TSTP Solution File: SWC398-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC398-1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 10:26:41 EDT 2024
% Result : Unsatisfiable 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 416
% Syntax : Number of formulae : 760 ( 251 unt; 0 def)
% Number of atoms : 2319 ( 287 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2827 (1268 ~;1329 |; 0 &)
% ( 230 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 251 ( 249 usr; 231 prp; 0-2 aty)
% Number of functors : 55 ( 55 usr; 9 con; 0-2 aty)
% Number of variables : 765 ( 765 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2924,plain,
$false,
inference(avatar_sat_refutation,[],[f239,f244,f249,f254,f259,f264,f269,f274,f283,f288,f293,f298,f303,f308,f313,f318,f323,f328,f333,f338,f342,f346,f350,f354,f358,f362,f366,f370,f374,f378,f382,f386,f390,f394,f398,f402,f406,f410,f414,f418,f422,f426,f430,f434,f438,f442,f446,f450,f454,f458,f462,f466,f470,f474,f478,f482,f487,f491,f495,f499,f503,f507,f511,f515,f519,f523,f527,f531,f535,f539,f543,f547,f551,f555,f559,f563,f567,f571,f575,f579,f583,f587,f591,f598,f602,f606,f672,f676,f680,f684,f689,f693,f697,f720,f724,f729,f733,f737,f741,f745,f749,f753,f757,f761,f765,f769,f774,f779,f783,f787,f791,f795,f799,f803,f807,f811,f816,f820,f824,f828,f832,f836,f851,f863,f867,f872,f876,f954,f958,f962,f966,f973,f977,f981,f985,f989,f993,f997,f1049,f1053,f1064,f1068,f1072,f1076,f1080,f1084,f1175,f1179,f1183,f1187,f1191,f1195,f1210,f1214,f1218,f1222,f1237,f1261,f1265,f1269,f1273,f1349,f1353,f1357,f1361,f1365,f1369,f1373,f1412,f1468,f1472,f1476,f1480,f1487,f1491,f1495,f1539,f1615,f1619,f1645,f1649,f1653,f1657,f1662,f1666,f1670,f1878,f1884,f1890,f1895,f1899,f1934,f1938,f1942,f1960,f2004,f2044,f2088,f2132,f2172,f2210,f2251,f2265,f2310,f2349,f2388,f2426,f2470,f2475,f2516,f2523,f2528,f2532,f2572,f2611,f2652,f2657,f2698,f2704,f2708,f2712,f2716,f2721,f2749,f2753,f2870,f2886,f2923]) ).
fof(f2923,plain,
( spl0_6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2524,f2521,f266,f246,f261]) ).
fof(f261,plain,
( spl0_6
<=> memberP(sk4,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f246,plain,
( spl0_3
<=> ssItem(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f266,plain,
( spl0_7
<=> memberP(sk3,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f2521,plain,
( spl0_213
<=> ! [X0] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2524,plain,
( ~ ssItem(sk6)
| memberP(sk4,sk6)
| ~ spl0_7
| ~ spl0_213 ),
inference(resolution,[],[f2522,f268]) ).
fof(f268,plain,
( memberP(sk3,sk6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f2522,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| memberP(sk4,X0) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2521]) ).
fof(f2886,plain,
( spl0_229
| spl0_230
| ~ spl0_4
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1702,f1643,f251,f2883,f2879]) ).
fof(f2879,plain,
( spl0_229
<=> sk3 = app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2883,plain,
( spl0_230
<=> duplicatefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f251,plain,
( spl0_4
<=> ssList(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1643,plain,
( spl0_182
<=> ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| app(app(skaf75(X0),cons(skaf74(X0),skaf76(X0))),cons(skaf74(X0),skaf77(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1702,plain,
( duplicatefreeP(sk3)
| sk3 = app(app(skaf75(sk3),cons(skaf74(sk3),skaf76(sk3))),cons(skaf74(sk3),skaf77(sk3)))
| ~ spl0_4
| ~ spl0_182 ),
inference(resolution,[],[f1644,f253]) ).
fof(f253,plain,
( ssList(sk3)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f1644,plain,
( ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| app(app(skaf75(X0),cons(skaf74(X0),skaf76(X0))),cons(skaf74(X0),skaf77(X0))) = X0 )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1643]) ).
fof(f2870,plain,
( ~ spl0_4
| ~ spl0_1
| spl0_228
| ~ spl0_8
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1520,f1485,f271,f2868,f236,f251]) ).
fof(f236,plain,
( spl0_1
<=> ssList(sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f2868,plain,
( spl0_228
<=> ! [X0,X1] :
( segmentP(app(sk4,X0),X1)
| ~ ssList(X0)
| ~ segmentP(sk5,X1)
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f271,plain,
( spl0_8
<=> sk4 = app(sk3,sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1485,plain,
( spl0_176
<=> ! [X0,X3,X2,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X3,X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1520,plain,
( ! [X0,X1] :
( segmentP(app(sk4,X0),X1)
| ~ ssList(sk5)
| ~ ssList(X1)
| ~ ssList(sk3)
| ~ segmentP(sk5,X1)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_176 ),
inference(superposition,[],[f1486,f273]) ).
fof(f273,plain,
( sk4 = app(sk3,sk5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f1486,plain,
( ! [X2,X3,X0,X1] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f2753,plain,
( ~ spl0_4
| ~ spl0_1
| spl0_227
| ~ spl0_8
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1630,f1617,f271,f2751,f236,f251]) ).
fof(f2751,plain,
( spl0_227
<=> ! [X0] :
( segmentP(app(sk4,X0),sk5)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1617,plain,
( spl0_181
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1630,plain,
( ! [X0] :
( segmentP(app(sk4,X0),sk5)
| ~ ssList(app(sk4,X0))
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_181 ),
inference(superposition,[],[f1618,f273]) ).
fof(f1618,plain,
( ! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1617]) ).
fof(f2749,plain,
( spl0_226
| ~ spl0_1
| ~ spl0_8
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2384,f2347,f271,f236,f2746]) ).
fof(f2746,plain,
( spl0_226
<=> hd(sk3) = hd(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2347,plain,
( spl0_207
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk3) = hd(app(sk3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2384,plain,
( hd(sk3) = hd(sk4)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_207 ),
inference(forward_demodulation,[],[f2383,f273]) ).
fof(f2383,plain,
( hd(sk3) = hd(app(sk3,sk5))
| ~ spl0_1
| ~ spl0_207 ),
inference(resolution,[],[f2348,f238]) ).
fof(f238,plain,
( ssList(sk5)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f2348,plain,
( ! [X0] :
( ~ ssList(X0)
| hd(sk3) = hd(app(sk3,X0)) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2347]) ).
fof(f2721,plain,
( spl0_225
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1501,f1470,f266,f251,f246,f2718]) ).
fof(f2718,plain,
( spl0_225
<=> sk3 = app(skaf42(sk3,sk6),cons(sk6,skaf43(sk6,sk3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1470,plain,
( spl0_173
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1501,plain,
( ~ ssList(sk3)
| ~ ssItem(sk6)
| sk3 = app(skaf42(sk3,sk6),cons(sk6,skaf43(sk6,sk3)))
| ~ spl0_7
| ~ spl0_173 ),
inference(resolution,[],[f1471,f268]) ).
fof(f1471,plain,
( ! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f2716,plain,
( ~ spl0_1
| ~ spl0_4
| spl0_224
| ~ spl0_8
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1453,f1359,f271,f2714,f251,f236]) ).
fof(f2714,plain,
( spl0_224
<=> ! [X0] :
( ~ memberP(sk4,X0)
| ~ ssItem(X0)
| memberP(sk3,X0)
| memberP(sk5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1359,plain,
( spl0_167
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X1,X2)
| memberP(X0,X2)
| ~ memberP(app(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1453,plain,
( ! [X0] :
( ~ memberP(sk4,X0)
| ~ ssList(sk3)
| ~ ssList(sk5)
| memberP(sk5,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_167 ),
inference(superposition,[],[f1360,f273]) ).
fof(f1360,plain,
( ! [X2,X0,X1] :
( ~ memberP(app(X0,X1),X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X1,X2)
| memberP(X0,X2)
| ~ ssItem(X2) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f2712,plain,
( spl0_223
| ~ spl0_1
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1446,f1351,f236,f2710]) ).
fof(f2710,plain,
( spl0_223
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk5,X1),X0) = app(sk5,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1351,plain,
( spl0_165
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1446,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk5,X1),X0) = app(sk5,app(X1,X0)) )
| ~ spl0_1
| ~ spl0_165 ),
inference(resolution,[],[f1352,f238]) ).
fof(f1352,plain,
( ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f2708,plain,
( spl0_222
| ~ spl0_5
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1445,f1351,f256,f2706]) ).
fof(f2706,plain,
( spl0_222
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f256,plain,
( spl0_5
<=> ssList(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1445,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) )
| ~ spl0_5
| ~ spl0_165 ),
inference(resolution,[],[f1352,f258]) ).
fof(f258,plain,
( ssList(sk4)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f2704,plain,
( spl0_221
| ~ spl0_4
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1444,f1351,f251,f2702]) ).
fof(f2702,plain,
( spl0_221
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1444,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) )
| ~ spl0_4
| ~ spl0_165 ),
inference(resolution,[],[f1352,f253]) ).
fof(f2698,plain,
( ~ spl0_4
| ~ spl0_1
| spl0_220
| ~ spl0_8
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1330,f1267,f271,f2696,f236,f251]) ).
fof(f2696,plain,
( spl0_220
<=> ! [X0] :
( sk4 != app(X0,sk5)
| sk3 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1267,plain,
( spl0_162
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1330,plain,
( ! [X0] :
( sk4 != app(X0,sk5)
| ~ ssList(X0)
| ~ ssList(sk5)
| sk3 = X0
| ~ ssList(sk3) )
| ~ spl0_8
| ~ spl0_162 ),
inference(superposition,[],[f1268,f273]) ).
fof(f1268,plain,
( ! [X2,X0,X1] :
( app(X0,X1) != app(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| ~ ssList(X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f2657,plain,
( spl0_219
| ~ spl0_8
| ~ spl0_93
| ~ spl0_200
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2653,f2650,f2001,f686,f271,f2655]) ).
fof(f2655,plain,
( spl0_219
<=> ! [X0] :
( sk4 != app(sk4,X0)
| sk5 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f686,plain,
( spl0_93
<=> sk3 = app(sk3,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2001,plain,
( spl0_200
<=> nil = sk5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2650,plain,
( spl0_218
<=> ! [X0] :
( sk4 != app(sk3,X0)
| sk5 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2653,plain,
( ! [X0] :
( sk4 != app(sk4,X0)
| sk5 = X0
| ~ ssList(X0) )
| ~ spl0_8
| ~ spl0_93
| ~ spl0_200
| ~ spl0_218 ),
inference(forward_demodulation,[],[f2651,f2613]) ).
fof(f2613,plain,
( sk3 = sk4
| ~ spl0_8
| ~ spl0_93
| ~ spl0_200 ),
inference(forward_demodulation,[],[f2456,f273]) ).
fof(f2456,plain,
( sk3 = app(sk3,sk5)
| ~ spl0_93
| ~ spl0_200 ),
inference(superposition,[],[f688,f2003]) ).
fof(f2003,plain,
( nil = sk5
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f688,plain,
( sk3 = app(sk3,nil)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f2651,plain,
( ! [X0] :
( sk4 != app(sk3,X0)
| sk5 = X0
| ~ ssList(X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2650]) ).
fof(f2652,plain,
( ~ spl0_1
| ~ spl0_4
| spl0_218
| ~ spl0_8
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1311,f1263,f271,f2650,f251,f236]) ).
fof(f1263,plain,
( spl0_161
<=> ! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1311,plain,
( ! [X0] :
( sk4 != app(sk3,X0)
| ~ ssList(X0)
| ~ ssList(sk3)
| sk5 = X0
| ~ ssList(sk5) )
| ~ spl0_8
| ~ spl0_161 ),
inference(superposition,[],[f1264,f273]) ).
fof(f1264,plain,
( ! [X2,X0,X1] :
( app(X0,X1) != app(X0,X2)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| ~ ssList(X1) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f2611,plain,
( spl0_200
| spl0_217
| ~ spl0_1
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1307,f1259,f236,f2609,f2001]) ).
fof(f2609,plain,
( spl0_217
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk5,X0)) = app(tl(sk5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1259,plain,
( spl0_160
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1307,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk5
| tl(app(sk5,X0)) = app(tl(sk5),X0) )
| ~ spl0_1
| ~ spl0_160 ),
inference(resolution,[],[f1260,f238]) ).
fof(f1260,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f2572,plain,
( spl0_198
| spl0_216
| ~ spl0_5
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1306,f1259,f256,f2570,f1957]) ).
fof(f1957,plain,
( spl0_198
<=> nil = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2570,plain,
( spl0_216
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk4,X0)) = app(tl(sk4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1306,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk4
| tl(app(sk4,X0)) = app(tl(sk4),X0) )
| ~ spl0_5
| ~ spl0_160 ),
inference(resolution,[],[f1260,f258]) ).
fof(f2532,plain,
( spl0_10
| spl0_215
| ~ spl0_4
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1305,f1259,f251,f2530,f280]) ).
fof(f280,plain,
( spl0_10
<=> nil = sk3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f2530,plain,
( spl0_215
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk3,X0)) = app(tl(sk3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1305,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk3
| tl(app(sk3,X0)) = app(tl(sk3),X0) )
| ~ spl0_4
| ~ spl0_160 ),
inference(resolution,[],[f1260,f253]) ).
fof(f2528,plain,
( ~ spl0_4
| ~ spl0_1
| spl0_214
| ~ spl0_8
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1168,f1082,f271,f2526,f236,f251]) ).
fof(f2526,plain,
( spl0_214
<=> ! [X0] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(sk5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1082,plain,
( spl0_148
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1168,plain,
( ! [X0] :
( memberP(sk4,X0)
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ memberP(sk5,X0)
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_148 ),
inference(superposition,[],[f1083,f273]) ).
fof(f1083,plain,
( ! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| ~ ssItem(X1) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f2523,plain,
( ~ spl0_4
| ~ spl0_1
| spl0_213
| ~ spl0_8
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1162,f1078,f271,f2521,f236,f251]) ).
fof(f1078,plain,
( spl0_147
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1162,plain,
( ! [X0] :
( memberP(sk4,X0)
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_8
| ~ spl0_147 ),
inference(superposition,[],[f1079,f273]) ).
fof(f1079,plain,
( ! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| ~ ssItem(X1) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f2516,plain,
( ~ spl0_1
| ~ spl0_4
| spl0_212
| ~ spl0_8
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1154,f1070,f271,f2514,f251,f236]) ).
fof(f2514,plain,
( spl0_212
<=> ! [X0] :
( frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1070,plain,
( spl0_145
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1154,plain,
( ! [X0] :
( frontsegP(sk4,X0)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ frontsegP(sk3,X0)
| ~ ssList(sk5) )
| ~ spl0_8
| ~ spl0_145 ),
inference(superposition,[],[f1071,f273]) ).
fof(f1071,plain,
( ! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f2475,plain,
( spl0_211
| ~ spl0_12
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2215,f2001,f290,f2472]) ).
fof(f2472,plain,
( spl0_211
<=> duplicatefreeP(sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f290,plain,
( spl0_12
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f2215,plain,
( duplicatefreeP(sk5)
| ~ spl0_12
| ~ spl0_200 ),
inference(superposition,[],[f292,f2003]) ).
fof(f292,plain,
( duplicatefreeP(nil)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f2470,plain,
( ~ spl0_4
| ~ spl0_1
| spl0_210
| ~ spl0_8
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1136,f1066,f271,f2468,f236,f251]) ).
fof(f2468,plain,
( spl0_210
<=> ! [X0] :
( rearsegP(sk4,X0)
| ~ rearsegP(sk5,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1066,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1136,plain,
( ! [X0] :
( rearsegP(sk4,X0)
| ~ ssList(sk5)
| ~ ssList(X0)
| ~ rearsegP(sk5,X0)
| ~ ssList(sk3) )
| ~ spl0_8
| ~ spl0_144 ),
inference(superposition,[],[f1067,f273]) ).
fof(f1067,plain,
( ! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f2426,plain,
( spl0_200
| spl0_209
| ~ spl0_1
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1118,f1047,f236,f2424,f2001]) ).
fof(f2424,plain,
( spl0_209
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk5) = hd(app(sk5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1047,plain,
( spl0_141
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1118,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk5
| hd(sk5) = hd(app(sk5,X0)) )
| ~ spl0_1
| ~ spl0_141 ),
inference(resolution,[],[f1048,f238]) ).
fof(f1048,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| hd(app(X1,X0)) = hd(X1) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f2388,plain,
( spl0_198
| spl0_208
| ~ spl0_5
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1117,f1047,f256,f2386,f1957]) ).
fof(f2386,plain,
( spl0_208
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk4) = hd(app(sk4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1117,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk4
| hd(sk4) = hd(app(sk4,X0)) )
| ~ spl0_5
| ~ spl0_141 ),
inference(resolution,[],[f1048,f258]) ).
fof(f2349,plain,
( spl0_10
| spl0_207
| ~ spl0_4
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1116,f1047,f251,f2347,f280]) ).
fof(f1116,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk3
| hd(sk3) = hd(app(sk3,X0)) )
| ~ spl0_4
| ~ spl0_141 ),
inference(resolution,[],[f1048,f253]) ).
fof(f2310,plain,
( spl0_206
| ~ spl0_11
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2214,f2001,f285,f2307]) ).
fof(f2307,plain,
( spl0_206
<=> equalelemsP(sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f285,plain,
( spl0_11
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f2214,plain,
( equalelemsP(sk5)
| ~ spl0_11
| ~ spl0_200 ),
inference(superposition,[],[f287,f2003]) ).
fof(f287,plain,
( equalelemsP(nil)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f2265,plain,
( ~ spl0_205
| spl0_198
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2260,f2001,f1957,f2262]) ).
fof(f2262,plain,
( spl0_205
<=> sk4 = sk5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2260,plain,
( sk4 != sk5
| spl0_198
| ~ spl0_200 ),
inference(forward_demodulation,[],[f1958,f2003]) ).
fof(f1958,plain,
( nil != sk4
| spl0_198 ),
inference(avatar_component_clause,[],[f1957]) ).
fof(f2251,plain,
( ~ spl0_1
| spl0_9
| ~ spl0_4
| ~ spl0_198
| ~ spl0_8
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f947,f870,f271,f1957,f251,f276,f236]) ).
fof(f276,plain,
( spl0_9
<=> sk3 = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f870,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f947,plain,
( nil != sk4
| ~ ssList(sk3)
| sk3 = sk4
| ~ ssList(sk5)
| ~ spl0_8
| ~ spl0_128 ),
inference(inner_rewriting,[],[f945]) ).
fof(f945,plain,
( nil != sk4
| ~ ssList(sk3)
| nil = sk3
| ~ ssList(sk5)
| ~ spl0_8
| ~ spl0_128 ),
inference(superposition,[],[f871,f273]) ).
fof(f871,plain,
( ! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X1) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f870]) ).
fof(f2210,plain,
( spl0_204
| spl0_200
| ~ spl0_1
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f944,f865,f236,f2001,f2207]) ).
fof(f2207,plain,
( spl0_204
<=> sk5 = cons(skaf83(sk5),skaf82(sk5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f865,plain,
( spl0_127
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f944,plain,
( nil = sk5
| sk5 = cons(skaf83(sk5),skaf82(sk5))
| ~ spl0_1
| ~ spl0_127 ),
inference(resolution,[],[f866,f238]) ).
fof(f866,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f2172,plain,
( spl0_203
| spl0_198
| ~ spl0_5
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f943,f865,f256,f1957,f2169]) ).
fof(f2169,plain,
( spl0_203
<=> sk4 = cons(skaf83(sk4),skaf82(sk4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f943,plain,
( nil = sk4
| sk4 = cons(skaf83(sk4),skaf82(sk4))
| ~ spl0_5
| ~ spl0_127 ),
inference(resolution,[],[f866,f258]) ).
fof(f2132,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f1542,f276,f266,f261]) ).
fof(f1542,plain,
( memberP(sk4,sk6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f268,f278]) ).
fof(f278,plain,
( sk3 = sk4
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f2088,plain,
( spl0_202
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f2049,f848,f280,f276,f271,f2085]) ).
fof(f2085,plain,
( spl0_202
<=> sk3 = sk5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f848,plain,
( spl0_125
<=> sk5 = app(nil,sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f2049,plain,
( sk3 = sk5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_125 ),
inference(forward_demodulation,[],[f278,f2047]) ).
fof(f2047,plain,
( sk4 = sk5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1543,f1611]) ).
fof(f1611,plain,
( sk5 = app(sk4,sk5)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1577,f278]) ).
fof(f1577,plain,
( sk5 = app(sk3,sk5)
| ~ spl0_10
| ~ spl0_125 ),
inference(superposition,[],[f850,f281]) ).
fof(f281,plain,
( nil = sk3
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f850,plain,
( sk5 = app(nil,sk5)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f1543,plain,
( sk4 = app(sk4,sk5)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f273,f278]) ).
fof(f2044,plain,
( spl0_201
| spl0_10
| ~ spl0_4
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f942,f865,f251,f280,f2041]) ).
fof(f2041,plain,
( spl0_201
<=> sk3 = cons(skaf83(sk3),skaf82(sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f942,plain,
( nil = sk3
| sk3 = cons(skaf83(sk3),skaf82(sk3))
| ~ spl0_4
| ~ spl0_127 ),
inference(resolution,[],[f866,f253]) ).
fof(f2004,plain,
( spl0_199
| spl0_200
| ~ spl0_1
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f910,f861,f236,f2001,f1997]) ).
fof(f1997,plain,
( spl0_199
<=> sk5 = cons(hd(sk5),tl(sk5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f861,plain,
( spl0_126
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f910,plain,
( nil = sk5
| sk5 = cons(hd(sk5),tl(sk5))
| ~ spl0_1
| ~ spl0_126 ),
inference(resolution,[],[f862,f238]) ).
fof(f862,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f1960,plain,
( spl0_197
| spl0_198
| ~ spl0_5
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f909,f861,f256,f1957,f1953]) ).
fof(f1953,plain,
( spl0_197
<=> sk4 = cons(hd(sk4),tl(sk4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f909,plain,
( nil = sk4
| sk4 = cons(hd(sk4),tl(sk4))
| ~ spl0_5
| ~ spl0_126 ),
inference(resolution,[],[f862,f258]) ).
fof(f1942,plain,
spl0_196,
inference(avatar_split_clause,[],[f227,f1940]) ).
fof(f1940,plain,
( spl0_196
<=> ! [X4,X0,X3,X2,X1] :
( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f227,plain,
! [X2,X3,X0,X1,X4] :
( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ totalorderP(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause184) ).
fof(f1938,plain,
spl0_195,
inference(avatar_split_clause,[],[f226,f1936]) ).
fof(f1936,plain,
( spl0_195
<=> ! [X4,X0,X3,X2,X1] :
( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f226,plain,
! [X2,X3,X0,X1,X4] :
( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ strictorderP(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause183) ).
fof(f1934,plain,
spl0_194,
inference(avatar_split_clause,[],[f225,f1932]) ).
fof(f1932,plain,
( spl0_194
<=> ! [X2,X4,X0,X3,X1] :
( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f225,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause185) ).
fof(f1899,plain,
spl0_193,
inference(avatar_split_clause,[],[f224,f1897]) ).
fof(f1897,plain,
( spl0_193
<=> ! [X4,X0,X3,X2,X1] :
( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f224,plain,
! [X2,X3,X0,X1,X4] :
( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3) ),
inference(equality_resolution,[],[f182]) ).
fof(f182,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ totalorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X5)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause182) ).
fof(f1895,plain,
spl0_192,
inference(avatar_split_clause,[],[f223,f1893]) ).
fof(f1893,plain,
( spl0_192
<=> ! [X4,X0,X3,X2,X1] :
( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f223,plain,
! [X2,X3,X0,X1,X4] :
( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3) ),
inference(equality_resolution,[],[f181]) ).
fof(f181,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ strictorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X5)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause181) ).
fof(f1890,plain,
spl0_191,
inference(avatar_split_clause,[],[f220,f1888]) ).
fof(f1888,plain,
( spl0_191
<=> ! [X0,X3,X2,X1] :
( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_resolution,[],[f179]) ).
fof(f179,axiom,
! [X2,X3,X0,X1,X4] :
( ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause179) ).
fof(f1884,plain,
spl0_190,
inference(avatar_split_clause,[],[f222,f1882]) ).
fof(f1882,plain,
( spl0_190
<=> ! [X0,X3,X2,X1] :
( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,cons(X2,X3))))
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,cons(X2,X3))))
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2 ),
inference(equality_resolution,[],[f180]) ).
fof(f180,axiom,
! [X2,X3,X0,X1,X4] :
( ~ equalelemsP(X4)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2
| app(X0,cons(X1,cons(X2,X3))) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause180) ).
fof(f1878,plain,
spl0_189,
inference(avatar_split_clause,[],[f177,f1876]) ).
fof(f1876,plain,
( spl0_189
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| nil = X0
| nil = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f177,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| nil = X0
| nil = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause177) ).
fof(f1670,plain,
spl0_188,
inference(avatar_split_clause,[],[f167,f1668]) ).
fof(f1668,plain,
( spl0_188
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f167,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause167) ).
fof(f1666,plain,
spl0_187,
inference(avatar_split_clause,[],[f166,f1664]) ).
fof(f1664,plain,
( spl0_187
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f166,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause166) ).
fof(f1662,plain,
( spl0_186
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f1540,f276,f241,f1659]) ).
fof(f1659,plain,
( spl0_186
<=> equalelemsP(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f241,plain,
( spl0_2
<=> equalelemsP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1540,plain,
( equalelemsP(sk4)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f243,f278]) ).
fof(f243,plain,
( equalelemsP(sk3)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f1657,plain,
spl0_185,
inference(avatar_split_clause,[],[f165,f1655]) ).
fof(f1655,plain,
( spl0_185
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f165,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause165) ).
fof(f1653,plain,
spl0_184,
inference(avatar_split_clause,[],[f164,f1651]) ).
fof(f1651,plain,
( spl0_184
<=> ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f164,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause164) ).
fof(f1649,plain,
spl0_183,
inference(avatar_split_clause,[],[f163,f1647]) ).
fof(f1647,plain,
( spl0_183
<=> ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f163,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause163) ).
fof(f1645,plain,
spl0_182,
inference(avatar_split_clause,[],[f162,f1643]) ).
fof(f162,axiom,
! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| app(app(skaf75(X0),cons(skaf74(X0),skaf76(X0))),cons(skaf74(X0),skaf77(X0))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause162) ).
fof(f1619,plain,
spl0_181,
inference(avatar_split_clause,[],[f219,f1617]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(equality_resolution,[],[f173]) ).
fof(f173,axiom,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(X3,X1)
| app(app(X0,X1),X2) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f1615,plain,
spl0_180,
inference(avatar_split_clause,[],[f218,f1613]) ).
fof(f1613,plain,
( spl0_180
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ),
inference(equality_resolution,[],[f175]) ).
fof(f175,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(X3,X1)
| app(X0,cons(X1,X2)) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).
fof(f1539,plain,
( spl0_179
| spl0_10
| ~ spl0_4
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f908,f861,f251,f280,f1536]) ).
fof(f1536,plain,
( spl0_179
<=> sk3 = cons(hd(sk3),tl(sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f908,plain,
( nil = sk3
| sk3 = cons(hd(sk3),tl(sk3))
| ~ spl0_4
| ~ spl0_126 ),
inference(resolution,[],[f862,f253]) ).
fof(f1495,plain,
spl0_178,
inference(avatar_split_clause,[],[f176,f1493]) ).
fof(f1493,plain,
( spl0_178
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f176,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause176) ).
fof(f1491,plain,
spl0_177,
inference(avatar_split_clause,[],[f174,f1489]) ).
fof(f1489,plain,
( spl0_177
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| frontsegP(X1,X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f174,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| frontsegP(X1,X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause174) ).
fof(f1487,plain,
spl0_176,
inference(avatar_split_clause,[],[f172,f1485]) ).
fof(f172,axiom,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X3,X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause172) ).
fof(f1480,plain,
spl0_175,
inference(avatar_split_clause,[],[f171,f1478]) ).
fof(f1478,plain,
( spl0_175
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3
| cons(X0,X1) != cons(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause171) ).
fof(f1476,plain,
spl0_174,
inference(avatar_split_clause,[],[f170,f1474]) ).
fof(f1474,plain,
( spl0_174
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| cons(X0,X1) != cons(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f170,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause170) ).
fof(f1472,plain,
spl0_173,
inference(avatar_split_clause,[],[f169,f1470]) ).
fof(f169,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause169) ).
fof(f1468,plain,
spl0_172,
inference(avatar_split_clause,[],[f168,f1466]) ).
fof(f1466,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1)
| app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f168,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1)
| app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause168) ).
fof(f1412,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| spl0_171
| ~ spl0_8
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1038,f995,f271,f1409,f256,f251,f236]) ).
fof(f1409,plain,
( spl0_171
<=> frontsegP(sk4,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f995,plain,
( spl0_140
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1038,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ spl0_8
| ~ spl0_140 ),
inference(superposition,[],[f996,f273]) ).
fof(f996,plain,
( ! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f1373,plain,
spl0_170,
inference(avatar_split_clause,[],[f161,f1371]) ).
fof(f1371,plain,
( spl0_170
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2)
| ~ memberP(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2)
| ~ memberP(cons(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause161) ).
fof(f1369,plain,
spl0_169,
inference(avatar_split_clause,[],[f160,f1367]) ).
fof(f1367,plain,
( spl0_169
<=> ! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f160,axiom,
! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause160) ).
fof(f1365,plain,
spl0_168,
inference(avatar_split_clause,[],[f159,f1363]) ).
fof(f1363,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f159,axiom,
! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause159) ).
fof(f1361,plain,
spl0_167,
inference(avatar_split_clause,[],[f158,f1359]) ).
fof(f158,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X1,X2)
| memberP(X0,X2)
| ~ memberP(app(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
fof(f1357,plain,
spl0_166,
inference(avatar_split_clause,[],[f157,f1355]) ).
fof(f1355,plain,
( spl0_166
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f157,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause157) ).
fof(f1353,plain,
spl0_165,
inference(avatar_split_clause,[],[f149,f1351]) ).
fof(f149,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
fof(f1349,plain,
spl0_164,
inference(avatar_split_clause,[],[f142,f1347]) ).
fof(f1347,plain,
( spl0_164
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f142,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause142) ).
fof(f1273,plain,
spl0_163,
inference(avatar_split_clause,[],[f228,f1271]) ).
fof(f1271,plain,
( spl0_163
<=> ! [X0,X1,X3] :
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f228,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f221,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(equality_resolution,[],[f178]) ).
fof(f178,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| X2 != X3
| ~ frontsegP(X0,X1)
| frontsegP(cons(X2,X0),cons(X3,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause178) ).
fof(f1269,plain,
spl0_162,
inference(avatar_split_clause,[],[f151,f1267]) ).
fof(f151,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause151) ).
fof(f1265,plain,
spl0_161,
inference(avatar_split_clause,[],[f150,f1263]) ).
fof(f150,axiom,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause150) ).
fof(f1261,plain,
spl0_160,
inference(avatar_split_clause,[],[f133,f1259]) ).
fof(f133,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause133) ).
fof(f1237,plain,
( ~ spl0_4
| ~ spl0_1
| ~ spl0_5
| spl0_159
| ~ spl0_8
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1029,f991,f271,f1234,f256,f236,f251]) ).
fof(f1234,plain,
( spl0_159
<=> rearsegP(sk4,sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f991,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1029,plain,
( rearsegP(sk4,sk5)
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ spl0_8
| ~ spl0_139 ),
inference(superposition,[],[f992,f273]) ).
fof(f992,plain,
( ! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f991]) ).
fof(f1222,plain,
spl0_158,
inference(avatar_split_clause,[],[f156,f1220]) ).
fof(f1220,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f156,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause156) ).
fof(f1218,plain,
spl0_157,
inference(avatar_split_clause,[],[f155,f1216]) ).
fof(f1216,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| lt(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| lt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause155) ).
fof(f1214,plain,
spl0_156,
inference(avatar_split_clause,[],[f154,f1212]) ).
fof(f1212,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| frontsegP(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f154,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| frontsegP(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause154) ).
fof(f1210,plain,
spl0_155,
inference(avatar_split_clause,[],[f153,f1208]) ).
fof(f1208,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f153,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause153) ).
fof(f1195,plain,
spl0_154,
inference(avatar_split_clause,[],[f152,f1193]) ).
fof(f1193,plain,
( spl0_154
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f152,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause152) ).
fof(f1191,plain,
spl0_153,
inference(avatar_split_clause,[],[f148,f1189]) ).
fof(f1189,plain,
( spl0_153
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| geq(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f148,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| geq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause148) ).
fof(f1187,plain,
spl0_152,
inference(avatar_split_clause,[],[f147,f1185]) ).
fof(f1185,plain,
( spl0_152
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| lt(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f147,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| lt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause147) ).
fof(f1183,plain,
spl0_151,
inference(avatar_split_clause,[],[f146,f1181]) ).
fof(f1181,plain,
( spl0_151
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f146,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause146) ).
fof(f1179,plain,
spl0_150,
inference(avatar_split_clause,[],[f135,f1177]) ).
fof(f1177,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f135,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause135) ).
fof(f1175,plain,
spl0_149,
inference(avatar_split_clause,[],[f134,f1173]) ).
fof(f1173,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f134,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause134) ).
fof(f1084,plain,
spl0_148,
inference(avatar_split_clause,[],[f141,f1082]) ).
fof(f141,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause141) ).
fof(f1080,plain,
spl0_147,
inference(avatar_split_clause,[],[f140,f1078]) ).
fof(f140,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause140) ).
fof(f1076,plain,
spl0_146,
inference(avatar_split_clause,[],[f139,f1074]) ).
fof(f1074,plain,
( spl0_146
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause139) ).
fof(f1072,plain,
spl0_145,
inference(avatar_split_clause,[],[f137,f1070]) ).
fof(f137,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause137) ).
fof(f1068,plain,
spl0_144,
inference(avatar_split_clause,[],[f136,f1066]) ).
fof(f136,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause136) ).
fof(f1064,plain,
spl0_143,
inference(avatar_split_clause,[],[f132,f1062]) ).
fof(f1062,plain,
( spl0_143
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f132,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause132) ).
fof(f1053,plain,
spl0_142,
inference(avatar_split_clause,[],[f131,f1051]) ).
fof(f1051,plain,
( spl0_142
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f131,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause131) ).
fof(f1049,plain,
spl0_141,
inference(avatar_split_clause,[],[f123,f1047]) ).
fof(f123,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause123) ).
fof(f997,plain,
spl0_140,
inference(avatar_split_clause,[],[f215,f995]) ).
fof(f215,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| frontsegP(X2,X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause144) ).
fof(f993,plain,
spl0_139,
inference(avatar_split_clause,[],[f214,f991]) ).
fof(f214,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ),
inference(equality_resolution,[],[f143]) ).
fof(f143,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X2,X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
fof(f989,plain,
spl0_138,
inference(avatar_split_clause,[],[f130,f987]) ).
fof(f987,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f130,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause130) ).
fof(f985,plain,
spl0_137,
inference(avatar_split_clause,[],[f129,f983]) ).
fof(f983,plain,
( spl0_137
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f129,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause129) ).
fof(f981,plain,
spl0_136,
inference(avatar_split_clause,[],[f128,f979]) ).
fof(f979,plain,
( spl0_136
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f128,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause128) ).
fof(f977,plain,
spl0_135,
inference(avatar_split_clause,[],[f127,f975]) ).
fof(f975,plain,
( spl0_135
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f127,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause127) ).
fof(f973,plain,
spl0_134,
inference(avatar_split_clause,[],[f126,f971]) ).
fof(f971,plain,
( spl0_134
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f126,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause126) ).
fof(f966,plain,
spl0_133,
inference(avatar_split_clause,[],[f125,f964]) ).
fof(f964,plain,
( spl0_133
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause125) ).
fof(f962,plain,
spl0_132,
inference(avatar_split_clause,[],[f124,f960]) ).
fof(f960,plain,
( spl0_132
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f124,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause124) ).
fof(f958,plain,
spl0_131,
inference(avatar_split_clause,[],[f122,f956]) ).
fof(f956,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f122,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause122) ).
fof(f954,plain,
spl0_130,
inference(avatar_split_clause,[],[f120,f952]) ).
fof(f952,plain,
( spl0_130
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f120,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f876,plain,
spl0_129,
inference(avatar_split_clause,[],[f119,f874]) ).
fof(f874,plain,
( spl0_129
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f119,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
fof(f872,plain,
spl0_128,
inference(avatar_split_clause,[],[f118,f870]) ).
fof(f118,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
fof(f867,plain,
spl0_127,
inference(avatar_split_clause,[],[f109,f865]) ).
fof(f109,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause109) ).
fof(f863,plain,
spl0_126,
inference(avatar_split_clause,[],[f104,f861]) ).
fof(f104,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
fof(f851,plain,
( spl0_125
| ~ spl0_1
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f668,f604,f236,f848]) ).
fof(f604,plain,
( spl0_88
<=> ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f668,plain,
( sk5 = app(nil,sk5)
| ~ spl0_1
| ~ spl0_88 ),
inference(resolution,[],[f605,f238]) ).
fof(f605,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f836,plain,
spl0_124,
inference(avatar_split_clause,[],[f209,f834]) ).
fof(f834,plain,
( spl0_124
<=> ! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f209,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ),
inference(equality_resolution,[],[f116]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause116) ).
fof(f832,plain,
spl0_123,
inference(avatar_split_clause,[],[f114,f830]) ).
fof(f830,plain,
( spl0_123
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f114,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause114) ).
fof(f828,plain,
spl0_122,
inference(avatar_split_clause,[],[f110,f826]) ).
fof(f826,plain,
( spl0_122
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f110,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause110) ).
fof(f824,plain,
spl0_121,
inference(avatar_split_clause,[],[f108,f822]) ).
fof(f822,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f108,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause108) ).
fof(f820,plain,
spl0_120,
inference(avatar_split_clause,[],[f107,f818]) ).
fof(f818,plain,
( spl0_120
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f107,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause107) ).
fof(f816,plain,
( spl0_119
| ~ spl0_5
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f667,f604,f256,f813]) ).
fof(f813,plain,
( spl0_119
<=> sk4 = app(nil,sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f667,plain,
( sk4 = app(nil,sk4)
| ~ spl0_5
| ~ spl0_88 ),
inference(resolution,[],[f605,f258]) ).
fof(f811,plain,
spl0_118,
inference(avatar_split_clause,[],[f106,f809]) ).
fof(f809,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f106,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause106) ).
fof(f807,plain,
spl0_117,
inference(avatar_split_clause,[],[f105,f805]) ).
fof(f805,plain,
( spl0_117
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause105) ).
fof(f803,plain,
spl0_116,
inference(avatar_split_clause,[],[f103,f801]) ).
fof(f801,plain,
( spl0_116
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f103,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
fof(f799,plain,
spl0_115,
inference(avatar_split_clause,[],[f102,f797]) ).
fof(f797,plain,
( spl0_115
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f102,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause102) ).
fof(f795,plain,
spl0_114,
inference(avatar_split_clause,[],[f101,f793]) ).
fof(f793,plain,
( spl0_114
<=> ! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f101,axiom,
! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause101) ).
fof(f791,plain,
spl0_113,
inference(avatar_split_clause,[],[f100,f789]) ).
fof(f789,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f100,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f787,plain,
spl0_112,
inference(avatar_split_clause,[],[f97,f785]) ).
fof(f785,plain,
( spl0_112
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause97) ).
fof(f783,plain,
spl0_111,
inference(avatar_split_clause,[],[f96,f781]) ).
fof(f781,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f96,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause96) ).
fof(f779,plain,
( spl0_110
| ~ spl0_4
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f666,f604,f251,f776]) ).
fof(f776,plain,
( spl0_110
<=> sk3 = app(nil,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f666,plain,
( sk3 = app(nil,sk3)
| ~ spl0_4
| ~ spl0_88 ),
inference(resolution,[],[f605,f253]) ).
fof(f774,plain,
( spl0_109
| ~ spl0_1
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f637,f600,f236,f771]) ).
fof(f771,plain,
( spl0_109
<=> sk5 = app(sk5,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f600,plain,
( spl0_87
<=> ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f637,plain,
( sk5 = app(sk5,nil)
| ~ spl0_1
| ~ spl0_87 ),
inference(resolution,[],[f601,f238]) ).
fof(f601,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f769,plain,
spl0_108,
inference(avatar_split_clause,[],[f230,f767]) ).
fof(f767,plain,
( spl0_108
<=> ! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f230,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(duplicate_literal_removal,[],[f213]) ).
fof(f213,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause138) ).
fof(f765,plain,
spl0_107,
inference(avatar_split_clause,[],[f99,f763]) ).
fof(f763,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f99,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
fof(f761,plain,
spl0_106,
inference(avatar_split_clause,[],[f98,f759]) ).
fof(f759,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause98) ).
fof(f757,plain,
spl0_105,
inference(avatar_split_clause,[],[f95,f755]) ).
fof(f755,plain,
( spl0_105
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f95,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause95) ).
fof(f753,plain,
spl0_104,
inference(avatar_split_clause,[],[f94,f751]) ).
fof(f751,plain,
( spl0_104
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f94,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause94) ).
fof(f749,plain,
spl0_103,
inference(avatar_split_clause,[],[f93,f747]) ).
fof(f747,plain,
( spl0_103
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f93,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause93) ).
fof(f745,plain,
spl0_102,
inference(avatar_split_clause,[],[f92,f743]) ).
fof(f743,plain,
( spl0_102
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f92,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause92) ).
fof(f741,plain,
spl0_101,
inference(avatar_split_clause,[],[f91,f739]) ).
fof(f739,plain,
( spl0_101
<=> ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f91,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause91) ).
fof(f737,plain,
spl0_100,
inference(avatar_split_clause,[],[f90,f735]) ).
fof(f735,plain,
( spl0_100
<=> ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f90,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause90) ).
fof(f733,plain,
spl0_99,
inference(avatar_split_clause,[],[f89,f731]) ).
fof(f731,plain,
( spl0_99
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f89,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause89) ).
fof(f729,plain,
( spl0_98
| ~ spl0_5
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f636,f600,f256,f726]) ).
fof(f726,plain,
( spl0_98
<=> sk4 = app(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f636,plain,
( sk4 = app(sk4,nil)
| ~ spl0_5
| ~ spl0_87 ),
inference(resolution,[],[f601,f258]) ).
fof(f724,plain,
spl0_97,
inference(avatar_split_clause,[],[f88,f722]) ).
fof(f722,plain,
( spl0_97
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f88,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause88) ).
fof(f720,plain,
spl0_96,
inference(avatar_split_clause,[],[f87,f718]) ).
fof(f718,plain,
( spl0_96
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f87,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause87) ).
fof(f697,plain,
spl0_95,
inference(avatar_split_clause,[],[f86,f695]) ).
fof(f695,plain,
( spl0_95
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f86,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f693,plain,
spl0_94,
inference(avatar_split_clause,[],[f85,f691]) ).
fof(f691,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f689,plain,
( spl0_93
| ~ spl0_4
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f635,f600,f251,f686]) ).
fof(f635,plain,
( sk3 = app(sk3,nil)
| ~ spl0_4
| ~ spl0_87 ),
inference(resolution,[],[f601,f253]) ).
fof(f684,plain,
spl0_92,
inference(avatar_split_clause,[],[f84,f682]) ).
fof(f682,plain,
( spl0_92
<=> ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f84,axiom,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause84) ).
fof(f680,plain,
spl0_91,
inference(avatar_split_clause,[],[f82,f678]) ).
fof(f678,plain,
( spl0_91
<=> ! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f82,axiom,
! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause82) ).
fof(f676,plain,
spl0_90,
inference(avatar_split_clause,[],[f80,f674]) ).
fof(f674,plain,
( spl0_90
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f80,axiom,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause80) ).
fof(f672,plain,
spl0_89,
inference(avatar_split_clause,[],[f77,f670]) ).
fof(f670,plain,
( spl0_89
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f77,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause77) ).
fof(f606,plain,
spl0_88,
inference(avatar_split_clause,[],[f74,f604]) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f602,plain,
spl0_87,
inference(avatar_split_clause,[],[f73,f600]) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f598,plain,
( spl0_85
| spl0_86 ),
inference(avatar_split_clause,[],[f72,f596,f593]) ).
fof(f593,plain,
( spl0_85
<=> ! [X1] : ssItem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f596,plain,
( spl0_86
<=> ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| ssItem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause72) ).
fof(f591,plain,
spl0_84,
inference(avatar_split_clause,[],[f70,f589]) ).
fof(f589,plain,
( spl0_84
<=> ! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f70,axiom,
! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
fof(f587,plain,
spl0_83,
inference(avatar_split_clause,[],[f69,f585]) ).
fof(f585,plain,
( spl0_83
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f69,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
fof(f583,plain,
spl0_82,
inference(avatar_split_clause,[],[f68,f581]) ).
fof(f581,plain,
( spl0_82
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f68,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
fof(f579,plain,
spl0_81,
inference(avatar_split_clause,[],[f67,f577]) ).
fof(f577,plain,
( spl0_81
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f67,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
fof(f575,plain,
spl0_80,
inference(avatar_split_clause,[],[f66,f573]) ).
fof(f573,plain,
( spl0_80
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f66,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
fof(f571,plain,
spl0_79,
inference(avatar_split_clause,[],[f65,f569]) ).
fof(f569,plain,
( spl0_79
<=> ! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f65,axiom,
! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
fof(f567,plain,
spl0_78,
inference(avatar_split_clause,[],[f64,f565]) ).
fof(f565,plain,
( spl0_78
<=> ! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f64,axiom,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
fof(f563,plain,
spl0_77,
inference(avatar_split_clause,[],[f233,f561]) ).
fof(f561,plain,
( spl0_77
<=> ! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f233,plain,
! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f207,plain,
! [X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause117) ).
fof(f559,plain,
spl0_76,
inference(avatar_split_clause,[],[f231,f557]) ).
fof(f557,plain,
( spl0_76
<=> ! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f231,plain,
! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f212]) ).
fof(f212,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f115]) ).
fof(f115,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f555,plain,
spl0_75,
inference(avatar_split_clause,[],[f71,f553]) ).
fof(f553,plain,
( spl0_75
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
fof(f551,plain,
spl0_74,
inference(avatar_split_clause,[],[f63,f549]) ).
fof(f549,plain,
( spl0_74
<=> ! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f63,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
fof(f547,plain,
spl0_73,
inference(avatar_split_clause,[],[f62,f545]) ).
fof(f545,plain,
( spl0_73
<=> ! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f62,axiom,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
fof(f543,plain,
spl0_72,
inference(avatar_split_clause,[],[f61,f541]) ).
fof(f541,plain,
( spl0_72
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f61,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause61) ).
fof(f539,plain,
spl0_71,
inference(avatar_split_clause,[],[f60,f537]) ).
fof(f537,plain,
( spl0_71
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f60,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
fof(f535,plain,
spl0_70,
inference(avatar_split_clause,[],[f59,f533]) ).
fof(f533,plain,
( spl0_70
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f59,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
fof(f531,plain,
spl0_69,
inference(avatar_split_clause,[],[f58,f529]) ).
fof(f529,plain,
( spl0_69
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f58,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
fof(f527,plain,
spl0_68,
inference(avatar_split_clause,[],[f57,f525]) ).
fof(f525,plain,
( spl0_68
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f57,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
fof(f523,plain,
spl0_67,
inference(avatar_split_clause,[],[f56,f521]) ).
fof(f521,plain,
( spl0_67
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f56,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
fof(f519,plain,
spl0_66,
inference(avatar_split_clause,[],[f55,f517]) ).
fof(f517,plain,
( spl0_66
<=> ! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f55,axiom,
! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
fof(f515,plain,
spl0_65,
inference(avatar_split_clause,[],[f195,f513]) ).
fof(f513,plain,
( spl0_65
<=> ! [X6,X8,X7] :
( ~ ssItem(X6)
| ~ ssList(X8)
| ~ ssList(X7)
| sk5 != app(cons(X6,nil),X7)
| sk3 != app(X8,cons(X6,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f195,axiom,
! [X8,X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X8)
| ~ ssList(X7)
| sk5 != app(cons(X6,nil),X7)
| sk3 != app(X8,cons(X6,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f511,plain,
spl0_64,
inference(avatar_split_clause,[],[f53,f509]) ).
fof(f509,plain,
( spl0_64
<=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f53,axiom,
! [X0,X1] : ssList(skaf42(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
fof(f507,plain,
spl0_63,
inference(avatar_split_clause,[],[f52,f505]) ).
fof(f505,plain,
( spl0_63
<=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f52,axiom,
! [X0,X1] : ssList(skaf43(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
fof(f503,plain,
spl0_62,
inference(avatar_split_clause,[],[f51,f501]) ).
fof(f501,plain,
( spl0_62
<=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
fof(f499,plain,
spl0_61,
inference(avatar_split_clause,[],[f50,f497]) ).
fof(f497,plain,
( spl0_61
<=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
fof(f495,plain,
spl0_60,
inference(avatar_split_clause,[],[f49,f493]) ).
fof(f493,plain,
( spl0_60
<=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f49,axiom,
! [X0,X1] : ssList(skaf47(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
fof(f491,plain,
spl0_59,
inference(avatar_split_clause,[],[f48,f489]) ).
fof(f489,plain,
( spl0_59
<=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f48,axiom,
! [X0,X1] : ssList(skaf48(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
fof(f487,plain,
~ spl0_58,
inference(avatar_split_clause,[],[f54,f484]) ).
fof(f484,plain,
( spl0_58
<=> skac3 = skac2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f54,axiom,
skac3 != skac2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
fof(f482,plain,
spl0_57,
inference(avatar_split_clause,[],[f47,f480]) ).
fof(f480,plain,
( spl0_57
<=> ! [X0] : ssItem(skaf44(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
fof(f478,plain,
spl0_56,
inference(avatar_split_clause,[],[f46,f476]) ).
fof(f476,plain,
( spl0_56
<=> ! [X0] : ssItem(skaf49(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f46,axiom,
! [X0] : ssItem(skaf49(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
fof(f474,plain,
spl0_55,
inference(avatar_split_clause,[],[f45,f472]) ).
fof(f472,plain,
( spl0_55
<=> ! [X0] : ssItem(skaf50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f45,axiom,
! [X0] : ssItem(skaf50(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
fof(f470,plain,
spl0_54,
inference(avatar_split_clause,[],[f44,f468]) ).
fof(f468,plain,
( spl0_54
<=> ! [X0] : ssList(skaf51(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f44,axiom,
! [X0] : ssList(skaf51(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
fof(f466,plain,
spl0_53,
inference(avatar_split_clause,[],[f43,f464]) ).
fof(f464,plain,
( spl0_53
<=> ! [X0] : ssList(skaf52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f43,axiom,
! [X0] : ssList(skaf52(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
fof(f462,plain,
spl0_52,
inference(avatar_split_clause,[],[f42,f460]) ).
fof(f460,plain,
( spl0_52
<=> ! [X0] : ssList(skaf53(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f42,axiom,
! [X0] : ssList(skaf53(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
fof(f458,plain,
spl0_51,
inference(avatar_split_clause,[],[f41,f456]) ).
fof(f456,plain,
( spl0_51
<=> ! [X0] : ssItem(skaf54(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f41,axiom,
! [X0] : ssItem(skaf54(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
fof(f454,plain,
spl0_50,
inference(avatar_split_clause,[],[f40,f452]) ).
fof(f452,plain,
( spl0_50
<=> ! [X0] : ssItem(skaf55(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f40,axiom,
! [X0] : ssItem(skaf55(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
fof(f450,plain,
spl0_49,
inference(avatar_split_clause,[],[f39,f448]) ).
fof(f448,plain,
( spl0_49
<=> ! [X0] : ssList(skaf56(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f39,axiom,
! [X0] : ssList(skaf56(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
fof(f446,plain,
spl0_48,
inference(avatar_split_clause,[],[f38,f444]) ).
fof(f444,plain,
( spl0_48
<=> ! [X0] : ssList(skaf57(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f38,axiom,
! [X0] : ssList(skaf57(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
fof(f442,plain,
spl0_47,
inference(avatar_split_clause,[],[f37,f440]) ).
fof(f440,plain,
( spl0_47
<=> ! [X0] : ssList(skaf58(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f37,axiom,
! [X0] : ssList(skaf58(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
fof(f438,plain,
spl0_46,
inference(avatar_split_clause,[],[f36,f436]) ).
fof(f436,plain,
( spl0_46
<=> ! [X0] : ssItem(skaf59(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f36,axiom,
! [X0] : ssItem(skaf59(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
fof(f434,plain,
spl0_45,
inference(avatar_split_clause,[],[f35,f432]) ).
fof(f432,plain,
( spl0_45
<=> ! [X0] : ssItem(skaf60(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f35,axiom,
! [X0] : ssItem(skaf60(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
fof(f430,plain,
spl0_44,
inference(avatar_split_clause,[],[f34,f428]) ).
fof(f428,plain,
( spl0_44
<=> ! [X0] : ssList(skaf61(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f34,axiom,
! [X0] : ssList(skaf61(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
fof(f426,plain,
spl0_43,
inference(avatar_split_clause,[],[f33,f424]) ).
fof(f424,plain,
( spl0_43
<=> ! [X0] : ssList(skaf62(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f33,axiom,
! [X0] : ssList(skaf62(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
fof(f422,plain,
spl0_42,
inference(avatar_split_clause,[],[f32,f420]) ).
fof(f420,plain,
( spl0_42
<=> ! [X0] : ssList(skaf63(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f32,axiom,
! [X0] : ssList(skaf63(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
fof(f418,plain,
spl0_41,
inference(avatar_split_clause,[],[f31,f416]) ).
fof(f416,plain,
( spl0_41
<=> ! [X0] : ssItem(skaf64(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f31,axiom,
! [X0] : ssItem(skaf64(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
fof(f414,plain,
spl0_40,
inference(avatar_split_clause,[],[f30,f412]) ).
fof(f412,plain,
( spl0_40
<=> ! [X0] : ssItem(skaf65(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f30,axiom,
! [X0] : ssItem(skaf65(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause30) ).
fof(f410,plain,
spl0_39,
inference(avatar_split_clause,[],[f29,f408]) ).
fof(f408,plain,
( spl0_39
<=> ! [X0] : ssList(skaf66(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f29,axiom,
! [X0] : ssList(skaf66(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause29) ).
fof(f406,plain,
spl0_38,
inference(avatar_split_clause,[],[f28,f404]) ).
fof(f404,plain,
( spl0_38
<=> ! [X0] : ssList(skaf67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f28,axiom,
! [X0] : ssList(skaf67(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause28) ).
fof(f402,plain,
spl0_37,
inference(avatar_split_clause,[],[f27,f400]) ).
fof(f400,plain,
( spl0_37
<=> ! [X0] : ssList(skaf68(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f27,axiom,
! [X0] : ssList(skaf68(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause27) ).
fof(f398,plain,
spl0_36,
inference(avatar_split_clause,[],[f26,f396]) ).
fof(f396,plain,
( spl0_36
<=> ! [X0] : ssItem(skaf69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f26,axiom,
! [X0] : ssItem(skaf69(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause26) ).
fof(f394,plain,
spl0_35,
inference(avatar_split_clause,[],[f25,f392]) ).
fof(f392,plain,
( spl0_35
<=> ! [X0] : ssItem(skaf70(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f25,axiom,
! [X0] : ssItem(skaf70(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause25) ).
fof(f390,plain,
spl0_34,
inference(avatar_split_clause,[],[f24,f388]) ).
fof(f388,plain,
( spl0_34
<=> ! [X0] : ssList(skaf71(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f24,axiom,
! [X0] : ssList(skaf71(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause24) ).
fof(f386,plain,
spl0_33,
inference(avatar_split_clause,[],[f23,f384]) ).
fof(f384,plain,
( spl0_33
<=> ! [X0] : ssList(skaf72(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f23,axiom,
! [X0] : ssList(skaf72(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause23) ).
fof(f382,plain,
spl0_32,
inference(avatar_split_clause,[],[f22,f380]) ).
fof(f380,plain,
( spl0_32
<=> ! [X0] : ssList(skaf73(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f22,axiom,
! [X0] : ssList(skaf73(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause22) ).
fof(f378,plain,
spl0_31,
inference(avatar_split_clause,[],[f21,f376]) ).
fof(f376,plain,
( spl0_31
<=> ! [X0] : ssItem(skaf74(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f21,axiom,
! [X0] : ssItem(skaf74(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause21) ).
fof(f374,plain,
spl0_30,
inference(avatar_split_clause,[],[f20,f372]) ).
fof(f372,plain,
( spl0_30
<=> ! [X0] : ssList(skaf75(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f20,axiom,
! [X0] : ssList(skaf75(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
fof(f370,plain,
spl0_29,
inference(avatar_split_clause,[],[f19,f368]) ).
fof(f368,plain,
( spl0_29
<=> ! [X0] : ssList(skaf76(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f19,axiom,
! [X0] : ssList(skaf76(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
fof(f366,plain,
spl0_28,
inference(avatar_split_clause,[],[f18,f364]) ).
fof(f364,plain,
( spl0_28
<=> ! [X0] : ssList(skaf77(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f18,axiom,
! [X0] : ssList(skaf77(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause18) ).
fof(f362,plain,
spl0_27,
inference(avatar_split_clause,[],[f17,f360]) ).
fof(f360,plain,
( spl0_27
<=> ! [X0] : ssItem(skaf78(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f17,axiom,
! [X0] : ssItem(skaf78(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
fof(f358,plain,
spl0_26,
inference(avatar_split_clause,[],[f16,f356]) ).
fof(f356,plain,
( spl0_26
<=> ! [X0] : ssItem(skaf79(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f16,axiom,
! [X0] : ssItem(skaf79(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause16) ).
fof(f354,plain,
spl0_25,
inference(avatar_split_clause,[],[f15,f352]) ).
fof(f352,plain,
( spl0_25
<=> ! [X0] : ssList(skaf80(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f15,axiom,
! [X0] : ssList(skaf80(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause15) ).
fof(f350,plain,
spl0_24,
inference(avatar_split_clause,[],[f14,f348]) ).
fof(f348,plain,
( spl0_24
<=> ! [X0] : ssList(skaf81(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f14,axiom,
! [X0] : ssList(skaf81(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause14) ).
fof(f346,plain,
spl0_23,
inference(avatar_split_clause,[],[f13,f344]) ).
fof(f344,plain,
( spl0_23
<=> ! [X0] : ssList(skaf82(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
fof(f342,plain,
spl0_22,
inference(avatar_split_clause,[],[f12,f340]) ).
fof(f340,plain,
( spl0_22
<=> ! [X0] : ssItem(skaf83(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
fof(f338,plain,
~ spl0_21,
inference(avatar_split_clause,[],[f11,f335]) ).
fof(f335,plain,
( spl0_21
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
fof(f333,plain,
spl0_20,
inference(avatar_split_clause,[],[f10,f330]) ).
fof(f330,plain,
( spl0_20
<=> ssItem(skac2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
fof(f328,plain,
spl0_19,
inference(avatar_split_clause,[],[f9,f325]) ).
fof(f325,plain,
( spl0_19
<=> ssItem(skac3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause9) ).
fof(f323,plain,
spl0_18,
inference(avatar_split_clause,[],[f8,f320]) ).
fof(f320,plain,
( spl0_18
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f318,plain,
spl0_17,
inference(avatar_split_clause,[],[f7,f315]) ).
fof(f315,plain,
( spl0_17
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f7,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
fof(f313,plain,
spl0_16,
inference(avatar_split_clause,[],[f6,f310]) ).
fof(f310,plain,
( spl0_16
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f6,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
fof(f308,plain,
spl0_15,
inference(avatar_split_clause,[],[f5,f305]) ).
fof(f305,plain,
( spl0_15
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f5,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
fof(f303,plain,
spl0_14,
inference(avatar_split_clause,[],[f4,f300]) ).
fof(f300,plain,
( spl0_14
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
fof(f298,plain,
spl0_13,
inference(avatar_split_clause,[],[f3,f295]) ).
fof(f295,plain,
( spl0_13
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
fof(f293,plain,
spl0_12,
inference(avatar_split_clause,[],[f2,f290]) ).
fof(f2,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
fof(f288,plain,
spl0_11,
inference(avatar_split_clause,[],[f1,f285]) ).
fof(f1,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
fof(f283,plain,
( spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f234,f280,f276]) ).
fof(f234,plain,
( nil != sk3
| sk3 = sk4 ),
inference(inner_rewriting,[],[f199]) ).
fof(f199,axiom,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f274,plain,
spl0_8,
inference(avatar_split_clause,[],[f193,f271]) ).
fof(f193,axiom,
sk4 = app(sk3,sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f269,plain,
spl0_7,
inference(avatar_split_clause,[],[f203,f266]) ).
fof(f203,plain,
memberP(sk3,sk6),
inference(definition_unfolding,[],[f197,f191]) ).
fof(f191,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f197,axiom,
memberP(sk1,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f264,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f202,f261]) ).
fof(f202,plain,
~ memberP(sk4,sk6),
inference(definition_unfolding,[],[f198,f190]) ).
fof(f190,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f198,axiom,
~ memberP(sk2,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f259,plain,
spl0_5,
inference(avatar_split_clause,[],[f201,f256]) ).
fof(f201,plain,
ssList(sk4),
inference(definition_unfolding,[],[f187,f190]) ).
fof(f187,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
fof(f254,plain,
spl0_4,
inference(avatar_split_clause,[],[f200,f251]) ).
fof(f200,plain,
ssList(sk3),
inference(definition_unfolding,[],[f186,f191]) ).
fof(f186,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
fof(f249,plain,
spl0_3,
inference(avatar_split_clause,[],[f196,f246]) ).
fof(f196,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f244,plain,
spl0_2,
inference(avatar_split_clause,[],[f194,f241]) ).
fof(f194,axiom,
equalelemsP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f239,plain,
spl0_1,
inference(avatar_split_clause,[],[f192,f236]) ).
fof(f192,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC398-1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 20:33:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (28935)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (28939)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (28938)WARNING: value z3 for option sas not known
% 0.21/0.38 % (28936)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (28937)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (28938)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)
% 0.21/0.38 % (28940)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)
% 0.21/0.38 % (28941)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)
% 0.21/0.38 % (28942)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)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [3]
% 0.21/0.42 TRYING [4]
% 0.21/0.43 TRYING [1]
% 0.21/0.44 TRYING [2]
% 0.21/0.47 TRYING [1]
% 0.21/0.47 TRYING [2]
% 0.21/0.48 % (28940)First to succeed.
% 0.21/0.48 TRYING [3]
% 0.21/0.49 % (28940)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28935"
% 0.21/0.49 % (28938)Also succeeded, but the first one will report.
% 0.21/0.49 % (28940)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49 % (28940)------------------------------
% 0.21/0.49 % (28940)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.49 % (28940)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (28940)Memory used [KB]: 2858
% 0.21/0.49 % (28940)Time elapsed: 0.110 s
% 0.21/0.49 % (28940)Instructions burned: 178 (million)
% 0.21/0.49 % (28935)Success in time 0.133 s
%------------------------------------------------------------------------------