TSTP Solution File: SWC118+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC118+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 : n025.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 09:59:20 EDT 2024
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 512
% Syntax : Number of formulae : 1556 ( 249 unt; 0 def)
% Number of atoms : 6225 (1022 equ)
% Maximal formula atoms : 60 ( 4 avg)
% Number of connectives : 7713 (3044 ~;3091 |; 858 &)
% ( 422 <=>; 298 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 384 ( 382 usr; 346 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 9 con; 0-2 aty)
% Number of variables : 2209 (1840 !; 369 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5051,plain,
$false,
inference(avatar_sat_refutation,[],[f654,f659,f664,f669,f674,f683,f692,f697,f702,f707,f712,f717,f722,f727,f732,f737,f742,f747,f752,f757,f762,f766,f770,f774,f778,f782,f786,f790,f794,f798,f808,f842,f846,f850,f854,f859,f863,f867,f871,f875,f879,f883,f887,f891,f895,f899,f904,f908,f912,f916,f920,f924,f928,f932,f936,f940,f944,f949,f953,f957,f961,f965,f969,f973,f977,f981,f985,f989,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1034,f1038,f1042,f1047,f1080,f1127,f1174,f1206,f1210,f1215,f1219,f1223,f1227,f1231,f1235,f1239,f1243,f1247,f1251,f1255,f1260,f1264,f1268,f1272,f1276,f1280,f1284,f1288,f1292,f1296,f1301,f1308,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1341,f1345,f1350,f1354,f1358,f1362,f1366,f1370,f1374,f1378,f1382,f1386,f1391,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1475,f1479,f1483,f1487,f1491,f1495,f1499,f1503,f1519,f1573,f1577,f1581,f1585,f1589,f1593,f1597,f1601,f1606,f1610,f1614,f1618,f1622,f1626,f1630,f1634,f1638,f1642,f1646,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1689,f1710,f1842,f1846,f1851,f1855,f1859,f1863,f1867,f1950,f1954,f1958,f1962,f1966,f1970,f1974,f2056,f2062,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2095,f2099,f2171,f2175,f2179,f2183,f2187,f2191,f2195,f2199,f2265,f2269,f2273,f2277,f2283,f2287,f2291,f2295,f2299,f2334,f2338,f2342,f2346,f2399,f2403,f2407,f2411,f2498,f2502,f2506,f2510,f2514,f2518,f2522,f2526,f2530,f2534,f2540,f2544,f2548,f2552,f2592,f2596,f2602,f2619,f2623,f2627,f2637,f2641,f2645,f2687,f2692,f2697,f2702,f2707,f2712,f2717,f2722,f2749,f2884,f2886,f2891,f2994,f3004,f3050,f3055,f3069,f3074,f3088,f3098,f3166,f3168,f3209,f3214,f3219,f3234,f3281,f3290,f3337,f3343,f3407,f3411,f3415,f3419,f3423,f3427,f3431,f3435,f3620,f3655,f3661,f3667,f3673,f3679,f3685,f3691,f3697,f3737,f3742,f3751,f3866,f3930,f3984,f3989,f4105,f4169,f4174,f4179,f4210,f4220,f4226,f4232,f4238,f4240,f4275,f4307,f4312,f4327,f4457,f4493,f4494,f4495,f4528,f4533,f4538,f4546,f4551,f4556,f4561,f4566,f4571,f4632,f4672,f4711,f4716,f4720,f4724,f4733,f4739,f4805,f4810,f4814,f4819,f4823,f4954,f4960,f4964,f4968,f4972,f4974,f5011,f5018,f5050]) ).
fof(f5050,plain,
( ~ spl71_2
| ~ spl71_1
| ~ spl71_3
| ~ spl71_4
| spl71_7
| ~ spl71_11
| ~ spl71_244 ),
inference(avatar_split_clause,[],[f2612,f2600,f699,f680,f666,f661,f651,f656]) ).
fof(f656,plain,
( spl71_2
<=> ssList(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_2])]) ).
fof(f651,plain,
( spl71_1
<=> ssList(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_1])]) ).
fof(f661,plain,
( spl71_3
<=> ssList(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_3])]) ).
fof(f666,plain,
( spl71_4
<=> ssList(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_4])]) ).
fof(f680,plain,
( spl71_7
<=> segmentP(sK21,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_7])]) ).
fof(f699,plain,
( spl71_11
<=> sK21 = app(app(sK22,sK20),sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_11])]) ).
fof(f2600,plain,
( spl71_244
<=> ! [X2,X1,X3] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_244])]) ).
fof(f2612,plain,
( segmentP(sK21,sK20)
| ~ ssList(sK23)
| ~ ssList(sK22)
| ~ ssList(sK20)
| ~ ssList(sK21)
| ~ spl71_11
| ~ spl71_244 ),
inference(superposition,[],[f2601,f701]) ).
fof(f701,plain,
( sK21 = app(app(sK22,sK20),sK23)
| ~ spl71_11 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f2601,plain,
( ! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) )
| ~ spl71_244 ),
inference(avatar_component_clause,[],[f2600]) ).
fof(f5018,plain,
( ~ spl71_2
| ~ spl71_4
| spl71_315
| ~ spl71_3
| ~ spl71_11
| ~ spl71_244
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4980,f4166,f2600,f699,f661,f4304,f666,f656]) ).
fof(f4304,plain,
( spl71_315
<=> segmentP(sK21,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_315])]) ).
fof(f4166,plain,
( spl71_307
<=> sK20 = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_307])]) ).
fof(f4980,plain,
( ~ ssList(sK22)
| segmentP(sK21,sK22)
| ~ ssList(sK23)
| ~ ssList(sK21)
| ~ spl71_11
| ~ spl71_244
| ~ spl71_307 ),
inference(duplicate_literal_removal,[],[f4979]) ).
fof(f4979,plain,
( ~ ssList(sK22)
| segmentP(sK21,sK22)
| ~ ssList(sK23)
| ~ ssList(sK22)
| ~ ssList(sK21)
| ~ spl71_11
| ~ spl71_244
| ~ spl71_307 ),
inference(forward_demodulation,[],[f4978,f4168]) ).
fof(f4168,plain,
( sK20 = sK22
| ~ spl71_307 ),
inference(avatar_component_clause,[],[f4166]) ).
fof(f4978,plain,
( segmentP(sK21,sK22)
| ~ ssList(sK23)
| ~ ssList(sK22)
| ~ ssList(sK20)
| ~ ssList(sK21)
| ~ spl71_11
| ~ spl71_244
| ~ spl71_307 ),
inference(forward_demodulation,[],[f2612,f4168]) ).
fof(f5011,plain,
( spl71_342
| ~ spl71_307
| ~ spl71_341 ),
inference(avatar_split_clause,[],[f4981,f4951,f4166,f4957]) ).
fof(f4957,plain,
( spl71_342
<=> frontsegP(sK21,app(sK22,sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_342])]) ).
fof(f4951,plain,
( spl71_341
<=> frontsegP(sK21,app(sK22,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_341])]) ).
fof(f4981,plain,
( frontsegP(sK21,app(sK22,sK22))
| ~ spl71_307
| ~ spl71_341 ),
inference(forward_demodulation,[],[f4953,f4168]) ).
fof(f4953,plain,
( frontsegP(sK21,app(sK22,sK20))
| ~ spl71_341 ),
inference(avatar_component_clause,[],[f4951]) ).
fof(f4974,plain,
( ~ spl71_3
| ~ spl71_147
| spl71_335 ),
inference(avatar_split_clause,[],[f4741,f4736,f1501,f661]) ).
fof(f1501,plain,
( spl71_147
<=> ! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_147])]) ).
fof(f4736,plain,
( spl71_335
<=> ssList(app(sK22,sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_335])]) ).
fof(f4741,plain,
( ~ ssList(sK22)
| ~ spl71_147
| spl71_335 ),
inference(duplicate_literal_removal,[],[f4740]) ).
fof(f4740,plain,
( ~ ssList(sK22)
| ~ ssList(sK22)
| ~ spl71_147
| spl71_335 ),
inference(resolution,[],[f4738,f1502]) ).
fof(f1502,plain,
( ! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl71_147 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f4738,plain,
( ~ ssList(app(sK22,sK22))
| spl71_335 ),
inference(avatar_component_clause,[],[f4736]) ).
fof(f4972,plain,
( spl71_345
| ~ spl71_1
| ~ spl71_220 ),
inference(avatar_split_clause,[],[f2351,f2332,f651,f4970]) ).
fof(f4970,plain,
( spl71_345
<=> ! [X0] :
( nil = X0
| tl(app(X0,sK20)) = app(tl(X0),sK20)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_345])]) ).
fof(f2332,plain,
( spl71_220
<=> ! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_220])]) ).
fof(f2351,plain,
( ! [X0] :
( nil = X0
| tl(app(X0,sK20)) = app(tl(X0),sK20)
| ~ ssList(X0) )
| ~ spl71_1
| ~ spl71_220 ),
inference(resolution,[],[f2333,f653]) ).
fof(f653,plain,
( ssList(sK20)
| ~ spl71_1 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f2333,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1)
| ~ ssList(X0) )
| ~ spl71_220 ),
inference(avatar_component_clause,[],[f2332]) ).
fof(f4968,plain,
( ~ spl71_4
| ~ spl71_333
| spl71_344
| ~ spl71_11
| ~ spl71_209 ),
inference(avatar_split_clause,[],[f2254,f2193,f699,f4966,f4726,f666]) ).
fof(f4726,plain,
( spl71_333
<=> ssList(app(sK22,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_333])]) ).
fof(f4966,plain,
( spl71_344
<=> ! [X0] :
( rearsegP(sK21,X0)
| ~ ssList(X0)
| ~ rearsegP(sK23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_344])]) ).
fof(f2193,plain,
( spl71_209
<=> ! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_209])]) ).
fof(f2254,plain,
( ! [X0] :
( rearsegP(sK21,X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(app(sK22,sK20))
| ~ ssList(X0)
| ~ ssList(sK23) )
| ~ spl71_11
| ~ spl71_209 ),
inference(superposition,[],[f2194,f701]) ).
fof(f2194,plain,
( ! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl71_209 ),
inference(avatar_component_clause,[],[f2193]) ).
fof(f4964,plain,
( ~ spl71_333
| ~ spl71_4
| spl71_343
| ~ spl71_11
| ~ spl71_205 ),
inference(avatar_split_clause,[],[f2203,f2177,f699,f4962,f666,f4726]) ).
fof(f4962,plain,
( spl71_343
<=> ! [X0] :
( memberP(sK21,X0)
| ~ ssItem(X0)
| ~ memberP(sK23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_343])]) ).
fof(f2177,plain,
( spl71_205
<=> ! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_205])]) ).
fof(f2203,plain,
( ! [X0] :
( memberP(sK21,X0)
| ~ memberP(sK23,X0)
| ~ ssList(sK23)
| ~ ssList(app(sK22,sK20))
| ~ ssItem(X0) )
| ~ spl71_11
| ~ spl71_205 ),
inference(superposition,[],[f2178,f701]) ).
fof(f2178,plain,
( ! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl71_205 ),
inference(avatar_component_clause,[],[f2177]) ).
fof(f4960,plain,
( ~ spl71_342
| ~ spl71_307
| spl71_341 ),
inference(avatar_split_clause,[],[f4955,f4951,f4166,f4957]) ).
fof(f4955,plain,
( ~ frontsegP(sK21,app(sK22,sK22))
| ~ spl71_307
| spl71_341 ),
inference(forward_demodulation,[],[f4952,f4168]) ).
fof(f4952,plain,
( ~ frontsegP(sK21,app(sK22,sK20))
| spl71_341 ),
inference(avatar_component_clause,[],[f4951]) ).
fof(f4954,plain,
( ~ spl71_2
| ~ spl71_333
| ~ spl71_4
| spl71_341
| ~ spl71_11
| ~ spl71_202 ),
inference(avatar_split_clause,[],[f2164,f2097,f699,f4951,f666,f4726,f656]) ).
fof(f2097,plain,
( spl71_202
<=> ! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_202])]) ).
fof(f2164,plain,
( frontsegP(sK21,app(sK22,sK20))
| ~ ssList(sK23)
| ~ ssList(app(sK22,sK20))
| ~ ssList(sK21)
| ~ spl71_11
| ~ spl71_202 ),
inference(superposition,[],[f2098,f701]) ).
fof(f2098,plain,
( ! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) )
| ~ spl71_202 ),
inference(avatar_component_clause,[],[f2097]) ).
fof(f4823,plain,
( spl71_340
| ~ spl71_4
| ~ spl71_206 ),
inference(avatar_split_clause,[],[f2211,f2181,f666,f4821]) ).
fof(f4821,plain,
( spl71_340
<=> ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK23))
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_340])]) ).
fof(f2181,plain,
( spl71_206
<=> ! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_206])]) ).
fof(f2211,plain,
( ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK23))
| ~ ssList(X0) )
| ~ spl71_4
| ~ spl71_206 ),
inference(resolution,[],[f2182,f668]) ).
fof(f668,plain,
( ssList(sK23)
| ~ spl71_4 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f2182,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1))
| ~ ssList(X0) )
| ~ spl71_206 ),
inference(avatar_component_clause,[],[f2181]) ).
fof(f4819,plain,
( ~ spl71_339
| spl71_261
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4192,f4166,f2877,f4816]) ).
fof(f4816,plain,
( spl71_339
<=> ssItem(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_339])]) ).
fof(f2877,plain,
( spl71_261
<=> ssItem(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_261])]) ).
fof(f4192,plain,
( ~ ssItem(sK22)
| spl71_261
| ~ spl71_307 ),
inference(superposition,[],[f2879,f4168]) ).
fof(f2879,plain,
( ~ ssItem(sK20)
| spl71_261 ),
inference(avatar_component_clause,[],[f2877]) ).
fof(f4814,plain,
( spl71_338
| ~ spl71_3
| ~ spl71_206 ),
inference(avatar_split_clause,[],[f2210,f2181,f661,f4812]) ).
fof(f4812,plain,
( spl71_338
<=> ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK22))
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_338])]) ).
fof(f2210,plain,
( ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK22))
| ~ ssList(X0) )
| ~ spl71_3
| ~ spl71_206 ),
inference(resolution,[],[f2182,f663]) ).
fof(f663,plain,
( ssList(sK22)
| ~ spl71_3 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f4810,plain,
( spl71_337
| ~ spl71_2
| ~ spl71_206 ),
inference(avatar_split_clause,[],[f2209,f2181,f656,f4808]) ).
fof(f4808,plain,
( spl71_337
<=> ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK21))
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_337])]) ).
fof(f2209,plain,
( ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK21))
| ~ ssList(X0) )
| ~ spl71_2
| ~ spl71_206 ),
inference(resolution,[],[f2182,f658]) ).
fof(f658,plain,
( ssList(sK21)
| ~ spl71_2 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f4805,plain,
( spl71_336
| ~ spl71_1
| ~ spl71_206 ),
inference(avatar_split_clause,[],[f2208,f2181,f651,f4803]) ).
fof(f4803,plain,
( spl71_336
<=> ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK20))
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_336])]) ).
fof(f2208,plain,
( ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK20))
| ~ ssList(X0) )
| ~ spl71_1
| ~ spl71_206 ),
inference(resolution,[],[f2182,f653]) ).
fof(f4739,plain,
( ~ spl71_335
| ~ spl71_307
| spl71_333 ),
inference(avatar_split_clause,[],[f4734,f4726,f4166,f4736]) ).
fof(f4734,plain,
( ~ ssList(app(sK22,sK22))
| ~ spl71_307
| spl71_333 ),
inference(forward_demodulation,[],[f4728,f4168]) ).
fof(f4728,plain,
( ~ ssList(app(sK22,sK20))
| spl71_333 ),
inference(avatar_component_clause,[],[f4726]) ).
fof(f4733,plain,
( ~ spl71_2
| ~ spl71_4
| ~ spl71_333
| spl71_334
| ~ spl71_11
| ~ spl71_200 ),
inference(avatar_split_clause,[],[f2161,f2088,f699,f4730,f4726,f666,f656]) ).
fof(f4730,plain,
( spl71_334
<=> rearsegP(sK21,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_334])]) ).
fof(f2088,plain,
( spl71_200
<=> ! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_200])]) ).
fof(f2161,plain,
( rearsegP(sK21,sK23)
| ~ ssList(app(sK22,sK20))
| ~ ssList(sK23)
| ~ ssList(sK21)
| ~ spl71_11
| ~ spl71_200 ),
inference(superposition,[],[f2089,f701]) ).
fof(f2089,plain,
( ! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) )
| ~ spl71_200 ),
inference(avatar_component_clause,[],[f2088]) ).
fof(f4724,plain,
( spl71_332
| ~ spl71_4
| ~ spl71_196 ),
inference(avatar_split_clause,[],[f2119,f2072,f666,f4722]) ).
fof(f4722,plain,
( spl71_332
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK23) = app(cons(X0,nil),sK23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_332])]) ).
fof(f2072,plain,
( spl71_196
<=> ! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_196])]) ).
fof(f2119,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK23) = app(cons(X0,nil),sK23) )
| ~ spl71_4
| ~ spl71_196 ),
inference(resolution,[],[f2073,f668]) ).
fof(f2073,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) )
| ~ spl71_196 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f4720,plain,
( spl71_331
| ~ spl71_3
| ~ spl71_196 ),
inference(avatar_split_clause,[],[f2118,f2072,f661,f4718]) ).
fof(f4718,plain,
( spl71_331
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK22) = app(cons(X0,nil),sK22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_331])]) ).
fof(f2118,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK22) = app(cons(X0,nil),sK22) )
| ~ spl71_3
| ~ spl71_196 ),
inference(resolution,[],[f2073,f663]) ).
fof(f4716,plain,
( spl71_330
| ~ spl71_2
| ~ spl71_196 ),
inference(avatar_split_clause,[],[f2117,f2072,f656,f4714]) ).
fof(f4714,plain,
( spl71_330
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK21) = app(cons(X0,nil),sK21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_330])]) ).
fof(f2117,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK21) = app(cons(X0,nil),sK21) )
| ~ spl71_2
| ~ spl71_196 ),
inference(resolution,[],[f2073,f658]) ).
fof(f4711,plain,
( spl71_329
| ~ spl71_1
| ~ spl71_196 ),
inference(avatar_split_clause,[],[f2116,f2072,f651,f4709]) ).
fof(f4709,plain,
( spl71_329
<=> ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK20) = app(cons(X0,nil),sK20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_329])]) ).
fof(f2116,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK20) = app(cons(X0,nil),sK20) )
| ~ spl71_1
| ~ spl71_196 ),
inference(resolution,[],[f2073,f653]) ).
fof(f4672,plain,
( spl71_9
| spl71_328
| ~ spl71_2
| ~ spl71_189
| ~ spl71_265
| ~ spl71_278 ),
inference(avatar_split_clause,[],[f3871,f3231,f3001,f1964,f656,f4669,f689]) ).
fof(f689,plain,
( spl71_9
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_9])]) ).
fof(f4669,plain,
( spl71_328
<=> sK21 = cons(sK26(sK21),sK27(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_328])]) ).
fof(f1964,plain,
( spl71_189
<=> ! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_189])]) ).
fof(f3001,plain,
( spl71_265
<=> hd(sK21) = sK26(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_265])]) ).
fof(f3231,plain,
( spl71_278
<=> tl(sK21) = sK27(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_278])]) ).
fof(f3871,plain,
( sK21 = cons(sK26(sK21),sK27(sK21))
| nil = sK21
| ~ spl71_2
| ~ spl71_189
| ~ spl71_265
| ~ spl71_278 ),
inference(forward_demodulation,[],[f3282,f3233]) ).
fof(f3233,plain,
( tl(sK21) = sK27(sK21)
| ~ spl71_278 ),
inference(avatar_component_clause,[],[f3231]) ).
fof(f3282,plain,
( sK21 = cons(sK26(sK21),tl(sK21))
| nil = sK21
| ~ spl71_2
| ~ spl71_189
| ~ spl71_265 ),
inference(forward_demodulation,[],[f2021,f3003]) ).
fof(f3003,plain,
( hd(sK21) = sK26(sK21)
| ~ spl71_265 ),
inference(avatar_component_clause,[],[f3001]) ).
fof(f2021,plain,
( nil = sK21
| sK21 = cons(hd(sK21),tl(sK21))
| ~ spl71_2
| ~ spl71_189 ),
inference(resolution,[],[f1965,f658]) ).
fof(f1965,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl71_189 ),
inference(avatar_component_clause,[],[f1964]) ).
fof(f4632,plain,
( spl71_272
| spl71_327
| ~ spl71_4
| ~ spl71_189
| ~ spl71_271
| ~ spl71_281 ),
inference(avatar_split_clause,[],[f3868,f3334,f3081,f1964,f666,f4629,f3085]) ).
fof(f3085,plain,
( spl71_272
<=> nil = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_272])]) ).
fof(f4629,plain,
( spl71_327
<=> sK23 = cons(sK26(sK23),sK27(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_327])]) ).
fof(f3081,plain,
( spl71_271
<=> hd(sK23) = sK26(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_271])]) ).
fof(f3334,plain,
( spl71_281
<=> tl(sK23) = sK27(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_281])]) ).
fof(f3868,plain,
( sK23 = cons(sK26(sK23),sK27(sK23))
| nil = sK23
| ~ spl71_4
| ~ spl71_189
| ~ spl71_271
| ~ spl71_281 ),
inference(forward_demodulation,[],[f3867,f3083]) ).
fof(f3083,plain,
( hd(sK23) = sK26(sK23)
| ~ spl71_271 ),
inference(avatar_component_clause,[],[f3081]) ).
fof(f3867,plain,
( sK23 = cons(hd(sK23),sK27(sK23))
| nil = sK23
| ~ spl71_4
| ~ spl71_189
| ~ spl71_281 ),
inference(forward_demodulation,[],[f2023,f3336]) ).
fof(f3336,plain,
( tl(sK23) = sK27(sK23)
| ~ spl71_281 ),
inference(avatar_component_clause,[],[f3334]) ).
fof(f2023,plain,
( nil = sK23
| sK23 = cons(hd(sK23),tl(sK23))
| ~ spl71_4
| ~ spl71_189 ),
inference(resolution,[],[f1965,f668]) ).
fof(f4571,plain,
( spl71_326
| ~ spl71_306
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4263,f4166,f4102,f4568]) ).
fof(f4568,plain,
( spl71_326
<=> sK22 = cons(sK26(sK22),sK27(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_326])]) ).
fof(f4102,plain,
( spl71_306
<=> sK20 = cons(sK26(sK20),sK27(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_306])]) ).
fof(f4263,plain,
( sK22 = cons(sK26(sK22),sK27(sK22))
| ~ spl71_306
| ~ spl71_307 ),
inference(forward_demodulation,[],[f4104,f4168]) ).
fof(f4104,plain,
( sK20 = cons(sK26(sK20),sK27(sK20))
| ~ spl71_306 ),
inference(avatar_component_clause,[],[f4102]) ).
fof(f4566,plain,
( spl71_325
| ~ spl71_11
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4182,f4166,f699,f4563]) ).
fof(f4563,plain,
( spl71_325
<=> sK21 = app(app(sK22,sK22),sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_325])]) ).
fof(f4182,plain,
( sK21 = app(app(sK22,sK22),sK23)
| ~ spl71_11
| ~ spl71_307 ),
inference(superposition,[],[f701,f4168]) ).
fof(f4561,plain,
( spl71_324
| ~ spl71_307
| ~ spl71_314 ),
inference(avatar_split_clause,[],[f4239,f4235,f4166,f4558]) ).
fof(f4558,plain,
( spl71_324
<=> strictorderedP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_324])]) ).
fof(f4235,plain,
( spl71_314
<=> strictorderedP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_314])]) ).
fof(f4239,plain,
( strictorderedP(sK22)
| ~ spl71_307
| ~ spl71_314 ),
inference(forward_demodulation,[],[f4237,f4168]) ).
fof(f4237,plain,
( strictorderedP(sK20)
| ~ spl71_314 ),
inference(avatar_component_clause,[],[f4235]) ).
fof(f4556,plain,
( spl71_323
| ~ spl71_307
| ~ spl71_313 ),
inference(avatar_split_clause,[],[f4233,f4229,f4166,f4553]) ).
fof(f4553,plain,
( spl71_323
<=> totalorderP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_323])]) ).
fof(f4229,plain,
( spl71_313
<=> totalorderP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_313])]) ).
fof(f4233,plain,
( totalorderP(sK22)
| ~ spl71_307
| ~ spl71_313 ),
inference(forward_demodulation,[],[f4231,f4168]) ).
fof(f4231,plain,
( totalorderP(sK20)
| ~ spl71_313 ),
inference(avatar_component_clause,[],[f4229]) ).
fof(f4551,plain,
( spl71_322
| ~ spl71_307
| ~ spl71_312 ),
inference(avatar_split_clause,[],[f4227,f4223,f4166,f4548]) ).
fof(f4548,plain,
( spl71_322
<=> strictorderP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_322])]) ).
fof(f4223,plain,
( spl71_312
<=> strictorderP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_312])]) ).
fof(f4227,plain,
( strictorderP(sK22)
| ~ spl71_307
| ~ spl71_312 ),
inference(forward_demodulation,[],[f4225,f4168]) ).
fof(f4225,plain,
( strictorderP(sK20)
| ~ spl71_312 ),
inference(avatar_component_clause,[],[f4223]) ).
fof(f4546,plain,
( spl71_321
| ~ spl71_307
| ~ spl71_311 ),
inference(avatar_split_clause,[],[f4221,f4217,f4166,f4543]) ).
fof(f4543,plain,
( spl71_321
<=> cyclefreeP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_321])]) ).
fof(f4217,plain,
( spl71_311
<=> cyclefreeP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_311])]) ).
fof(f4221,plain,
( cyclefreeP(sK22)
| ~ spl71_307
| ~ spl71_311 ),
inference(forward_demodulation,[],[f4219,f4168]) ).
fof(f4219,plain,
( cyclefreeP(sK20)
| ~ spl71_311 ),
inference(avatar_component_clause,[],[f4217]) ).
fof(f4538,plain,
( spl71_320
| ~ spl71_307
| ~ spl71_310 ),
inference(avatar_split_clause,[],[f4211,f4207,f4166,f4535]) ).
fof(f4535,plain,
( spl71_320
<=> duplicatefreeP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_320])]) ).
fof(f4207,plain,
( spl71_310
<=> duplicatefreeP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_310])]) ).
fof(f4211,plain,
( duplicatefreeP(sK22)
| ~ spl71_307
| ~ spl71_310 ),
inference(forward_demodulation,[],[f4209,f4168]) ).
fof(f4209,plain,
( duplicatefreeP(sK20)
| ~ spl71_310 ),
inference(avatar_component_clause,[],[f4207]) ).
fof(f4533,plain,
( spl71_319
| ~ spl71_5
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4181,f4166,f671,f4530]) ).
fof(f4530,plain,
( spl71_319
<=> totalorderedP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_319])]) ).
fof(f671,plain,
( spl71_5
<=> totalorderedP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_5])]) ).
fof(f4181,plain,
( totalorderedP(sK22)
| ~ spl71_5
| ~ spl71_307 ),
inference(superposition,[],[f673,f4168]) ).
fof(f673,plain,
( totalorderedP(sK20)
| ~ spl71_5 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f4528,plain,
( ~ spl71_318
| spl71_8
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4277,f4166,f685,f4525]) ).
fof(f4525,plain,
( spl71_318
<=> sK21 = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_318])]) ).
fof(f685,plain,
( spl71_8
<=> sK20 = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_8])]) ).
fof(f4277,plain,
( sK21 != sK22
| spl71_8
| ~ spl71_307 ),
inference(forward_demodulation,[],[f687,f4168]) ).
fof(f687,plain,
( sK20 != sK21
| spl71_8 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f4495,plain,
( ~ spl71_1
| ~ spl71_3
| spl71_307
| ~ spl71_174
| spl71_317 ),
inference(avatar_split_clause,[],[f4335,f4324,f1673,f4166,f661,f651]) ).
fof(f1673,plain,
( spl71_174
<=> ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_174])]) ).
fof(f4324,plain,
( spl71_317
<=> neq(sK20,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_317])]) ).
fof(f4335,plain,
( sK20 = sK22
| ~ ssList(sK22)
| ~ ssList(sK20)
| ~ spl71_174
| spl71_317 ),
inference(resolution,[],[f4325,f1674]) ).
fof(f1674,plain,
( ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl71_174 ),
inference(avatar_component_clause,[],[f1673]) ).
fof(f4325,plain,
( ~ neq(sK20,sK22)
| spl71_317 ),
inference(avatar_component_clause,[],[f4324]) ).
fof(f4494,plain,
( spl71_317
| ~ spl71_6
| ~ spl71_269 ),
inference(avatar_split_clause,[],[f4273,f3066,f676,f4324]) ).
fof(f676,plain,
( spl71_6
<=> neq(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_6])]) ).
fof(f3066,plain,
( spl71_269
<=> nil = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_269])]) ).
fof(f4273,plain,
( neq(sK20,sK22)
| ~ spl71_6
| ~ spl71_269 ),
inference(forward_demodulation,[],[f677,f3068]) ).
fof(f3068,plain,
( nil = sK22
| ~ spl71_269 ),
inference(avatar_component_clause,[],[f3066]) ).
fof(f677,plain,
( neq(sK20,nil)
| ~ spl71_6 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f4493,plain,
( ~ spl71_3
| ~ spl71_20
| spl71_269
| ~ spl71_174
| spl71_316 ),
inference(avatar_split_clause,[],[f4331,f4309,f1673,f3066,f744,f661]) ).
fof(f744,plain,
( spl71_20
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_20])]) ).
fof(f4309,plain,
( spl71_316
<=> neq(sK22,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_316])]) ).
fof(f4331,plain,
( nil = sK22
| ~ ssList(nil)
| ~ ssList(sK22)
| ~ spl71_174
| spl71_316 ),
inference(resolution,[],[f4310,f1674]) ).
fof(f4310,plain,
( ~ neq(sK22,nil)
| spl71_316 ),
inference(avatar_component_clause,[],[f4309]) ).
fof(f4457,plain,
( ~ spl71_3
| spl71_282
| ~ spl71_4
| ~ spl71_174
| ~ spl71_272
| spl71_316 ),
inference(avatar_split_clause,[],[f4334,f4309,f3085,f1673,f666,f3340,f661]) ).
fof(f3340,plain,
( spl71_282
<=> sK22 = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_282])]) ).
fof(f4334,plain,
( ~ ssList(sK23)
| sK22 = sK23
| ~ ssList(sK22)
| ~ spl71_174
| ~ spl71_272
| spl71_316 ),
inference(forward_demodulation,[],[f4333,f3087]) ).
fof(f3087,plain,
( nil = sK23
| ~ spl71_272 ),
inference(avatar_component_clause,[],[f3085]) ).
fof(f4333,plain,
( sK22 = sK23
| ~ ssList(nil)
| ~ ssList(sK22)
| ~ spl71_174
| ~ spl71_272
| spl71_316 ),
inference(forward_demodulation,[],[f4331,f3087]) ).
fof(f4327,plain,
( spl71_317
| ~ spl71_6
| ~ spl71_272
| ~ spl71_282 ),
inference(avatar_split_clause,[],[f4315,f3340,f3085,f676,f4324]) ).
fof(f4315,plain,
( neq(sK20,sK22)
| ~ spl71_6
| ~ spl71_272
| ~ spl71_282 ),
inference(forward_demodulation,[],[f677,f4084]) ).
fof(f4084,plain,
( nil = sK22
| ~ spl71_272
| ~ spl71_282 ),
inference(forward_demodulation,[],[f3087,f3342]) ).
fof(f3342,plain,
( sK22 = sK23
| ~ spl71_282 ),
inference(avatar_component_clause,[],[f3340]) ).
fof(f4312,plain,
( spl71_316
| ~ spl71_6
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4276,f4166,f676,f4309]) ).
fof(f4276,plain,
( neq(sK22,nil)
| ~ spl71_6
| ~ spl71_307 ),
inference(forward_demodulation,[],[f677,f4168]) ).
fof(f4307,plain,
( ~ spl71_315
| spl71_7
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4267,f4166,f680,f4304]) ).
fof(f4267,plain,
( ~ segmentP(sK21,sK22)
| spl71_7
| ~ spl71_307 ),
inference(forward_demodulation,[],[f682,f4168]) ).
fof(f682,plain,
( ~ segmentP(sK21,sK20)
| spl71_7 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f4275,plain,
( ~ spl71_269
| spl71_10
| ~ spl71_307 ),
inference(avatar_split_clause,[],[f4265,f4166,f694,f3066]) ).
fof(f694,plain,
( spl71_10
<=> nil = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_10])]) ).
fof(f4265,plain,
( nil != sK22
| spl71_10
| ~ spl71_307 ),
inference(forward_demodulation,[],[f696,f4168]) ).
fof(f696,plain,
( nil != sK20
| spl71_10 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f4240,plain,
( ~ spl71_8
| spl71_9
| ~ spl71_10 ),
inference(avatar_split_clause,[],[f2911,f694,f689,f685]) ).
fof(f2911,plain,
( sK20 != sK21
| spl71_9
| ~ spl71_10 ),
inference(superposition,[],[f691,f695]) ).
fof(f695,plain,
( nil = sK20
| ~ spl71_10 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f691,plain,
( nil != sK21
| spl71_9 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f4238,plain,
( spl71_314
| ~ spl71_10
| ~ spl71_18 ),
inference(avatar_split_clause,[],[f2918,f734,f694,f4235]) ).
fof(f734,plain,
( spl71_18
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_18])]) ).
fof(f2918,plain,
( strictorderedP(sK20)
| ~ spl71_10
| ~ spl71_18 ),
inference(superposition,[],[f736,f695]) ).
fof(f736,plain,
( strictorderedP(nil)
| ~ spl71_18 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f4232,plain,
( spl71_313
| ~ spl71_10
| ~ spl71_17 ),
inference(avatar_split_clause,[],[f2917,f729,f694,f4229]) ).
fof(f729,plain,
( spl71_17
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_17])]) ).
fof(f2917,plain,
( totalorderP(sK20)
| ~ spl71_10
| ~ spl71_17 ),
inference(superposition,[],[f731,f695]) ).
fof(f731,plain,
( totalorderP(nil)
| ~ spl71_17 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f4226,plain,
( spl71_312
| ~ spl71_10
| ~ spl71_16 ),
inference(avatar_split_clause,[],[f2916,f724,f694,f4223]) ).
fof(f724,plain,
( spl71_16
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_16])]) ).
fof(f2916,plain,
( strictorderP(sK20)
| ~ spl71_10
| ~ spl71_16 ),
inference(superposition,[],[f726,f695]) ).
fof(f726,plain,
( strictorderP(nil)
| ~ spl71_16 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f4220,plain,
( spl71_311
| ~ spl71_10
| ~ spl71_15 ),
inference(avatar_split_clause,[],[f2915,f719,f694,f4217]) ).
fof(f719,plain,
( spl71_15
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_15])]) ).
fof(f2915,plain,
( cyclefreeP(sK20)
| ~ spl71_10
| ~ spl71_15 ),
inference(superposition,[],[f721,f695]) ).
fof(f721,plain,
( cyclefreeP(nil)
| ~ spl71_15 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f4210,plain,
( spl71_310
| ~ spl71_10
| ~ spl71_14 ),
inference(avatar_split_clause,[],[f2914,f714,f694,f4207]) ).
fof(f714,plain,
( spl71_14
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_14])]) ).
fof(f2914,plain,
( duplicatefreeP(sK20)
| ~ spl71_10
| ~ spl71_14 ),
inference(superposition,[],[f716,f695]) ).
fof(f716,plain,
( duplicatefreeP(nil)
| ~ spl71_14 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f4179,plain,
( ~ spl71_309
| spl71_6
| ~ spl71_10
| ~ spl71_269 ),
inference(avatar_split_clause,[],[f4164,f3066,f694,f676,f4176]) ).
fof(f4176,plain,
( spl71_309
<=> neq(sK22,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_309])]) ).
fof(f4164,plain,
( ~ neq(sK22,sK22)
| spl71_6
| ~ spl71_10
| ~ spl71_269 ),
inference(forward_demodulation,[],[f4163,f4111]) ).
fof(f4111,plain,
( sK20 = sK22
| ~ spl71_10
| ~ spl71_269 ),
inference(forward_demodulation,[],[f695,f3068]) ).
fof(f4163,plain,
( ~ neq(sK20,sK22)
| spl71_6
| ~ spl71_269 ),
inference(forward_demodulation,[],[f678,f3068]) ).
fof(f678,plain,
( ~ neq(sK20,nil)
| spl71_6 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f4174,plain,
( spl71_308
| ~ spl71_7
| ~ spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_253
| ~ spl71_258
| ~ spl71_269
| ~ spl71_282 ),
inference(avatar_split_clause,[],[f4161,f3340,f3066,f2719,f2694,f699,f694,f685,f680,f4171]) ).
fof(f4171,plain,
( spl71_308
<=> segmentP(sK22,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_308])]) ).
fof(f2694,plain,
( spl71_253
<=> sK22 = app(sK22,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_253])]) ).
fof(f2719,plain,
( spl71_258
<=> sK23 = app(nil,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_258])]) ).
fof(f4161,plain,
( segmentP(sK22,sK22)
| ~ spl71_7
| ~ spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_253
| ~ spl71_258
| ~ spl71_269
| ~ spl71_282 ),
inference(forward_demodulation,[],[f4160,f4119]) ).
fof(f4119,plain,
( sK21 = sK22
| ~ spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_253
| ~ spl71_258
| ~ spl71_269
| ~ spl71_282 ),
inference(forward_demodulation,[],[f4118,f3342]) ).
fof(f4118,plain,
( sK21 = sK23
| ~ spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_253
| ~ spl71_258
| ~ spl71_269 ),
inference(forward_demodulation,[],[f3099,f3329]) ).
fof(f3329,plain,
( sK23 = app(sK22,sK23)
| ~ spl71_258
| ~ spl71_269 ),
inference(superposition,[],[f2721,f3068]) ).
fof(f2721,plain,
( sK23 = app(nil,sK23)
| ~ spl71_258 ),
inference(avatar_component_clause,[],[f2719]) ).
fof(f3099,plain,
( sK21 = app(sK22,sK23)
| ~ spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_253 ),
inference(forward_demodulation,[],[f2896,f2984]) ).
fof(f2984,plain,
( sK22 = app(sK22,sK21)
| ~ spl71_8
| ~ spl71_10
| ~ spl71_253 ),
inference(forward_demodulation,[],[f2942,f686]) ).
fof(f686,plain,
( sK20 = sK21
| ~ spl71_8 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f2942,plain,
( sK22 = app(sK22,sK20)
| ~ spl71_10
| ~ spl71_253 ),
inference(superposition,[],[f2696,f695]) ).
fof(f2696,plain,
( sK22 = app(sK22,nil)
| ~ spl71_253 ),
inference(avatar_component_clause,[],[f2694]) ).
fof(f2896,plain,
( sK21 = app(app(sK22,sK21),sK23)
| ~ spl71_8
| ~ spl71_11 ),
inference(superposition,[],[f701,f686]) ).
fof(f4160,plain,
( segmentP(sK21,sK22)
| ~ spl71_7
| ~ spl71_10
| ~ spl71_269 ),
inference(forward_demodulation,[],[f681,f4111]) ).
fof(f681,plain,
( segmentP(sK21,sK20)
| ~ spl71_7 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f4169,plain,
( spl71_307
| ~ spl71_10
| ~ spl71_269 ),
inference(avatar_split_clause,[],[f4111,f3066,f694,f4166]) ).
fof(f4105,plain,
( spl71_10
| spl71_306
| ~ spl71_1
| ~ spl71_189
| ~ spl71_263
| ~ spl71_273 ),
inference(avatar_split_clause,[],[f3221,f3095,f2888,f1964,f651,f4102,f694]) ).
fof(f2888,plain,
( spl71_263
<=> hd(sK20) = sK26(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_263])]) ).
fof(f3095,plain,
( spl71_273
<=> tl(sK20) = sK27(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_273])]) ).
fof(f3221,plain,
( sK20 = cons(sK26(sK20),sK27(sK20))
| nil = sK20
| ~ spl71_1
| ~ spl71_189
| ~ spl71_263
| ~ spl71_273 ),
inference(forward_demodulation,[],[f3220,f2890]) ).
fof(f2890,plain,
( hd(sK20) = sK26(sK20)
| ~ spl71_263 ),
inference(avatar_component_clause,[],[f2888]) ).
fof(f3220,plain,
( sK20 = cons(hd(sK20),sK27(sK20))
| nil = sK20
| ~ spl71_1
| ~ spl71_189
| ~ spl71_273 ),
inference(forward_demodulation,[],[f2020,f3097]) ).
fof(f3097,plain,
( tl(sK20) = sK27(sK20)
| ~ spl71_273 ),
inference(avatar_component_clause,[],[f3095]) ).
fof(f2020,plain,
( nil = sK20
| sK20 = cons(hd(sK20),tl(sK20))
| ~ spl71_1
| ~ spl71_189 ),
inference(resolution,[],[f1965,f653]) ).
fof(f3989,plain,
( spl71_305
| spl71_272
| ~ spl71_4
| ~ spl71_188 ),
inference(avatar_split_clause,[],[f1987,f1960,f666,f3085,f3986]) ).
fof(f3986,plain,
( spl71_305
<=> sK23 = cons(sK25(sK23),sK24(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_305])]) ).
fof(f1960,plain,
( spl71_188
<=> ! [X0] :
( cons(sK25(X0),sK24(X0)) = X0
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_188])]) ).
fof(f1987,plain,
( nil = sK23
| sK23 = cons(sK25(sK23),sK24(sK23))
| ~ spl71_4
| ~ spl71_188 ),
inference(resolution,[],[f1961,f668]) ).
fof(f1961,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK25(X0),sK24(X0)) = X0 )
| ~ spl71_188 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f3984,plain,
( ~ spl71_304
| spl71_12
| ~ spl71_269 ),
inference(avatar_split_clause,[],[f3294,f3066,f704,f3981]) ).
fof(f3981,plain,
( spl71_304
<=> singletonP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_304])]) ).
fof(f704,plain,
( spl71_12
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_12])]) ).
fof(f3294,plain,
( ~ singletonP(sK22)
| spl71_12
| ~ spl71_269 ),
inference(superposition,[],[f706,f3068]) ).
fof(f706,plain,
( ~ singletonP(nil)
| spl71_12 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f3930,plain,
( spl71_303
| spl71_269
| ~ spl71_3
| ~ spl71_188 ),
inference(avatar_split_clause,[],[f1986,f1960,f661,f3066,f3927]) ).
fof(f3927,plain,
( spl71_303
<=> sK22 = cons(sK25(sK22),sK24(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_303])]) ).
fof(f1986,plain,
( nil = sK22
| sK22 = cons(sK25(sK22),sK24(sK22))
| ~ spl71_3
| ~ spl71_188 ),
inference(resolution,[],[f1961,f663]) ).
fof(f3866,plain,
( spl71_302
| ~ spl71_9
| ~ spl71_15 ),
inference(avatar_split_clause,[],[f3012,f719,f689,f3863]) ).
fof(f3863,plain,
( spl71_302
<=> cyclefreeP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_302])]) ).
fof(f3012,plain,
( cyclefreeP(sK21)
| ~ spl71_9
| ~ spl71_15 ),
inference(superposition,[],[f721,f690]) ).
fof(f690,plain,
( nil = sK21
| ~ spl71_9 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f3751,plain,
( spl71_301
| ~ spl71_9
| ~ spl71_272 ),
inference(avatar_split_clause,[],[f3746,f3085,f689,f3748]) ).
fof(f3748,plain,
( spl71_301
<=> sK21 = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_301])]) ).
fof(f3746,plain,
( sK21 = sK23
| ~ spl71_9
| ~ spl71_272 ),
inference(forward_demodulation,[],[f690,f3087]) ).
fof(f3742,plain,
( spl71_300
| spl71_9
| ~ spl71_2
| ~ spl71_188 ),
inference(avatar_split_clause,[],[f1985,f1960,f656,f689,f3739]) ).
fof(f3739,plain,
( spl71_300
<=> sK21 = cons(sK25(sK21),sK24(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_300])]) ).
fof(f1985,plain,
( nil = sK21
| sK21 = cons(sK25(sK21),sK24(sK21))
| ~ spl71_2
| ~ spl71_188 ),
inference(resolution,[],[f1961,f658]) ).
fof(f3737,plain,
( ~ spl71_299
| spl71_12
| ~ spl71_272 ),
inference(avatar_split_clause,[],[f3356,f3085,f704,f3734]) ).
fof(f3734,plain,
( spl71_299
<=> singletonP(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_299])]) ).
fof(f3356,plain,
( ~ singletonP(sK23)
| spl71_12
| ~ spl71_272 ),
inference(superposition,[],[f706,f3087]) ).
fof(f3697,plain,
( spl71_298
| spl71_10
| ~ spl71_1
| ~ spl71_188 ),
inference(avatar_split_clause,[],[f1984,f1960,f651,f694,f3694]) ).
fof(f3694,plain,
( spl71_298
<=> sK20 = cons(sK25(sK20),sK24(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_298])]) ).
fof(f1984,plain,
( nil = sK20
| sK20 = cons(sK25(sK20),sK24(sK20))
| ~ spl71_1
| ~ spl71_188 ),
inference(resolution,[],[f1961,f653]) ).
fof(f3691,plain,
( spl71_297
| ~ spl71_20
| ~ spl71_32 ),
inference(avatar_split_clause,[],[f834,f796,f744,f3688]) ).
fof(f3688,plain,
( spl71_297
<=> sP17(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_297])]) ).
fof(f796,plain,
( spl71_32
<=> ! [X0] :
( sP17(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_32])]) ).
fof(f834,plain,
( sP17(nil)
| ~ spl71_20
| ~ spl71_32 ),
inference(resolution,[],[f797,f746]) ).
fof(f746,plain,
( ssList(nil)
| ~ spl71_20 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f797,plain,
( ! [X0] :
( ~ ssList(X0)
| sP17(X0) )
| ~ spl71_32 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f3685,plain,
( spl71_296
| ~ spl71_20
| ~ spl71_31 ),
inference(avatar_split_clause,[],[f829,f792,f744,f3682]) ).
fof(f3682,plain,
( spl71_296
<=> sP15(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_296])]) ).
fof(f792,plain,
( spl71_31
<=> ! [X0] :
( sP15(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_31])]) ).
fof(f829,plain,
( sP15(nil)
| ~ spl71_20
| ~ spl71_31 ),
inference(resolution,[],[f793,f746]) ).
fof(f793,plain,
( ! [X0] :
( ~ ssList(X0)
| sP15(X0) )
| ~ spl71_31 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f3679,plain,
( spl71_295
| ~ spl71_20
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f824,f788,f744,f3676]) ).
fof(f3676,plain,
( spl71_295
<=> sP13(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_295])]) ).
fof(f788,plain,
( spl71_30
<=> ! [X0] :
( sP13(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_30])]) ).
fof(f824,plain,
( sP13(nil)
| ~ spl71_20
| ~ spl71_30 ),
inference(resolution,[],[f789,f746]) ).
fof(f789,plain,
( ! [X0] :
( ~ ssList(X0)
| sP13(X0) )
| ~ spl71_30 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f3673,plain,
( spl71_294
| ~ spl71_20
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f819,f784,f744,f3670]) ).
fof(f3670,plain,
( spl71_294
<=> sP11(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_294])]) ).
fof(f784,plain,
( spl71_29
<=> ! [X0] :
( sP11(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_29])]) ).
fof(f819,plain,
( sP11(nil)
| ~ spl71_20
| ~ spl71_29 ),
inference(resolution,[],[f785,f746]) ).
fof(f785,plain,
( ! [X0] :
( ~ ssList(X0)
| sP11(X0) )
| ~ spl71_29 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f3667,plain,
( spl71_293
| ~ spl71_20
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f814,f780,f744,f3664]) ).
fof(f3664,plain,
( spl71_293
<=> sP9(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_293])]) ).
fof(f780,plain,
( spl71_28
<=> ! [X0] :
( sP9(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_28])]) ).
fof(f814,plain,
( sP9(nil)
| ~ spl71_20
| ~ spl71_28 ),
inference(resolution,[],[f781,f746]) ).
fof(f781,plain,
( ! [X0] :
( ~ ssList(X0)
| sP9(X0) )
| ~ spl71_28 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f3661,plain,
( spl71_292
| ~ spl71_20
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f809,f776,f744,f3658]) ).
fof(f3658,plain,
( spl71_292
<=> sP7(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_292])]) ).
fof(f776,plain,
( spl71_27
<=> ! [X0] :
( sP7(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_27])]) ).
fof(f809,plain,
( sP7(nil)
| ~ spl71_20
| ~ spl71_27 ),
inference(resolution,[],[f777,f746]) ).
fof(f777,plain,
( ! [X0] :
( ~ ssList(X0)
| sP7(X0) )
| ~ spl71_27 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f3655,plain,
( spl71_291
| ~ spl71_20
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f799,f772,f744,f3652]) ).
fof(f3652,plain,
( spl71_291
<=> sP5(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_291])]) ).
fof(f772,plain,
( spl71_26
<=> ! [X0] :
( sP5(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_26])]) ).
fof(f799,plain,
( sP5(nil)
| ~ spl71_20
| ~ spl71_26 ),
inference(resolution,[],[f773,f746]) ).
fof(f773,plain,
( ! [X0] :
( ~ ssList(X0)
| sP5(X0) )
| ~ spl71_26 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f3620,plain,
( ~ spl71_2
| ~ spl71_42
| spl71_276 ),
inference(avatar_split_clause,[],[f3222,f3211,f873,f656]) ).
fof(f873,plain,
( spl71_42
<=> ! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_42])]) ).
fof(f3211,plain,
( spl71_276
<=> segmentP(sK21,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_276])]) ).
fof(f3222,plain,
( ~ ssList(sK21)
| ~ spl71_42
| spl71_276 ),
inference(resolution,[],[f3213,f874]) ).
fof(f874,plain,
( ! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) )
| ~ spl71_42 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f3213,plain,
( ~ segmentP(sK21,sK21)
| spl71_276 ),
inference(avatar_component_clause,[],[f3211]) ).
fof(f3435,plain,
( spl71_290
| ~ spl71_4
| ~ spl71_173 ),
inference(avatar_split_clause,[],[f1809,f1669,f666,f3433]) ).
fof(f3433,plain,
( spl71_290
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK23)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_290])]) ).
fof(f1669,plain,
( spl71_173
<=> ! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_173])]) ).
fof(f1809,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK23)) = X0 )
| ~ spl71_4
| ~ spl71_173 ),
inference(resolution,[],[f1670,f668]) ).
fof(f1670,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 )
| ~ spl71_173 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f3431,plain,
( spl71_289
| ~ spl71_3
| ~ spl71_173 ),
inference(avatar_split_clause,[],[f1808,f1669,f661,f3429]) ).
fof(f3429,plain,
( spl71_289
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_289])]) ).
fof(f1808,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22)) = X0 )
| ~ spl71_3
| ~ spl71_173 ),
inference(resolution,[],[f1670,f663]) ).
fof(f3427,plain,
( spl71_288
| ~ spl71_2
| ~ spl71_173 ),
inference(avatar_split_clause,[],[f1807,f1669,f656,f3425]) ).
fof(f3425,plain,
( spl71_288
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_288])]) ).
fof(f1807,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 )
| ~ spl71_2
| ~ spl71_173 ),
inference(resolution,[],[f1670,f658]) ).
fof(f3423,plain,
( spl71_287
| ~ spl71_1
| ~ spl71_173 ),
inference(avatar_split_clause,[],[f1806,f1669,f651,f3421]) ).
fof(f3421,plain,
( spl71_287
<=> ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_287])]) ).
fof(f1806,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 )
| ~ spl71_1
| ~ spl71_173 ),
inference(resolution,[],[f1670,f653]) ).
fof(f3419,plain,
( spl71_286
| ~ spl71_4
| ~ spl71_172 ),
inference(avatar_split_clause,[],[f1779,f1665,f666,f3417]) ).
fof(f3417,plain,
( spl71_286
<=> ! [X0] :
( ~ ssItem(X0)
| sK23 = tl(cons(X0,sK23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_286])]) ).
fof(f1665,plain,
( spl71_172
<=> ! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_172])]) ).
fof(f1779,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK23 = tl(cons(X0,sK23)) )
| ~ spl71_4
| ~ spl71_172 ),
inference(resolution,[],[f1666,f668]) ).
fof(f1666,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 )
| ~ spl71_172 ),
inference(avatar_component_clause,[],[f1665]) ).
fof(f3415,plain,
( spl71_285
| ~ spl71_3
| ~ spl71_172 ),
inference(avatar_split_clause,[],[f1778,f1665,f661,f3413]) ).
fof(f3413,plain,
( spl71_285
<=> ! [X0] :
( ~ ssItem(X0)
| sK22 = tl(cons(X0,sK22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_285])]) ).
fof(f1778,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK22 = tl(cons(X0,sK22)) )
| ~ spl71_3
| ~ spl71_172 ),
inference(resolution,[],[f1666,f663]) ).
fof(f3411,plain,
( spl71_284
| ~ spl71_2
| ~ spl71_172 ),
inference(avatar_split_clause,[],[f1777,f1665,f656,f3409]) ).
fof(f3409,plain,
( spl71_284
<=> ! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_284])]) ).
fof(f1777,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) )
| ~ spl71_2
| ~ spl71_172 ),
inference(resolution,[],[f1666,f658]) ).
fof(f3407,plain,
( spl71_283
| ~ spl71_1
| ~ spl71_172 ),
inference(avatar_split_clause,[],[f1776,f1665,f651,f3405]) ).
fof(f3405,plain,
( spl71_283
<=> ! [X0] :
( ~ ssItem(X0)
| sK20 = tl(cons(X0,sK20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_283])]) ).
fof(f1776,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK20 = tl(cons(X0,sK20)) )
| ~ spl71_1
| ~ spl71_172 ),
inference(resolution,[],[f1666,f653]) ).
fof(f3343,plain,
( spl71_282
| ~ spl71_269
| ~ spl71_272 ),
inference(avatar_split_clause,[],[f3338,f3085,f3066,f3340]) ).
fof(f3338,plain,
( sK22 = sK23
| ~ spl71_269
| ~ spl71_272 ),
inference(forward_demodulation,[],[f3087,f3068]) ).
fof(f3337,plain,
( spl71_281
| spl71_272
| ~ spl71_4
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1749,f1657,f666,f3085,f3334]) ).
fof(f1657,plain,
( spl71_170
<=> ! [X0] :
( tl(X0) = sK27(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_170])]) ).
fof(f1749,plain,
( nil = sK23
| tl(sK23) = sK27(sK23)
| ~ spl71_4
| ~ spl71_170 ),
inference(resolution,[],[f1658,f668]) ).
fof(f1658,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK27(X0) )
| ~ spl71_170 ),
inference(avatar_component_clause,[],[f1657]) ).
fof(f3290,plain,
( spl71_280
| spl71_269
| ~ spl71_3
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1748,f1657,f661,f3066,f3287]) ).
fof(f3287,plain,
( spl71_280
<=> tl(sK22) = sK27(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_280])]) ).
fof(f1748,plain,
( nil = sK22
| tl(sK22) = sK27(sK22)
| ~ spl71_3
| ~ spl71_170 ),
inference(resolution,[],[f1658,f663]) ).
fof(f3281,plain,
( spl71_279
| ~ spl71_9
| ~ spl71_14 ),
inference(avatar_split_clause,[],[f3011,f714,f689,f3278]) ).
fof(f3278,plain,
( spl71_279
<=> duplicatefreeP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_279])]) ).
fof(f3011,plain,
( duplicatefreeP(sK21)
| ~ spl71_9
| ~ spl71_14 ),
inference(superposition,[],[f716,f690]) ).
fof(f3234,plain,
( spl71_278
| spl71_9
| ~ spl71_2
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1747,f1657,f656,f689,f3231]) ).
fof(f1747,plain,
( nil = sK21
| tl(sK21) = sK27(sK21)
| ~ spl71_2
| ~ spl71_170 ),
inference(resolution,[],[f1658,f658]) ).
fof(f3219,plain,
( spl71_277
| ~ spl71_6
| ~ spl71_8 ),
inference(avatar_split_clause,[],[f3103,f685,f676,f3216]) ).
fof(f3216,plain,
( spl71_277
<=> neq(sK21,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_277])]) ).
fof(f3103,plain,
( neq(sK21,nil)
| ~ spl71_6
| ~ spl71_8 ),
inference(superposition,[],[f677,f686]) ).
fof(f3214,plain,
( ~ spl71_276
| spl71_7
| ~ spl71_8 ),
inference(avatar_split_clause,[],[f2895,f685,f680,f3211]) ).
fof(f2895,plain,
( ~ segmentP(sK21,sK21)
| spl71_7
| ~ spl71_8 ),
inference(superposition,[],[f682,f686]) ).
fof(f3209,plain,
( ~ spl71_275
| ~ spl71_8
| spl71_261 ),
inference(avatar_split_clause,[],[f2907,f2877,f685,f3206]) ).
fof(f3206,plain,
( spl71_275
<=> ssItem(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_275])]) ).
fof(f2907,plain,
( ~ ssItem(sK21)
| ~ spl71_8
| spl71_261 ),
inference(superposition,[],[f2879,f686]) ).
fof(f3168,plain,
( spl71_260
| ~ spl71_10
| ~ spl71_13 ),
inference(avatar_split_clause,[],[f2913,f709,f694,f2746]) ).
fof(f2746,plain,
( spl71_260
<=> equalelemsP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_260])]) ).
fof(f709,plain,
( spl71_13
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_13])]) ).
fof(f2913,plain,
( equalelemsP(sK20)
| ~ spl71_10
| ~ spl71_13 ),
inference(superposition,[],[f711,f695]) ).
fof(f711,plain,
( equalelemsP(nil)
| ~ spl71_13 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f3166,plain,
( ~ spl71_274
| ~ spl71_10
| spl71_12 ),
inference(avatar_split_clause,[],[f2912,f704,f694,f3163]) ).
fof(f3163,plain,
( spl71_274
<=> singletonP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_274])]) ).
fof(f2912,plain,
( ~ singletonP(sK20)
| ~ spl71_10
| spl71_12 ),
inference(superposition,[],[f706,f695]) ).
fof(f3098,plain,
( spl71_273
| spl71_10
| ~ spl71_1
| ~ spl71_170 ),
inference(avatar_split_clause,[],[f1746,f1657,f651,f694,f3095]) ).
fof(f1746,plain,
( nil = sK20
| tl(sK20) = sK27(sK20)
| ~ spl71_1
| ~ spl71_170 ),
inference(resolution,[],[f1658,f653]) ).
fof(f3088,plain,
( spl71_271
| spl71_272
| ~ spl71_4
| ~ spl71_169 ),
inference(avatar_split_clause,[],[f1719,f1653,f666,f3085,f3081]) ).
fof(f1653,plain,
( spl71_169
<=> ! [X0] :
( hd(X0) = sK26(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_169])]) ).
fof(f1719,plain,
( nil = sK23
| hd(sK23) = sK26(sK23)
| ~ spl71_4
| ~ spl71_169 ),
inference(resolution,[],[f1654,f668]) ).
fof(f1654,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK26(X0) )
| ~ spl71_169 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f3074,plain,
( spl71_267
| ~ spl71_270
| ~ spl71_38
| ~ spl71_97 ),
inference(avatar_split_clause,[],[f2166,f1241,f856,f3071,f3052]) ).
fof(f3052,plain,
( spl71_267
<=> equalelemsP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_267])]) ).
fof(f3071,plain,
( spl71_270
<=> sP4(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_270])]) ).
fof(f856,plain,
( spl71_38
<=> sP5(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_38])]) ).
fof(f1241,plain,
( spl71_97
<=> ! [X0] :
( equalelemsP(X0)
| ~ sP4(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_97])]) ).
fof(f2166,plain,
( ~ sP4(sK21)
| equalelemsP(sK21)
| ~ spl71_38
| ~ spl71_97 ),
inference(resolution,[],[f858,f1242]) ).
fof(f1242,plain,
( ! [X0] :
( ~ sP5(X0)
| ~ sP4(X0)
| equalelemsP(X0) )
| ~ spl71_97 ),
inference(avatar_component_clause,[],[f1241]) ).
fof(f858,plain,
( sP5(sK21)
| ~ spl71_38 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f3069,plain,
( spl71_268
| spl71_269
| ~ spl71_3
| ~ spl71_169 ),
inference(avatar_split_clause,[],[f1718,f1653,f661,f3066,f3062]) ).
fof(f3062,plain,
( spl71_268
<=> hd(sK22) = sK26(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_268])]) ).
fof(f1718,plain,
( nil = sK22
| hd(sK22) = sK26(sK22)
| ~ spl71_3
| ~ spl71_169 ),
inference(resolution,[],[f1654,f663]) ).
fof(f3055,plain,
( spl71_267
| ~ spl71_9
| ~ spl71_13 ),
inference(avatar_split_clause,[],[f3010,f709,f689,f3052]) ).
fof(f3010,plain,
( equalelemsP(sK21)
| ~ spl71_9
| ~ spl71_13 ),
inference(superposition,[],[f711,f690]) ).
fof(f3050,plain,
( ~ spl71_266
| ~ spl71_9
| spl71_12 ),
inference(avatar_split_clause,[],[f3009,f704,f689,f3047]) ).
fof(f3047,plain,
( spl71_266
<=> singletonP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_266])]) ).
fof(f3009,plain,
( ~ singletonP(sK21)
| ~ spl71_9
| spl71_12 ),
inference(superposition,[],[f706,f690]) ).
fof(f3004,plain,
( spl71_265
| spl71_9
| ~ spl71_2
| ~ spl71_169 ),
inference(avatar_split_clause,[],[f1717,f1653,f656,f689,f3001]) ).
fof(f1717,plain,
( nil = sK21
| hd(sK21) = sK26(sK21)
| ~ spl71_2
| ~ spl71_169 ),
inference(resolution,[],[f1654,f658]) ).
fof(f2994,plain,
( spl71_264
| ~ spl71_5
| ~ spl71_8 ),
inference(avatar_split_clause,[],[f2893,f685,f671,f2991]) ).
fof(f2991,plain,
( spl71_264
<=> totalorderedP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_264])]) ).
fof(f2893,plain,
( totalorderedP(sK21)
| ~ spl71_5
| ~ spl71_8 ),
inference(superposition,[],[f673,f686]) ).
fof(f2891,plain,
( spl71_263
| spl71_10
| ~ spl71_1
| ~ spl71_169 ),
inference(avatar_split_clause,[],[f1716,f1653,f651,f694,f2888]) ).
fof(f1716,plain,
( nil = sK20
| hd(sK20) = sK26(sK20)
| ~ spl71_1
| ~ spl71_169 ),
inference(resolution,[],[f1654,f653]) ).
fof(f2886,plain,
( ~ spl71_1
| ~ spl71_20
| spl71_10
| spl71_6
| ~ spl71_174 ),
inference(avatar_split_clause,[],[f1832,f1673,f676,f694,f744,f651]) ).
fof(f1832,plain,
( nil = sK20
| ~ ssList(nil)
| ~ ssList(sK20)
| spl71_6
| ~ spl71_174 ),
inference(resolution,[],[f1674,f678]) ).
fof(f2884,plain,
( ~ spl71_261
| ~ spl71_262
| spl71_10
| spl71_6
| ~ spl71_155 ),
inference(avatar_split_clause,[],[f1680,f1595,f676,f694,f2881,f2877]) ).
fof(f2881,plain,
( spl71_262
<=> ssItem(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_262])]) ).
fof(f1595,plain,
( spl71_155
<=> ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_155])]) ).
fof(f1680,plain,
( nil = sK20
| ~ ssItem(nil)
| ~ ssItem(sK20)
| spl71_6
| ~ spl71_155 ),
inference(resolution,[],[f1596,f678]) ).
fof(f1596,plain,
( ! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) )
| ~ spl71_155 ),
inference(avatar_component_clause,[],[f1595]) ).
fof(f2749,plain,
( spl71_259
| ~ spl71_260
| ~ spl71_33
| ~ spl71_96 ),
inference(avatar_split_clause,[],[f1302,f1237,f805,f2746,f2742]) ).
fof(f2742,plain,
( spl71_259
<=> sP4(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_259])]) ).
fof(f805,plain,
( spl71_33
<=> sP5(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_33])]) ).
fof(f1237,plain,
( spl71_96
<=> ! [X0] :
( sP4(X0)
| ~ equalelemsP(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_96])]) ).
fof(f1302,plain,
( ~ equalelemsP(sK20)
| sP4(sK20)
| ~ spl71_33
| ~ spl71_96 ),
inference(resolution,[],[f1238,f807]) ).
fof(f807,plain,
( sP5(sK20)
| ~ spl71_33 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f1238,plain,
( ! [X0] :
( ~ sP5(X0)
| ~ equalelemsP(X0)
| sP4(X0) )
| ~ spl71_96 ),
inference(avatar_component_clause,[],[f1237]) ).
fof(f2722,plain,
( spl71_258
| ~ spl71_4
| ~ spl71_119 ),
inference(avatar_split_clause,[],[f1421,f1335,f666,f2719]) ).
fof(f1335,plain,
( spl71_119
<=> ! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_119])]) ).
fof(f1421,plain,
( sK23 = app(nil,sK23)
| ~ spl71_4
| ~ spl71_119 ),
inference(resolution,[],[f1336,f668]) ).
fof(f1336,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl71_119 ),
inference(avatar_component_clause,[],[f1335]) ).
fof(f2717,plain,
( spl71_257
| ~ spl71_3
| ~ spl71_119 ),
inference(avatar_split_clause,[],[f1420,f1335,f661,f2714]) ).
fof(f2714,plain,
( spl71_257
<=> sK22 = app(nil,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_257])]) ).
fof(f1420,plain,
( sK22 = app(nil,sK22)
| ~ spl71_3
| ~ spl71_119 ),
inference(resolution,[],[f1336,f663]) ).
fof(f2712,plain,
( spl71_256
| ~ spl71_2
| ~ spl71_119 ),
inference(avatar_split_clause,[],[f1419,f1335,f656,f2709]) ).
fof(f2709,plain,
( spl71_256
<=> sK21 = app(nil,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_256])]) ).
fof(f1419,plain,
( sK21 = app(nil,sK21)
| ~ spl71_2
| ~ spl71_119 ),
inference(resolution,[],[f1336,f658]) ).
fof(f2707,plain,
( spl71_255
| ~ spl71_1
| ~ spl71_119 ),
inference(avatar_split_clause,[],[f1418,f1335,f651,f2704]) ).
fof(f2704,plain,
( spl71_255
<=> sK20 = app(nil,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_255])]) ).
fof(f1418,plain,
( sK20 = app(nil,sK20)
| ~ spl71_1
| ~ spl71_119 ),
inference(resolution,[],[f1336,f653]) ).
fof(f2702,plain,
( spl71_254
| ~ spl71_4
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1396,f1331,f666,f2699]) ).
fof(f2699,plain,
( spl71_254
<=> sK23 = app(sK23,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_254])]) ).
fof(f1331,plain,
( spl71_118
<=> ! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_118])]) ).
fof(f1396,plain,
( sK23 = app(sK23,nil)
| ~ spl71_4
| ~ spl71_118 ),
inference(resolution,[],[f1332,f668]) ).
fof(f1332,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl71_118 ),
inference(avatar_component_clause,[],[f1331]) ).
fof(f2697,plain,
( spl71_253
| ~ spl71_3
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1395,f1331,f661,f2694]) ).
fof(f1395,plain,
( sK22 = app(sK22,nil)
| ~ spl71_3
| ~ spl71_118 ),
inference(resolution,[],[f1332,f663]) ).
fof(f2692,plain,
( spl71_252
| ~ spl71_2
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1394,f1331,f656,f2689]) ).
fof(f2689,plain,
( spl71_252
<=> sK21 = app(sK21,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_252])]) ).
fof(f1394,plain,
( sK21 = app(sK21,nil)
| ~ spl71_2
| ~ spl71_118 ),
inference(resolution,[],[f1332,f658]) ).
fof(f2687,plain,
( spl71_251
| ~ spl71_1
| ~ spl71_118 ),
inference(avatar_split_clause,[],[f1393,f1331,f651,f2684]) ).
fof(f2684,plain,
( spl71_251
<=> sK20 = app(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_251])]) ).
fof(f1393,plain,
( sK20 = app(sK20,nil)
| ~ spl71_1
| ~ spl71_118 ),
inference(resolution,[],[f1332,f653]) ).
fof(f2645,plain,
spl71_250,
inference(avatar_split_clause,[],[f627,f2643]) ).
fof(f2643,plain,
( spl71_250
<=> ! [X10,X9,X7,X6,X8] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_250])]) ).
fof(f627,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f524]) ).
fof(f524,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0] :
( ( sP12(X0)
| ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssList(sK50(X0))
& ssItem(sK49(X0))
& ssItem(sK48(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51,sK52])],[f325,f330,f329,f328,f327,f326]) ).
fof(f326,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f328,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f329,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(rectify,[],[f324]) ).
fof(f324,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP12(X0) ) ),
inference(nnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0] :
( sP12(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f2641,plain,
spl71_249,
inference(avatar_split_clause,[],[f626,f2639]) ).
fof(f2639,plain,
( spl71_249
<=> ! [X10,X9,X7,X6,X8] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_249])]) ).
fof(f626,plain,
! [X10,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f512]) ).
fof(f512,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f322]) ).
fof(f322,plain,
! [X0] :
( ( sP10(X0)
| ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssList(sK45(X0))
& ssItem(sK44(X0))
& ssItem(sK43(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45,sK46,sK47])],[f316,f321,f320,f319,f318,f317]) ).
fof(f317,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f319,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(rectify,[],[f315]) ).
fof(f315,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP10(X0) ) ),
inference(nnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] :
( sP10(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f2637,plain,
spl71_248,
inference(avatar_split_clause,[],[f625,f2635]) ).
fof(f2635,plain,
( spl71_248
<=> ! [X10,X9,X7,X6,X8] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_248])]) ).
fof(f625,plain,
! [X10,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f500]) ).
fof(f500,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0] :
( ( sP8(X0)
| ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssList(sK40(X0))
& ssItem(sK39(X0))
& ssItem(sK38(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40,sK41,sK42])],[f307,f312,f311,f310,f309,f308]) ).
fof(f308,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f310,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(rectify,[],[f306]) ).
fof(f306,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( sP8(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f2627,plain,
spl71_247,
inference(avatar_split_clause,[],[f629,f2625]) ).
fof(f2625,plain,
( spl71_247
<=> ! [X10,X9,X7,X6,X8] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_247])]) ).
fof(f629,plain,
! [X10,X8,X6,X9,X7] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ( sP16(X0)
| ( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssList(sK60(X0))
& ssItem(sK59(X0))
& ssItem(sK58(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61,sK62])],[f343,f348,f347,f346,f345,f344]) ).
fof(f344,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP16(X0) ) ),
inference(rectify,[],[f342]) ).
fof(f342,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP16(X0) ) ),
inference(nnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( sP16(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f2623,plain,
spl71_246,
inference(avatar_split_clause,[],[f628,f2621]) ).
fof(f2621,plain,
( spl71_246
<=> ! [X10,X9,X7,X6,X8] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_246])]) ).
fof(f628,plain,
! [X10,X8,X6,X9,X7] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f536]) ).
fof(f536,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0] :
( ( sP14(X0)
| ( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssList(sK55(X0))
& ssItem(sK54(X0))
& ssItem(sK53(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f334,f339,f338,f337,f336,f335]) ).
fof(f335,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f337,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f338,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(rectify,[],[f333]) ).
fof(f333,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP14(X0) ) ),
inference(nnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( sP14(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f2619,plain,
spl71_245,
inference(avatar_split_clause,[],[f575,f2617]) ).
fof(f2617,plain,
( spl71_245
<=> ! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_245])]) ).
fof(f575,plain,
! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( tl(X0) = tl(X1)
& hd(X0) = hd(X1)
& nil != X0
& nil != X1 )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77) ).
fof(f2602,plain,
spl71_244,
inference(avatar_split_clause,[],[f637,f2600]) ).
fof(f637,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f590]) ).
fof(f590,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1))
& ssList(sK67(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f368,f370,f369]) ).
fof(f369,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f370,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f368,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f367]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f2596,plain,
spl71_243,
inference(avatar_split_clause,[],[f633,f2594]) ).
fof(f2594,plain,
( spl71_243
<=> ! [X2,X1,X3] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_243])]) ).
fof(f633,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f571]) ).
fof(f571,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1))
& ssList(sK63(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f354,f356,f355]) ).
fof(f355,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK63(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
! [X0,X1] :
( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f2592,plain,
spl71_242,
inference(avatar_split_clause,[],[f622,f2590]) ).
fof(f2590,plain,
( spl71_242
<=> ! [X5,X7,X6,X8] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(app(X7,cons(X5,cons(X6,X8)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_242])]) ).
fof(f622,plain,
! [X8,X6,X7,X5] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(app(X7,cons(X5,cons(X6,X8)))) ),
inference(equality_resolution,[],[f479]) ).
fof(f479,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ( sP4(X0)
| ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0))
& ssList(sK31(X0))
& ssItem(sK30(X0))
& ssItem(sK29(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f290,f294,f293,f292,f291]) ).
fof(f291,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f293,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
=> ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f290,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP4(X0) ) ),
inference(rectify,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0] :
( sP4(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f2552,plain,
spl71_241,
inference(avatar_split_clause,[],[f642,f2550]) ).
fof(f2550,plain,
( spl71_241
<=> ! [X10,X7,X9,X8] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_241])]) ).
fof(f642,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f624]) ).
fof(f624,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f623]) ).
fof(f623,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP6(X0) ),
inference(equality_resolution,[],[f489]) ).
fof(f489,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f304]) ).
fof(f304,plain,
! [X0] :
( ( sP6(X0)
| ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssList(sK35(X0))
& ssItem(sK34(X0))
& ssItem(sK33(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36,sK37])],[f298,f303,f302,f301,f300,f299]) ).
fof(f299,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f300,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f301,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f302,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
=> ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP6(X0) ) ),
inference(rectify,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0] :
( sP6(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f2548,plain,
spl71_240,
inference(avatar_split_clause,[],[f605,f2546]) ).
fof(f2546,plain,
( spl71_240
<=> ! [X0,X3,X2,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_240])]) ).
fof(f605,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f2544,plain,
spl71_239,
inference(avatar_split_clause,[],[f596,f2542]) ).
fof(f2542,plain,
( spl71_239
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_239])]) ).
fof(f596,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X0 = X1
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
fof(f2540,plain,
spl71_238,
inference(avatar_split_clause,[],[f595,f2538]) ).
fof(f2538,plain,
( spl71_238
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_238])]) ).
fof(f595,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f2534,plain,
spl71_237,
inference(avatar_split_clause,[],[f589,f2532]) ).
fof(f2532,plain,
( spl71_237
<=> ! [X0,X1] :
( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_237])]) ).
fof(f589,plain,
! [X0,X1] :
( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f2530,plain,
spl71_236,
inference(avatar_split_clause,[],[f570,f2528]) ).
fof(f2528,plain,
( spl71_236
<=> ! [X0,X1] :
( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_236])]) ).
fof(f570,plain,
! [X0,X1] :
( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f2526,plain,
spl71_235,
inference(avatar_split_clause,[],[f553,f2524]) ).
fof(f2524,plain,
( spl71_235
<=> ! [X0] :
( sP16(X0)
| app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_235])]) ).
fof(f553,plain,
! [X0] :
( sP16(X0)
| app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ),
inference(cnf_transformation,[],[f349]) ).
fof(f2522,plain,
spl71_234,
inference(avatar_split_clause,[],[f542,f2520]) ).
fof(f2520,plain,
( spl71_234
<=> ! [X0] :
( sP14(X0)
| app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_234])]) ).
fof(f542,plain,
! [X0] :
( sP14(X0)
| app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ),
inference(cnf_transformation,[],[f340]) ).
fof(f2518,plain,
spl71_233,
inference(avatar_split_clause,[],[f530,f2516]) ).
fof(f2516,plain,
( spl71_233
<=> ! [X0] :
( sP12(X0)
| app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_233])]) ).
fof(f530,plain,
! [X0] :
( sP12(X0)
| app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ),
inference(cnf_transformation,[],[f331]) ).
fof(f2514,plain,
spl71_232,
inference(avatar_split_clause,[],[f518,f2512]) ).
fof(f2512,plain,
( spl71_232
<=> ! [X0] :
( sP10(X0)
| app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_232])]) ).
fof(f518,plain,
! [X0] :
( sP10(X0)
| app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ),
inference(cnf_transformation,[],[f322]) ).
fof(f2510,plain,
spl71_231,
inference(avatar_split_clause,[],[f506,f2508]) ).
fof(f2508,plain,
( spl71_231
<=> ! [X0] :
( sP8(X0)
| app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_231])]) ).
fof(f506,plain,
! [X0] :
( sP8(X0)
| app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ),
inference(cnf_transformation,[],[f313]) ).
fof(f2506,plain,
spl71_230,
inference(avatar_split_clause,[],[f495,f2504]) ).
fof(f2504,plain,
( spl71_230
<=> ! [X0] :
( sP6(X0)
| app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_230])]) ).
fof(f495,plain,
! [X0] :
( sP6(X0)
| app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ),
inference(cnf_transformation,[],[f304]) ).
fof(f2502,plain,
spl71_229,
inference(avatar_split_clause,[],[f435,f2500]) ).
fof(f2500,plain,
( spl71_229
<=> ! [X0,X3,X2,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_229])]) ).
fof(f435,plain,
! [X2,X3,X0,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
fof(f2498,plain,
spl71_228,
inference(avatar_split_clause,[],[f434,f2496]) ).
fof(f2496,plain,
( spl71_228
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_228])]) ).
fof(f434,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f2411,plain,
spl71_227,
inference(avatar_split_clause,[],[f597,f2409]) ).
fof(f2409,plain,
( spl71_227
<=> ! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_227])]) ).
fof(f597,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f2407,plain,
spl71_226,
inference(avatar_split_clause,[],[f594,f2405]) ).
fof(f2405,plain,
( spl71_226
<=> ! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_226])]) ).
fof(f594,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
fof(f2403,plain,
spl71_225,
inference(avatar_split_clause,[],[f453,f2401]) ).
fof(f2401,plain,
( spl71_225
<=> ! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_225])]) ).
fof(f453,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f275]) ).
fof(f275,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f2399,plain,
spl71_224,
inference(avatar_split_clause,[],[f431,f2397]) ).
fof(f2397,plain,
( spl71_224
<=> ! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_224])]) ).
fof(f431,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f263]) ).
fof(f263,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f2346,plain,
spl71_223,
inference(avatar_split_clause,[],[f643,f2344]) ).
fof(f2344,plain,
( spl71_223
<=> ! [X2,X1,X3] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_223])]) ).
fof(f643,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f616,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f436]) ).
fof(f436,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f2342,plain,
spl71_222,
inference(avatar_split_clause,[],[f601,f2340]) ).
fof(f2340,plain,
( spl71_222
<=> ! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_222])]) ).
fof(f601,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
fof(f2338,plain,
spl71_221,
inference(avatar_split_clause,[],[f600,f2336]) ).
fof(f2336,plain,
( spl71_221
<=> ! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_221])]) ).
fof(f600,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
fof(f2334,plain,
spl71_220,
inference(avatar_split_clause,[],[f574,f2332]) ).
fof(f574,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
fof(f2299,plain,
spl71_219,
inference(avatar_split_clause,[],[f604,f2297]) ).
fof(f2297,plain,
( spl71_219
<=> ! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_219])]) ).
fof(f604,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f2295,plain,
spl71_218,
inference(avatar_split_clause,[],[f603,f2293]) ).
fof(f2293,plain,
( spl71_218
<=> ! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_218])]) ).
fof(f603,plain,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
fof(f2291,plain,
spl71_217,
inference(avatar_split_clause,[],[f602,f2289]) ).
fof(f2289,plain,
( spl71_217
<=> ! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_217])]) ).
fof(f602,plain,
! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f2287,plain,
spl71_216,
inference(avatar_split_clause,[],[f484,f2285]) ).
fof(f2285,plain,
( spl71_216
<=> ! [X0] :
( sP4(X0)
| app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_216])]) ).
fof(f484,plain,
! [X0] :
( sP4(X0)
| app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ),
inference(cnf_transformation,[],[f295]) ).
fof(f2283,plain,
spl71_215,
inference(avatar_split_clause,[],[f430,f2281]) ).
fof(f2281,plain,
( spl71_215
<=> ! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_215])]) ).
fof(f430,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& lt(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
fof(f2277,plain,
spl71_214,
inference(avatar_split_clause,[],[f429,f2275]) ).
fof(f2275,plain,
( spl71_214
<=> ! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_214])]) ).
fof(f429,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).
fof(f2273,plain,
spl71_213,
inference(avatar_split_clause,[],[f428,f2271]) ).
fof(f2271,plain,
( spl71_213
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_213])]) ).
fof(f428,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
fof(f2269,plain,
spl71_212,
inference(avatar_split_clause,[],[f427,f2267]) ).
fof(f2267,plain,
( spl71_212
<=> ! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_212])]) ).
fof(f427,plain,
! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X0,X1) )
=> geq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).
fof(f2265,plain,
spl71_211,
inference(avatar_split_clause,[],[f426,f2263]) ).
fof(f2263,plain,
( spl71_211
<=> ! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_211])]) ).
fof(f426,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).
fof(f2199,plain,
spl71_210,
inference(avatar_split_clause,[],[f599,f2197]) ).
fof(f2197,plain,
( spl71_210
<=> ! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_210])]) ).
fof(f599,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f2195,plain,
spl71_209,
inference(avatar_split_clause,[],[f598,f2193]) ).
fof(f598,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f2191,plain,
spl71_208,
inference(avatar_split_clause,[],[f585,f2189]) ).
fof(f2189,plain,
( spl71_208
<=> ! [X0,X1] :
( app(X1,sK66(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_208])]) ).
fof(f585,plain,
! [X0,X1] :
( app(X1,sK66(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK66(X0,X1)) = X0
& ssList(sK66(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f364,f365]) ).
fof(f365,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK66(X0,X1)) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f364,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f2187,plain,
spl71_207,
inference(avatar_split_clause,[],[f582,f2185]) ).
fof(f2185,plain,
( spl71_207
<=> ! [X0,X1] :
( app(sK65(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_207])]) ).
fof(f582,plain,
! [X0,X1] :
( app(sK65(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f360,f361]) ).
fof(f361,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f360,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f2183,plain,
spl71_206,
inference(avatar_split_clause,[],[f573,f2181]) ).
fof(f573,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
fof(f2179,plain,
spl71_205,
inference(avatar_split_clause,[],[f455,f2177]) ).
fof(f455,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f2175,plain,
spl71_204,
inference(avatar_split_clause,[],[f454,f2173]) ).
fof(f2173,plain,
( spl71_204
<=> ! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_204])]) ).
fof(f454,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f2171,plain,
spl71_203,
inference(avatar_split_clause,[],[f433,f2169]) ).
fof(f2169,plain,
( spl71_203
<=> ! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_203])]) ).
fof(f433,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f2099,plain,
spl71_202,
inference(avatar_split_clause,[],[f636,f2097]) ).
fof(f636,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f586]) ).
fof(f586,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f2095,plain,
( spl71_201
| ~ spl71_4
| ~ spl71_32 ),
inference(avatar_split_clause,[],[f838,f796,f666,f2092]) ).
fof(f2092,plain,
( spl71_201
<=> sP17(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_201])]) ).
fof(f838,plain,
( sP17(sK23)
| ~ spl71_4
| ~ spl71_32 ),
inference(resolution,[],[f797,f668]) ).
fof(f2090,plain,
spl71_200,
inference(avatar_split_clause,[],[f635,f2088]) ).
fof(f635,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f583]) ).
fof(f583,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f2086,plain,
spl71_199,
inference(avatar_split_clause,[],[f578,f2084]) ).
fof(f2084,plain,
( spl71_199
<=> ! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_199])]) ).
fof(f578,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f2082,plain,
spl71_198,
inference(avatar_split_clause,[],[f577,f2080]) ).
fof(f2080,plain,
( spl71_198
<=> ! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_198])]) ).
fof(f577,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f2078,plain,
spl71_197,
inference(avatar_split_clause,[],[f576,f2076]) ).
fof(f2076,plain,
( spl71_197
<=> ! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_197])]) ).
fof(f576,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f2074,plain,
spl71_196,
inference(avatar_split_clause,[],[f567,f2072]) ).
fof(f567,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f2070,plain,
spl71_195,
inference(avatar_split_clause,[],[f416,f2068]) ).
fof(f2068,plain,
( spl71_195
<=> ! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_195])]) ).
fof(f416,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f2066,plain,
spl71_194,
inference(avatar_split_clause,[],[f415,f2064]) ).
fof(f2064,plain,
( spl71_194
<=> ! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_194])]) ).
fof(f415,plain,
! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( geq(X1,X0)
& geq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
fof(f2062,plain,
spl71_193,
inference(avatar_split_clause,[],[f413,f2060]) ).
fof(f2060,plain,
( spl71_193
<=> ! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_193])]) ).
fof(f413,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( leq(X0,X1)
=> ( lt(X0,X1)
| X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).
fof(f2056,plain,
( spl71_192
| ~ spl71_3
| ~ spl71_32 ),
inference(avatar_split_clause,[],[f837,f796,f661,f2053]) ).
fof(f2053,plain,
( spl71_192
<=> sP17(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_192])]) ).
fof(f837,plain,
( sP17(sK22)
| ~ spl71_3
| ~ spl71_32 ),
inference(resolution,[],[f797,f663]) ).
fof(f1974,plain,
spl71_191,
inference(avatar_split_clause,[],[f592,f1972]) ).
fof(f1972,plain,
( spl71_191
<=> ! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_191])]) ).
fof(f592,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f1970,plain,
spl71_190,
inference(avatar_split_clause,[],[f591,f1968]) ).
fof(f1968,plain,
( spl71_190
<=> ! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_190])]) ).
fof(f591,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f1966,plain,
spl71_189,
inference(avatar_split_clause,[],[f469,f1964]) ).
fof(f469,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f1962,plain,
spl71_188,
inference(avatar_split_clause,[],[f466,f1960]) ).
fof(f466,plain,
! [X0] :
( cons(sK25(X0),sK24(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0] :
( ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0))
& ssList(sK24(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f150,f278,f277]) ).
fof(f277,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
& ssList(sK24(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f278,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
=> ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f1958,plain,
spl71_187,
inference(avatar_split_clause,[],[f451,f1956]) ).
fof(f1956,plain,
( spl71_187
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_187])]) ).
fof(f451,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f273]) ).
fof(f273,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1954,plain,
spl71_186,
inference(avatar_split_clause,[],[f443,f1952]) ).
fof(f1952,plain,
( spl71_186
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_186])]) ).
fof(f443,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f269]) ).
fof(f269,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1950,plain,
( spl71_185
| ~ spl71_2
| ~ spl71_32 ),
inference(avatar_split_clause,[],[f836,f796,f656,f1947]) ).
fof(f1947,plain,
( spl71_185
<=> sP17(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_185])]) ).
fof(f836,plain,
( sP17(sK21)
| ~ spl71_2
| ~ spl71_32 ),
inference(resolution,[],[f797,f658]) ).
fof(f1867,plain,
spl71_184,
inference(avatar_split_clause,[],[f588,f1865]) ).
fof(f1865,plain,
( spl71_184
<=> ! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_184])]) ).
fof(f588,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f1863,plain,
spl71_183,
inference(avatar_split_clause,[],[f587,f1861]) ).
fof(f1861,plain,
( spl71_183
<=> ! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_183])]) ).
fof(f587,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f1859,plain,
spl71_182,
inference(avatar_split_clause,[],[f584,f1857]) ).
fof(f1857,plain,
( spl71_182
<=> ! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_182])]) ).
fof(f584,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f1855,plain,
spl71_181,
inference(avatar_split_clause,[],[f581,f1853]) ).
fof(f1853,plain,
( spl71_181
<=> ! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_181])]) ).
fof(f581,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f1851,plain,
( spl71_180
| ~ spl71_1
| ~ spl71_32 ),
inference(avatar_split_clause,[],[f835,f796,f651,f1848]) ).
fof(f1848,plain,
( spl71_180
<=> sP17(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_180])]) ).
fof(f835,plain,
( sP17(sK20)
| ~ spl71_1
| ~ spl71_32 ),
inference(resolution,[],[f797,f653]) ).
fof(f1846,plain,
spl71_179,
inference(avatar_split_clause,[],[f569,f1844]) ).
fof(f1844,plain,
( spl71_179
<=> ! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_179])]) ).
fof(f569,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f1842,plain,
spl71_178,
inference(avatar_split_clause,[],[f568,f1840]) ).
fof(f1840,plain,
( spl71_178
<=> ! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_178])]) ).
fof(f568,plain,
! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f1710,plain,
( spl71_177
| ~ spl71_4
| ~ spl71_31 ),
inference(avatar_split_clause,[],[f833,f792,f666,f1707]) ).
fof(f1707,plain,
( spl71_177
<=> sP15(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_177])]) ).
fof(f833,plain,
( sP15(sK23)
| ~ spl71_4
| ~ spl71_31 ),
inference(resolution,[],[f793,f668]) ).
fof(f1689,plain,
( spl71_176
| ~ spl71_3
| ~ spl71_31 ),
inference(avatar_split_clause,[],[f832,f792,f661,f1686]) ).
fof(f1686,plain,
( spl71_176
<=> sP15(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_176])]) ).
fof(f832,plain,
( sP15(sK22)
| ~ spl71_3
| ~ spl71_31 ),
inference(resolution,[],[f793,f663]) ).
fof(f1679,plain,
spl71_175,
inference(avatar_split_clause,[],[f621,f1677]) ).
fof(f1677,plain,
( spl71_175
<=> ! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_175])]) ).
fof(f621,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f476]) ).
fof(f476,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f285,f286]) ).
fof(f286,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f285,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f1675,plain,
spl71_174,
inference(avatar_split_clause,[],[f580,f1673]) ).
fof(f580,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f1671,plain,
spl71_173,
inference(avatar_split_clause,[],[f566,f1669]) ).
fof(f566,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f1667,plain,
spl71_172,
inference(avatar_split_clause,[],[f565,f1665]) ).
fof(f565,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f1663,plain,
spl71_171,
inference(avatar_split_clause,[],[f475,f1661]) ).
fof(f1661,plain,
( spl71_171
<=> ! [X0] :
( cons(sK28(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_171])]) ).
fof(f475,plain,
! [X0] :
( cons(sK28(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f1659,plain,
spl71_170,
inference(avatar_split_clause,[],[f473,f1657]) ).
fof(f473,plain,
! [X0] :
( tl(X0) = sK27(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f160,f282]) ).
fof(f282,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f1655,plain,
spl71_169,
inference(avatar_split_clause,[],[f471,f1653]) ).
fof(f471,plain,
! [X0] :
( hd(X0) = sK26(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f158,f280]) ).
fof(f280,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f1651,plain,
( spl71_168
| ~ spl71_2
| ~ spl71_31 ),
inference(avatar_split_clause,[],[f831,f792,f656,f1648]) ).
fof(f1648,plain,
( spl71_168
<=> sP15(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_168])]) ).
fof(f831,plain,
( sP15(sK21)
| ~ spl71_2
| ~ spl71_31 ),
inference(resolution,[],[f793,f658]) ).
fof(f1646,plain,
spl71_167,
inference(avatar_split_clause,[],[f449,f1644]) ).
fof(f1644,plain,
( spl71_167
<=> ! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_167])]) ).
fof(f449,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1642,plain,
spl71_166,
inference(avatar_split_clause,[],[f446,f1640]) ).
fof(f1640,plain,
( spl71_166
<=> ! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_166])]) ).
fof(f446,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f1638,plain,
spl71_165,
inference(avatar_split_clause,[],[f445,f1636]) ).
fof(f1636,plain,
( spl71_165
<=> ! [X0,X1] :
( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_165])]) ).
fof(f445,plain,
! [X0,X1] :
( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f1634,plain,
spl71_164,
inference(avatar_split_clause,[],[f441,f1632]) ).
fof(f1632,plain,
( spl71_164
<=> ! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_164])]) ).
fof(f441,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1630,plain,
spl71_163,
inference(avatar_split_clause,[],[f438,f1628]) ).
fof(f1628,plain,
( spl71_163
<=> ! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_163])]) ).
fof(f438,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f1626,plain,
spl71_162,
inference(avatar_split_clause,[],[f437,f1624]) ).
fof(f1624,plain,
( spl71_162
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ strictorderedP(cons(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_162])]) ).
fof(f437,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ strictorderedP(cons(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f1622,plain,
spl71_161,
inference(avatar_split_clause,[],[f424,f1620]) ).
fof(f1620,plain,
( spl71_161
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_161])]) ).
fof(f424,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f261]) ).
fof(f261,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
fof(f1618,plain,
spl71_160,
inference(avatar_split_clause,[],[f422,f1616]) ).
fof(f1616,plain,
( spl71_160
<=> ! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_160])]) ).
fof(f422,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( geq(X0,X1)
<=> leq(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( geq(X0,X1)
<=> leq(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
fof(f1614,plain,
spl71_159,
inference(avatar_split_clause,[],[f421,f1612]) ).
fof(f1612,plain,
( spl71_159
<=> ! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_159])]) ).
fof(f421,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f1610,plain,
spl71_158,
inference(avatar_split_clause,[],[f420,f1608]) ).
fof(f1608,plain,
( spl71_158
<=> ! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_158])]) ).
fof(f420,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
fof(f1606,plain,
( spl71_157
| ~ spl71_1
| ~ spl71_31 ),
inference(avatar_split_clause,[],[f830,f792,f651,f1603]) ).
fof(f1603,plain,
( spl71_157
<=> sP15(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_157])]) ).
fof(f830,plain,
( sP15(sK20)
| ~ spl71_1
| ~ spl71_31 ),
inference(resolution,[],[f793,f653]) ).
fof(f1601,plain,
spl71_156,
inference(avatar_split_clause,[],[f419,f1599]) ).
fof(f1599,plain,
( spl71_156
<=> ! [X0,X1] :
( lt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_156])]) ).
fof(f419,plain,
! [X0,X1] :
( lt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f1597,plain,
spl71_155,
inference(avatar_split_clause,[],[f418,f1595]) ).
fof(f418,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f1593,plain,
spl71_154,
inference(avatar_split_clause,[],[f414,f1591]) ).
fof(f1591,plain,
( spl71_154
<=> ! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_154])]) ).
fof(f414,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
=> ~ lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f1589,plain,
spl71_153,
inference(avatar_split_clause,[],[f412,f1587]) ).
fof(f1587,plain,
( spl71_153
<=> ! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_153])]) ).
fof(f412,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
=> ~ gt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
fof(f1585,plain,
spl71_152,
inference(avatar_split_clause,[],[f644,f1583]) ).
fof(f1583,plain,
( spl71_152
<=> ! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_152])]) ).
fof(f644,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f615,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f432]) ).
fof(f432,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f1581,plain,
spl71_151,
inference(avatar_split_clause,[],[f564,f1579]) ).
fof(f1579,plain,
( spl71_151
<=> ! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_151])]) ).
fof(f564,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f1577,plain,
spl71_150,
inference(avatar_split_clause,[],[f563,f1575]) ).
fof(f1575,plain,
( spl71_150
<=> ! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_150])]) ).
fof(f563,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f1573,plain,
( spl71_149
| ~ spl71_4
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f828,f788,f666,f1570]) ).
fof(f1570,plain,
( spl71_149
<=> sP13(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_149])]) ).
fof(f828,plain,
( sP13(sK23)
| ~ spl71_4
| ~ spl71_30 ),
inference(resolution,[],[f789,f668]) ).
fof(f1519,plain,
( spl71_148
| ~ spl71_3
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f827,f788,f661,f1516]) ).
fof(f1516,plain,
( spl71_148
<=> sP13(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_148])]) ).
fof(f827,plain,
( sP13(sK22)
| ~ spl71_3
| ~ spl71_30 ),
inference(resolution,[],[f789,f663]) ).
fof(f1503,plain,
spl71_147,
inference(avatar_split_clause,[],[f572,f1501]) ).
fof(f572,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f1499,plain,
spl71_146,
inference(avatar_split_clause,[],[f562,f1497]) ).
fof(f1497,plain,
( spl71_146
<=> ! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_146])]) ).
fof(f562,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f1495,plain,
spl71_145,
inference(avatar_split_clause,[],[f560,f1493]) ).
fof(f1493,plain,
( spl71_145
<=> ! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_145])]) ).
fof(f560,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f1491,plain,
spl71_144,
inference(avatar_split_clause,[],[f558,f1489]) ).
fof(f1489,plain,
( spl71_144
<=> ! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_144])]) ).
fof(f558,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f1487,plain,
spl71_143,
inference(avatar_split_clause,[],[f556,f1485]) ).
fof(f1485,plain,
( spl71_143
<=> ! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_143])]) ).
fof(f556,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f1483,plain,
spl71_142,
inference(avatar_split_clause,[],[f472,f1481]) ).
fof(f1481,plain,
( spl71_142
<=> ! [X0] :
( ssList(sK27(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_142])]) ).
fof(f472,plain,
! [X0] :
( ssList(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f1479,plain,
spl71_141,
inference(avatar_split_clause,[],[f470,f1477]) ).
fof(f1477,plain,
( spl71_141
<=> ! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_141])]) ).
fof(f470,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f1475,plain,
( spl71_140
| ~ spl71_2
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f826,f788,f656,f1472]) ).
fof(f1472,plain,
( spl71_140
<=> sP13(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_140])]) ).
fof(f826,plain,
( sP13(sK21)
| ~ spl71_2
| ~ spl71_30 ),
inference(resolution,[],[f789,f658]) ).
fof(f1470,plain,
spl71_139,
inference(avatar_split_clause,[],[f468,f1468]) ).
fof(f1468,plain,
( spl71_139
<=> ! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_139])]) ).
fof(f468,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f1466,plain,
spl71_138,
inference(avatar_split_clause,[],[f467,f1464]) ).
fof(f1464,plain,
( spl71_138
<=> ! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_138])]) ).
fof(f467,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f1462,plain,
spl71_137,
inference(avatar_split_clause,[],[f465,f1460]) ).
fof(f1460,plain,
( spl71_137
<=> ! [X0] :
( ssItem(sK25(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_137])]) ).
fof(f465,plain,
! [X0] :
( ssItem(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f1458,plain,
spl71_136,
inference(avatar_split_clause,[],[f464,f1456]) ).
fof(f1456,plain,
( spl71_136
<=> ! [X0] :
( ssList(sK24(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_136])]) ).
fof(f464,plain,
! [X0] :
( ssList(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f1454,plain,
spl71_135,
inference(avatar_split_clause,[],[f448,f1452]) ).
fof(f1452,plain,
( spl71_135
<=> ! [X0,X1] :
( totalorderedP(X0)
| nil = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_135])]) ).
fof(f448,plain,
! [X0,X1] :
( totalorderedP(X0)
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1450,plain,
spl71_134,
inference(avatar_split_clause,[],[f440,f1448]) ).
fof(f1448,plain,
( spl71_134
<=> ! [X0,X1] :
( strictorderedP(X0)
| nil = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_134])]) ).
fof(f440,plain,
! [X0,X1] :
( strictorderedP(X0)
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1446,plain,
( spl71_133
| ~ spl71_1
| ~ spl71_30 ),
inference(avatar_split_clause,[],[f825,f788,f651,f1443]) ).
fof(f1443,plain,
( spl71_133
<=> sP13(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_133])]) ).
fof(f825,plain,
( sP13(sK20)
| ~ spl71_1
| ~ spl71_30 ),
inference(resolution,[],[f789,f653]) ).
fof(f1391,plain,
( spl71_132
| ~ spl71_4
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f823,f784,f666,f1388]) ).
fof(f1388,plain,
( spl71_132
<=> sP11(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_132])]) ).
fof(f823,plain,
( sP11(sK23)
| ~ spl71_4
| ~ spl71_29 ),
inference(resolution,[],[f785,f668]) ).
fof(f1386,plain,
spl71_131,
inference(avatar_split_clause,[],[f554,f1384]) ).
fof(f1384,plain,
( spl71_131
<=> ! [X0] :
( sP16(X0)
| ~ leq(sK58(X0),sK59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_131])]) ).
fof(f554,plain,
! [X0] :
( sP16(X0)
| ~ leq(sK58(X0),sK59(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1382,plain,
spl71_130,
inference(avatar_split_clause,[],[f543,f1380]) ).
fof(f1380,plain,
( spl71_130
<=> ! [X0] :
( sP14(X0)
| ~ lt(sK53(X0),sK54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_130])]) ).
fof(f543,plain,
! [X0] :
( sP14(X0)
| ~ lt(sK53(X0),sK54(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f1378,plain,
spl71_129,
inference(avatar_split_clause,[],[f532,f1376]) ).
fof(f1376,plain,
( spl71_129
<=> ! [X0] :
( sP12(X0)
| leq(sK49(X0),sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_129])]) ).
fof(f532,plain,
! [X0] :
( sP12(X0)
| leq(sK49(X0),sK48(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f1374,plain,
spl71_128,
inference(avatar_split_clause,[],[f531,f1372]) ).
fof(f1372,plain,
( spl71_128
<=> ! [X0] :
( sP12(X0)
| leq(sK48(X0),sK49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_128])]) ).
fof(f531,plain,
! [X0] :
( sP12(X0)
| leq(sK48(X0),sK49(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f1370,plain,
spl71_127,
inference(avatar_split_clause,[],[f520,f1368]) ).
fof(f1368,plain,
( spl71_127
<=> ! [X0] :
( sP10(X0)
| ~ lt(sK44(X0),sK43(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_127])]) ).
fof(f520,plain,
! [X0] :
( sP10(X0)
| ~ lt(sK44(X0),sK43(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f1366,plain,
spl71_126,
inference(avatar_split_clause,[],[f519,f1364]) ).
fof(f1364,plain,
( spl71_126
<=> ! [X0] :
( sP10(X0)
| ~ lt(sK43(X0),sK44(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_126])]) ).
fof(f519,plain,
! [X0] :
( sP10(X0)
| ~ lt(sK43(X0),sK44(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f1362,plain,
spl71_125,
inference(avatar_split_clause,[],[f508,f1360]) ).
fof(f1360,plain,
( spl71_125
<=> ! [X0] :
( sP8(X0)
| ~ leq(sK39(X0),sK38(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_125])]) ).
fof(f508,plain,
! [X0] :
( sP8(X0)
| ~ leq(sK39(X0),sK38(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f1358,plain,
spl71_124,
inference(avatar_split_clause,[],[f507,f1356]) ).
fof(f1356,plain,
( spl71_124
<=> ! [X0] :
( sP8(X0)
| ~ leq(sK38(X0),sK39(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_124])]) ).
fof(f507,plain,
! [X0] :
( sP8(X0)
| ~ leq(sK38(X0),sK39(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f1354,plain,
spl71_123,
inference(avatar_split_clause,[],[f496,f1352]) ).
fof(f1352,plain,
( spl71_123
<=> ! [X0] :
( sP6(X0)
| sK33(X0) = sK34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_123])]) ).
fof(f496,plain,
! [X0] :
( sP6(X0)
| sK33(X0) = sK34(X0) ),
inference(cnf_transformation,[],[f304]) ).
fof(f1350,plain,
( spl71_122
| ~ spl71_3
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f822,f784,f661,f1347]) ).
fof(f1347,plain,
( spl71_122
<=> sP11(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_122])]) ).
fof(f822,plain,
( sP11(sK22)
| ~ spl71_3
| ~ spl71_29 ),
inference(resolution,[],[f785,f663]) ).
fof(f1345,plain,
spl71_121,
inference(avatar_split_clause,[],[f485,f1343]) ).
fof(f1343,plain,
( spl71_121
<=> ! [X0] :
( sP4(X0)
| sK29(X0) != sK30(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_121])]) ).
fof(f485,plain,
! [X0] :
( sP4(X0)
| sK29(X0) != sK30(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f1341,plain,
spl71_120,
inference(avatar_split_clause,[],[f474,f1339]) ).
fof(f1339,plain,
( spl71_120
<=> ! [X0] :
( ssItem(sK28(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_120])]) ).
fof(f474,plain,
! [X0] :
( ssItem(sK28(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f1337,plain,
spl71_119,
inference(avatar_split_clause,[],[f463,f1335]) ).
fof(f463,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f1333,plain,
spl71_118,
inference(avatar_split_clause,[],[f462,f1331]) ).
fof(f462,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f1329,plain,
spl71_117,
inference(avatar_split_clause,[],[f452,f1327]) ).
fof(f1327,plain,
( spl71_117
<=> ! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_117])]) ).
fof(f452,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f139,f228,f227]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).
fof(f1325,plain,
spl71_116,
inference(avatar_split_clause,[],[f444,f1323]) ).
fof(f1323,plain,
( spl71_116
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_116])]) ).
fof(f444,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0] :
( ! [X1] :
( sP1(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f225,f224]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).
fof(f1321,plain,
spl71_115,
inference(avatar_split_clause,[],[f388,f1319]) ).
fof(f1319,plain,
( spl71_115
<=> ! [X9,X7,X6,X8] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9)
| ~ ssItem(X8)
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7)
| ~ ssItem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_115])]) ).
fof(f388,plain,
! [X8,X6,X9,X7] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9)
| ~ ssItem(X8)
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
( ( ~ segmentP(sK19,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != sK19 )
& ( nil != sK20
| nil = sK21 )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),sK23)
& ssList(sK23)
& ssList(sK22)
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23])],[f100,f256,f255,f254,f253,f252,f251]) ).
fof(f251,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ~ segmentP(sK19,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != sK19 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(sK19,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != sK19 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ~ segmentP(sK19,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != sK19 )
& ( nil != sK20
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X3] :
( ( ~ segmentP(sK19,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != sK19 )
& ( nil != sK20
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ( ~ segmentP(sK19,sK18)
| ~ neq(sK18,nil) )
& ( nil != sK18
| nil != sK19 )
& ( nil != sK20
| nil = sK21 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = sK21
& ssList(X5) )
& ssList(X4) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& app(app(X4,sK20),X5) = sK21
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),X5)
& ssList(X5) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f256,plain,
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),X5)
& ssList(X5) )
=> ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK20
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK20)
& sK21 = app(app(sK22,sK20),sK23)
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X2
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X10,X12)
& app(cons(X12,nil),X13) = X2
& ssList(X13) )
& ssItem(X12) )
& app(X11,cons(X10,nil)) = X4
& ssList(X11) )
& ssItem(X10) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f1317,plain,
spl71_114,
inference(avatar_split_clause,[],[f387,f1315]) ).
fof(f1315,plain,
( spl71_114
<=> ! [X10,X11,X13,X12] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13)
| ~ ssItem(X12)
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11)
| ~ ssItem(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_114])]) ).
fof(f387,plain,
! [X10,X11,X12,X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK20
| ~ ssList(X13)
| ~ ssItem(X12)
| app(X11,cons(X10,nil)) != sK22
| ~ ssList(X11)
| ~ ssItem(X10) ),
inference(cnf_transformation,[],[f257]) ).
fof(f1313,plain,
( spl71_113
| ~ spl71_2
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f821,f784,f656,f1310]) ).
fof(f1310,plain,
( spl71_113
<=> sP11(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_113])]) ).
fof(f821,plain,
( sP11(sK21)
| ~ spl71_2
| ~ spl71_29 ),
inference(resolution,[],[f785,f658]) ).
fof(f1308,plain,
( spl71_112
| ~ spl71_1
| ~ spl71_29 ),
inference(avatar_split_clause,[],[f820,f784,f651,f1305]) ).
fof(f1305,plain,
( spl71_112
<=> sP11(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_112])]) ).
fof(f820,plain,
( sP11(sK20)
| ~ spl71_1
| ~ spl71_29 ),
inference(resolution,[],[f785,f653]) ).
fof(f1301,plain,
( spl71_111
| ~ spl71_4
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f818,f780,f666,f1298]) ).
fof(f1298,plain,
( spl71_111
<=> sP9(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_111])]) ).
fof(f818,plain,
( sP9(sK23)
| ~ spl71_4
| ~ spl71_28 ),
inference(resolution,[],[f781,f668]) ).
fof(f1296,plain,
spl71_110,
inference(avatar_split_clause,[],[f546,f1294]) ).
fof(f1294,plain,
( spl71_110
<=> ! [X0] :
( totalorderedP(X0)
| ~ sP16(X0)
| ~ sP17(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_110])]) ).
fof(f546,plain,
! [X0] :
( totalorderedP(X0)
| ~ sP16(X0)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ totalorderedP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP16(X0) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f1292,plain,
spl71_109,
inference(avatar_split_clause,[],[f545,f1290]) ).
fof(f1290,plain,
( spl71_109
<=> ! [X0] :
( sP16(X0)
| ~ totalorderedP(X0)
| ~ sP17(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_109])]) ).
fof(f545,plain,
! [X0] :
( sP16(X0)
| ~ totalorderedP(X0)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f1288,plain,
spl71_108,
inference(avatar_split_clause,[],[f535,f1286]) ).
fof(f1286,plain,
( spl71_108
<=> ! [X0] :
( strictorderedP(X0)
| ~ sP14(X0)
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_108])]) ).
fof(f535,plain,
! [X0] :
( strictorderedP(X0)
| ~ sP14(X0)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ strictorderedP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP14(X0) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f1284,plain,
spl71_107,
inference(avatar_split_clause,[],[f534,f1282]) ).
fof(f1282,plain,
( spl71_107
<=> ! [X0] :
( sP14(X0)
| ~ strictorderedP(X0)
| ~ sP15(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_107])]) ).
fof(f534,plain,
! [X0] :
( sP14(X0)
| ~ strictorderedP(X0)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f1280,plain,
spl71_106,
inference(avatar_split_clause,[],[f523,f1278]) ).
fof(f1278,plain,
( spl71_106
<=> ! [X0] :
( cyclefreeP(X0)
| ~ sP12(X0)
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_106])]) ).
fof(f523,plain,
! [X0] :
( cyclefreeP(X0)
| ~ sP12(X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP12(X0) )
& ( sP12(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP12(X0) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f1276,plain,
spl71_105,
inference(avatar_split_clause,[],[f522,f1274]) ).
fof(f1274,plain,
( spl71_105
<=> ! [X0] :
( sP12(X0)
| ~ cyclefreeP(X0)
| ~ sP13(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_105])]) ).
fof(f522,plain,
! [X0] :
( sP12(X0)
| ~ cyclefreeP(X0)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f1272,plain,
spl71_104,
inference(avatar_split_clause,[],[f511,f1270]) ).
fof(f1270,plain,
( spl71_104
<=> ! [X0] :
( strictorderP(X0)
| ~ sP10(X0)
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_104])]) ).
fof(f511,plain,
! [X0] :
( strictorderP(X0)
| ~ sP10(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP10(X0) )
& ( sP10(X0)
| ~ strictorderP(X0) ) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP10(X0) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f1268,plain,
spl71_103,
inference(avatar_split_clause,[],[f510,f1266]) ).
fof(f1266,plain,
( spl71_103
<=> ! [X0] :
( sP10(X0)
| ~ strictorderP(X0)
| ~ sP11(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_103])]) ).
fof(f510,plain,
! [X0] :
( sP10(X0)
| ~ strictorderP(X0)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f1264,plain,
spl71_102,
inference(avatar_split_clause,[],[f499,f1262]) ).
fof(f1262,plain,
( spl71_102
<=> ! [X0] :
( totalorderP(X0)
| ~ sP8(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_102])]) ).
fof(f499,plain,
! [X0] :
( totalorderP(X0)
| ~ sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ totalorderP(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP8(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f1260,plain,
( spl71_101
| ~ spl71_3
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f817,f780,f661,f1257]) ).
fof(f1257,plain,
( spl71_101
<=> sP9(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_101])]) ).
fof(f817,plain,
( sP9(sK22)
| ~ spl71_3
| ~ spl71_28 ),
inference(resolution,[],[f781,f663]) ).
fof(f1255,plain,
spl71_100,
inference(avatar_split_clause,[],[f498,f1253]) ).
fof(f1253,plain,
( spl71_100
<=> ! [X0] :
( sP8(X0)
| ~ totalorderP(X0)
| ~ sP9(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_100])]) ).
fof(f498,plain,
! [X0] :
( sP8(X0)
| ~ totalorderP(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f1251,plain,
spl71_99,
inference(avatar_split_clause,[],[f488,f1249]) ).
fof(f1249,plain,
( spl71_99
<=> ! [X0] :
( duplicatefreeP(X0)
| ~ sP6(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_99])]) ).
fof(f488,plain,
! [X0] :
( duplicatefreeP(X0)
| ~ sP6(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f296,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f1247,plain,
spl71_98,
inference(avatar_split_clause,[],[f487,f1245]) ).
fof(f1245,plain,
( spl71_98
<=> ! [X0] :
( sP6(X0)
| ~ duplicatefreeP(X0)
| ~ sP7(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_98])]) ).
fof(f487,plain,
! [X0] :
( sP6(X0)
| ~ duplicatefreeP(X0)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f1243,plain,
spl71_97,
inference(avatar_split_clause,[],[f478,f1241]) ).
fof(f478,plain,
! [X0] :
( equalelemsP(X0)
| ~ sP4(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ equalelemsP(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f1239,plain,
spl71_96,
inference(avatar_split_clause,[],[f477,f1237]) ).
fof(f477,plain,
! [X0] :
( sP4(X0)
| ~ equalelemsP(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f1235,plain,
spl71_95,
inference(avatar_split_clause,[],[f411,f1233]) ).
fof(f1233,plain,
( spl71_95
<=> ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_95])]) ).
fof(f411,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f1231,plain,
spl71_94,
inference(avatar_split_clause,[],[f410,f1229]) ).
fof(f1229,plain,
( spl71_94
<=> ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_94])]) ).
fof(f410,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
fof(f1227,plain,
spl71_93,
inference(avatar_split_clause,[],[f409,f1225]) ).
fof(f1225,plain,
( spl71_93
<=> ! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_93])]) ).
fof(f409,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(f1223,plain,
spl71_92,
inference(avatar_split_clause,[],[f408,f1221]) ).
fof(f1221,plain,
( spl71_92
<=> ! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_92])]) ).
fof(f408,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
fof(f1219,plain,
spl71_91,
inference(avatar_split_clause,[],[f407,f1217]) ).
fof(f1217,plain,
( spl71_91
<=> ! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_91])]) ).
fof(f407,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
fof(f1215,plain,
( spl71_90
| ~ spl71_2
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f816,f780,f656,f1212]) ).
fof(f1212,plain,
( spl71_90
<=> sP9(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_90])]) ).
fof(f816,plain,
( sP9(sK21)
| ~ spl71_2
| ~ spl71_28 ),
inference(resolution,[],[f781,f658]) ).
fof(f1210,plain,
spl71_89,
inference(avatar_split_clause,[],[f406,f1208]) ).
fof(f1208,plain,
( spl71_89
<=> ! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_89])]) ).
fof(f406,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
fof(f1206,plain,
spl71_88,
inference(avatar_split_clause,[],[f405,f1204]) ).
fof(f1204,plain,
( spl71_88
<=> ! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_88])]) ).
fof(f405,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f1174,plain,
( spl71_87
| ~ spl71_1
| ~ spl71_28 ),
inference(avatar_split_clause,[],[f815,f780,f651,f1171]) ).
fof(f1171,plain,
( spl71_87
<=> sP9(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_87])]) ).
fof(f815,plain,
( sP9(sK20)
| ~ spl71_1
| ~ spl71_28 ),
inference(resolution,[],[f781,f653]) ).
fof(f1127,plain,
( spl71_86
| ~ spl71_4
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f813,f776,f666,f1124]) ).
fof(f1124,plain,
( spl71_86
<=> sP7(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_86])]) ).
fof(f813,plain,
( sP7(sK23)
| ~ spl71_4
| ~ spl71_27 ),
inference(resolution,[],[f777,f668]) ).
fof(f1080,plain,
( spl71_85
| ~ spl71_3
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f812,f776,f661,f1077]) ).
fof(f1077,plain,
( spl71_85
<=> sP7(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_85])]) ).
fof(f812,plain,
( sP7(sK22)
| ~ spl71_3
| ~ spl71_27 ),
inference(resolution,[],[f777,f663]) ).
fof(f1047,plain,
( spl71_84
| ~ spl71_2
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f811,f776,f656,f1044]) ).
fof(f1044,plain,
( spl71_84
<=> sP7(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_84])]) ).
fof(f811,plain,
( sP7(sK21)
| ~ spl71_2
| ~ spl71_27 ),
inference(resolution,[],[f777,f658]) ).
fof(f1042,plain,
spl71_83,
inference(avatar_split_clause,[],[f646,f1040]) ).
fof(f1040,plain,
( spl71_83
<=> ! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_83])]) ).
fof(f646,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f613]) ).
fof(f613,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f417]) ).
fof(f417,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f1038,plain,
spl71_82,
inference(avatar_split_clause,[],[f641,f1036]) ).
fof(f1036,plain,
( spl71_82
<=> ! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_82])]) ).
fof(f641,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f634]) ).
fof(f634,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f579]) ).
fof(f579,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f1034,plain,
( spl71_81
| ~ spl71_1
| ~ spl71_27 ),
inference(avatar_split_clause,[],[f810,f776,f651,f1031]) ).
fof(f1031,plain,
( spl71_81
<=> sP7(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_81])]) ).
fof(f810,plain,
( sP7(sK20)
| ~ spl71_1
| ~ spl71_27 ),
inference(resolution,[],[f777,f653]) ).
fof(f1029,plain,
spl71_80,
inference(avatar_split_clause,[],[f552,f1027]) ).
fof(f1027,plain,
( spl71_80
<=> ! [X0] :
( sP16(X0)
| ssList(sK62(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_80])]) ).
fof(f552,plain,
! [X0] :
( sP16(X0)
| ssList(sK62(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1025,plain,
spl71_79,
inference(avatar_split_clause,[],[f551,f1023]) ).
fof(f1023,plain,
( spl71_79
<=> ! [X0] :
( sP16(X0)
| ssList(sK61(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_79])]) ).
fof(f551,plain,
! [X0] :
( sP16(X0)
| ssList(sK61(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1021,plain,
spl71_78,
inference(avatar_split_clause,[],[f550,f1019]) ).
fof(f1019,plain,
( spl71_78
<=> ! [X0] :
( sP16(X0)
| ssList(sK60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_78])]) ).
fof(f550,plain,
! [X0] :
( sP16(X0)
| ssList(sK60(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1017,plain,
spl71_77,
inference(avatar_split_clause,[],[f549,f1015]) ).
fof(f1015,plain,
( spl71_77
<=> ! [X0] :
( sP16(X0)
| ssItem(sK59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_77])]) ).
fof(f549,plain,
! [X0] :
( sP16(X0)
| ssItem(sK59(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1013,plain,
spl71_76,
inference(avatar_split_clause,[],[f548,f1011]) ).
fof(f1011,plain,
( spl71_76
<=> ! [X0] :
( sP16(X0)
| ssItem(sK58(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_76])]) ).
fof(f548,plain,
! [X0] :
( sP16(X0)
| ssItem(sK58(X0)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1009,plain,
spl71_75,
inference(avatar_split_clause,[],[f541,f1007]) ).
fof(f1007,plain,
( spl71_75
<=> ! [X0] :
( sP14(X0)
| ssList(sK57(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_75])]) ).
fof(f541,plain,
! [X0] :
( sP14(X0)
| ssList(sK57(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f1005,plain,
spl71_74,
inference(avatar_split_clause,[],[f540,f1003]) ).
fof(f1003,plain,
( spl71_74
<=> ! [X0] :
( sP14(X0)
| ssList(sK56(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_74])]) ).
fof(f540,plain,
! [X0] :
( sP14(X0)
| ssList(sK56(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f1001,plain,
spl71_73,
inference(avatar_split_clause,[],[f539,f999]) ).
fof(f999,plain,
( spl71_73
<=> ! [X0] :
( sP14(X0)
| ssList(sK55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_73])]) ).
fof(f539,plain,
! [X0] :
( sP14(X0)
| ssList(sK55(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f997,plain,
spl71_72,
inference(avatar_split_clause,[],[f538,f995]) ).
fof(f995,plain,
( spl71_72
<=> ! [X0] :
( sP14(X0)
| ssItem(sK54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_72])]) ).
fof(f538,plain,
! [X0] :
( sP14(X0)
| ssItem(sK54(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f993,plain,
spl71_71,
inference(avatar_split_clause,[],[f537,f991]) ).
fof(f991,plain,
( spl71_71
<=> ! [X0] :
( sP14(X0)
| ssItem(sK53(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_71])]) ).
fof(f537,plain,
! [X0] :
( sP14(X0)
| ssItem(sK53(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f989,plain,
spl71_70,
inference(avatar_split_clause,[],[f529,f987]) ).
fof(f987,plain,
( spl71_70
<=> ! [X0] :
( sP12(X0)
| ssList(sK52(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_70])]) ).
fof(f529,plain,
! [X0] :
( sP12(X0)
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f985,plain,
spl71_69,
inference(avatar_split_clause,[],[f528,f983]) ).
fof(f983,plain,
( spl71_69
<=> ! [X0] :
( sP12(X0)
| ssList(sK51(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_69])]) ).
fof(f528,plain,
! [X0] :
( sP12(X0)
| ssList(sK51(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f981,plain,
spl71_68,
inference(avatar_split_clause,[],[f527,f979]) ).
fof(f979,plain,
( spl71_68
<=> ! [X0] :
( sP12(X0)
| ssList(sK50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_68])]) ).
fof(f527,plain,
! [X0] :
( sP12(X0)
| ssList(sK50(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f977,plain,
spl71_67,
inference(avatar_split_clause,[],[f526,f975]) ).
fof(f975,plain,
( spl71_67
<=> ! [X0] :
( sP12(X0)
| ssItem(sK49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_67])]) ).
fof(f526,plain,
! [X0] :
( sP12(X0)
| ssItem(sK49(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f973,plain,
spl71_66,
inference(avatar_split_clause,[],[f525,f971]) ).
fof(f971,plain,
( spl71_66
<=> ! [X0] :
( sP12(X0)
| ssItem(sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_66])]) ).
fof(f525,plain,
! [X0] :
( sP12(X0)
| ssItem(sK48(X0)) ),
inference(cnf_transformation,[],[f331]) ).
fof(f969,plain,
spl71_65,
inference(avatar_split_clause,[],[f517,f967]) ).
fof(f967,plain,
( spl71_65
<=> ! [X0] :
( sP10(X0)
| ssList(sK47(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_65])]) ).
fof(f517,plain,
! [X0] :
( sP10(X0)
| ssList(sK47(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f965,plain,
spl71_64,
inference(avatar_split_clause,[],[f516,f963]) ).
fof(f963,plain,
( spl71_64
<=> ! [X0] :
( sP10(X0)
| ssList(sK46(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_64])]) ).
fof(f516,plain,
! [X0] :
( sP10(X0)
| ssList(sK46(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f961,plain,
spl71_63,
inference(avatar_split_clause,[],[f515,f959]) ).
fof(f959,plain,
( spl71_63
<=> ! [X0] :
( sP10(X0)
| ssList(sK45(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_63])]) ).
fof(f515,plain,
! [X0] :
( sP10(X0)
| ssList(sK45(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f957,plain,
spl71_62,
inference(avatar_split_clause,[],[f514,f955]) ).
fof(f955,plain,
( spl71_62
<=> ! [X0] :
( sP10(X0)
| ssItem(sK44(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_62])]) ).
fof(f514,plain,
! [X0] :
( sP10(X0)
| ssItem(sK44(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f953,plain,
spl71_61,
inference(avatar_split_clause,[],[f513,f951]) ).
fof(f951,plain,
( spl71_61
<=> ! [X0] :
( sP10(X0)
| ssItem(sK43(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_61])]) ).
fof(f513,plain,
! [X0] :
( sP10(X0)
| ssItem(sK43(X0)) ),
inference(cnf_transformation,[],[f322]) ).
fof(f949,plain,
( spl71_60
| ~ spl71_4
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f803,f772,f666,f946]) ).
fof(f946,plain,
( spl71_60
<=> sP5(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_60])]) ).
fof(f803,plain,
( sP5(sK23)
| ~ spl71_4
| ~ spl71_26 ),
inference(resolution,[],[f773,f668]) ).
fof(f944,plain,
spl71_59,
inference(avatar_split_clause,[],[f505,f942]) ).
fof(f942,plain,
( spl71_59
<=> ! [X0] :
( sP8(X0)
| ssList(sK42(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_59])]) ).
fof(f505,plain,
! [X0] :
( sP8(X0)
| ssList(sK42(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f940,plain,
spl71_58,
inference(avatar_split_clause,[],[f504,f938]) ).
fof(f938,plain,
( spl71_58
<=> ! [X0] :
( sP8(X0)
| ssList(sK41(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_58])]) ).
fof(f504,plain,
! [X0] :
( sP8(X0)
| ssList(sK41(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f936,plain,
spl71_57,
inference(avatar_split_clause,[],[f503,f934]) ).
fof(f934,plain,
( spl71_57
<=> ! [X0] :
( sP8(X0)
| ssList(sK40(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_57])]) ).
fof(f503,plain,
! [X0] :
( sP8(X0)
| ssList(sK40(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f932,plain,
spl71_56,
inference(avatar_split_clause,[],[f502,f930]) ).
fof(f930,plain,
( spl71_56
<=> ! [X0] :
( sP8(X0)
| ssItem(sK39(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_56])]) ).
fof(f502,plain,
! [X0] :
( sP8(X0)
| ssItem(sK39(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f928,plain,
spl71_55,
inference(avatar_split_clause,[],[f501,f926]) ).
fof(f926,plain,
( spl71_55
<=> ! [X0] :
( sP8(X0)
| ssItem(sK38(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_55])]) ).
fof(f501,plain,
! [X0] :
( sP8(X0)
| ssItem(sK38(X0)) ),
inference(cnf_transformation,[],[f313]) ).
fof(f924,plain,
spl71_54,
inference(avatar_split_clause,[],[f494,f922]) ).
fof(f922,plain,
( spl71_54
<=> ! [X0] :
( sP6(X0)
| ssList(sK37(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_54])]) ).
fof(f494,plain,
! [X0] :
( sP6(X0)
| ssList(sK37(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f920,plain,
spl71_53,
inference(avatar_split_clause,[],[f493,f918]) ).
fof(f918,plain,
( spl71_53
<=> ! [X0] :
( sP6(X0)
| ssList(sK36(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_53])]) ).
fof(f493,plain,
! [X0] :
( sP6(X0)
| ssList(sK36(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f916,plain,
spl71_52,
inference(avatar_split_clause,[],[f492,f914]) ).
fof(f914,plain,
( spl71_52
<=> ! [X0] :
( sP6(X0)
| ssList(sK35(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_52])]) ).
fof(f492,plain,
! [X0] :
( sP6(X0)
| ssList(sK35(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f912,plain,
spl71_51,
inference(avatar_split_clause,[],[f491,f910]) ).
fof(f910,plain,
( spl71_51
<=> ! [X0] :
( sP6(X0)
| ssItem(sK34(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_51])]) ).
fof(f491,plain,
! [X0] :
( sP6(X0)
| ssItem(sK34(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f908,plain,
spl71_50,
inference(avatar_split_clause,[],[f490,f906]) ).
fof(f906,plain,
( spl71_50
<=> ! [X0] :
( sP6(X0)
| ssItem(sK33(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_50])]) ).
fof(f490,plain,
! [X0] :
( sP6(X0)
| ssItem(sK33(X0)) ),
inference(cnf_transformation,[],[f304]) ).
fof(f904,plain,
( spl71_49
| ~ spl71_3
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f802,f772,f661,f901]) ).
fof(f901,plain,
( spl71_49
<=> sP5(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_49])]) ).
fof(f802,plain,
( sP5(sK22)
| ~ spl71_3
| ~ spl71_26 ),
inference(resolution,[],[f773,f663]) ).
fof(f899,plain,
spl71_48,
inference(avatar_split_clause,[],[f483,f897]) ).
fof(f897,plain,
( spl71_48
<=> ! [X0] :
( sP4(X0)
| ssList(sK32(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_48])]) ).
fof(f483,plain,
! [X0] :
( sP4(X0)
| ssList(sK32(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f895,plain,
spl71_47,
inference(avatar_split_clause,[],[f482,f893]) ).
fof(f893,plain,
( spl71_47
<=> ! [X0] :
( sP4(X0)
| ssList(sK31(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_47])]) ).
fof(f482,plain,
! [X0] :
( sP4(X0)
| ssList(sK31(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f891,plain,
spl71_46,
inference(avatar_split_clause,[],[f481,f889]) ).
fof(f889,plain,
( spl71_46
<=> ! [X0] :
( sP4(X0)
| ssItem(sK30(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_46])]) ).
fof(f481,plain,
! [X0] :
( sP4(X0)
| ssItem(sK30(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f887,plain,
spl71_45,
inference(avatar_split_clause,[],[f480,f885]) ).
fof(f885,plain,
( spl71_45
<=> ! [X0] :
( sP4(X0)
| ssItem(sK29(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_45])]) ).
fof(f480,plain,
! [X0] :
( sP4(X0)
| ssItem(sK29(X0)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f883,plain,
spl71_44,
inference(avatar_split_clause,[],[f461,f881]) ).
fof(f881,plain,
( spl71_44
<=> ! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_44])]) ).
fof(f461,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f879,plain,
spl71_43,
inference(avatar_split_clause,[],[f460,f877]) ).
fof(f877,plain,
( spl71_43
<=> ! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_43])]) ).
fof(f460,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f875,plain,
spl71_42,
inference(avatar_split_clause,[],[f459,f873]) ).
fof(f459,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f871,plain,
spl71_41,
inference(avatar_split_clause,[],[f458,f869]) ).
fof(f869,plain,
( spl71_41
<=> ! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_41])]) ).
fof(f458,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f867,plain,
spl71_40,
inference(avatar_split_clause,[],[f457,f865]) ).
fof(f865,plain,
( spl71_40
<=> ! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_40])]) ).
fof(f457,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f863,plain,
spl71_39,
inference(avatar_split_clause,[],[f456,f861]) ).
fof(f861,plain,
( spl71_39
<=> ! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_39])]) ).
fof(f456,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f859,plain,
( spl71_38
| ~ spl71_2
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f801,f772,f656,f856]) ).
fof(f801,plain,
( sP5(sK21)
| ~ spl71_2
| ~ spl71_26 ),
inference(resolution,[],[f773,f658]) ).
fof(f854,plain,
spl71_37,
inference(avatar_split_clause,[],[f404,f852]) ).
fof(f852,plain,
( spl71_37
<=> ! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_37])]) ).
fof(f404,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f850,plain,
spl71_36,
inference(avatar_split_clause,[],[f403,f848]) ).
fof(f848,plain,
( spl71_36
<=> ! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_36])]) ).
fof(f403,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
fof(f846,plain,
spl71_35,
inference(avatar_split_clause,[],[f402,f844]) ).
fof(f844,plain,
( spl71_35
<=> ! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_35])]) ).
fof(f402,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
fof(f842,plain,
spl71_34,
inference(avatar_split_clause,[],[f401,f840]) ).
fof(f840,plain,
( spl71_34
<=> ! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_34])]) ).
fof(f401,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f808,plain,
( spl71_33
| ~ spl71_1
| ~ spl71_26 ),
inference(avatar_split_clause,[],[f800,f772,f651,f805]) ).
fof(f800,plain,
( sP5(sK20)
| ~ spl71_1
| ~ spl71_26 ),
inference(resolution,[],[f773,f653]) ).
fof(f798,plain,
spl71_32,
inference(avatar_split_clause,[],[f555,f796]) ).
fof(f555,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f175,f249,f248]) ).
fof(f175,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
fof(f794,plain,
spl71_31,
inference(avatar_split_clause,[],[f544,f792]) ).
fof(f544,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f173,f246,f245]) ).
fof(f173,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
fof(f790,plain,
spl71_30,
inference(avatar_split_clause,[],[f533,f788]) ).
fof(f533,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f171,f243,f242]) ).
fof(f171,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f786,plain,
spl71_29,
inference(avatar_split_clause,[],[f521,f784]) ).
fof(f521,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f169,f240,f239]) ).
fof(f169,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( lt(X2,X1)
| lt(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
fof(f782,plain,
spl71_28,
inference(avatar_split_clause,[],[f509,f780]) ).
fof(f509,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f167,f237,f236]) ).
fof(f167,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( leq(X2,X1)
| leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
fof(f778,plain,
spl71_27,
inference(avatar_split_clause,[],[f497,f776]) ).
fof(f497,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f165,f234,f233]) ).
fof(f165,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(f774,plain,
spl71_26,
inference(avatar_split_clause,[],[f486,f772]) ).
fof(f486,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f163,f231,f230]) ).
fof(f163,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ssList(X0)
=> ( equalelemsP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(X3,cons(X1,cons(X2,X4))) = X0
=> X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
fof(f770,plain,
spl71_25,
inference(avatar_split_clause,[],[f619,f768]) ).
fof(f768,plain,
( spl71_25
<=> ! [X1] : sP2(nil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_25])]) ).
fof(f619,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f450]) ).
fof(f450,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f766,plain,
spl71_24,
inference(avatar_split_clause,[],[f617,f764]) ).
fof(f764,plain,
( spl71_24
<=> ! [X1] : sP0(nil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_24])]) ).
fof(f617,plain,
! [X1] : sP0(nil,X1),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
! [X0,X1] :
( sP0(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f270]) ).
fof(f762,plain,
~ spl71_23,
inference(avatar_split_clause,[],[f608,f759]) ).
fof(f759,plain,
( spl71_23
<=> sK69 = sK70 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_23])]) ).
fof(f608,plain,
sK69 != sK70,
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
( sK69 != sK70
& ssItem(sK70)
& ssItem(sK69) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f2,f375,f374]) ).
fof(f374,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK69 != X1
& ssItem(X1) )
& ssItem(sK69) ) ),
introduced(choice_axiom,[]) ).
fof(f375,plain,
( ? [X1] :
( sK69 != X1
& ssItem(X1) )
=> ( sK69 != sK70
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f757,plain,
spl71_22,
inference(avatar_split_clause,[],[f607,f754]) ).
fof(f754,plain,
( spl71_22
<=> ssItem(sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_22])]) ).
fof(f607,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f376]) ).
fof(f752,plain,
spl71_21,
inference(avatar_split_clause,[],[f606,f749]) ).
fof(f749,plain,
( spl71_21
<=> ssItem(sK69) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_21])]) ).
fof(f606,plain,
ssItem(sK69),
inference(cnf_transformation,[],[f376]) ).
fof(f747,plain,
spl71_20,
inference(avatar_split_clause,[],[f400,f744]) ).
fof(f400,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f742,plain,
spl71_19,
inference(avatar_split_clause,[],[f399,f739]) ).
fof(f739,plain,
( spl71_19
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_19])]) ).
fof(f399,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f737,plain,
spl71_18,
inference(avatar_split_clause,[],[f398,f734]) ).
fof(f398,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f732,plain,
spl71_17,
inference(avatar_split_clause,[],[f397,f729]) ).
fof(f397,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f727,plain,
spl71_16,
inference(avatar_split_clause,[],[f396,f724]) ).
fof(f396,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f722,plain,
spl71_15,
inference(avatar_split_clause,[],[f395,f719]) ).
fof(f395,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f717,plain,
spl71_14,
inference(avatar_split_clause,[],[f394,f714]) ).
fof(f394,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f712,plain,
spl71_13,
inference(avatar_split_clause,[],[f393,f709]) ).
fof(f393,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f707,plain,
~ spl71_12,
inference(avatar_split_clause,[],[f392,f704]) ).
fof(f392,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f702,plain,
spl71_11,
inference(avatar_split_clause,[],[f385,f699]) ).
fof(f385,plain,
sK21 = app(app(sK22,sK20),sK23),
inference(cnf_transformation,[],[f257]) ).
fof(f697,plain,
( spl71_8
| ~ spl71_10 ),
inference(avatar_split_clause,[],[f649,f694,f685]) ).
fof(f649,plain,
( nil != sK20
| sK20 = sK21 ),
inference(inner_rewriting,[],[f389]) ).
fof(f389,plain,
( nil != sK20
| nil = sK21 ),
inference(cnf_transformation,[],[f257]) ).
fof(f692,plain,
( ~ spl71_8
| ~ spl71_9 ),
inference(avatar_split_clause,[],[f648,f689,f685]) ).
fof(f648,plain,
( nil != sK21
| sK20 != sK21 ),
inference(inner_rewriting,[],[f647]) ).
fof(f647,plain,
( nil != sK20
| sK20 != sK21 ),
inference(inner_rewriting,[],[f610]) ).
fof(f610,plain,
( nil != sK20
| nil != sK21 ),
inference(definition_unfolding,[],[f390,f382,f381]) ).
fof(f381,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f257]) ).
fof(f382,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f257]) ).
fof(f390,plain,
( nil != sK18
| nil != sK19 ),
inference(cnf_transformation,[],[f257]) ).
fof(f683,plain,
( ~ spl71_6
| ~ spl71_7 ),
inference(avatar_split_clause,[],[f609,f680,f676]) ).
fof(f609,plain,
( ~ segmentP(sK21,sK20)
| ~ neq(sK20,nil) ),
inference(definition_unfolding,[],[f391,f381,f382,f382]) ).
fof(f391,plain,
( ~ segmentP(sK19,sK18)
| ~ neq(sK18,nil) ),
inference(cnf_transformation,[],[f257]) ).
fof(f674,plain,
spl71_5,
inference(avatar_split_clause,[],[f386,f671]) ).
fof(f386,plain,
totalorderedP(sK20),
inference(cnf_transformation,[],[f257]) ).
fof(f669,plain,
spl71_4,
inference(avatar_split_clause,[],[f384,f666]) ).
fof(f384,plain,
ssList(sK23),
inference(cnf_transformation,[],[f257]) ).
fof(f664,plain,
spl71_3,
inference(avatar_split_clause,[],[f383,f661]) ).
fof(f383,plain,
ssList(sK22),
inference(cnf_transformation,[],[f257]) ).
fof(f659,plain,
spl71_2,
inference(avatar_split_clause,[],[f380,f656]) ).
fof(f380,plain,
ssList(sK21),
inference(cnf_transformation,[],[f257]) ).
fof(f654,plain,
spl71_1,
inference(avatar_split_clause,[],[f379,f651]) ).
fof(f379,plain,
ssList(sK20),
inference(cnf_transformation,[],[f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC118+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 20:35:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (17495)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (17498)WARNING: value z3 for option sas not known
% 0.21/0.37 % (17497)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (17496)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (17499)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (17498)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)
% 0.21/0.37 % (17500)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37 % (17501)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37 % (17502)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.41 TRYING [3]
% 0.21/0.45 TRYING [1]
% 0.21/0.46 TRYING [2]
% 0.21/0.46 TRYING [4]
% 0.21/0.47 TRYING [4]
% 0.21/0.47 TRYING [3]
% 0.21/0.50 % (17500)First to succeed.
% 0.21/0.52 % (17500)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17495"
% 0.21/0.52 % (17500)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (17500)------------------------------
% 0.21/0.53 % (17500)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.53 % (17500)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (17500)Memory used [KB]: 3646
% 0.21/0.53 % (17500)Time elapsed: 0.143 s
% 0.21/0.53 % (17500)Instructions burned: 271 (million)
% 0.21/0.53 % (17495)Success in time 0.159 s
%------------------------------------------------------------------------------