof(f4425,plain,
( spl0_8
| spl0_348
| ~ spl0_263
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4304,f3235,f3055,f4309,f278]) ).
fof(f4304,plain,
( sk6 = app(app(sk6,sk3),sk6)
| nil = sk3
| ~ spl0_263
| ~ spl0_278 ),
inference(forward_demodulation,[],[f4284,f3237]) ).
fof(f3237,plain,
( sk4 = sk6
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f3235]) ).
fof(f4424,plain,
( ~ spl0_348
| spl0_32
| ~ spl0_263
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4420,f3235,f3055,f415,f4309]) ).
fof(f4420,plain,
( sk6 != app(app(sk6,sk3),sk6)
| spl0_32
| ~ spl0_263
| ~ spl0_278 ),
inference(forward_demodulation,[],[f3231,f3237]) ).
fof(f4418,plain,
( ~ spl0_278
| spl0_32
| ~ spl0_263
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4415,f4309,f3055,f415,f3235]) ).
fof(f4414,plain,
( spl0_347
| ~ spl0_166
| ~ spl0_263
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4412,f4309,f3055,f1326,f4299]) ).
fof(f4299,plain,
( spl0_347
<=> sk6 = app(sk6,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f1326,plain,
( spl0_166
<=> sk7 = app(sk7,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f4412,plain,
( sk6 = app(sk6,sk6)
| ~ spl0_166
| ~ spl0_263
| ~ spl0_348 ),
inference(forward_demodulation,[],[f4311,f3063]) ).
fof(f3063,plain,
( sk6 = app(sk6,sk3)
| ~ spl0_166
| ~ spl0_263 ),
inference(superposition,[],[f1328,f3057]) ).
fof(f1328,plain,
( sk7 = app(sk7,sk3)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f4409,plain,
( ~ spl0_349
| ~ spl0_263
| spl0_319 ),
inference(avatar_split_clause,[],[f3774,f3766,f3055,f4313]) ).
fof(f4313,plain,
( spl0_349
<=> sk3 = sk6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f3766,plain,
( spl0_319
<=> sk3 = sk7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f3774,plain,
( sk3 != sk6
| ~ spl0_263
| spl0_319 ),
inference(forward_demodulation,[],[f3767,f3057]) ).
fof(f3767,plain,
( sk3 != sk7
| spl0_319 ),
inference(avatar_component_clause,[],[f3766]) ).
fof(f4401,plain,
( ~ spl0_351
| spl0_10
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3242,f3235,f297,f4398]) ).
fof(f4398,plain,
( spl0_351
<=> segmentP(sk6,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f297,plain,
( spl0_10
<=> segmentP(sk4,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f3242,plain,
( ~ segmentP(sk6,sk3)
| spl0_10
| ~ spl0_278 ),
inference(superposition,[],[f299,f3237]) ).
fof(f299,plain,
( ~ segmentP(sk4,sk3)
| spl0_10 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f4365,plain,
( ~ spl0_6
| ~ spl0_82
| spl0_281 ),
inference(avatar_split_clause,[],[f3273,f3267,f620,f267]) ).
fof(f267,plain,
( spl0_6
<=> ssList(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f620,plain,
( spl0_82
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f3267,plain,
( spl0_281
<=> segmentP(sk6,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f3273,plain,
( ~ ssList(sk6)
| ~ spl0_82
| spl0_281 ),
inference(resolution,[],[f3269,f621]) ).
fof(f621,plain,
( ! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f3269,plain,
( ~ segmentP(sk6,sk6)
| spl0_281 ),
inference(avatar_component_clause,[],[f3267]) ).
fof(f4363,plain,
( spl0_350
| ~ spl0_3
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3240,f3235,f253,f4360]) ).
fof(f4360,plain,
( spl0_350
<=> neq(sk6,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f253,plain,
( spl0_3
<=> neq(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f3240,plain,
( neq(sk6,nil)
| ~ spl0_3
| ~ spl0_278 ),
inference(superposition,[],[f255,f3237]) ).
fof(f255,plain,
( neq(sk4,nil)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f4358,plain,
( spl0_314
| ~ spl0_11
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4323,f4313,f301,f3695]) ).
fof(f3695,plain,
( spl0_314
<=> singletonP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f301,plain,
( spl0_11
<=> singletonP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f4323,plain,
( singletonP(sk6)
| ~ spl0_11
| ~ spl0_349 ),
inference(superposition,[],[f302,f4315]) ).
fof(f4315,plain,
( sk3 = sk6
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f4313]) ).
fof(f302,plain,
( singletonP(sk3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f4318,plain,
( spl0_347
| ~ spl0_160
| ~ spl0_278
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4317,f4309,f3235,f1197,f4299]) ).
fof(f1197,plain,
( spl0_160
<=> sk4 = app(sk4,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f4317,plain,
( sk6 = app(sk6,sk6)
| ~ spl0_160
| ~ spl0_278
| ~ spl0_348 ),
inference(forward_demodulation,[],[f4311,f3245]) ).
fof(f3245,plain,
( sk6 = app(sk6,sk3)
| ~ spl0_160
| ~ spl0_278 ),
inference(superposition,[],[f1199,f3237]) ).
fof(f1199,plain,
( sk4 = app(sk4,sk3)
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f4316,plain,
( spl0_348
| spl0_349
| ~ spl0_262
| ~ spl0_263
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4305,f3235,f3055,f3048,f4313,f4309]) ).
fof(f3048,plain,
( spl0_262
<=> nil = sk7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f4305,plain,
( sk3 = sk6
| sk6 = app(app(sk6,sk3),sk6)
| ~ spl0_262
| ~ spl0_263
| ~ spl0_278 ),
inference(forward_demodulation,[],[f4304,f4290]) ).
fof(f4290,plain,
( nil = sk6
| ~ spl0_262
| ~ spl0_263 ),
inference(forward_demodulation,[],[f3050,f3057]) ).
fof(f3050,plain,
( nil = sk7
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f3048]) ).
fof(f4303,plain,
( spl0_8
| spl0_347
| ~ spl0_161
| ~ spl0_263
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4286,f3235,f3055,f1260,f4299,f278]) ).
fof(f1260,plain,
( spl0_161
<=> sk6 = app(sk6,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f4286,plain,
( sk6 = app(sk6,sk6)
| nil = sk3
| ~ spl0_161
| ~ spl0_263
| ~ spl0_278 ),
inference(forward_demodulation,[],[f4285,f3237]) ).
fof(f4285,plain,
( sk4 = app(sk6,sk6)
| nil = sk3
| ~ spl0_161
| ~ spl0_263 ),
inference(forward_demodulation,[],[f4284,f1262]) ).
fof(f1262,plain,
( sk6 = app(sk6,sk3)
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1260]) ).
fof(f4302,plain,
( ~ spl0_347
| spl0_32
| ~ spl0_161
| ~ spl0_263
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f4279,f3235,f3055,f1260,f415,f4299]) ).
fof(f4279,plain,
( sk6 != app(sk6,sk6)
| spl0_32
| ~ spl0_161
| ~ spl0_263
| ~ spl0_278 ),
inference(forward_demodulation,[],[f3232,f3237]) ).
fof(f3232,plain,
( sk4 != app(sk6,sk6)
| spl0_32
| ~ spl0_161
| ~ spl0_263 ),
inference(forward_demodulation,[],[f3231,f1262]) ).
fof(f4219,plain,
( ~ spl0_6
| ~ spl0_93
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3272,f3257,f668,f267]) ).
fof(f668,plain,
( spl0_93
<=> ! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f3257,plain,
( spl0_279
<=> neq(sk6,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3272,plain,
( ~ ssList(sk6)
| ~ spl0_93
| ~ spl0_279 ),
inference(resolution,[],[f3259,f669]) ).
fof(f669,plain,
( ! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f3259,plain,
( neq(sk6,sk6)
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f3257]) ).
fof(f4217,plain,
( spl0_346
| ~ spl0_41
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1733,f1726,f452,f4215]) ).
fof(f4215,plain,
( spl0_346
<=> ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf77(X1)
| tl(app(skaf77(X1),X0)) = app(tl(skaf77(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f452,plain,
( spl0_41
<=> ! [X0] : ssList(skaf77(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1726,plain,
( spl0_204
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| tl(app(X1,X0)) = app(tl(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1733,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf77(X1)
| tl(app(skaf77(X1),X0)) = app(tl(skaf77(X1)),X0) )
| ~ spl0_41
| ~ spl0_204 ),
inference(resolution,[],[f1727,f453]) ).
fof(f453,plain,
( ! [X0] : ssList(skaf77(X0))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f1727,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| sk3 = X1
| tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f1726]) ).
fof(f4212,plain,
( spl0_345
| ~ spl0_38
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1732,f1726,f440,f4210]) ).
fof(f4210,plain,
( spl0_345
<=> ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf80(X1)
| tl(app(skaf80(X1),X0)) = app(tl(skaf80(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f440,plain,
( spl0_38
<=> ! [X0] : ssList(skaf80(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1732,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf80(X1)
| tl(app(skaf80(X1),X0)) = app(tl(skaf80(X1)),X0) )
| ~ spl0_38
| ~ spl0_204 ),
inference(resolution,[],[f1727,f441]) ).
fof(f441,plain,
( ! [X0] : ssList(skaf80(X0))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f4207,plain,
( spl0_344
| ~ spl0_37
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1731,f1726,f436,f4205]) ).
fof(f4205,plain,
( spl0_344
<=> ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf81(X1)
| tl(app(skaf81(X1),X0)) = app(tl(skaf81(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f436,plain,
( spl0_37
<=> ! [X0] : ssList(skaf81(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1731,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf81(X1)
| tl(app(skaf81(X1),X0)) = app(tl(skaf81(X1)),X0) )
| ~ spl0_37
| ~ spl0_204 ),
inference(resolution,[],[f1727,f437]) ).
fof(f437,plain,
( ! [X0] : ssList(skaf81(X0))
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f4202,plain,
( spl0_343
| ~ spl0_36
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1730,f1726,f432,f4200]) ).
fof(f4200,plain,
( spl0_343
<=> ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf82(X1)
| tl(app(skaf82(X1),X0)) = app(tl(skaf82(X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f432,plain,
( spl0_36
<=> ! [X0] : ssList(skaf82(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1730,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| sk3 = skaf82(X1)
| tl(app(skaf82(X1),X0)) = app(tl(skaf82(X1)),X0) )
| ~ spl0_36
| ~ spl0_204 ),
inference(resolution,[],[f1727,f433]) ).
fof(f433,plain,
( ! [X0] : ssList(skaf82(X0))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f4198,plain,
( ~ spl0_342
| ~ spl0_94
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3271,f3257,f672,f4195]) ).
fof(f4195,plain,
( spl0_342
<=> ssItem(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f672,plain,
( spl0_94
<=> ! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f3271,plain,
( ~ ssItem(sk6)
| ~ spl0_94
| ~ spl0_279 ),
inference(resolution,[],[f3259,f673]) ).
fof(f673,plain,
( ! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f4193,plain,
( spl0_341
| ~ spl0_78
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f780,f751,f602,f4191]) ).
fof(f4191,plain,
( spl0_341
<=> ! [X0,X1] : duplicatefreeP(skaf42(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f602,plain,
( spl0_78
<=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f751,plain,
( spl0_110
<=> ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f780,plain,
( ! [X0,X1] : duplicatefreeP(skaf42(X0,X1))
| ~ spl0_78
| ~ spl0_110 ),
inference(resolution,[],[f752,f603]) ).
fof(f603,plain,
( ! [X0,X1] : ssList(skaf42(X0,X1))
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f752,plain,
( ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f4189,plain,
( spl0_340
| ~ spl0_77
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f779,f751,f598,f4187]) ).
fof(f4187,plain,
( spl0_340
<=> ! [X0,X1] : duplicatefreeP(skaf43(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f598,plain,
( spl0_77
<=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f779,plain,
( ! [X0,X1] : duplicatefreeP(skaf43(X0,X1))
| ~ spl0_77
| ~ spl0_110 ),
inference(resolution,[],[f752,f599]) ).
fof(f599,plain,
( ! [X0,X1] : ssList(skaf43(X0,X1))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f4185,plain,
( spl0_339
| ~ spl0_76
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f778,f751,f594,f4183]) ).
fof(f4183,plain,
( spl0_339
<=> ! [X0,X1] : duplicatefreeP(skaf45(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f594,plain,
( spl0_76
<=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f778,plain,
( ! [X0,X1] : duplicatefreeP(skaf45(X0,X1))
| ~ spl0_76
| ~ spl0_110 ),
inference(resolution,[],[f752,f595]) ).
fof(f595,plain,
( ! [X0,X1] : ssList(skaf45(X0,X1))
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f4181,plain,
( spl0_338
| ~ spl0_75
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f777,f751,f590,f4179]) ).
fof(f4179,plain,
( spl0_338
<=> ! [X0,X1] : duplicatefreeP(skaf46(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f590,plain,
( spl0_75
<=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f777,plain,
( ! [X0,X1] : duplicatefreeP(skaf46(X0,X1))
| ~ spl0_75
| ~ spl0_110 ),
inference(resolution,[],[f752,f591]) ).
fof(f591,plain,
( ! [X0,X1] : ssList(skaf46(X0,X1))
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f4177,plain,
( spl0_337
| ~ spl0_74
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f776,f751,f586,f4175]) ).
fof(f4175,plain,
( spl0_337
<=> ! [X0,X1] : duplicatefreeP(skaf47(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f586,plain,
( spl0_74
<=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f776,plain,
( ! [X0,X1] : duplicatefreeP(skaf47(X0,X1))
| ~ spl0_74
| ~ spl0_110 ),
inference(resolution,[],[f752,f587]) ).
fof(f587,plain,
( ! [X0,X1] : ssList(skaf47(X0,X1))
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f4173,plain,
( spl0_336
| ~ spl0_73
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f775,f751,f582,f4171]) ).
fof(f4171,plain,
( spl0_336
<=> ! [X0,X1] : duplicatefreeP(skaf48(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f582,plain,
( spl0_73
<=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f775,plain,
( ! [X0,X1] : duplicatefreeP(skaf48(X0,X1))
| ~ spl0_73
| ~ spl0_110 ),
inference(resolution,[],[f752,f583]) ).
fof(f583,plain,
( ! [X0,X1] : ssList(skaf48(X0,X1))
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f3983,plain,
( spl0_335
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f3929,f3926,f2998,f2879,f1462,f1085,f267,f3981]) ).
fof(f3981,plain,
( spl0_335
<=> ! [X0,X1] :
( sk6 = X1
| ~ ssList(X0)
| hd(X1) = hd(cons(hd(X1),X0))
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f1085,plain,
( spl0_158
<=> sk3 = cons(sk5,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1462,plain,
( spl0_179
<=> sk6 = app(sk3,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f2879,plain,
( spl0_253
<=> ! [X0] :
( app(sk3,X0) = cons(sk5,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2998,plain,
( spl0_260
<=> nil = sk6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f3926,plain,
( spl0_324
<=> ! [X0,X1] :
( ~ ssList(X0)
| hd(X1) = hd(cons(hd(X1),X0))
| ~ ssList(X1)
| sk3 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f3929,plain,
( ! [X0,X1] :
( sk6 = X1
| ~ ssList(X0)
| hd(X1) = hd(cons(hd(X1),X0))
| ~ ssList(X1) )
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_324 ),
inference(forward_demodulation,[],[f3927,f3039]) ).
fof(f3039,plain,
( sk3 = sk6
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260 ),
inference(forward_demodulation,[],[f3029,f2937]) ).
fof(f2937,plain,
( sk6 = cons(sk5,sk6)
| ~ spl0_6
| ~ spl0_179
| ~ spl0_253 ),
inference(forward_demodulation,[],[f2932,f1464]) ).
fof(f1464,plain,
( sk6 = app(sk3,sk6)
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f2932,plain,
( app(sk3,sk6) = cons(sk5,sk6)
| ~ spl0_6
| ~ spl0_253 ),
inference(resolution,[],[f2880,f269]) ).
fof(f269,plain,
( ssList(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f2880,plain,
( ! [X0] :
( ~ ssList(X0)
| app(sk3,X0) = cons(sk5,X0) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2879]) ).
fof(f3029,plain,
( sk3 = cons(sk5,sk6)
| ~ spl0_158
| ~ spl0_260 ),
inference(superposition,[],[f1087,f3000]) ).
fof(f3000,plain,
( nil = sk6
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f2998]) ).
fof(f1087,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f3927,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| hd(X1) = hd(cons(hd(X1),X0))
| ~ ssList(X1)
| sk3 = X1 )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3926]) ).
fof(f3979,plain,
( spl0_334
| ~ spl0_5
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1982,f1846,f262,f3977]) ).
fof(f3977,plain,
( spl0_334
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| cons(sk5,app(X1,X0)) = app(cons(sk5,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f262,plain,
( spl0_5
<=> ssItem(sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1846,plain,
( spl0_210
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1982,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| cons(sk5,app(X1,X0)) = app(cons(sk5,X1),X0) )
| ~ spl0_5
| ~ spl0_210 ),
inference(resolution,[],[f1847,f264]) ).
fof(f264,plain,
( ssItem(sk5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f1847,plain,
( ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f1846]) ).
fof(f3974,plain,
( spl0_333
| ~ spl0_12
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1962,f1842,f306,f3972]) ).
fof(f3972,plain,
( spl0_333
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk7,X1),X0) = app(sk7,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f306,plain,
( spl0_12
<=> ssList(sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1842,plain,
( spl0_209
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1962,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk7,X1),X0) = app(sk7,app(X1,X0)) )
| ~ spl0_12
| ~ spl0_209 ),
inference(resolution,[],[f1843,f308]) ).
fof(f308,plain,
( ssList(sk7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f1843,plain,
( ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1842]) ).
fof(f3970,plain,
( spl0_332
| ~ spl0_6
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1961,f1842,f267,f3968]) ).
fof(f3968,plain,
( spl0_332
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk6,X1),X0) = app(sk6,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f1961,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk6,X1),X0) = app(sk6,app(X1,X0)) )
| ~ spl0_6
| ~ spl0_209 ),
inference(resolution,[],[f1843,f269]) ).
fof(f3965,plain,
( spl0_331
| ~ spl0_2
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1960,f1842,f248,f3963]) ).
fof(f3963,plain,
( spl0_331
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f248,plain,
( spl0_2
<=> ssList(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1960,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) )
| ~ spl0_2
| ~ spl0_209 ),
inference(resolution,[],[f1843,f250]) ).
fof(f250,plain,
( ssList(sk4)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f3960,plain,
( spl0_330
| ~ spl0_1
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1959,f1842,f243,f3958]) ).
fof(f3958,plain,
( spl0_330
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f243,plain,
( spl0_1
<=> ssList(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1959,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) )
| ~ spl0_1
| ~ spl0_209 ),
inference(resolution,[],[f1843,f245]) ).
fof(f245,plain,
( ssList(sk3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f3954,plain,
( spl0_328
| spl0_329
| ~ spl0_12
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1926,f1838,f306,f3951,f3947]) ).
fof(f3947,plain,
( spl0_328
<=> sk7 = app(skaf80(sk7),cons(skaf78(sk7),cons(skaf79(sk7),skaf81(sk7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f3951,plain,
( spl0_329
<=> equalelemsP(sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f1838,plain,
( spl0_208
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1926,plain,
( equalelemsP(sk7)
| sk7 = app(skaf80(sk7),cons(skaf78(sk7),cons(skaf79(sk7),skaf81(sk7))))
| ~ spl0_12
| ~ spl0_208 ),
inference(resolution,[],[f1839,f308]) ).
fof(f1839,plain,
( ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f1838]) ).
fof(f3945,plain,
( ~ spl0_327
| ~ spl0_278
| spl0_325 ),
inference(avatar_split_clause,[],[f3940,f3931,f3235,f3942]) ).
fof(f3942,plain,
( spl0_327
<=> sk6 = app(skaf80(sk6),cons(skaf78(sk6),cons(skaf79(sk6),skaf81(sk6)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f3931,plain,
( spl0_325
<=> sk4 = app(skaf80(sk4),cons(skaf78(sk4),cons(skaf79(sk4),skaf81(sk4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f3940,plain,
( sk6 != app(skaf80(sk6),cons(skaf78(sk6),cons(skaf79(sk6),skaf81(sk6))))
| ~ spl0_278
| spl0_325 ),
inference(forward_demodulation,[],[f3932,f3237]) ).
fof(f3932,plain,
( sk4 != app(skaf80(sk4),cons(skaf78(sk4),cons(skaf79(sk4),skaf81(sk4))))
| spl0_325 ),
inference(avatar_component_clause,[],[f3931]) ).
fof(f3938,plain,
( spl0_325
| spl0_326
| ~ spl0_2
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1924,f1838,f248,f3935,f3931]) ).
fof(f3935,plain,
( spl0_326
<=> equalelemsP(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f1924,plain,
( equalelemsP(sk4)
| sk4 = app(skaf80(sk4),cons(skaf78(sk4),cons(skaf79(sk4),skaf81(sk4))))
| ~ spl0_2
| ~ spl0_208 ),
inference(resolution,[],[f1839,f250]) ).
fof(f3928,plain,
( spl0_324
| ~ spl0_117
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1245,f1022,f876,f3926]) ).
fof(f876,plain,
( spl0_117
<=> ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssItem(hd(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1022,plain,
( spl0_144
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1245,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| hd(X1) = hd(cons(hd(X1),X0))
| ~ ssList(X1)
| sk3 = X1 )
| ~ spl0_117
| ~ spl0_144 ),
inference(resolution,[],[f1023,f877]) ).
fof(f877,plain,
( ! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f1023,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f3875,plain,
( ~ spl0_5
| ~ spl0_90
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f3206,f3192,f655,f262]) ).
fof(f655,plain,
( spl0_90
<=> ! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f3192,plain,
( spl0_275
<=> ! [X0] :
( lt(X0,sk5)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f3206,plain,
( ~ ssItem(sk5)
| ~ spl0_90
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f3195]) ).
fof(f3195,plain,
( ~ ssItem(sk5)
| ~ ssItem(sk5)
| ~ spl0_90
| ~ spl0_275 ),
inference(resolution,[],[f3193,f656]) ).
fof(f656,plain,
( ! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f3193,plain,
( ! [X0] :
( lt(X0,sk5)
| ~ ssItem(X0) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f3192]) ).
fof(f3836,plain,
( spl0_323
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3703,f3700,f2998,f2879,f1462,f1085,f267,f3834]) ).
fof(f3834,plain,
( spl0_323
<=> ! [X0,X1] :
( sk6 = X1
| ~ ssList(X0)
| tl(cons(hd(X1),X0)) = X0
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3700,plain,
( spl0_315
<=> ! [X0,X1] :
( ~ ssList(X0)
| tl(cons(hd(X1),X0)) = X0
| ~ ssList(X1)
| sk3 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3703,plain,
( ! [X0,X1] :
( sk6 = X1
| ~ ssList(X0)
| tl(cons(hd(X1),X0)) = X0
| ~ ssList(X1) )
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_315 ),
inference(forward_demodulation,[],[f3701,f3039]) ).
fof(f3701,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| tl(cons(hd(X1),X0)) = X0
| ~ ssList(X1)
| sk3 = X1 )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3700]) ).
fof(f3832,plain,
( spl0_262
| spl0_320
| ~ spl0_12
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1815,f1721,f306,f3770,f3048]) ).
fof(f3770,plain,
( spl0_320
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk7,X0)) = app(tl(sk7),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f1721,plain,
( spl0_203
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1815,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk7
| tl(app(sk7,X0)) = app(tl(sk7),X0) )
| ~ spl0_12
| ~ spl0_203 ),
inference(resolution,[],[f1722,f308]) ).
fof(f1722,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f1721]) ).
fof(f3831,plain,
( spl0_4
| spl0_318
| ~ spl0_2
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1813,f1721,f248,f3761,f258]) ).
fof(f3761,plain,
( spl0_318
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk4,X0)) = app(tl(sk4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1813,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk4
| tl(app(sk4,X0)) = app(tl(sk4),X0) )
| ~ spl0_2
| ~ spl0_203 ),
inference(resolution,[],[f1722,f250]) ).
fof(f3785,plain,
( spl0_322
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_257
| ~ spl0_260
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3781,f3776,f2998,f2947,f2879,f1462,f1085,f267,f3783]) ).
fof(f3783,plain,
( spl0_322
<=> ! [X0] :
( app(sk6,X0) = tl(app(sk6,X0))
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2947,plain,
( spl0_257
<=> nil = tl(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3776,plain,
( spl0_321
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk3,X0)) = app(tl(sk3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f3781,plain,
( ! [X0] :
( app(sk6,X0) = tl(app(sk6,X0))
| ~ ssList(X0) )
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_257
| ~ spl0_260
| ~ spl0_321 ),
inference(forward_demodulation,[],[f3780,f3000]) ).
fof(f3780,plain,
( ! [X0] :
( app(nil,X0) = tl(app(sk6,X0))
| ~ ssList(X0) )
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_257
| ~ spl0_260
| ~ spl0_321 ),
inference(forward_demodulation,[],[f3779,f3039]) ).
fof(f3779,plain,
( ! [X0] :
( app(nil,X0) = tl(app(sk3,X0))
| ~ ssList(X0) )
| ~ spl0_257
| ~ spl0_321 ),
inference(forward_demodulation,[],[f3777,f2949]) ).
fof(f2949,plain,
( nil = tl(sk3)
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2947]) ).
fof(f3777,plain,
( ! [X0] :
( ~ ssList(X0)
| tl(app(sk3,X0)) = app(tl(sk3),X0) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3776]) ).
fof(f3778,plain,
( spl0_8
| spl0_321
| ~ spl0_1
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1812,f1721,f243,f3776,f278]) ).
fof(f1812,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk3
| tl(app(sk3,X0)) = app(tl(sk3),X0) )
| ~ spl0_1
| ~ spl0_203 ),
inference(resolution,[],[f1722,f245]) ).
fof(f3772,plain,
( spl0_319
| spl0_320
| ~ spl0_12
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1764,f1726,f306,f3770,f3766]) ).
fof(f1764,plain,
( ! [X0] :
( ~ ssList(X0)
| sk3 = sk7
| tl(app(sk7,X0)) = app(tl(sk7),X0) )
| ~ spl0_12
| ~ spl0_204 ),
inference(resolution,[],[f1727,f308]) ).
fof(f3763,plain,
( spl0_9
| spl0_318
| ~ spl0_2
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1762,f1726,f248,f3761,f284]) ).
fof(f284,plain,
( spl0_9
<=> sk3 = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1762,plain,
( ! [X0] :
( ~ ssList(X0)
| sk3 = sk4
| tl(app(sk4,X0)) = app(tl(sk4),X0) )
| ~ spl0_2
| ~ spl0_204 ),
inference(resolution,[],[f1727,f250]) ).
fof(f3712,plain,
( spl0_317
| ~ spl0_260
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f3708,f3705,f2998,f3710]) ).
fof(f3710,plain,
( spl0_317
<=> ! [X0] :
( tl(app(sk6,X0)) = app(tl(sk6),X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f3705,plain,
( spl0_316
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(nil,X0)) = app(tl(nil),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f3708,plain,
( ! [X0] :
( tl(app(sk6,X0)) = app(tl(sk6),X0)
| ~ ssList(X0) )
| ~ spl0_260
| ~ spl0_316 ),
inference(forward_demodulation,[],[f3706,f3000]) ).
fof(f3706,plain,
( ! [X0] :
( ~ ssList(X0)
| tl(app(nil,X0)) = app(tl(nil),X0) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f3705]) ).
fof(f3707,plain,
( spl0_8
| spl0_316
| ~ spl0_28
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1729,f1726,f393,f3705,f278]) ).
fof(f393,plain,
( spl0_28
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1729,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk3
| tl(app(nil,X0)) = app(tl(nil),X0) )
| ~ spl0_28
| ~ spl0_204 ),
inference(resolution,[],[f1727,f395]) ).
fof(f395,plain,
( ssList(nil)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f3702,plain,
( spl0_315
| ~ spl0_117
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1225,f1018,f876,f3700]) ).
fof(f1018,plain,
( spl0_143
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1225,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| tl(cons(hd(X1),X0)) = X0
| ~ ssList(X1)
| sk3 = X1 )
| ~ spl0_117
| ~ spl0_143 ),
inference(resolution,[],[f1019,f877]) ).
fof(f1019,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f3698,plain,
( ~ spl0_314
| spl0_31
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3013,f2998,f409,f3695]) ).
fof(f409,plain,
( spl0_31
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f3013,plain,
( ~ singletonP(sk6)
| spl0_31
| ~ spl0_260 ),
inference(superposition,[],[f411,f3000]) ).
fof(f411,plain,
( ~ singletonP(nil)
| spl0_31 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f3693,plain,
( spl0_313
| ~ spl0_68
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f774,f751,f561,f3691]) ).
fof(f3691,plain,
( spl0_313
<=> ! [X0] : duplicatefreeP(skaf51(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f561,plain,
( spl0_68
<=> ! [X0] : ssList(skaf51(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f774,plain,
( ! [X0] : duplicatefreeP(skaf51(X0))
| ~ spl0_68
| ~ spl0_110 ),
inference(resolution,[],[f752,f562]) ).
fof(f562,plain,
( ! [X0] : ssList(skaf51(X0))
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f3689,plain,
( spl0_312
| ~ spl0_67
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f773,f751,f557,f3687]) ).
fof(f3687,plain,
( spl0_312
<=> ! [X0] : duplicatefreeP(skaf52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f557,plain,
( spl0_67
<=> ! [X0] : ssList(skaf52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f773,plain,
( ! [X0] : duplicatefreeP(skaf52(X0))
| ~ spl0_67
| ~ spl0_110 ),
inference(resolution,[],[f752,f558]) ).
fof(f558,plain,
( ! [X0] : ssList(skaf52(X0))
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f3685,plain,
( spl0_311
| ~ spl0_66
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f772,f751,f553,f3683]) ).
fof(f3683,plain,
( spl0_311
<=> ! [X0] : duplicatefreeP(skaf53(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f553,plain,
( spl0_66
<=> ! [X0] : ssList(skaf53(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f772,plain,
( ! [X0] : duplicatefreeP(skaf53(X0))
| ~ spl0_66
| ~ spl0_110 ),
inference(resolution,[],[f752,f554]) ).
fof(f554,plain,
( ! [X0] : ssList(skaf53(X0))
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f3681,plain,
( spl0_310
| ~ spl0_63
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f771,f751,f541,f3679]) ).
fof(f3679,plain,
( spl0_310
<=> ! [X0] : duplicatefreeP(skaf56(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f541,plain,
( spl0_63
<=> ! [X0] : ssList(skaf56(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f771,plain,
( ! [X0] : duplicatefreeP(skaf56(X0))
| ~ spl0_63
| ~ spl0_110 ),
inference(resolution,[],[f752,f542]) ).
fof(f542,plain,
( ! [X0] : ssList(skaf56(X0))
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f3677,plain,
( spl0_309
| ~ spl0_62
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f770,f751,f537,f3675]) ).
fof(f3675,plain,
( spl0_309
<=> ! [X0] : duplicatefreeP(skaf57(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f537,plain,
( spl0_62
<=> ! [X0] : ssList(skaf57(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f770,plain,
( ! [X0] : duplicatefreeP(skaf57(X0))
| ~ spl0_62
| ~ spl0_110 ),
inference(resolution,[],[f752,f538]) ).
fof(f538,plain,
( ! [X0] : ssList(skaf57(X0))
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f3673,plain,
( spl0_308
| ~ spl0_61
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f769,f751,f533,f3671]) ).
fof(f3671,plain,
( spl0_308
<=> ! [X0] : duplicatefreeP(skaf58(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f533,plain,
( spl0_61
<=> ! [X0] : ssList(skaf58(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f769,plain,
( ! [X0] : duplicatefreeP(skaf58(X0))
| ~ spl0_61
| ~ spl0_110 ),
inference(resolution,[],[f752,f534]) ).
fof(f534,plain,
( ! [X0] : ssList(skaf58(X0))
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f3669,plain,
( spl0_307
| ~ spl0_26
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3011,f2998,f382,f3666]) ).
fof(f3666,plain,
( spl0_307
<=> cyclefreeP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f382,plain,
( spl0_26
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f3011,plain,
( cyclefreeP(sk6)
| ~ spl0_26
| ~ spl0_260 ),
inference(superposition,[],[f384,f3000]) ).
fof(f384,plain,
( cyclefreeP(nil)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f3664,plain,
( spl0_306
| ~ spl0_58
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f768,f751,f521,f3662]) ).
fof(f3662,plain,
( spl0_306
<=> ! [X0] : duplicatefreeP(skaf61(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f521,plain,
( spl0_58
<=> ! [X0] : ssList(skaf61(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f768,plain,
( ! [X0] : duplicatefreeP(skaf61(X0))
| ~ spl0_58
| ~ spl0_110 ),
inference(resolution,[],[f752,f522]) ).
fof(f522,plain,
( ! [X0] : ssList(skaf61(X0))
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f3660,plain,
( spl0_305
| ~ spl0_57
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f767,f751,f517,f3658]) ).
fof(f3658,plain,
( spl0_305
<=> ! [X0] : duplicatefreeP(skaf62(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f517,plain,
( spl0_57
<=> ! [X0] : ssList(skaf62(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f767,plain,
( ! [X0] : duplicatefreeP(skaf62(X0))
| ~ spl0_57
| ~ spl0_110 ),
inference(resolution,[],[f752,f518]) ).
fof(f518,plain,
( ! [X0] : ssList(skaf62(X0))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f3656,plain,
( spl0_304
| ~ spl0_56
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f766,f751,f513,f3654]) ).
fof(f3654,plain,
( spl0_304
<=> ! [X0] : duplicatefreeP(skaf63(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f513,plain,
( spl0_56
<=> ! [X0] : ssList(skaf63(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f766,plain,
( ! [X0] : duplicatefreeP(skaf63(X0))
| ~ spl0_56
| ~ spl0_110 ),
inference(resolution,[],[f752,f514]) ).
fof(f514,plain,
( ! [X0] : ssList(skaf63(X0))
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f3652,plain,
( spl0_303
| ~ spl0_53
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f765,f751,f501,f3650]) ).
fof(f3650,plain,
( spl0_303
<=> ! [X0] : duplicatefreeP(skaf66(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f501,plain,
( spl0_53
<=> ! [X0] : ssList(skaf66(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f765,plain,
( ! [X0] : duplicatefreeP(skaf66(X0))
| ~ spl0_53
| ~ spl0_110 ),
inference(resolution,[],[f752,f502]) ).
fof(f502,plain,
( ! [X0] : ssList(skaf66(X0))
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f3648,plain,
( spl0_302
| ~ spl0_52
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f764,f751,f497,f3646]) ).
fof(f3646,plain,
( spl0_302
<=> ! [X0] : duplicatefreeP(skaf67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f497,plain,
( spl0_52
<=> ! [X0] : ssList(skaf67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f764,plain,
( ! [X0] : duplicatefreeP(skaf67(X0))
| ~ spl0_52
| ~ spl0_110 ),
inference(resolution,[],[f752,f498]) ).
fof(f498,plain,
( ! [X0] : ssList(skaf67(X0))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f3644,plain,
( spl0_301
| ~ spl0_51
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f763,f751,f493,f3642]) ).
fof(f3642,plain,
( spl0_301
<=> ! [X0] : duplicatefreeP(skaf68(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f493,plain,
( spl0_51
<=> ! [X0] : ssList(skaf68(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f763,plain,
( ! [X0] : duplicatefreeP(skaf68(X0))
| ~ spl0_51
| ~ spl0_110 ),
inference(resolution,[],[f752,f494]) ).
fof(f494,plain,
( ! [X0] : ssList(skaf68(X0))
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f3640,plain,
( spl0_300
| ~ spl0_48
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f762,f751,f481,f3638]) ).
fof(f3638,plain,
( spl0_300
<=> ! [X0] : duplicatefreeP(skaf71(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f481,plain,
( spl0_48
<=> ! [X0] : ssList(skaf71(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f762,plain,
( ! [X0] : duplicatefreeP(skaf71(X0))
| ~ spl0_48
| ~ spl0_110 ),
inference(resolution,[],[f752,f482]) ).
fof(f482,plain,
( ! [X0] : ssList(skaf71(X0))
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f3636,plain,
( spl0_299
| ~ spl0_47
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f761,f751,f477,f3634]) ).
fof(f3634,plain,
( spl0_299
<=> ! [X0] : duplicatefreeP(skaf72(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f477,plain,
( spl0_47
<=> ! [X0] : ssList(skaf72(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f761,plain,
( ! [X0] : duplicatefreeP(skaf72(X0))
| ~ spl0_47
| ~ spl0_110 ),
inference(resolution,[],[f752,f478]) ).
fof(f478,plain,
( ! [X0] : ssList(skaf72(X0))
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f3632,plain,
( spl0_298
| ~ spl0_46
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f760,f751,f473,f3630]) ).
fof(f3630,plain,
( spl0_298
<=> ! [X0] : duplicatefreeP(skaf73(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f473,plain,
( spl0_46
<=> ! [X0] : ssList(skaf73(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f760,plain,
( ! [X0] : duplicatefreeP(skaf73(X0))
| ~ spl0_46
| ~ spl0_110 ),
inference(resolution,[],[f752,f474]) ).
fof(f474,plain,
( ! [X0] : ssList(skaf73(X0))
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f3628,plain,
( spl0_297
| ~ spl0_44
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f759,f751,f465,f3626]) ).
fof(f3626,plain,
( spl0_297
<=> ! [X0] : duplicatefreeP(skaf75(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f465,plain,
( spl0_44
<=> ! [X0] : ssList(skaf75(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f759,plain,
( ! [X0] : duplicatefreeP(skaf75(X0))
| ~ spl0_44
| ~ spl0_110 ),
inference(resolution,[],[f752,f466]) ).
fof(f466,plain,
( ! [X0] : ssList(skaf75(X0))
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f3624,plain,
( spl0_296
| ~ spl0_24
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3010,f2998,f371,f3621]) ).
fof(f3621,plain,
( spl0_296
<=> totalorderP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f371,plain,
( spl0_24
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f3010,plain,
( totalorderP(sk6)
| ~ spl0_24
| ~ spl0_260 ),
inference(superposition,[],[f373,f3000]) ).
fof(f373,plain,
( totalorderP(nil)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f3619,plain,
( spl0_295
| ~ spl0_43
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f758,f751,f461,f3617]) ).
fof(f3617,plain,
( spl0_295
<=> ! [X0] : duplicatefreeP(skaf76(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f461,plain,
( spl0_43
<=> ! [X0] : ssList(skaf76(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f758,plain,
( ! [X0] : duplicatefreeP(skaf76(X0))
| ~ spl0_43
| ~ spl0_110 ),
inference(resolution,[],[f752,f462]) ).
fof(f462,plain,
( ! [X0] : ssList(skaf76(X0))
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f3615,plain,
( spl0_294
| ~ spl0_41
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f757,f751,f452,f3613]) ).
fof(f3613,plain,
( spl0_294
<=> ! [X0] : duplicatefreeP(skaf77(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f757,plain,
( ! [X0] : duplicatefreeP(skaf77(X0))
| ~ spl0_41
| ~ spl0_110 ),
inference(resolution,[],[f752,f453]) ).
fof(f3611,plain,
( spl0_293
| ~ spl0_38
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f756,f751,f440,f3609]) ).
fof(f3609,plain,
( spl0_293
<=> ! [X0] : duplicatefreeP(skaf80(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f756,plain,
( ! [X0] : duplicatefreeP(skaf80(X0))
| ~ spl0_38
| ~ spl0_110 ),
inference(resolution,[],[f752,f441]) ).
fof(f3607,plain,
( spl0_292
| ~ spl0_37
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f755,f751,f436,f3605]) ).
fof(f3605,plain,
( spl0_292
<=> ! [X0] : duplicatefreeP(skaf81(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f755,plain,
( ! [X0] : duplicatefreeP(skaf81(X0))
| ~ spl0_37
| ~ spl0_110 ),
inference(resolution,[],[f752,f437]) ).
fof(f3603,plain,
( spl0_291
| ~ spl0_36
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f754,f751,f432,f3601]) ).
fof(f3601,plain,
( spl0_291
<=> ! [X0] : duplicatefreeP(skaf82(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f754,plain,
( ! [X0] : duplicatefreeP(skaf82(X0))
| ~ spl0_36
| ~ spl0_110 ),
inference(resolution,[],[f752,f433]) ).
fof(f3523,plain,
( spl0_290
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3452,f3448,f2998,f2879,f1462,f1085,f267,f3521]) ).
fof(f3521,plain,
( spl0_290
<=> ! [X0] :
( sk6 = X0
| tl(X0) = app(sk6,tl(X0))
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f3448,plain,
( spl0_283
<=> ! [X0] :
( tl(X0) = app(nil,tl(X0))
| ~ ssList(X0)
| sk3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3452,plain,
( ! [X0] :
( sk6 = X0
| tl(X0) = app(sk6,tl(X0))
| ~ ssList(X0) )
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_283 ),
inference(forward_demodulation,[],[f3451,f3039]) ).
fof(f3451,plain,
( ! [X0] :
( tl(X0) = app(sk6,tl(X0))
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_260
| ~ spl0_283 ),
inference(forward_demodulation,[],[f3449,f3000]) ).
fof(f3449,plain,
( ! [X0] :
( tl(X0) = app(nil,tl(X0))
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f3448]) ).
fof(f3519,plain,
( spl0_289
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3446,f3442,f2998,f2879,f1462,f1085,f267,f3517]) ).
fof(f3517,plain,
( spl0_289
<=> ! [X0] :
( sk6 = X0
| tl(X0) = app(tl(X0),sk6)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3442,plain,
( spl0_282
<=> ! [X0] :
( tl(X0) = app(tl(X0),nil)
| ~ ssList(X0)
| sk3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3446,plain,
( ! [X0] :
( sk6 = X0
| tl(X0) = app(tl(X0),sk6)
| ~ ssList(X0) )
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_282 ),
inference(forward_demodulation,[],[f3445,f3039]) ).
fof(f3445,plain,
( ! [X0] :
( tl(X0) = app(tl(X0),sk6)
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_260
| ~ spl0_282 ),
inference(forward_demodulation,[],[f3443,f3000]) ).
fof(f3443,plain,
( ! [X0] :
( tl(X0) = app(tl(X0),nil)
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f3442]) ).
fof(f3515,plain,
( spl0_262
| spl0_288
| ~ spl0_12
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1563,f1492,f306,f3513,f3048]) ).
fof(f3513,plain,
( spl0_288
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk7) = hd(app(sk7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f1492,plain,
( spl0_180
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1563,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk7
| hd(sk7) = hd(app(sk7,X0)) )
| ~ spl0_12
| ~ spl0_180 ),
inference(resolution,[],[f1493,f308]) ).
fof(f1493,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| hd(app(X1,X0)) = hd(X1) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f3511,plain,
( spl0_287
| ~ spl0_22
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3009,f2998,f360,f3508]) ).
fof(f3508,plain,
( spl0_287
<=> strictorderP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f360,plain,
( spl0_22
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f3009,plain,
( strictorderP(sk6)
| ~ spl0_22
| ~ spl0_260 ),
inference(superposition,[],[f362,f3000]) ).
fof(f362,plain,
( strictorderP(nil)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f3505,plain,
( spl0_4
| spl0_286
| ~ spl0_2
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1561,f1492,f248,f3503,f258]) ).
fof(f3503,plain,
( spl0_286
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk4) = hd(app(sk4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f1561,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk4
| hd(sk4) = hd(app(sk4,X0)) )
| ~ spl0_2
| ~ spl0_180 ),
inference(resolution,[],[f1493,f250]) ).
fof(f3461,plain,
( spl0_285
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3457,f3454,f2998,f2879,f1462,f1085,f267,f3459]) ).
fof(f3459,plain,
( spl0_285
<=> ! [X0] :
( hd(sk6) = hd(app(sk6,X0))
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f3454,plain,
( spl0_284
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk3) = hd(app(sk3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3457,plain,
( ! [X0] :
( hd(sk6) = hd(app(sk6,X0))
| ~ ssList(X0) )
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_284 ),
inference(forward_demodulation,[],[f3455,f3039]) ).
fof(f3455,plain,
( ! [X0] :
( ~ ssList(X0)
| hd(sk3) = hd(app(sk3,X0)) )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f3454]) ).
fof(f3456,plain,
( spl0_8
| spl0_284
| ~ spl0_1
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1560,f1492,f243,f3454,f278]) ).
fof(f1560,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk3
| hd(sk3) = hd(app(sk3,X0)) )
| ~ spl0_1
| ~ spl0_180 ),
inference(resolution,[],[f1493,f245]) ).
fof(f3450,plain,
( spl0_283
| ~ spl0_113
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1176,f885,f826,f3448]) ).
fof(f826,plain,
( spl0_113
<=> ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f885,plain,
( spl0_119
<=> ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssList(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1176,plain,
( ! [X0] :
( tl(X0) = app(nil,tl(X0))
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_113
| ~ spl0_119 ),
inference(resolution,[],[f827,f886]) ).
fof(f886,plain,
( ! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f827,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f3444,plain,
( spl0_282
| ~ spl0_111
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1141,f885,f786,f3442]) ).
fof(f786,plain,
( spl0_111
<=> ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1141,plain,
( ! [X0] :
( tl(X0) = app(tl(X0),nil)
| ~ ssList(X0)
| sk3 = X0 )
| ~ spl0_111
| ~ spl0_119 ),
inference(resolution,[],[f787,f886]) ).
fof(f787,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f786]) ).
fof(f3270,plain,
( ~ spl0_281
| ~ spl0_6
| spl0_10
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3253,f3235,f2998,f2879,f1462,f1085,f297,f267,f3267]) ).
fof(f3253,plain,
( ~ segmentP(sk6,sk6)
| ~ spl0_6
| spl0_10
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_278 ),
inference(forward_demodulation,[],[f3242,f3039]) ).
fof(f3265,plain,
( spl0_280
| ~ spl0_20
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3008,f2998,f349,f3262]) ).
fof(f3262,plain,
( spl0_280
<=> totalorderedP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f349,plain,
( spl0_20
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f3008,plain,
( totalorderedP(sk6)
| ~ spl0_20
| ~ spl0_260 ),
inference(superposition,[],[f351,f3000]) ).
fof(f351,plain,
( totalorderedP(nil)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f3260,plain,
( spl0_279
| ~ spl0_3
| ~ spl0_260
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3252,f3235,f2998,f253,f3257]) ).
fof(f3252,plain,
( neq(sk6,sk6)
| ~ spl0_3
| ~ spl0_260
| ~ spl0_278 ),
inference(forward_demodulation,[],[f3240,f3000]) ).
fof(f3238,plain,
( spl0_278
| ~ spl0_161
| ~ spl0_229
| ~ spl0_260
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f3230,f3055,f2998,f2121,f1260,f3235]) ).
fof(f2121,plain,
( spl0_229
<=> sk6 = app(sk6,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f3230,plain,
( sk4 = sk6
| ~ spl0_161
| ~ spl0_229
| ~ spl0_260
| ~ spl0_263 ),
inference(duplicate_literal_removal,[],[f3229]) ).
fof(f3229,plain,
( sk4 = sk6
| sk4 = sk6
| ~ spl0_161
| ~ spl0_229
| ~ spl0_260
| ~ spl0_263 ),
inference(forward_demodulation,[],[f3228,f3032]) ).
fof(f3032,plain,
( sk6 = app(sk6,sk6)
| ~ spl0_229
| ~ spl0_260 ),
inference(superposition,[],[f2123,f3000]) ).
fof(f2123,plain,
( sk6 = app(sk6,nil)
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f3228,plain,
( sk4 = app(sk6,sk6)
| sk4 = sk6
| ~ spl0_161
| ~ spl0_260
| ~ spl0_263 ),
inference(forward_demodulation,[],[f3227,f1262]) ).
fof(f3227,plain,
( sk4 = app(app(sk6,sk3),sk6)
| sk4 = sk6
| ~ spl0_260
| ~ spl0_263 ),
inference(forward_demodulation,[],[f3226,f3057]) ).
fof(f3226,plain,
( sk4 = sk6
| sk4 = app(app(sk6,sk3),sk7)
| ~ spl0_260 ),
inference(forward_demodulation,[],[f198,f3000]) ).
fof(f3224,plain,
( ~ spl0_12
| ~ spl0_6
| ~ spl0_1
| ~ spl0_2
| spl0_10
| ~ spl0_32
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2102,f2089,f415,f297,f248,f243,f267,f306]) ).
fof(f2089,plain,
( spl0_225
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2102,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ spl0_32
| ~ spl0_225 ),
inference(superposition,[],[f2090,f417]) ).
fof(f417,plain,
( sk4 = app(app(sk6,sk3),sk7)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f2090,plain,
( ! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2089]) ).
fof(f3215,plain,
( spl0_277
| ~ spl0_28
| ~ spl0_158
| ~ spl0_249
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3211,f3208,f2697,f1085,f393,f3213]) ).
fof(f3213,plain,
( spl0_277
<=> ! [X0] :
( leq(X0,sk5)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2697,plain,
( spl0_249
<=> ! [X0] :
( ~ ssList(X0)
| sk5 = hd(cons(sk5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f3208,plain,
( spl0_276
<=> ! [X0] :
( ~ ssItem(X0)
| leq(X0,hd(sk3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f3211,plain,
( ! [X0] :
( leq(X0,sk5)
| ~ ssItem(X0) )
| ~ spl0_28
| ~ spl0_158
| ~ spl0_249
| ~ spl0_276 ),
inference(forward_demodulation,[],[f3209,f2877]) ).
fof(f2877,plain,
( sk5 = hd(sk3)
| ~ spl0_28
| ~ spl0_158
| ~ spl0_249 ),
inference(forward_demodulation,[],[f2841,f1087]) ).
fof(f2841,plain,
( sk5 = hd(cons(sk5,nil))
| ~ spl0_28
| ~ spl0_249 ),
inference(resolution,[],[f2698,f395]) ).
fof(f2698,plain,
( ! [X0] :
( ~ ssList(X0)
| sk5 = hd(cons(sk5,X0)) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2697]) ).
fof(f3209,plain,
( ! [X0] :
( ~ ssItem(X0)
| leq(X0,hd(sk3)) )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f3208]) ).
fof(f3210,plain,
( spl0_276
| spl0_8
| ~ spl0_1
| ~ spl0_102
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1680,f1624,f713,f243,f278,f3208]) ).
fof(f713,plain,
( spl0_102
<=> ! [X0] :
( totalorderedP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1624,plain,
( spl0_192
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1680,plain,
( ! [X0] :
( ~ ssList(sk3)
| nil = sk3
| ~ ssItem(X0)
| leq(X0,hd(sk3)) )
| ~ spl0_102
| ~ spl0_192 ),
inference(duplicate_literal_removal,[],[f1676]) ).
fof(f1676,plain,
( ! [X0] :
( ~ ssList(sk3)
| nil = sk3
| ~ ssItem(X0)
| leq(X0,hd(sk3))
| ~ ssItem(X0) )
| ~ spl0_102
| ~ spl0_192 ),
inference(resolution,[],[f1625,f714]) ).
fof(f714,plain,
( ! [X0] :
( totalorderedP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f1625,plain,
( ! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| ~ ssList(X1)
| nil = X1
| ~ ssItem(X0)
| leq(X0,hd(X1)) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1624]) ).
fof(f3194,plain,
( spl0_275
| ~ spl0_28
| ~ spl0_158
| ~ spl0_249
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3190,f3187,f2697,f1085,f393,f3192]) ).
fof(f3187,plain,
( spl0_274
<=> ! [X0] :
( ~ ssItem(X0)
| lt(X0,hd(sk3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3190,plain,
( ! [X0] :
( lt(X0,sk5)
| ~ ssItem(X0) )
| ~ spl0_28
| ~ spl0_158
| ~ spl0_249
| ~ spl0_274 ),
inference(forward_demodulation,[],[f3188,f2877]) ).
fof(f3188,plain,
( ! [X0] :
( ~ ssItem(X0)
| lt(X0,hd(sk3)) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f3187]) ).
fof(f3189,plain,
( spl0_274
| spl0_8
| ~ spl0_1
| ~ spl0_100
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1675,f1610,f703,f243,f278,f3187]) ).
fof(f703,plain,
( spl0_100
<=> ! [X0] :
( strictorderedP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1610,plain,
( spl0_190
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1675,plain,
( ! [X0] :
( ~ ssList(sk3)
| nil = sk3
| ~ ssItem(X0)
| lt(X0,hd(sk3)) )
| ~ spl0_100
| ~ spl0_190 ),
inference(duplicate_literal_removal,[],[f1671]) ).
fof(f1671,plain,
( ! [X0] :
( ~ ssList(sk3)
| nil = sk3
| ~ ssItem(X0)
| lt(X0,hd(sk3))
| ~ ssItem(X0) )
| ~ spl0_100
| ~ spl0_190 ),
inference(resolution,[],[f1611,f704]) ).
fof(f704,plain,
( ! [X0] :
( strictorderedP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f1611,plain,
( ! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| ~ ssList(X1)
| nil = X1
| ~ ssItem(X0)
| lt(X0,hd(X1)) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1610]) ).
fof(f3185,plain,
( spl0_273
| ~ spl0_18
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3007,f2998,f338,f3182]) ).
fof(f3182,plain,
( spl0_273
<=> strictorderedP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f338,plain,
( spl0_18
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f3007,plain,
( strictorderedP(sk6)
| ~ spl0_18
| ~ spl0_260 ),
inference(superposition,[],[f340,f3000]) ).
fof(f340,plain,
( strictorderedP(nil)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f3170,plain,
( spl0_272
| ~ spl0_260
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3166,f3163,f2998,f3168]) ).
fof(f3168,plain,
( spl0_272
<=> ! [X0] :
( leq(X0,hd(sk6))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f3163,plain,
( spl0_271
<=> ! [X0] :
( ~ ssItem(X0)
| leq(X0,hd(nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3166,plain,
( ! [X0] :
( leq(X0,hd(sk6))
| ~ ssItem(X0) )
| ~ spl0_260
| ~ spl0_271 ),
inference(forward_demodulation,[],[f3164,f3000]) ).
fof(f3164,plain,
( ! [X0] :
( ~ ssItem(X0)
| leq(X0,hd(nil)) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f3163]) ).
fof(f3165,plain,
( spl0_8
| ~ spl0_28
| spl0_271
| ~ spl0_101
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1635,f1629,f708,f3163,f393,f278]) ).
fof(f708,plain,
( spl0_101
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1629,plain,
( spl0_193
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1635,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| nil = sk3
| leq(X0,hd(nil)) )
| ~ spl0_101
| ~ spl0_193 ),
inference(duplicate_literal_removal,[],[f1633]) ).
fof(f1633,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| nil = sk3
| leq(X0,hd(nil))
| ~ ssItem(X0) )
| ~ spl0_101
| ~ spl0_193 ),
inference(resolution,[],[f1630,f709]) ).
fof(f709,plain,
( ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f1630,plain,
( ! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| sk3 = X1
| leq(X0,hd(X1)) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f3147,plain,
( spl0_270
| ~ spl0_260
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3143,f3140,f2998,f3145]) ).
fof(f3145,plain,
( spl0_270
<=> ! [X0] :
( lt(X0,hd(sk6))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f3140,plain,
( spl0_269
<=> ! [X0] :
( ~ ssItem(X0)
| lt(X0,hd(nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f3143,plain,
( ! [X0] :
( lt(X0,hd(sk6))
| ~ ssItem(X0) )
| ~ spl0_260
| ~ spl0_269 ),
inference(forward_demodulation,[],[f3141,f3000]) ).
fof(f3141,plain,
( ! [X0] :
( ~ ssItem(X0)
| lt(X0,hd(nil)) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f3140]) ).
fof(f3142,plain,
( spl0_8
| ~ spl0_28
| spl0_269
| ~ spl0_99
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1621,f1615,f698,f3140,f393,f278]) ).
fof(f698,plain,
( spl0_99
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1615,plain,
( spl0_191
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1621,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| nil = sk3
| lt(X0,hd(nil)) )
| ~ spl0_99
| ~ spl0_191 ),
inference(duplicate_literal_removal,[],[f1619]) ).
fof(f1619,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| nil = sk3
| lt(X0,hd(nil))
| ~ ssItem(X0) )
| ~ spl0_99
| ~ spl0_191 ),
inference(resolution,[],[f1616,f699]) ).
fof(f699,plain,
( ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f1616,plain,
( ! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| sk3 = X1
| lt(X0,hd(X1)) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1615]) ).
fof(f3137,plain,
( ~ spl0_265
| ~ spl0_263
| spl0_268 ),
inference(avatar_split_clause,[],[f3136,f3132,f3055,f3078]) ).
fof(f3078,plain,
( spl0_265
<=> sk6 = cons(skaf83(sk6),skaf82(sk6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f3132,plain,
( spl0_268
<=> sk7 = cons(skaf83(sk7),skaf82(sk7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3136,plain,
( sk6 != cons(skaf83(sk6),skaf82(sk6))
| ~ spl0_263
| spl0_268 ),
inference(forward_demodulation,[],[f3133,f3057]) ).
fof(f3133,plain,
( sk7 != cons(skaf83(sk7),skaf82(sk7))
| spl0_268 ),
inference(avatar_component_clause,[],[f3132]) ).
fof(f3135,plain,
( spl0_268
| spl0_262
| ~ spl0_12
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1365,f1278,f306,f3048,f3132]) ).
fof(f1278,plain,
( spl0_163
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1365,plain,
( nil = sk7
| sk7 = cons(skaf83(sk7),skaf82(sk7))
| ~ spl0_12
| ~ spl0_163 ),
inference(resolution,[],[f1279,f308]) ).
fof(f1279,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1278]) ).
fof(f3129,plain,
( spl0_267
| spl0_4
| ~ spl0_2
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1363,f1278,f248,f258,f3126]) ).
fof(f3126,plain,
( spl0_267
<=> sk4 = cons(skaf83(sk4),skaf82(sk4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1363,plain,
( nil = sk4
| sk4 = cons(skaf83(sk4),skaf82(sk4))
| ~ spl0_2
| ~ spl0_163 ),
inference(resolution,[],[f1279,f250]) ).
fof(f3086,plain,
( spl0_266
| ~ spl0_14
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f3005,f2998,f316,f3083]) ).
fof(f3083,plain,
( spl0_266
<=> equalelemsP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f316,plain,
( spl0_14
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f3005,plain,
( equalelemsP(sk6)
| ~ spl0_14
| ~ spl0_260 ),
inference(superposition,[],[f318,f3000]) ).
fof(f318,plain,
( equalelemsP(nil)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f3081,plain,
( spl0_265
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f3076,f3072,f2998,f2879,f1462,f1085,f267,f3078]) ).
fof(f3072,plain,
( spl0_264
<=> sk3 = cons(skaf83(sk3),skaf82(sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f3076,plain,
( sk6 = cons(skaf83(sk6),skaf82(sk6))
| ~ spl0_6
| ~ spl0_158
| ~ spl0_179
| ~ spl0_253
| ~ spl0_260
| ~ spl0_264 ),
inference(forward_demodulation,[],[f3074,f3039]) ).
fof(f3074,plain,
( sk3 = cons(skaf83(sk3),skaf82(sk3))
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f3072]) ).
fof(f3075,plain,
( spl0_264
| spl0_8
| ~ spl0_1
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1362,f1278,f243,f278,f3072]) ).
fof(f1362,plain,
( nil = sk3
| sk3 = cons(skaf83(sk3),skaf82(sk3))
| ~ spl0_1
| ~ spl0_163 ),
inference(resolution,[],[f1279,f245]) ).
fof(f3058,plain,
( spl0_263
| ~ spl0_260
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f3052,f3048,f2998,f3055]) ).
fof(f3052,plain,
( sk6 = sk7
| ~ spl0_260
| ~ spl0_262 ),
inference(forward_demodulation,[],[f3050,f3000]) ).
fof(f3051,plain,
( spl0_261
| spl0_262
| ~ spl0_12
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1324,f1274,f306,f3048,f3044]) ).
fof(f3044,plain,
( spl0_261
<=> sk7 = cons(hd(sk7),tl(sk7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1274,plain,
( spl0_162
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1324,plain,
( nil = sk7
| sk7 = cons(hd(sk7),tl(sk7))
| ~ spl0_12
| ~ spl0_162 ),
inference(resolution,[],[f1275,f308]) ).
fof(f1275,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1274]) ).
fof(f3001,plain,
( spl0_259
| spl0_260
| ~ spl0_6
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1323,f1274,f267,f2998,f2994]) ).
fof(f2994,plain,
( spl0_259
<=> sk6 = cons(hd(sk6),tl(sk6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1323,plain,
( nil = sk6
| sk6 = cons(hd(sk6),tl(sk6))
| ~ spl0_6
| ~ spl0_162 ),
inference(resolution,[],[f1275,f269]) ).
fof(f2955,plain,
( spl0_258
| spl0_4
| ~ spl0_2
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1322,f1274,f248,f258,f2952]) ).
fof(f2952,plain,
( spl0_258
<=> sk4 = cons(hd(sk4),tl(sk4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1322,plain,
( nil = sk4
| sk4 = cons(hd(sk4),tl(sk4))
| ~ spl0_2
| ~ spl0_162 ),
inference(resolution,[],[f1275,f250]) ).
fof(f2950,plain,
( spl0_257
| ~ spl0_28
| ~ spl0_158
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2840,f2693,f1085,f393,f2947]) ).
fof(f2693,plain,
( spl0_248
<=> ! [X0] :
( ~ ssList(X0)
| tl(cons(sk5,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2840,plain,
( nil = tl(sk3)
| ~ spl0_28
| ~ spl0_158
| ~ spl0_248 ),
inference(forward_demodulation,[],[f2804,f1087]) ).
fof(f2804,plain,
( nil = tl(cons(sk5,nil))
| ~ spl0_28
| ~ spl0_248 ),
inference(resolution,[],[f2694,f395]) ).
fof(f2694,plain,
( ! [X0] :
( ~ ssList(X0)
| tl(cons(sk5,X0)) = X0 )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2693]) ).
fof(f2943,plain,
( spl0_256
| spl0_8
| ~ spl0_1
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1321,f1274,f243,f278,f2940]) ).
fof(f2940,plain,
( spl0_256
<=> sk3 = cons(hd(sk3),tl(sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1321,plain,
( nil = sk3
| sk3 = cons(hd(sk3),tl(sk3))
| ~ spl0_1
| ~ spl0_162 ),
inference(resolution,[],[f1275,f245]) ).
fof(f2894,plain,
( ~ spl0_12
| ~ spl0_2
| spl0_255
| ~ spl0_6
| ~ spl0_32
| ~ spl0_161
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1490,f1414,f1260,f415,f267,f2891,f248,f306]) ).
fof(f2891,plain,
( spl0_255
<=> frontsegP(sk4,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1414,plain,
( spl0_178
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1490,plain,
( ~ ssList(sk6)
| frontsegP(sk4,sk6)
| ~ ssList(sk4)
| ~ ssList(sk7)
| ~ spl0_32
| ~ spl0_161
| ~ spl0_178 ),
inference(forward_demodulation,[],[f1489,f1262]) ).
fof(f1489,plain,
( frontsegP(sk4,sk6)
| ~ ssList(sk4)
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7)
| ~ spl0_32
| ~ spl0_161
| ~ spl0_178 ),
inference(forward_demodulation,[],[f1487,f1262]) ).
fof(f1487,plain,
( frontsegP(sk4,app(sk6,sk3))
| ~ ssList(sk4)
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7)
| ~ spl0_32
| ~ spl0_178 ),
inference(superposition,[],[f1415,f417]) ).
fof(f1415,plain,
( ! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1414]) ).
fof(f2886,plain,
( ~ spl0_12
| ~ spl0_2
| spl0_254
| ~ spl0_6
| ~ spl0_32
| ~ spl0_161
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1485,f1410,f1260,f415,f267,f2883,f248,f306]) ).
fof(f2883,plain,
( spl0_254
<=> rearsegP(sk4,sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1410,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1485,plain,
( ~ ssList(sk6)
| rearsegP(sk4,sk7)
| ~ ssList(sk4)
| ~ ssList(sk7)
| ~ spl0_32
| ~ spl0_161
| ~ spl0_177 ),
inference(forward_demodulation,[],[f1483,f1262]) ).
fof(f1483,plain,
( rearsegP(sk4,sk7)
| ~ ssList(sk4)
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| ~ spl0_32
| ~ spl0_177 ),
inference(superposition,[],[f1411,f417]) ).
fof(f1411,plain,
( ! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1410]) ).
fof(f2881,plain,
( spl0_253
| ~ spl0_5
| ~ spl0_158
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1437,f1369,f1085,f262,f2879]) ).
fof(f1369,plain,
( spl0_167
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1437,plain,
( ! [X0] :
( app(sk3,X0) = cons(sk5,X0)
| ~ ssList(X0) )
| ~ spl0_5
| ~ spl0_158
| ~ spl0_167 ),
inference(forward_demodulation,[],[f1436,f1087]) ).
fof(f1436,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(sk5,X0) = app(cons(sk5,nil),X0) )
| ~ spl0_5
| ~ spl0_167 ),
inference(resolution,[],[f1370,f264]) ).
fof(f1370,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1369]) ).
fof(f2803,plain,
( spl0_252
| ~ spl0_32
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2427,f1260,f415,f2800]) ).
fof(f2800,plain,
( spl0_252
<=> sk4 = app(sk6,sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2427,plain,
( sk4 = app(sk6,sk7)
| ~ spl0_32
| ~ spl0_161 ),
inference(superposition,[],[f417,f1262]) ).
fof(f2753,plain,
( ~ spl0_1
| spl0_251
| ~ spl0_11
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f2668,f1035,f301,f2750,f243]) ).
fof(f2750,plain,
( spl0_251
<=> sk3 = cons(skaf44(sk3),sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1035,plain,
( spl0_147
<=> ! [X0] :
( cons(skaf44(X0),sk3) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f2668,plain,
( sk3 = cons(skaf44(sk3),sk3)
| ~ ssList(sk3)
| ~ spl0_11
| ~ spl0_147 ),
inference(resolution,[],[f302,f1036]) ).
fof(f1036,plain,
( ! [X0] :
( ~ singletonP(X0)
| cons(skaf44(X0),sk3) = X0
| ~ ssList(X0) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1035]) ).
fof(f2704,plain,
( spl0_250
| ~ spl0_1
| ~ spl0_11
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f2667,f1030,f301,f243,f2701]) ).
fof(f2701,plain,
( spl0_250
<=> sk3 = cons(skaf44(sk3),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1030,plain,
( spl0_146
<=> ! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f2667,plain,
( ~ ssList(sk3)
| sk3 = cons(skaf44(sk3),nil)
| ~ spl0_11
| ~ spl0_146 ),
inference(resolution,[],[f302,f1031]) ).
fof(f1031,plain,
( ! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f2699,plain,
( spl0_249
| ~ spl0_5
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1246,f1022,f262,f2697]) ).
fof(f1246,plain,
( ! [X0] :
( ~ ssList(X0)
| sk5 = hd(cons(sk5,X0)) )
| ~ spl0_5
| ~ spl0_144 ),
inference(resolution,[],[f1023,f264]) ).
fof(f2695,plain,
( spl0_248
| ~ spl0_5
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1226,f1018,f262,f2693]) ).
fof(f1226,plain,
( ! [X0] :
( ~ ssList(X0)
| tl(cons(sk5,X0)) = X0 )
| ~ spl0_5
| ~ spl0_143 ),
inference(resolution,[],[f1019,f264]) ).
fof(f2689,plain,
( ~ spl0_1
| spl0_247
| ~ spl0_128
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1082,f1077,f943,f2687,f243]) ).
fof(f2687,plain,
( spl0_247
<=> ! [X0] :
( singletonP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f943,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1077,plain,
( spl0_157
<=> ! [X0] :
( singletonP(cons(X0,sk3))
| ~ ssList(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1082,plain,
( ! [X0] :
( singletonP(cons(X0,sk3))
| ~ ssItem(X0)
| ~ ssList(sk3) )
| ~ spl0_128
| ~ spl0_157 ),
inference(duplicate_literal_removal,[],[f1080]) ).
fof(f1080,plain,
( ! [X0] :
( singletonP(cons(X0,sk3))
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssItem(X0) )
| ~ spl0_128
| ~ spl0_157 ),
inference(resolution,[],[f1078,f944]) ).
fof(f944,plain,
( ! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f1078,plain,
( ! [X0] :
( ~ ssList(cons(X0,sk3))
| singletonP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f2685,plain,
( spl0_246
| ~ spl0_110
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f890,f885,f751,f2683]) ).
fof(f2683,plain,
( spl0_246
<=> ! [X0] :
( ~ ssList(X0)
| sk3 = X0
| duplicatefreeP(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f890,plain,
( ! [X0] :
( ~ ssList(X0)
| sk3 = X0
| duplicatefreeP(tl(X0)) )
| ~ spl0_110
| ~ spl0_119 ),
inference(resolution,[],[f886,f752]) ).
fof(f2681,plain,
( ~ spl0_28
| spl0_8
| ~ spl0_1
| ~ spl0_86
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1098,f931,f638,f243,f278,f393]) ).
fof(f638,plain,
( spl0_86
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f931,plain,
( spl0_126
<=> ! [X0] :
( sk3 = X0
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1098,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ ssList(nil)
| ~ spl0_86
| ~ spl0_126 ),
inference(resolution,[],[f639,f932]) ).
fof(f932,plain,
( ! [X0] :
( ~ frontsegP(sk3,X0)
| sk3 = X0
| ~ ssList(X0) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f931]) ).
fof(f639,plain,
( ! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f2680,plain,
( ~ spl0_5
| ~ spl0_92
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2674,f2670,f664,f262]) ).
fof(f664,plain,
( spl0_92
<=> ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2670,plain,
( spl0_245
<=> memberP(sk3,sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2674,plain,
( ~ ssItem(sk5)
| ~ spl0_92
| ~ spl0_245 ),
inference(resolution,[],[f2672,f665]) ).
fof(f665,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f2672,plain,
( memberP(sk3,sk5)
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2670]) ).
fof(f2679,plain,
( ~ spl0_28
| spl0_8
| ~ spl0_1
| ~ spl0_84
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f1191,f906,f629,f243,f278,f393]) ).
fof(f629,plain,
( spl0_84
<=> ! [X0] :
( rearsegP(X0,sk3)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f906,plain,
( spl0_122
<=> ! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1191,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ ssList(nil)
| ~ spl0_84
| ~ spl0_122 ),
inference(resolution,[],[f907,f630]) ).
fof(f630,plain,
( ! [X0] :
( rearsegP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f907,plain,
( ! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f906]) ).
fof(f2678,plain,
( ~ spl0_28
| spl0_8
| ~ spl0_1
| ~ spl0_83
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1097,f912,f624,f243,f278,f393]) ).
fof(f624,plain,
( spl0_83
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f912,plain,
( spl0_123
<=> ! [X0] :
( sk3 = X0
| ~ rearsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1097,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ ssList(nil)
| ~ spl0_83
| ~ spl0_123 ),
inference(resolution,[],[f625,f913]) ).
fof(f913,plain,
( ! [X0] :
( ~ rearsegP(sk3,X0)
| sk3 = X0
| ~ ssList(X0) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f625,plain,
( ! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f2677,plain,
( ~ spl0_28
| spl0_8
| ~ spl0_1
| ~ spl0_87
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1201,f925,f643,f243,f278,f393]) ).
fof(f643,plain,
( spl0_87
<=> ! [X0] :
( frontsegP(X0,sk3)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f925,plain,
( spl0_125
<=> ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1201,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ ssList(nil)
| ~ spl0_87
| ~ spl0_125 ),
inference(resolution,[],[f926,f644]) ).
fof(f644,plain,
( ! [X0] :
( frontsegP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f926,plain,
( ! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f2676,plain,
( ~ spl0_28
| spl0_8
| ~ spl0_1
| ~ spl0_80
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1096,f898,f610,f243,f278,f393]) ).
fof(f610,plain,
( spl0_80
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f898,plain,
( spl0_121
<=> ! [X0] :
( sk3 = X0
| ~ segmentP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1096,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ ssList(nil)
| ~ spl0_80
| ~ spl0_121 ),
inference(resolution,[],[f611,f899]) ).
fof(f899,plain,
( ! [X0] :
( ~ segmentP(sk3,X0)
| sk3 = X0
| ~ ssList(X0) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f611,plain,
( ! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f2673,plain,
( ~ spl0_5
| ~ spl0_28
| spl0_245
| ~ spl0_142
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1089,f1085,f1011,f2670,f393,f262]) ).
fof(f1011,plain,
( spl0_142
<=> ! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1089,plain,
( memberP(sk3,sk5)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ spl0_142
| ~ spl0_158 ),
inference(superposition,[],[f1012,f1087]) ).
fof(f1012,plain,
( ! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f2666,plain,
( spl0_11
| ~ spl0_5
| ~ spl0_1
| ~ spl0_156
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1271,f1085,f1071,f243,f262,f301]) ).
fof(f1071,plain,
( spl0_156
<=> ! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1271,plain,
( ~ ssList(sk3)
| ~ ssItem(sk5)
| singletonP(sk3)
| ~ spl0_156
| ~ spl0_158 ),
inference(superposition,[],[f1072,f1087]) ).
fof(f1072,plain,
( ! [X0] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1071]) ).
fof(f2393,plain,
( spl0_4
| spl0_12 ),
inference(avatar_split_clause,[],[f196,f306,f258]) ).
fof(f196,axiom,
( ssList(sk7)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f2392,plain,
( spl0_244
| ~ spl0_12
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1180,f826,f306,f2389]) ).
fof(f2389,plain,
( spl0_244
<=> sk7 = app(nil,sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1180,plain,
( sk7 = app(nil,sk7)
| ~ spl0_12
| ~ spl0_113 ),
inference(resolution,[],[f827,f308]) ).
fof(f2387,plain,
( spl0_243
| ~ spl0_6
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1179,f826,f267,f2384]) ).
fof(f2384,plain,
( spl0_243
<=> sk6 = app(nil,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f1179,plain,
( sk6 = app(nil,sk6)
| ~ spl0_6
| ~ spl0_113 ),
inference(resolution,[],[f827,f269]) ).
fof(f2382,plain,
( spl0_242
| ~ spl0_2
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1178,f826,f248,f2379]) ).
fof(f2379,plain,
( spl0_242
<=> sk4 = app(nil,sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f1178,plain,
( sk4 = app(nil,sk4)
| ~ spl0_2
| ~ spl0_113 ),
inference(resolution,[],[f827,f250]) ).
fof(f2368,plain,
( spl0_241
| ~ spl0_1
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1177,f826,f243,f2365]) ).
fof(f2365,plain,
( spl0_241
<=> sk3 = app(nil,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1177,plain,
( sk3 = app(nil,sk3)
| ~ spl0_1
| ~ spl0_113 ),
inference(resolution,[],[f827,f245]) ).
fof(f2363,plain,
spl0_240,
inference(avatar_split_clause,[],[f235,f2361]) ).
fof(f2361,plain,
( spl0_240
<=> ! [X4,X0,X3,X2,X1] :
( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f235,plain,
! [X2,X3,X0,X1,X4] :
( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ totalorderP(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause184) ).
fof(f2359,plain,
spl0_239,
inference(avatar_split_clause,[],[f234,f2357]) ).
fof(f2357,plain,
( spl0_239
<=> ! [X4,X0,X3,X2,X1] :
( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f234,plain,
! [X2,X3,X0,X1,X4] :
( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ strictorderP(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause183) ).
fof(f2355,plain,
spl0_238,
inference(avatar_split_clause,[],[f233,f2353]) ).
fof(f2353,plain,
( spl0_238
<=> ! [X2,X4,X0,X3,X1] :
( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f233,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).
fof(f2345,plain,
spl0_237,
inference(avatar_split_clause,[],[f232,f2343]) ).
fof(f2343,plain,
( spl0_237
<=> ! [X4,X0,X3,X2,X1] :
( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f232,plain,
! [X2,X3,X0,X1,X4] :
( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3) ),
inference(equality_resolution,[],[f182]) ).
fof(f182,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ totalorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X5)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause182) ).
fof(f2341,plain,
spl0_236,
inference(avatar_split_clause,[],[f231,f2339]) ).
fof(f2339,plain,
( spl0_236
<=> ! [X4,X0,X3,X2,X1] :
( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f231,plain,
! [X2,X3,X0,X1,X4] :
( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3) ),
inference(equality_resolution,[],[f181]) ).
fof(f181,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ strictorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X5)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause181) ).
fof(f2334,plain,
spl0_235,
inference(avatar_split_clause,[],[f228,f2332]) ).
fof(f2332,plain,
( spl0_235
<=> ! [X0,X3,X2,X1] :
( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_resolution,[],[f179]) ).
fof(f179,axiom,
! [X2,X3,X0,X1,X4] :
( ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).
fof(f2327,plain,
( spl0_234
| ~ spl0_12
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1145,f786,f306,f2324]) ).
fof(f2324,plain,
( spl0_234
<=> sk7 = app(sk7,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1145,plain,
( sk7 = app(sk7,nil)
| ~ spl0_12
| ~ spl0_111 ),
inference(resolution,[],[f787,f308]) ).
fof(f2322,plain,
spl0_233,
inference(avatar_split_clause,[],[f230,f2320]) ).
fof(f2320,plain,
( spl0_233
<=> ! [X0,X3,X2,X1] :
( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,cons(X2,X3))))
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f230,plain,
! [X2,X3,X0,X1] :
( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,cons(X2,X3))))
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2 ),
inference(equality_resolution,[],[f180]) ).
fof(f180,axiom,
! [X2,X3,X0,X1,X4] :
( ~ equalelemsP(X4)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2
| app(X0,cons(X1,cons(X2,X3))) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause180) ).
fof(f2316,plain,
spl0_232,
inference(avatar_split_clause,[],[f177,f2314]) ).
fof(f2314,plain,
( spl0_232
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| nil = X0
| nil = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f177,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| nil = X0
| nil = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause177) ).
fof(f2132,plain,
spl0_231,
inference(avatar_split_clause,[],[f167,f2130]) ).
fof(f2130,plain,
( spl0_231
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f167,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause167) ).
fof(f2128,plain,
spl0_230,
inference(avatar_split_clause,[],[f166,f2126]) ).
fof(f2126,plain,
( spl0_230
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f166,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause166) ).
fof(f2124,plain,
( spl0_229
| ~ spl0_6
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1144,f786,f267,f2121]) ).
fof(f1144,plain,
( sk6 = app(sk6,nil)
| ~ spl0_6
| ~ spl0_111 ),
inference(resolution,[],[f787,f269]) ).
fof(f2119,plain,
spl0_228,
inference(avatar_split_clause,[],[f165,f2117]) ).
fof(f2117,plain,
( spl0_228
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f165,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause165) ).
fof(f2115,plain,
spl0_227,
inference(avatar_split_clause,[],[f164,f2113]) ).
fof(f2113,plain,
( spl0_227
<=> ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f164,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause164) ).
fof(f2111,plain,
spl0_226,
inference(avatar_split_clause,[],[f163,f2109]) ).
fof(f2109,plain,
( spl0_226
<=> ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f163,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause163) ).
fof(f2091,plain,
spl0_225,
inference(avatar_split_clause,[],[f227,f2089]) ).
fof(f227,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(equality_resolution,[],[f173]) ).
fof(f173,axiom,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(X3,X1)
| app(app(X0,X1),X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
fof(f2087,plain,
spl0_224,
inference(avatar_split_clause,[],[f226,f2085]) ).
fof(f2085,plain,
( spl0_224
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ),
inference(equality_resolution,[],[f175]) ).
fof(f175,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(X3,X1)
| app(X0,cons(X1,X2)) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause175) ).
fof(f2060,plain,
( spl0_223
| ~ spl0_2
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1143,f786,f248,f2057]) ).
fof(f2057,plain,
( spl0_223
<=> sk4 = app(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1143,plain,
( sk4 = app(sk4,nil)
| ~ spl0_2
| ~ spl0_111 ),
inference(resolution,[],[f787,f250]) ).
fof(f2031,plain,
spl0_222,
inference(avatar_split_clause,[],[f176,f2029]) ).
fof(f2029,plain,
( spl0_222
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f176,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause176) ).
fof(f2027,plain,
spl0_221,
inference(avatar_split_clause,[],[f174,f2025]) ).
fof(f2025,plain,
( spl0_221
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| frontsegP(X1,X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f174,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| frontsegP(X1,X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause174) ).
fof(f2023,plain,
spl0_220,
inference(avatar_split_clause,[],[f172,f2021]) ).
fof(f2021,plain,
( spl0_220
<=> ! [X0,X3,X2,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X3,X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f172,axiom,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X3,X0),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause172) ).
fof(f2019,plain,
spl0_219,
inference(avatar_split_clause,[],[f171,f2017]) ).
fof(f2017,plain,
( spl0_219
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3
| cons(X0,X1) != cons(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause171) ).
fof(f2015,plain,
spl0_218,
inference(avatar_split_clause,[],[f170,f2013]) ).
fof(f2013,plain,
( spl0_218
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| cons(X0,X1) != cons(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f170,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause170) ).
fof(f2011,plain,
spl0_217,
inference(avatar_split_clause,[],[f169,f2009]) ).
fof(f2009,plain,
( spl0_217
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f169,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause169) ).
fof(f2007,plain,
( spl0_216
| ~ spl0_1
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1142,f786,f243,f2004]) ).
fof(f2004,plain,
( spl0_216
<=> sk3 = app(sk3,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1142,plain,
( sk3 = app(sk3,nil)
| ~ spl0_1
| ~ spl0_111 ),
inference(resolution,[],[f787,f245]) ).
fof(f2002,plain,
spl0_215,
inference(avatar_split_clause,[],[f168,f2000]) ).
fof(f2000,plain,
( spl0_215
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1)
| app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f168,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1)
| app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause168) ).
fof(f1890,plain,
spl0_214,
inference(avatar_split_clause,[],[f161,f1888]) ).
fof(f1888,plain,
( spl0_214
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2)
| ~ memberP(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2)
| ~ memberP(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
fof(f1886,plain,
spl0_213,
inference(avatar_split_clause,[],[f160,f1884]) ).
fof(f1884,plain,
( spl0_213
<=> ! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f160,axiom,
! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).
fof(f1856,plain,
spl0_212,
inference(avatar_split_clause,[],[f159,f1854]) ).
fof(f1854,plain,
( spl0_212
<=> ! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f159,axiom,
! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).
fof(f1852,plain,
spl0_211,
inference(avatar_split_clause,[],[f158,f1850]) ).
fof(f1850,plain,
( spl0_211
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X1,X2)
| memberP(X0,X2)
| ~ memberP(app(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f158,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X1,X2)
| memberP(X0,X2)
| ~ memberP(app(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
fof(f1848,plain,
spl0_210,
inference(avatar_split_clause,[],[f157,f1846]) ).
fof(f157,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).
fof(f1844,plain,
spl0_209,
inference(avatar_split_clause,[],[f149,f1842]) ).
fof(f149,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
fof(f1840,plain,
spl0_208,
inference(avatar_split_clause,[],[f142,f1838]) ).
fof(f142,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
fof(f1779,plain,
spl0_207,
inference(avatar_split_clause,[],[f236,f1777]) ).
fof(f1777,plain,
( spl0_207
<=> ! [X0,X1,X3] :
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f236,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(duplicate_literal_removal,[],[f229]) ).
fof(f229,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(equality_resolution,[],[f178]) ).
fof(f178,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| X2 != X3
| ~ frontsegP(X0,X1)
| frontsegP(cons(X2,X0),cons(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause178) ).
fof(f1774,plain,
( spl0_8
| ~ spl0_1
| ~ spl0_113
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1688,f1684,f826,f243,f278]) ).
fof(f1684,plain,
( spl0_202
<=> nil = app(nil,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1688,plain,
( nil = sk3
| ~ spl0_1
| ~ spl0_113
| ~ spl0_202 ),
inference(forward_demodulation,[],[f1686,f1177]) ).
fof(f1686,plain,
( nil = app(nil,sk3)
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f1684]) ).
fof(f1773,plain,
spl0_206,
inference(avatar_split_clause,[],[f151,f1771]) ).
fof(f1771,plain,
( spl0_206
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f151,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
fof(f1769,plain,
spl0_205,
inference(avatar_split_clause,[],[f150,f1767]) ).
fof(f1767,plain,
( spl0_205
<=> ! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f150,axiom,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
fof(f1728,plain,
( spl0_204
| ~ spl0_1
| ~ spl0_113
| ~ spl0_202
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1724,f1721,f1684,f826,f243,f1726]) ).
fof(f1724,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ spl0_1
| ~ spl0_113
| ~ spl0_202
| ~ spl0_203 ),
inference(forward_demodulation,[],[f1722,f1688]) ).
fof(f1723,plain,
spl0_203,
inference(avatar_split_clause,[],[f133,f1721]) ).
fof(f133,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
fof(f1687,plain,
( spl0_202
| ~ spl0_28
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1094,f791,f393,f1684]) ).
fof(f791,plain,
( spl0_112
<=> ! [X0] :
( app(X0,sk3) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1094,plain,
( nil = app(nil,sk3)
| ~ spl0_28
| ~ spl0_112 ),
inference(resolution,[],[f395,f792]) ).
fof(f792,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,sk3) = X0 )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f1670,plain,
spl0_201,
inference(avatar_split_clause,[],[f156,f1668]) ).
fof(f1668,plain,
( spl0_201
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f156,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).
fof(f1666,plain,
spl0_200,
inference(avatar_split_clause,[],[f155,f1664]) ).
fof(f1664,plain,
( spl0_200
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| lt(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| lt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).
fof(f1662,plain,
spl0_199,
inference(avatar_split_clause,[],[f154,f1660]) ).
fof(f1660,plain,
( spl0_199
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| frontsegP(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f154,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| frontsegP(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause154) ).
fof(f1658,plain,
spl0_198,
inference(avatar_split_clause,[],[f153,f1656]) ).
fof(f1656,plain,
( spl0_198
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f153,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause153) ).
fof(f1654,plain,
spl0_197,
inference(avatar_split_clause,[],[f152,f1652]) ).
fof(f1652,plain,
( spl0_197
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f152,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause152) ).
fof(f1649,plain,
( spl0_8
| ~ spl0_1
| ~ spl0_111
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1606,f1602,f786,f243,f278]) ).
fof(f1602,plain,
( spl0_189
<=> nil = app(sk3,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1606,plain,
( nil = sk3
| ~ spl0_1
| ~ spl0_111
| ~ spl0_189 ),
inference(forward_demodulation,[],[f1604,f1142]) ).
fof(f1604,plain,
( nil = app(sk3,nil)
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1602]) ).
fof(f1648,plain,
spl0_196,
inference(avatar_split_clause,[],[f148,f1646]) ).
fof(f1646,plain,
( spl0_196
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| geq(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f148,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| geq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).
fof(f1644,plain,
spl0_195,
inference(avatar_split_clause,[],[f147,f1642]) ).
fof(f1642,plain,
( spl0_195
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| lt(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f147,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| lt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause147) ).
fof(f1640,plain,
spl0_194,
inference(avatar_split_clause,[],[f146,f1638]) ).
fof(f1638,plain,
( spl0_194
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f146,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause146) ).
fof(f1631,plain,
( spl0_193
| ~ spl0_1
| ~ spl0_111
| ~ spl0_189
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1627,f1624,f1602,f786,f243,f1629]) ).
fof(f1627,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) )
| ~ spl0_1
| ~ spl0_111
| ~ spl0_189
| ~ spl0_192 ),
inference(forward_demodulation,[],[f1625,f1606]) ).
fof(f1626,plain,
spl0_192,
inference(avatar_split_clause,[],[f135,f1624]) ).
fof(f135,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
fof(f1617,plain,
( spl0_191
| ~ spl0_1
| ~ spl0_111
| ~ spl0_189
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1613,f1610,f1602,f786,f243,f1615]) ).
fof(f1613,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) )
| ~ spl0_1
| ~ spl0_111
| ~ spl0_189
| ~ spl0_190 ),
inference(forward_demodulation,[],[f1611,f1606]) ).
fof(f1612,plain,
spl0_190,
inference(avatar_split_clause,[],[f134,f1610]) ).
fof(f134,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).
fof(f1605,plain,
( spl0_189
| ~ spl0_28
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1093,f831,f393,f1602]) ).
fof(f831,plain,
( spl0_114
<=> ! [X0] :
( app(sk3,X0) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1093,plain,
( nil = app(sk3,nil)
| ~ spl0_28
| ~ spl0_114 ),
inference(resolution,[],[f395,f832]) ).
fof(f832,plain,
( ! [X0] :
( ~ ssList(X0)
| app(sk3,X0) = X0 )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f1527,plain,
spl0_188,
inference(avatar_split_clause,[],[f141,f1525]) ).
fof(f1525,plain,
( spl0_188
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f141,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
fof(f1523,plain,
spl0_187,
inference(avatar_split_clause,[],[f140,f1521]) ).
fof(f1521,plain,
( spl0_187
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f140,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
fof(f1519,plain,
spl0_186,
inference(avatar_split_clause,[],[f139,f1517]) ).
fof(f1517,plain,
( spl0_186
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).
fof(f1515,plain,
( spl0_185
| ~ spl0_12
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f864,f831,f306,f1512]) ).
fof(f1512,plain,
( spl0_185
<=> sk7 = app(sk3,sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f864,plain,
( sk7 = app(sk3,sk7)
| ~ spl0_12
| ~ spl0_114 ),
inference(resolution,[],[f832,f308]) ).
fof(f1510,plain,
spl0_184,
inference(avatar_split_clause,[],[f137,f1508]) ).
fof(f1508,plain,
( spl0_184
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f137,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
fof(f1506,plain,
spl0_183,
inference(avatar_split_clause,[],[f136,f1504]) ).
fof(f1504,plain,
( spl0_183
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f136,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
fof(f1502,plain,
spl0_182,
inference(avatar_split_clause,[],[f132,f1500]) ).
fof(f1500,plain,
( spl0_182
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f132,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
fof(f1498,plain,
spl0_181,
inference(avatar_split_clause,[],[f131,f1496]) ).
fof(f1496,plain,
( spl0_181
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f131,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
fof(f1494,plain,
spl0_180,
inference(avatar_split_clause,[],[f123,f1492]) ).
fof(f123,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
fof(f1465,plain,
( spl0_179
| ~ spl0_6
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f863,f831,f267,f1462]) ).
fof(f863,plain,
( sk6 = app(sk3,sk6)
| ~ spl0_6
| ~ spl0_114 ),
inference(resolution,[],[f832,f269]) ).
fof(f1416,plain,
spl0_178,
inference(avatar_split_clause,[],[f223,f1414]) ).
fof(f223,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| frontsegP(X2,X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
fof(f1412,plain,
spl0_177,
inference(avatar_split_clause,[],[f222,f1410]) ).
fof(f222,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ),
inference(equality_resolution,[],[f143]) ).
fof(f143,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X2,X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
fof(f1408,plain,
spl0_176,
inference(avatar_split_clause,[],[f130,f1406]) ).
fof(f1406,plain,
( spl0_176
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f130,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).
fof(f1404,plain,
spl0_175,
inference(avatar_split_clause,[],[f129,f1402]) ).
fof(f1402,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f129,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
fof(f1400,plain,
( spl0_174
| ~ spl0_2
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f862,f831,f248,f1397]) ).
fof(f1397,plain,
( spl0_174
<=> sk4 = app(sk3,sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f862,plain,
( sk4 = app(sk3,sk4)
| ~ spl0_2
| ~ spl0_114 ),
inference(resolution,[],[f832,f250]) ).
fof(f1395,plain,
spl0_173,
inference(avatar_split_clause,[],[f128,f1393]) ).
fof(f1393,plain,
( spl0_173
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f128,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
fof(f1391,plain,
spl0_172,
inference(avatar_split_clause,[],[f127,f1389]) ).
fof(f1389,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f127,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
fof(f1387,plain,
spl0_171,
inference(avatar_split_clause,[],[f126,f1385]) ).
fof(f1385,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f126,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
fof(f1383,plain,
spl0_170,
inference(avatar_split_clause,[],[f125,f1381]) ).
fof(f1381,plain,
( spl0_170
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).
fof(f1379,plain,
spl0_169,
inference(avatar_split_clause,[],[f124,f1377]) ).
fof(f1377,plain,
( spl0_169
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f124,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).
fof(f1375,plain,
spl0_168,
inference(avatar_split_clause,[],[f122,f1373]) ).
fof(f1373,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f122,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).
fof(f1371,plain,
spl0_167,
inference(avatar_split_clause,[],[f120,f1369]) ).
fof(f120,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
fof(f1329,plain,
( spl0_166
| ~ spl0_12
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f824,f791,f306,f1326]) ).
fof(f824,plain,
( sk7 = app(sk7,sk3)
| ~ spl0_12
| ~ spl0_112 ),
inference(resolution,[],[f792,f308]) ).
fof(f1288,plain,
spl0_165,
inference(avatar_split_clause,[],[f119,f1286]) ).
fof(f1286,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f119,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
fof(f1284,plain,
spl0_164,
inference(avatar_split_clause,[],[f118,f1282]) ).
fof(f1282,plain,
( spl0_164
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f118,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
fof(f1280,plain,
spl0_163,
inference(avatar_split_clause,[],[f109,f1278]) ).
fof(f109,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
fof(f1276,plain,
spl0_162,
inference(avatar_split_clause,[],[f104,f1274]) ).
fof(f104,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
fof(f1263,plain,
( spl0_161
| ~ spl0_6
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f823,f791,f267,f1260]) ).
fof(f823,plain,
( sk6 = app(sk6,sk3)
| ~ spl0_6
| ~ spl0_112 ),
inference(resolution,[],[f792,f269]) ).
fof(f1200,plain,
( spl0_160
| ~ spl0_2
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f822,f791,f248,f1197]) ).
fof(f822,plain,
( sk4 = app(sk4,sk3)
| ~ spl0_2
| ~ spl0_112 ),
inference(resolution,[],[f792,f250]) ).
fof(f1106,plain,
( spl0_159
| ~ spl0_1
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f821,f791,f243,f1103]) ).
fof(f1103,plain,
( spl0_159
<=> sk3 = app(sk3,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f821,plain,
( sk3 = app(sk3,sk3)
| ~ spl0_1
| ~ spl0_112 ),
inference(resolution,[],[f792,f245]) ).
fof(f1092,plain,
( ~ spl0_5
| ~ spl0_1
| ~ spl0_13
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1015,f1007,f311,f243,f262]) ).
fof(f311,plain,
( spl0_13
<=> sk3 = cons(sk5,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1007,plain,
( spl0_141
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1015,plain,
( ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ spl0_13
| ~ spl0_141 ),
inference(trivial_inequality_removal,[],[f1014]) ).
fof(f1014,plain,
( sk3 != sk3
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ spl0_13
| ~ spl0_141 ),
inference(superposition,[],[f1008,f313]) ).
fof(f313,plain,
( sk3 = cons(sk5,sk3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f1008,plain,
( ! [X0,X1] :
( cons(X0,X1) != X1
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f1088,plain,
( spl0_158
| spl0_4 ),
inference(avatar_split_clause,[],[f197,f258,f1085]) ).
fof(f197,axiom,
( nil = sk4
| sk3 = cons(sk5,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f1083,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_13
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1005,f1001,f311,f262,f243]) ).
fof(f1001,plain,
( spl0_140
<=> ! [X0,X1] :
( cons(X0,X1) != sk3
| ~ ssItem(X0)
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1005,plain,
( ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ spl0_13
| ~ spl0_140 ),
inference(trivial_inequality_removal,[],[f1004]) ).
fof(f1004,plain,
( sk3 != sk3
| ~ ssItem(sk5)
| ~ ssList(sk3)
| ~ spl0_13
| ~ spl0_140 ),
inference(superposition,[],[f1002,f313]) ).
fof(f1002,plain,
( ! [X0,X1] :
( cons(X0,X1) != sk3
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1079,plain,
( spl0_157
| ~ spl0_8
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1075,f1071,f278,f1077]) ).
fof(f1075,plain,
( ! [X0] :
( singletonP(cons(X0,sk3))
| ~ ssList(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_156 ),
inference(forward_demodulation,[],[f1074,f280]) ).
fof(f280,plain,
( nil = sk3
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f1074,plain,
( ! [X0] :
( ~ ssList(cons(X0,sk3))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) )
| ~ spl0_8
| ~ spl0_156 ),
inference(forward_demodulation,[],[f1072,f280]) ).
fof(f1073,plain,
spl0_156,
inference(avatar_split_clause,[],[f217,f1071]) ).
fof(f217,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ),
inference(equality_resolution,[],[f116]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
fof(f1069,plain,
spl0_155,
inference(avatar_split_clause,[],[f114,f1067]) ).
fof(f1067,plain,
( spl0_155
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f114,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
fof(f1065,plain,
spl0_154,
inference(avatar_split_clause,[],[f110,f1063]) ).
fof(f1063,plain,
( spl0_154
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f110,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
fof(f1061,plain,
spl0_153,
inference(avatar_split_clause,[],[f108,f1059]) ).
fof(f1059,plain,
( spl0_153
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f108,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
fof(f1057,plain,
spl0_152,
inference(avatar_split_clause,[],[f107,f1055]) ).
fof(f1055,plain,
( spl0_152
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f107,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
fof(f1053,plain,
spl0_151,
inference(avatar_split_clause,[],[f106,f1051]) ).
fof(f1051,plain,
( spl0_151
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f106,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
fof(f1049,plain,
spl0_150,
inference(avatar_split_clause,[],[f105,f1047]) ).
fof(f1047,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
fof(f1045,plain,
spl0_149,
inference(avatar_split_clause,[],[f103,f1043]) ).
fof(f1043,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f103,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
fof(f1041,plain,
spl0_148,
inference(avatar_split_clause,[],[f102,f1039]) ).
fof(f1039,plain,
( spl0_148
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f102,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
fof(f1037,plain,
( spl0_147
| ~ spl0_8
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1033,f1030,f278,f1035]) ).
fof(f1033,plain,
( ! [X0] :
( cons(skaf44(X0),sk3) = X0
| ~ singletonP(X0)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_146 ),
inference(forward_demodulation,[],[f1031,f280]) ).
fof(f1032,plain,
spl0_146,
inference(avatar_split_clause,[],[f101,f1030]) ).
fof(f101,axiom,
! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
fof(f1028,plain,
spl0_145,
inference(avatar_split_clause,[],[f100,f1026]) ).
fof(f1026,plain,
( spl0_145
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f100,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f1024,plain,
spl0_144,
inference(avatar_split_clause,[],[f97,f1022]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
fof(f1020,plain,
spl0_143,
inference(avatar_split_clause,[],[f96,f1018]) ).
fof(f96,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
fof(f1013,plain,
spl0_142,
inference(avatar_split_clause,[],[f238,f1011]) ).
fof(f238,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f221,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
fof(f1009,plain,
spl0_141,
inference(avatar_split_clause,[],[f99,f1007]) ).
fof(f99,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
fof(f1003,plain,
( spl0_140
| ~ spl0_8
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f999,f996,f278,f1001]) ).
fof(f996,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f999,plain,
( ! [X0,X1] :
( cons(X0,X1) != sk3
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl0_8
| ~ spl0_139 ),
inference(forward_demodulation,[],[f997,f280]) ).
fof(f997,plain,
( ! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f998,plain,
spl0_139,
inference(avatar_split_clause,[],[f98,f996]) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f994,plain,
spl0_138,
inference(avatar_split_clause,[],[f95,f992]) ).
fof(f992,plain,
( spl0_138
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f95,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
fof(f990,plain,
spl0_137,
inference(avatar_split_clause,[],[f94,f988]) ).
fof(f988,plain,
( spl0_137
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f94,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
fof(f986,plain,
spl0_136,
inference(avatar_split_clause,[],[f93,f984]) ).
fof(f984,plain,
( spl0_136
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f93,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
fof(f982,plain,
spl0_135,
inference(avatar_split_clause,[],[f92,f980]) ).
fof(f980,plain,
( spl0_135
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f92,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
fof(f978,plain,
spl0_134,
inference(avatar_split_clause,[],[f91,f976]) ).
fof(f976,plain,
( spl0_134
<=> ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f91,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
fof(f974,plain,
spl0_133,
inference(avatar_split_clause,[],[f90,f972]) ).
fof(f972,plain,
( spl0_133
<=> ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f90,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
fof(f970,plain,
spl0_132,
inference(avatar_split_clause,[],[f89,f968]) ).
fof(f968,plain,
( spl0_132
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f89,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
fof(f966,plain,
( spl0_131
| ~ spl0_12
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f784,f751,f306,f963]) ).
fof(f963,plain,
( spl0_131
<=> duplicatefreeP(sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f784,plain,
( duplicatefreeP(sk7)
| ~ spl0_12
| ~ spl0_110 ),
inference(resolution,[],[f752,f308]) ).
fof(f961,plain,
spl0_130,
inference(avatar_split_clause,[],[f88,f959]) ).
fof(f959,plain,
( spl0_130
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f88,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
fof(f957,plain,
spl0_129,
inference(avatar_split_clause,[],[f87,f955]) ).
fof(f955,plain,
( spl0_129
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f87,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
fof(f945,plain,
spl0_128,
inference(avatar_split_clause,[],[f86,f943]) ).
fof(f86,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f941,plain,
spl0_127,
inference(avatar_split_clause,[],[f85,f939]) ).
fof(f939,plain,
( spl0_127
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f933,plain,
( spl0_126
| ~ spl0_8
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f929,f925,f278,f931]) ).
fof(f929,plain,
( ! [X0] :
( sk3 = X0
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_125 ),
inference(forward_demodulation,[],[f928,f280]) ).
fof(f928,plain,
( ! [X0] :
( ~ frontsegP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_8
| ~ spl0_125 ),
inference(forward_demodulation,[],[f926,f280]) ).
fof(f927,plain,
spl0_125,
inference(avatar_split_clause,[],[f84,f925]) ).
fof(f84,axiom,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
fof(f919,plain,
( spl0_124
| ~ spl0_6
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f783,f751,f267,f916]) ).
fof(f916,plain,
( spl0_124
<=> duplicatefreeP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f783,plain,
( duplicatefreeP(sk6)
| ~ spl0_6
| ~ spl0_110 ),
inference(resolution,[],[f752,f269]) ).
fof(f914,plain,
( spl0_123
| ~ spl0_8
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f910,f906,f278,f912]) ).
fof(f910,plain,
( ! [X0] :
( sk3 = X0
| ~ rearsegP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_122 ),
inference(forward_demodulation,[],[f909,f280]) ).
fof(f909,plain,
( ! [X0] :
( ~ rearsegP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_8
| ~ spl0_122 ),
inference(forward_demodulation,[],[f907,f280]) ).
fof(f908,plain,
spl0_122,
inference(avatar_split_clause,[],[f82,f906]) ).
fof(f82,axiom,
! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
fof(f900,plain,
( spl0_121
| ~ spl0_8
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f896,f892,f278,f898]) ).
fof(f892,plain,
( spl0_120
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f896,plain,
( ! [X0] :
( sk3 = X0
| ~ segmentP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_120 ),
inference(forward_demodulation,[],[f895,f280]) ).
fof(f895,plain,
( ! [X0] :
( ~ segmentP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_8
| ~ spl0_120 ),
inference(forward_demodulation,[],[f893,f280]) ).
fof(f893,plain,
( ! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f894,plain,
spl0_120,
inference(avatar_split_clause,[],[f80,f892]) ).
fof(f80,axiom,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
fof(f887,plain,
( spl0_119
| ~ spl0_8
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f883,f880,f278,f885]) ).
fof(f880,plain,
( spl0_118
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f883,plain,
( ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssList(tl(X0)) )
| ~ spl0_8
| ~ spl0_118 ),
inference(forward_demodulation,[],[f881,f280]) ).
fof(f881,plain,
( ! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f882,plain,
spl0_118,
inference(avatar_split_clause,[],[f77,f880]) ).
fof(f77,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
fof(f878,plain,
( spl0_117
| ~ spl0_8
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f869,f866,f278,f876]) ).
fof(f866,plain,
( spl0_115
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f869,plain,
( ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssItem(hd(X0)) )
| ~ spl0_8
| ~ spl0_115 ),
inference(forward_demodulation,[],[f867,f280]) ).
fof(f867,plain,
( ! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f874,plain,
( spl0_116
| ~ spl0_2
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f782,f751,f248,f871]) ).
fof(f871,plain,
( spl0_116
<=> duplicatefreeP(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f782,plain,
( duplicatefreeP(sk4)
| ~ spl0_2
| ~ spl0_110 ),
inference(resolution,[],[f752,f250]) ).
fof(f868,plain,
spl0_115,
inference(avatar_split_clause,[],[f76,f866]) ).
fof(f76,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
fof(f833,plain,
( spl0_114
| ~ spl0_8
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f829,f826,f278,f831]) ).
fof(f829,plain,
( ! [X0] :
( app(sk3,X0) = X0
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_113 ),
inference(forward_demodulation,[],[f827,f280]) ).
fof(f828,plain,
spl0_113,
inference(avatar_split_clause,[],[f74,f826]) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f793,plain,
( spl0_112
| ~ spl0_8
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f789,f786,f278,f791]) ).
fof(f789,plain,
( ! [X0] :
( app(X0,sk3) = X0
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_111 ),
inference(forward_demodulation,[],[f787,f280]) ).
fof(f788,plain,
spl0_111,
inference(avatar_split_clause,[],[f73,f786]) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f753,plain,
( spl0_109
| spl0_110 ),
inference(avatar_split_clause,[],[f72,f751,f748]) ).
fof(f748,plain,
( spl0_109
<=> ! [X1] : ssItem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
fof(f745,plain,
( spl0_108
| ~ spl0_8
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f741,f738,f278,f743]) ).
fof(f743,plain,
( spl0_108
<=> ! [X0] :
( cyclefreeP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f738,plain,
( spl0_107
<=> ! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f741,plain,
( ! [X0] :
( cyclefreeP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_107 ),
inference(forward_demodulation,[],[f739,f280]) ).
fof(f739,plain,
( ! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f740,plain,
spl0_107,
inference(avatar_split_clause,[],[f70,f738]) ).
fof(f70,axiom,
! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
fof(f735,plain,
( spl0_106
| ~ spl0_8
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f731,f728,f278,f733]) ).
fof(f733,plain,
( spl0_106
<=> ! [X0] :
( totalorderP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f728,plain,
( spl0_105
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f731,plain,
( ! [X0] :
( totalorderP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_105 ),
inference(forward_demodulation,[],[f729,f280]) ).
fof(f729,plain,
( ! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f728]) ).
fof(f730,plain,
spl0_105,
inference(avatar_split_clause,[],[f69,f728]) ).
fof(f69,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
fof(f725,plain,
( spl0_104
| ~ spl0_8
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f721,f718,f278,f723]) ).
fof(f723,plain,
( spl0_104
<=> ! [X0] :
( strictorderP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f718,plain,
( spl0_103
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f721,plain,
( ! [X0] :
( strictorderP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_103 ),
inference(forward_demodulation,[],[f719,f280]) ).
fof(f719,plain,
( ! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f720,plain,
spl0_103,
inference(avatar_split_clause,[],[f68,f718]) ).
fof(f68,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
fof(f715,plain,
( spl0_102
| ~ spl0_8
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f711,f708,f278,f713]) ).
fof(f711,plain,
( ! [X0] :
( totalorderedP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_101 ),
inference(forward_demodulation,[],[f709,f280]) ).
fof(f710,plain,
spl0_101,
inference(avatar_split_clause,[],[f67,f708]) ).
fof(f67,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
fof(f705,plain,
( spl0_100
| ~ spl0_8
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f701,f698,f278,f703]) ).
fof(f701,plain,
( ! [X0] :
( strictorderedP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_99 ),
inference(forward_demodulation,[],[f699,f280]) ).
fof(f700,plain,
spl0_99,
inference(avatar_split_clause,[],[f66,f698]) ).
fof(f66,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
fof(f695,plain,
( spl0_98
| ~ spl0_8
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f691,f688,f278,f693]) ).
fof(f693,plain,
( spl0_98
<=> ! [X0] :
( duplicatefreeP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f688,plain,
( spl0_97
<=> ! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f691,plain,
( ! [X0] :
( duplicatefreeP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_97 ),
inference(forward_demodulation,[],[f689,f280]) ).
fof(f689,plain,
( ! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f690,plain,
spl0_97,
inference(avatar_split_clause,[],[f65,f688]) ).
fof(f65,axiom,
! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
fof(f685,plain,
( spl0_96
| ~ spl0_8
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f681,f678,f278,f683]) ).
fof(f683,plain,
( spl0_96
<=> ! [X0] :
( equalelemsP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f678,plain,
( spl0_95
<=> ! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f681,plain,
( ! [X0] :
( equalelemsP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_95 ),
inference(forward_demodulation,[],[f679,f280]) ).
fof(f679,plain,
( ! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f680,plain,
spl0_95,
inference(avatar_split_clause,[],[f64,f678]) ).
fof(f64,axiom,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
fof(f676,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f675,f668,f273,f248]) ).
fof(f273,plain,
( spl0_7
<=> neq(sk4,sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f675,plain,
( ~ ssList(sk4)
| ~ spl0_7
| ~ spl0_93 ),
inference(resolution,[],[f669,f275]) ).
fof(f275,plain,
( neq(sk4,sk4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f674,plain,
spl0_94,
inference(avatar_split_clause,[],[f241,f672]) ).
fof(f241,plain,
! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f215,plain,
! [X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
fof(f670,plain,
spl0_93,
inference(avatar_split_clause,[],[f239,f668]) ).
fof(f239,plain,
! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f220,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f115]) ).
fof(f115,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f666,plain,
( spl0_92
| ~ spl0_8
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f662,f659,f278,f664]) ).
fof(f659,plain,
( spl0_91
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f662,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_91 ),
inference(forward_demodulation,[],[f660,f280]) ).
fof(f660,plain,
( ! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f661,plain,
spl0_91,
inference(avatar_split_clause,[],[f71,f659]) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f657,plain,
spl0_90,
inference(avatar_split_clause,[],[f63,f655]) ).
fof(f63,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
fof(f653,plain,
spl0_89,
inference(avatar_split_clause,[],[f62,f651]) ).
fof(f651,plain,
( spl0_89
<=> ! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f62,axiom,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
fof(f649,plain,
spl0_88,
inference(avatar_split_clause,[],[f61,f647]) ).
fof(f647,plain,
( spl0_88
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f61,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
fof(f645,plain,
( spl0_87
| ~ spl0_8
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f641,f638,f278,f643]) ).
fof(f641,plain,
( ! [X0] :
( frontsegP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_86 ),
inference(forward_demodulation,[],[f639,f280]) ).
fof(f640,plain,
spl0_86,
inference(avatar_split_clause,[],[f60,f638]) ).
fof(f60,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
fof(f636,plain,
spl0_85,
inference(avatar_split_clause,[],[f59,f634]) ).
fof(f634,plain,
( spl0_85
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f59,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
fof(f632,plain,
( ~ spl0_2
| spl0_10
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f618,f615,f297,f248]) ).
fof(f615,plain,
( spl0_81
<=> ! [X0] :
( segmentP(X0,sk3)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f618,plain,
( ~ ssList(sk4)
| spl0_10
| ~ spl0_81 ),
inference(resolution,[],[f616,f299]) ).
fof(f616,plain,
( ! [X0] :
( segmentP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f631,plain,
( spl0_84
| ~ spl0_8
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f627,f624,f278,f629]) ).
fof(f627,plain,
( ! [X0] :
( rearsegP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_83 ),
inference(forward_demodulation,[],[f625,f280]) ).
fof(f626,plain,
spl0_83,
inference(avatar_split_clause,[],[f58,f624]) ).
fof(f58,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
fof(f622,plain,
spl0_82,
inference(avatar_split_clause,[],[f57,f620]) ).
fof(f57,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
fof(f617,plain,
( spl0_81
| ~ spl0_8
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f613,f610,f278,f615]) ).
fof(f613,plain,
( ! [X0] :
( segmentP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_80 ),
inference(forward_demodulation,[],[f611,f280]) ).
fof(f612,plain,
spl0_80,
inference(avatar_split_clause,[],[f56,f610]) ).
fof(f56,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
fof(f608,plain,
spl0_79,
inference(avatar_split_clause,[],[f55,f606]) ).
fof(f606,plain,
( spl0_79
<=> ! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f55,axiom,
! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
fof(f604,plain,
spl0_78,
inference(avatar_split_clause,[],[f53,f602]) ).
fof(f53,axiom,
! [X0,X1] : ssList(skaf42(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
fof(f600,plain,
spl0_77,
inference(avatar_split_clause,[],[f52,f598]) ).
fof(f52,axiom,
! [X0,X1] : ssList(skaf43(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
fof(f596,plain,
spl0_76,
inference(avatar_split_clause,[],[f51,f594]) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
fof(f592,plain,
spl0_75,
inference(avatar_split_clause,[],[f50,f590]) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
fof(f588,plain,
spl0_74,
inference(avatar_split_clause,[],[f49,f586]) ).
fof(f49,axiom,
! [X0,X1] : ssList(skaf47(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
fof(f584,plain,
spl0_73,
inference(avatar_split_clause,[],[f48,f582]) ).
fof(f48,axiom,
! [X0,X1] : ssList(skaf48(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
fof(f580,plain,
~ spl0_72,
inference(avatar_split_clause,[],[f54,f577]) ).
fof(f577,plain,
( spl0_72
<=> skac3 = skac2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f54,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
fof(f575,plain,
spl0_71,
inference(avatar_split_clause,[],[f47,f573]) ).
fof(f573,plain,
( spl0_71
<=> ! [X0] : ssItem(skaf44(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
fof(f571,plain,
spl0_70,
inference(avatar_split_clause,[],[f46,f569]) ).
fof(f569,plain,
( spl0_70
<=> ! [X0] : ssItem(skaf49(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f46,axiom,
! [X0] : ssItem(skaf49(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
fof(f567,plain,
spl0_69,
inference(avatar_split_clause,[],[f45,f565]) ).
fof(f565,plain,
( spl0_69
<=> ! [X0] : ssItem(skaf50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f45,axiom,
! [X0] : ssItem(skaf50(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
fof(f563,plain,
spl0_68,
inference(avatar_split_clause,[],[f44,f561]) ).
fof(f44,axiom,
! [X0] : ssList(skaf51(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
fof(f559,plain,
spl0_67,
inference(avatar_split_clause,[],[f43,f557]) ).
fof(f43,axiom,
! [X0] : ssList(skaf52(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
fof(f555,plain,
spl0_66,
inference(avatar_split_clause,[],[f42,f553]) ).
fof(f42,axiom,
! [X0] : ssList(skaf53(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
fof(f551,plain,
spl0_65,
inference(avatar_split_clause,[],[f41,f549]) ).
fof(f549,plain,
( spl0_65
<=> ! [X0] : ssItem(skaf54(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f41,axiom,
! [X0] : ssItem(skaf54(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
fof(f547,plain,
spl0_64,
inference(avatar_split_clause,[],[f40,f545]) ).
fof(f545,plain,
( spl0_64
<=> ! [X0] : ssItem(skaf55(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f40,axiom,
! [X0] : ssItem(skaf55(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
fof(f543,plain,
spl0_63,
inference(avatar_split_clause,[],[f39,f541]) ).
fof(f39,axiom,
! [X0] : ssList(skaf56(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
fof(f539,plain,
spl0_62,
inference(avatar_split_clause,[],[f38,f537]) ).
fof(f38,axiom,
! [X0] : ssList(skaf57(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
fof(f535,plain,
spl0_61,
inference(avatar_split_clause,[],[f37,f533]) ).
fof(f37,axiom,
! [X0] : ssList(skaf58(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
fof(f531,plain,
spl0_60,
inference(avatar_split_clause,[],[f36,f529]) ).
fof(f529,plain,
( spl0_60
<=> ! [X0] : ssItem(skaf59(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f36,axiom,
! [X0] : ssItem(skaf59(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
fof(f527,plain,
spl0_59,
inference(avatar_split_clause,[],[f35,f525]) ).
fof(f525,plain,
( spl0_59
<=> ! [X0] : ssItem(skaf60(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f35,axiom,
! [X0] : ssItem(skaf60(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
fof(f523,plain,
spl0_58,
inference(avatar_split_clause,[],[f34,f521]) ).
fof(f34,axiom,
! [X0] : ssList(skaf61(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
fof(f519,plain,
spl0_57,
inference(avatar_split_clause,[],[f33,f517]) ).
fof(f33,axiom,
! [X0] : ssList(skaf62(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
fof(f515,plain,
spl0_56,
inference(avatar_split_clause,[],[f32,f513]) ).
fof(f32,axiom,
! [X0] : ssList(skaf63(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
fof(f511,plain,
spl0_55,
inference(avatar_split_clause,[],[f31,f509]) ).
fof(f509,plain,
( spl0_55
<=> ! [X0] : ssItem(skaf64(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f31,axiom,
! [X0] : ssItem(skaf64(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
fof(f507,plain,
spl0_54,
inference(avatar_split_clause,[],[f30,f505]) ).
fof(f505,plain,
( spl0_54
<=> ! [X0] : ssItem(skaf65(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f30,axiom,
! [X0] : ssItem(skaf65(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
fof(f503,plain,
spl0_53,
inference(avatar_split_clause,[],[f29,f501]) ).
fof(f29,axiom,
! [X0] : ssList(skaf66(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
fof(f499,plain,
spl0_52,
inference(avatar_split_clause,[],[f28,f497]) ).
fof(f28,axiom,
! [X0] : ssList(skaf67(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
fof(f495,plain,
spl0_51,
inference(avatar_split_clause,[],[f27,f493]) ).
fof(f27,axiom,
! [X0] : ssList(skaf68(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
fof(f491,plain,
spl0_50,
inference(avatar_split_clause,[],[f26,f489]) ).
fof(f489,plain,
( spl0_50
<=> ! [X0] : ssItem(skaf69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f26,axiom,
! [X0] : ssItem(skaf69(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
fof(f487,plain,
spl0_49,
inference(avatar_split_clause,[],[f25,f485]) ).
fof(f485,plain,
( spl0_49
<=> ! [X0] : ssItem(skaf70(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f25,axiom,
! [X0] : ssItem(skaf70(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
fof(f483,plain,
spl0_48,
inference(avatar_split_clause,[],[f24,f481]) ).
fof(f24,axiom,
! [X0] : ssList(skaf71(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
fof(f479,plain,
spl0_47,
inference(avatar_split_clause,[],[f23,f477]) ).
fof(f23,axiom,
! [X0] : ssList(skaf72(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
fof(f475,plain,
spl0_46,
inference(avatar_split_clause,[],[f22,f473]) ).
fof(f22,axiom,
! [X0] : ssList(skaf73(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
fof(f471,plain,
spl0_45,
inference(avatar_split_clause,[],[f21,f469]) ).
fof(f469,plain,
( spl0_45
<=> ! [X0] : ssItem(skaf74(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f21,axiom,
! [X0] : ssItem(skaf74(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
fof(f467,plain,
spl0_44,
inference(avatar_split_clause,[],[f20,f465]) ).
fof(f20,axiom,
! [X0] : ssList(skaf75(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
fof(f463,plain,
spl0_43,
inference(avatar_split_clause,[],[f19,f461]) ).
fof(f19,axiom,
! [X0] : ssList(skaf76(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
fof(f459,plain,
( spl0_42
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f295,f278,f253,f456]) ).
fof(f456,plain,
( spl0_42
<=> neq(sk4,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f295,plain,
( neq(sk4,sk3)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f255,f280]) ).
fof(f454,plain,
spl0_41,
inference(avatar_split_clause,[],[f18,f452]) ).
fof(f18,axiom,
! [X0] : ssList(skaf77(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
fof(f450,plain,
spl0_40,
inference(avatar_split_clause,[],[f17,f448]) ).
fof(f448,plain,
( spl0_40
<=> ! [X0] : ssItem(skaf78(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f17,axiom,
! [X0] : ssItem(skaf78(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
fof(f446,plain,
spl0_39,
inference(avatar_split_clause,[],[f16,f444]) ).
fof(f444,plain,
( spl0_39
<=> ! [X0] : ssItem(skaf79(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f16,axiom,
! [X0] : ssItem(skaf79(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
fof(f442,plain,
spl0_38,
inference(avatar_split_clause,[],[f15,f440]) ).
fof(f15,axiom,
! [X0] : ssList(skaf80(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
fof(f438,plain,
spl0_37,
inference(avatar_split_clause,[],[f14,f436]) ).
fof(f14,axiom,
! [X0] : ssList(skaf81(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
fof(f434,plain,
spl0_36,
inference(avatar_split_clause,[],[f13,f432]) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
fof(f430,plain,
spl0_35,
inference(avatar_split_clause,[],[f12,f428]) ).
fof(f428,plain,
( spl0_35
<=> ! [X0] : ssItem(skaf83(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
fof(f426,plain,
( spl0_34
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f293,f278,f284,f424]) ).
fof(f424,plain,
( spl0_34
<=> ! [X6] :
( ~ ssItem(X6)
| ~ lt(X6,sk5)
| ~ memberP(sk7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f293,plain,
( ! [X6] :
( sk3 = sk4
| ~ ssItem(X6)
| ~ memberP(sk7,X6)
| ~ lt(X6,sk5) )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f200,f280]) ).
fof(f200,axiom,
! [X6] :
( ~ ssItem(X6)
| ~ memberP(sk7,X6)
| ~ lt(X6,sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f422,plain,
( spl0_33
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f292,f278,f284,f420]) ).
fof(f420,plain,
( spl0_33
<=> ! [X6] :
( ~ ssItem(X6)
| ~ lt(sk5,X6)
| ~ memberP(sk6,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f292,plain,
( ! [X6] :
( sk3 = sk4
| ~ ssItem(X6)
| ~ memberP(sk6,X6)
| ~ lt(sk5,X6) )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f199,f280]) ).
fof(f199,axiom,
! [X6] :
( ~ ssItem(X6)
| ~ memberP(sk6,X6)
| ~ lt(sk5,X6)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f418,plain,
( spl0_32
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f291,f278,f284,f415]) ).
fof(f291,plain,
( sk3 = sk4
| sk4 = app(app(sk6,sk3),sk7)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f198,f280]) ).
fof(f412,plain,
~ spl0_31,
inference(avatar_split_clause,[],[f11,f409]) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
fof(f407,plain,
spl0_30,
inference(avatar_split_clause,[],[f10,f404]) ).
fof(f404,plain,
( spl0_30
<=> ssItem(skac2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
fof(f402,plain,
spl0_29,
inference(avatar_split_clause,[],[f9,f399]) ).
fof(f399,plain,
( spl0_29
<=> ssItem(skac3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
fof(f396,plain,
spl0_28,
inference(avatar_split_clause,[],[f8,f393]) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f391,plain,
( spl0_27
| ~ spl0_8
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f386,f382,f278,f388]) ).
fof(f388,plain,
( spl0_27
<=> cyclefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f386,plain,
( cyclefreeP(sk3)
| ~ spl0_8
| ~ spl0_26 ),
inference(forward_demodulation,[],[f384,f280]) ).
fof(f385,plain,
spl0_26,
inference(avatar_split_clause,[],[f7,f382]) ).
fof(f7,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
fof(f380,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f375,f371,f278,f377]) ).
fof(f377,plain,
( spl0_25
<=> totalorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f375,plain,
( totalorderP(sk3)
| ~ spl0_8
| ~ spl0_24 ),
inference(forward_demodulation,[],[f373,f280]) ).
fof(f374,plain,
spl0_24,
inference(avatar_split_clause,[],[f6,f371]) ).
fof(f6,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
fof(f369,plain,
( spl0_23
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f364,f360,f278,f366]) ).
fof(f366,plain,
( spl0_23
<=> strictorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f364,plain,
( strictorderP(sk3)
| ~ spl0_8
| ~ spl0_22 ),
inference(forward_demodulation,[],[f362,f280]) ).
fof(f363,plain,
spl0_22,
inference(avatar_split_clause,[],[f5,f360]) ).
fof(f5,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
fof(f358,plain,
( spl0_21
| ~ spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f353,f349,f278,f355]) ).
fof(f355,plain,
( spl0_21
<=> totalorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f353,plain,
( totalorderedP(sk3)
| ~ spl0_8
| ~ spl0_20 ),
inference(forward_demodulation,[],[f351,f280]) ).
fof(f352,plain,
spl0_20,
inference(avatar_split_clause,[],[f4,f349]) ).
fof(f4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
fof(f347,plain,
( spl0_19
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f342,f338,f278,f344]) ).
fof(f344,plain,
( spl0_19
<=> strictorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f342,plain,
( strictorderedP(sk3)
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f340,f280]) ).
fof(f341,plain,
spl0_18,
inference(avatar_split_clause,[],[f3,f338]) ).
fof(f3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
fof(f336,plain,
( spl0_17
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f331,f327,f278,f333]) ).
fof(f333,plain,
( spl0_17
<=> duplicatefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f327,plain,
( spl0_16
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f331,plain,
( duplicatefreeP(sk3)
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f329,f280]) ).
fof(f329,plain,
( duplicatefreeP(nil)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f330,plain,
spl0_16,
inference(avatar_split_clause,[],[f2,f327]) ).
fof(f2,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
fof(f325,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f320,f316,f278,f322]) ).
fof(f322,plain,
( spl0_15
<=> equalelemsP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f320,plain,
( equalelemsP(sk3)
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f318,f280]) ).
fof(f319,plain,
spl0_14,
inference(avatar_split_clause,[],[f1,f316]) ).
fof(f1,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
fof(f314,plain,
( spl0_9
| spl0_13
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f290,f278,f311,f284]) ).
fof(f290,plain,
( sk3 = cons(sk5,sk3)
| sk3 = sk4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f289,f280]) ).
fof(f289,plain,
( sk3 = sk4
| sk3 = cons(sk5,nil)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f197,f280]) ).
fof(f309,plain,
( spl0_12
| spl0_9
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f288,f278,f284,f306]) ).
fof(f288,plain,
( sk3 = sk4
| ssList(sk7)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f196,f280]) ).
fof(f304,plain,
( ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f211,f301,f297]) ).
fof(f211,plain,
( ~ singletonP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f207,f191,f190,f191]) ).
fof(f190,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f191,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f207,axiom,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
fof(f287,plain,
( spl0_9
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f282,f278,f258,f284]) ).
fof(f282,plain,
( sk3 = sk4
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f280,f260]) ).
fof(f260,plain,
( nil = sk4
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f281,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f201,f267,f278]) ).
fof(f201,axiom,
( ssList(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f276,plain,
( spl0_7
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f271,f258,f253,f273]) ).
fof(f271,plain,
( neq(sk4,sk4)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f255,f260]) ).
fof(f270,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f195,f267,f258]) ).
fof(f195,axiom,
( ssList(sk6)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f265,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f193,f262,f258]) ).
fof(f193,axiom,
( ssItem(sk5)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f256,plain,
spl0_3,
inference(avatar_split_clause,[],[f210,f253]) ).
fof(f210,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f192,f190]) ).
fof(f192,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f251,plain,
spl0_2,
inference(avatar_split_clause,[],[f209,f248]) ).
fof(f209,plain,
ssList(sk4),
inference(definition_unfolding,[],[f187,f190]) ).
fof(f187,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
fof(f246,plain,
spl0_1,
inference(avatar_split_clause,[],[f208,f243]) ).
fof(f208,plain,
ssList(sk3),
inference(definition_unfolding,[],[f186,f191]) ).
fof(f186,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC384-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 20:30:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (10286)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (10287)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (10289)WARNING: value z3 for option sas not known
% 0.15/0.39 % (10290)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (10288)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (10291)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)
% 0.15/0.39 % (10292)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)
% 0.15/0.39 % (10293)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)
% 0.15/0.39 % (10289)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)
% 0.21/0.41 TRYING [1]
% 0.21/0.41 TRYING [2]
% 0.21/0.42 TRYING [3]
% 0.21/0.45 TRYING [1]
% 0.21/0.46 TRYING [1]
% 0.21/0.46 TRYING [2]
% 0.21/0.46 TRYING [3]
% 0.21/0.47 TRYING [2]
% 0.21/0.47 TRYING [4]
% 0.21/0.51 TRYING [4]
% 0.21/0.53 % (10291)First to succeed.
% 0.21/0.55 % (10291)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10286"
% 0.21/0.55 % (10291)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56 % (10291)------------------------------
% 0.21/0.56 % (10291)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.56 % (10291)Termination reason: Refutation
% 0.21/0.56
% 0.21/0.56 % (10291)Memory used [KB]: 3517
% 0.21/0.56 % (10291)Time elapsed: 0.157 s
% 0.21/0.56 % (10291)Instructions burned: 256 (million)
% 0.21/0.56 % (10286)Success in time 0.198 s
%------------------------------------------------------------------------------