TSTP Solution File: SWC012-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC012-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:39:55 EDT 2024
% Result : Unsatisfiable 0.25s 0.50s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 412
% Syntax : Number of formulae : 744 ( 237 unt; 0 def)
% Number of atoms : 2233 ( 281 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2685 (1196 ~;1259 |; 0 &)
% ( 230 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 251 ( 249 usr; 231 prp; 0-2 aty)
% Number of functors : 54 ( 54 usr; 8 con; 0-2 aty)
% Number of variables : 749 ( 749 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2637,plain,
$false,
inference(avatar_sat_refutation,[],[f243,f248,f253,f258,f263,f268,f273,f278,f283,f288,f293,f298,f303,f308,f313,f318,f322,f326,f330,f334,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,f467,f471,f475,f479,f483,f487,f491,f495,f499,f503,f507,f511,f515,f519,f523,f527,f531,f535,f539,f543,f548,f552,f556,f560,f564,f568,f572,f576,f583,f618,f622,f626,f691,f695,f699,f703,f707,f711,f715,f738,f742,f746,f750,f754,f758,f762,f766,f770,f774,f778,f782,f787,f791,f795,f799,f804,f808,f812,f816,f820,f824,f828,f832,f836,f840,f844,f849,f870,f876,f880,f884,f888,f965,f969,f973,f977,f981,f985,f989,f993,f997,f1004,f1008,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1095,f1174,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1211,f1215,f1219,f1253,f1267,f1271,f1275,f1341,f1345,f1349,f1358,f1362,f1366,f1370,f1374,f1454,f1463,f1467,f1471,f1475,f1479,f1483,f1487,f1535,f1539,f1560,f1569,f1573,f1577,f1581,f1585,f1589,f1791,f1797,f1804,f1812,f1816,f1857,f1861,f1865,f1888,f1925,f1965,f2006,f2012,f2022,f2071,f2075,f2079,f2125,f2129,f2133,f2137,f2142,f2190,f2231,f2344,f2357,f2396,f2435,f2474,f2509,f2514,f2519,f2558,f2563,f2621,f2626,f2635,f2636]) ).
fof(f2636,plain,
( ~ spl0_12
| ~ spl0_73
| ~ spl0_105
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f2017,f801,f784,f546,f295]) ).
fof(f295,plain,
( spl0_12
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f546,plain,
( spl0_73
<=> ! [X0] :
( sk4 != app(sk4,X0)
| sk3 != app(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f784,plain,
( spl0_105
<=> sk3 = app(sk3,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f801,plain,
( spl0_109
<=> sk4 = app(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f2017,plain,
( ~ ssList(nil)
| ~ spl0_73
| ~ spl0_105
| ~ spl0_109 ),
inference(trivial_inequality_removal,[],[f2016]) ).
fof(f2016,plain,
( sk3 != sk3
| ~ ssList(nil)
| ~ spl0_73
| ~ spl0_105
| ~ spl0_109 ),
inference(forward_demodulation,[],[f2015,f786]) ).
fof(f786,plain,
( sk3 = app(sk3,nil)
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f2015,plain,
( sk3 != app(sk3,nil)
| ~ ssList(nil)
| ~ spl0_73
| ~ spl0_109 ),
inference(trivial_inequality_removal,[],[f2014]) ).
fof(f2014,plain,
( sk4 != sk4
| sk3 != app(sk3,nil)
| ~ ssList(nil)
| ~ spl0_73
| ~ spl0_109 ),
inference(superposition,[],[f547,f803]) ).
fof(f803,plain,
( sk4 = app(sk4,nil)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f547,plain,
( ! [X0] :
( sk4 != app(sk4,X0)
| sk3 != app(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f2635,plain,
( spl0_229
| spl0_230
| ~ spl0_1
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1655,f1571,f240,f2632,f2628]) ).
fof(f2628,plain,
( spl0_229
<=> sk4 = app(app(skaf71(sk4),cons(skaf69(sk4),skaf72(sk4))),cons(skaf70(sk4),skaf73(sk4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2632,plain,
( spl0_230
<=> strictorderedP(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f240,plain,
( spl0_1
<=> ssList(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1571,plain,
( spl0_182
<=> ! [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_182])]) ).
fof(f1655,plain,
( strictorderedP(sk4)
| sk4 = app(app(skaf71(sk4),cons(skaf69(sk4),skaf72(sk4))),cons(skaf70(sk4),skaf73(sk4)))
| ~ spl0_1
| ~ spl0_182 ),
inference(resolution,[],[f1572,f242]) ).
fof(f242,plain,
( ssList(sk4)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f1572,plain,
( ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1571]) ).
fof(f2626,plain,
( spl0_228
| spl0_86
| ~ spl0_1
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1622,f1558,f240,f688,f2623]) ).
fof(f2623,plain,
( spl0_228
<=> sk4 = app(app(skaf75(sk4),cons(skaf74(sk4),skaf76(sk4))),cons(skaf74(sk4),skaf77(sk4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f688,plain,
( spl0_86
<=> duplicatefreeP(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1558,plain,
( spl0_179
<=> ! [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_179])]) ).
fof(f1622,plain,
( duplicatefreeP(sk4)
| sk4 = app(app(skaf75(sk4),cons(skaf74(sk4),skaf76(sk4))),cons(skaf74(sk4),skaf77(sk4)))
| ~ spl0_1
| ~ spl0_179 ),
inference(resolution,[],[f1559,f242]) ).
fof(f1559,plain,
( ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| app(app(skaf75(X0),cons(skaf74(X0),skaf76(X0))),cons(skaf74(X0),skaf77(X0))) = X0 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1558]) ).
fof(f2621,plain,
( spl0_227
| spl0_226
| ~ spl0_1
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1407,f1339,f240,f2560,f2618]) ).
fof(f2618,plain,
( spl0_227
<=> sk4 = app(skaf80(sk4),cons(skaf78(sk4),cons(skaf79(sk4),skaf81(sk4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2560,plain,
( spl0_226
<=> equalelemsP(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1339,plain,
( spl0_161
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1407,plain,
( equalelemsP(sk4)
| sk4 = app(skaf80(sk4),cons(skaf78(sk4),cons(skaf79(sk4),skaf81(sk4))))
| ~ spl0_1
| ~ spl0_161 ),
inference(resolution,[],[f1340,f242]) ).
fof(f1340,plain,
( ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f2563,plain,
( spl0_226
| ~ spl0_5
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1967,f1566,f260,f2560]) ).
fof(f260,plain,
( spl0_5
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1566,plain,
( spl0_181
<=> nil = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1967,plain,
( equalelemsP(sk4)
| ~ spl0_5
| ~ spl0_181 ),
inference(superposition,[],[f262,f1568]) ).
fof(f1568,plain,
( nil = sk4
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1566]) ).
fof(f262,plain,
( equalelemsP(nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f2558,plain,
( spl0_181
| spl0_225
| ~ spl0_1
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1308,f1251,f240,f2556,f1566]) ).
fof(f2556,plain,
( spl0_225
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk4,X0)) = app(tl(sk4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1251,plain,
( spl0_157
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1308,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk4
| tl(app(sk4,X0)) = app(tl(sk4),X0) )
| ~ spl0_1
| ~ spl0_157 ),
inference(resolution,[],[f1252,f242]) ).
fof(f1252,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f2519,plain,
( spl0_224
| ~ spl0_181
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2515,f2512,f1566,f2517]) ).
fof(f2517,plain,
( spl0_224
<=> ! [X0] : skaf82(X0) = app(skaf82(X0),sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2512,plain,
( spl0_223
<=> ! [X0] : skaf82(X0) = app(skaf82(X0),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2515,plain,
( ! [X0] : skaf82(X0) = app(skaf82(X0),sk4)
| ~ spl0_181
| ~ spl0_223 ),
inference(forward_demodulation,[],[f2513,f1568]) ).
fof(f2513,plain,
( ! [X0] : skaf82(X0) = app(skaf82(X0),nil)
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2512]) ).
fof(f2514,plain,
( spl0_223
| ~ spl0_18
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f628,f620,f324,f2512]) ).
fof(f324,plain,
( spl0_18
<=> ! [X0] : ssList(skaf82(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f620,plain,
( spl0_84
<=> ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f628,plain,
( ! [X0] : skaf82(X0) = app(skaf82(X0),nil)
| ~ spl0_18
| ~ spl0_84 ),
inference(resolution,[],[f621,f325]) ).
fof(f325,plain,
( ! [X0] : ssList(skaf82(X0))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f621,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f2509,plain,
( spl0_222
| ~ spl0_12
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f627,f620,f295,f2506]) ).
fof(f2506,plain,
( spl0_222
<=> nil = app(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f627,plain,
( nil = app(nil,nil)
| ~ spl0_12
| ~ spl0_84 ),
inference(resolution,[],[f621,f297]) ).
fof(f297,plain,
( ssList(nil)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f2474,plain,
( spl0_220
| spl0_221
| ~ spl0_2
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1786,f1587,f245,f2471,f2467]) ).
fof(f2467,plain,
( spl0_220
<=> sk3 = app(app(skaf51(sk3),cons(skaf49(sk3),skaf52(sk3))),cons(skaf50(sk3),skaf53(sk3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2471,plain,
( spl0_221
<=> cyclefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f245,plain,
( spl0_2
<=> ssList(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1587,plain,
( spl0_186
<=> ! [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_186])]) ).
fof(f1786,plain,
( cyclefreeP(sk3)
| sk3 = app(app(skaf51(sk3),cons(skaf49(sk3),skaf52(sk3))),cons(skaf50(sk3),skaf53(sk3)))
| ~ spl0_2
| ~ spl0_186 ),
inference(resolution,[],[f1588,f247]) ).
fof(f247,plain,
( ssList(sk3)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f1588,plain,
( ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1587]) ).
fof(f2435,plain,
( spl0_218
| spl0_219
| ~ spl0_2
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1753,f1583,f245,f2432,f2428]) ).
fof(f2428,plain,
( spl0_218
<=> sk3 = app(app(skaf56(sk3),cons(skaf54(sk3),skaf57(sk3))),cons(skaf55(sk3),skaf58(sk3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2432,plain,
( spl0_219
<=> totalorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1583,plain,
( spl0_185
<=> ! [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_185])]) ).
fof(f1753,plain,
( totalorderP(sk3)
| sk3 = app(app(skaf56(sk3),cons(skaf54(sk3),skaf57(sk3))),cons(skaf55(sk3),skaf58(sk3)))
| ~ spl0_2
| ~ spl0_185 ),
inference(resolution,[],[f1584,f247]) ).
fof(f1584,plain,
( ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1583]) ).
fof(f2396,plain,
( spl0_216
| spl0_217
| ~ spl0_2
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1720,f1579,f245,f2393,f2389]) ).
fof(f2389,plain,
( spl0_216
<=> sk3 = app(app(skaf61(sk3),cons(skaf59(sk3),skaf62(sk3))),cons(skaf60(sk3),skaf63(sk3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2393,plain,
( spl0_217
<=> strictorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1579,plain,
( spl0_184
<=> ! [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_184])]) ).
fof(f1720,plain,
( strictorderP(sk3)
| sk3 = app(app(skaf61(sk3),cons(skaf59(sk3),skaf62(sk3))),cons(skaf60(sk3),skaf63(sk3)))
| ~ spl0_2
| ~ spl0_184 ),
inference(resolution,[],[f1580,f247]) ).
fof(f1580,plain,
( ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1579]) ).
fof(f2357,plain,
( spl0_214
| spl0_215
| ~ spl0_2
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1687,f1575,f245,f2354,f2350]) ).
fof(f2350,plain,
( spl0_214
<=> sk3 = app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2354,plain,
( spl0_215
<=> totalorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1575,plain,
( spl0_183
<=> ! [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_183])]) ).
fof(f1687,plain,
( totalorderedP(sk3)
| sk3 = app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3)))
| ~ spl0_2
| ~ spl0_183 ),
inference(resolution,[],[f1576,f247]) ).
fof(f1576,plain,
( ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1575]) ).
fof(f2344,plain,
( spl0_213
| spl0_209
| ~ spl0_2
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1654,f1571,f245,f2139,f2341]) ).
fof(f2341,plain,
( spl0_213
<=> sk3 = app(app(skaf71(sk3),cons(skaf69(sk3),skaf72(sk3))),cons(skaf70(sk3),skaf73(sk3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2139,plain,
( spl0_209
<=> strictorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1654,plain,
( strictorderedP(sk3)
| sk3 = app(app(skaf71(sk3),cons(skaf69(sk3),skaf72(sk3))),cons(skaf70(sk3),skaf73(sk3)))
| ~ spl0_2
| ~ spl0_182 ),
inference(resolution,[],[f1572,f247]) ).
fof(f2231,plain,
( spl0_181
| spl0_212
| ~ spl0_1
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1128,f1058,f240,f2229,f1566]) ).
fof(f2229,plain,
( spl0_212
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk4) = hd(app(sk4,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1058,plain,
( spl0_137
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1128,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk4
| hd(sk4) = hd(app(sk4,X0)) )
| ~ spl0_1
| ~ spl0_137 ),
inference(resolution,[],[f1059,f242]) ).
fof(f1059,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| hd(app(X1,X0)) = hd(X1) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f2190,plain,
( spl0_210
| spl0_211
| ~ spl0_2
| ~ spl0_157
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f2145,f1566,f1251,f245,f2187,f2184]) ).
fof(f2184,plain,
( spl0_210
<=> ! [X0] :
( ~ ssList(X0)
| tl(app(sk3,X0)) = app(tl(sk3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f2187,plain,
( spl0_211
<=> sk3 = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2145,plain,
( ! [X0] :
( sk3 = sk4
| ~ ssList(X0)
| tl(app(sk3,X0)) = app(tl(sk3),X0) )
| ~ spl0_2
| ~ spl0_157
| ~ spl0_181 ),
inference(forward_demodulation,[],[f1307,f1568]) ).
fof(f1307,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk3
| tl(app(sk3,X0)) = app(tl(sk3),X0) )
| ~ spl0_2
| ~ spl0_157 ),
inference(resolution,[],[f1252,f247]) ).
fof(f2142,plain,
( spl0_209
| ~ spl0_7
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1892,f1180,f270,f2139]) ).
fof(f270,plain,
( spl0_7
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1180,plain,
( spl0_147
<=> nil = sk3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1892,plain,
( strictorderedP(sk3)
| ~ spl0_7
| ~ spl0_147 ),
inference(superposition,[],[f272,f1182]) ).
fof(f1182,plain,
( nil = sk3
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f272,plain,
( strictorderedP(nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f2137,plain,
( ~ spl0_2
| ~ spl0_198
| spl0_208
| ~ spl0_16
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1321,f1269,f315,f2135,f1999,f245]) ).
fof(f1999,plain,
( spl0_198
<=> ssList(cons(sk5,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2135,plain,
( spl0_208
<=> ! [X0] :
( sk4 != app(X0,cons(sk5,nil))
| sk3 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f315,plain,
( spl0_16
<=> sk4 = app(sk3,cons(sk5,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1269,plain,
( spl0_159
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1321,plain,
( ! [X0] :
( sk4 != app(X0,cons(sk5,nil))
| ~ ssList(X0)
| ~ ssList(cons(sk5,nil))
| sk3 = X0
| ~ ssList(sk3) )
| ~ spl0_16
| ~ spl0_159 ),
inference(superposition,[],[f1270,f317]) ).
fof(f317,plain,
( sk4 = app(sk3,cons(sk5,nil))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f1270,plain,
( ! [X2,X0,X1] :
( app(X0,X1) != app(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| ~ ssList(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1269]) ).
fof(f2133,plain,
( ~ spl0_198
| ~ spl0_2
| spl0_207
| ~ spl0_16
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1309,f1265,f315,f2131,f245,f1999]) ).
fof(f2131,plain,
( spl0_207
<=> ! [X0] :
( sk4 != app(sk3,X0)
| cons(sk5,nil) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1265,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1309,plain,
( ! [X0] :
( sk4 != app(sk3,X0)
| ~ ssList(X0)
| ~ ssList(sk3)
| cons(sk5,nil) = X0
| ~ ssList(cons(sk5,nil)) )
| ~ spl0_16
| ~ spl0_158 ),
inference(superposition,[],[f1266,f317]) ).
fof(f1266,plain,
( ! [X2,X0,X1] :
( app(X0,X1) != app(X0,X2)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| ~ ssList(X1) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1265]) ).
fof(f2129,plain,
( ~ spl0_2
| ~ spl0_198
| spl0_206
| ~ spl0_16
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1166,f1093,f315,f2127,f1999,f245]) ).
fof(f2127,plain,
( spl0_206
<=> ! [X0] :
( memberP(sk4,X0)
| ~ ssItem(X0)
| ~ memberP(cons(sk5,nil),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1093,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1166,plain,
( ! [X0] :
( memberP(sk4,X0)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk3)
| ~ memberP(cons(sk5,nil),X0)
| ~ ssItem(X0) )
| ~ spl0_16
| ~ spl0_144 ),
inference(superposition,[],[f1094,f317]) ).
fof(f1094,plain,
( ! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| ~ ssItem(X1) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f2125,plain,
( ~ spl0_2
| ~ spl0_198
| spl0_205
| ~ spl0_16
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1145,f1070,f315,f2123,f1999,f245]) ).
fof(f2123,plain,
( spl0_205
<=> ! [X0] :
( rearsegP(sk4,X0)
| ~ rearsegP(cons(sk5,nil),X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1070,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1145,plain,
( ! [X0] :
( rearsegP(sk4,X0)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| ~ rearsegP(cons(sk5,nil),X0)
| ~ ssList(sk3) )
| ~ spl0_16
| ~ spl0_140 ),
inference(superposition,[],[f1071,f317]) ).
fof(f1071,plain,
( ! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f2079,plain,
( spl0_204
| ~ spl0_1
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1440,f1343,f240,f2077]) ).
fof(f2077,plain,
( spl0_204
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1343,plain,
( spl0_162
<=> ! [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_162])]) ).
fof(f1440,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk4,X1),X0) = app(sk4,app(X1,X0)) )
| ~ spl0_1
| ~ spl0_162 ),
inference(resolution,[],[f1344,f242]) ).
fof(f1344,plain,
( ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1343]) ).
fof(f2075,plain,
( spl0_203
| ~ spl0_2
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1439,f1343,f245,f2073]) ).
fof(f2073,plain,
( spl0_203
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1439,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(sk3,X1),X0) = app(sk3,app(X1,X0)) )
| ~ spl0_2
| ~ spl0_162 ),
inference(resolution,[],[f1344,f247]) ).
fof(f2071,plain,
( ~ spl0_198
| ~ spl0_2
| spl0_202
| ~ spl0_16
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1154,f1074,f315,f2069,f245,f1999]) ).
fof(f2069,plain,
( spl0_202
<=> ! [X0] :
( frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1074,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1154,plain,
( ! [X0] :
( frontsegP(sk4,X0)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ frontsegP(sk3,X0)
| ~ ssList(cons(sk5,nil)) )
| ~ spl0_16
| ~ spl0_141 ),
inference(superposition,[],[f1075,f317]) ).
fof(f1075,plain,
( ! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1074]) ).
fof(f2022,plain,
( spl0_147
| spl0_201
| ~ spl0_2
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1127,f1058,f245,f2020,f1180]) ).
fof(f2020,plain,
( spl0_201
<=> ! [X0] :
( ~ ssList(X0)
| hd(sk3) = hd(app(sk3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1127,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = sk3
| hd(sk3) = hd(app(sk3,X0)) )
| ~ spl0_2
| ~ spl0_137 ),
inference(resolution,[],[f1059,f247]) ).
fof(f2012,plain,
( ~ spl0_200
| ~ spl0_181
| spl0_198 ),
inference(avatar_split_clause,[],[f2007,f1999,f1566,f2009]) ).
fof(f2009,plain,
( spl0_200
<=> ssList(cons(sk5,sk4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2007,plain,
( ~ ssList(cons(sk5,sk4))
| ~ spl0_181
| spl0_198 ),
inference(forward_demodulation,[],[f2001,f1568]) ).
fof(f2001,plain,
( ~ ssList(cons(sk5,nil))
| spl0_198 ),
inference(avatar_component_clause,[],[f1999]) ).
fof(f2006,plain,
( ~ spl0_198
| ~ spl0_2
| ~ spl0_1
| spl0_199
| ~ spl0_16
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1049,f1006,f315,f2003,f240,f245,f1999]) ).
fof(f2003,plain,
( spl0_199
<=> frontsegP(sk4,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1006,plain,
( spl0_136
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1049,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ~ spl0_16
| ~ spl0_136 ),
inference(superposition,[],[f1007,f317]) ).
fof(f1007,plain,
( ! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1965,plain,
( spl0_197
| spl0_181
| ~ spl0_1
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f954,f878,f240,f1566,f1962]) ).
fof(f1962,plain,
( spl0_197
<=> sk4 = cons(skaf83(sk4),skaf82(sk4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f878,plain,
( spl0_123
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f954,plain,
( nil = sk4
| sk4 = cons(skaf83(sk4),skaf82(sk4))
| ~ spl0_1
| ~ spl0_123 ),
inference(resolution,[],[f879,f242]) ).
fof(f879,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f1925,plain,
( spl0_196
| ~ spl0_5
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1890,f1180,f260,f1922]) ).
fof(f1922,plain,
( spl0_196
<=> equalelemsP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1890,plain,
( equalelemsP(sk3)
| ~ spl0_5
| ~ spl0_147 ),
inference(superposition,[],[f262,f1182]) ).
fof(f1888,plain,
( spl0_195
| spl0_147
| ~ spl0_2
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f953,f878,f245,f1180,f1885]) ).
fof(f1885,plain,
( spl0_195
<=> sk3 = cons(skaf83(sk3),skaf82(sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f953,plain,
( nil = sk3
| sk3 = cons(skaf83(sk3),skaf82(sk3))
| ~ spl0_2
| ~ spl0_123 ),
inference(resolution,[],[f879,f247]) ).
fof(f1865,plain,
spl0_194,
inference(avatar_split_clause,[],[f231,f1863]) ).
fof(f1863,plain,
( spl0_194
<=> ! [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_194])]) ).
fof(f231,plain,
! [X2,X3,X0,X1,X4] :
( ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ totalorderP(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| leq(X1,X3)
| leq(X3,X1)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause184) ).
fof(f1861,plain,
spl0_193,
inference(avatar_split_clause,[],[f230,f1859]) ).
fof(f1859,plain,
( spl0_193
<=> ! [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_193])]) ).
fof(f230,plain,
! [X2,X3,X0,X1,X4] :
( ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ strictorderP(X5)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| lt(X1,X3)
| lt(X3,X1)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause183) ).
fof(f1857,plain,
spl0_192,
inference(avatar_split_clause,[],[f229,f1855]) ).
fof(f1855,plain,
( spl0_192
<=> ! [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_192])]) ).
fof(f229,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclefreeP(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(app(app(X2,cons(X0,X3)),cons(X1,X4)))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0) ),
inference(equality_resolution,[],[f185]) ).
fof(f185,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X5)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ leq(X0,X1)
| ~ leq(X1,X0)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).
fof(f1816,plain,
spl0_191,
inference(avatar_split_clause,[],[f228,f1814]) ).
fof(f1814,plain,
( spl0_191
<=> ! [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_191])]) ).
fof(f228,plain,
! [X2,X3,X0,X1,X4] :
( ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3) ),
inference(equality_resolution,[],[f182]) ).
fof(f182,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ totalorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X5)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| leq(X1,X3)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause182) ).
fof(f1812,plain,
spl0_190,
inference(avatar_split_clause,[],[f227,f1810]) ).
fof(f1810,plain,
( spl0_190
<=> ! [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_190])]) ).
fof(f227,plain,
! [X2,X3,X0,X1,X4] :
( ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3) ),
inference(equality_resolution,[],[f181]) ).
fof(f181,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ strictorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X5)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| lt(X1,X3)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause181) ).
fof(f1804,plain,
spl0_189,
inference(avatar_split_clause,[],[f224,f1802]) ).
fof(f1802,plain,
( spl0_189
<=> ! [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_189])]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_resolution,[],[f179]) ).
fof(f179,axiom,
! [X2,X3,X0,X1,X4] :
( ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).
fof(f1797,plain,
spl0_188,
inference(avatar_split_clause,[],[f226,f1795]) ).
fof(f1795,plain,
( spl0_188
<=> ! [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_188])]) ).
fof(f226,plain,
! [X2,X3,X0,X1] :
( ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,cons(X2,X3))))
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2 ),
inference(equality_resolution,[],[f180]) ).
fof(f180,axiom,
! [X2,X3,X0,X1,X4] :
( ~ equalelemsP(X4)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X0)
| ~ ssList(X3)
| X1 = X2
| app(X0,cons(X1,cons(X2,X3))) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause180) ).
fof(f1791,plain,
spl0_187,
inference(avatar_split_clause,[],[f177,f1789]) ).
fof(f1789,plain,
( spl0_187
<=> ! [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_187])]) ).
fof(f177,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| nil = X0
| nil = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause177) ).
fof(f1589,plain,
spl0_186,
inference(avatar_split_clause,[],[f167,f1587]) ).
fof(f167,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause167) ).
fof(f1585,plain,
spl0_185,
inference(avatar_split_clause,[],[f166,f1583]) ).
fof(f166,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause166) ).
fof(f1581,plain,
spl0_184,
inference(avatar_split_clause,[],[f165,f1579]) ).
fof(f165,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| app(app(skaf61(X0),cons(skaf59(X0),skaf62(X0))),cons(skaf60(X0),skaf63(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause165) ).
fof(f1577,plain,
spl0_183,
inference(avatar_split_clause,[],[f164,f1575]) ).
fof(f164,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause164) ).
fof(f1573,plain,
spl0_182,
inference(avatar_split_clause,[],[f163,f1571]) ).
fof(f163,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause163) ).
fof(f1569,plain,
( spl0_180
| spl0_181
| ~ spl0_1
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f921,f874,f240,f1566,f1562]) ).
fof(f1562,plain,
( spl0_180
<=> sk4 = cons(hd(sk4),tl(sk4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f874,plain,
( spl0_122
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f921,plain,
( nil = sk4
| sk4 = cons(hd(sk4),tl(sk4))
| ~ spl0_1
| ~ spl0_122 ),
inference(resolution,[],[f875,f242]) ).
fof(f875,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f1560,plain,
spl0_179,
inference(avatar_split_clause,[],[f162,f1558]) ).
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/sandbox2/benchmark/theBenchmark.p',clause162) ).
fof(f1539,plain,
spl0_178,
inference(avatar_split_clause,[],[f223,f1537]) ).
fof(f1537,plain,
( spl0_178
<=> ! [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_178])]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(equality_resolution,[],[f173]) ).
fof(f173,axiom,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(X3,X1)
| app(app(X0,X1),X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
fof(f1535,plain,
spl0_177,
inference(avatar_split_clause,[],[f222,f1533]) ).
fof(f1533,plain,
( spl0_177
<=> ! [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_177])]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ),
inference(equality_resolution,[],[f175]) ).
fof(f175,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(X3,X1)
| app(X0,cons(X1,X2)) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause175) ).
fof(f1487,plain,
spl0_176,
inference(avatar_split_clause,[],[f176,f1485]) ).
fof(f1485,plain,
( spl0_176
<=> ! [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_176])]) ).
fof(f176,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause176) ).
fof(f1483,plain,
spl0_175,
inference(avatar_split_clause,[],[f174,f1481]) ).
fof(f1481,plain,
( spl0_175
<=> ! [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_175])]) ).
fof(f174,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| frontsegP(X1,X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause174) ).
fof(f1479,plain,
spl0_174,
inference(avatar_split_clause,[],[f172,f1477]) ).
fof(f1477,plain,
( spl0_174
<=> ! [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_174])]) ).
fof(f172,axiom,
! [X2,X3,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X3,X0),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause172) ).
fof(f1475,plain,
spl0_173,
inference(avatar_split_clause,[],[f171,f1473]) ).
fof(f1473,plain,
( spl0_173
<=> ! [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_173])]) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause171) ).
fof(f1471,plain,
spl0_172,
inference(avatar_split_clause,[],[f170,f1469]) ).
fof(f1469,plain,
( spl0_172
<=> ! [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_172])]) ).
fof(f170,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause170) ).
fof(f1467,plain,
spl0_171,
inference(avatar_split_clause,[],[f169,f1465]) ).
fof(f1465,plain,
( spl0_171
<=> ! [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_171])]) ).
fof(f169,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause169) ).
fof(f1463,plain,
spl0_170,
inference(avatar_split_clause,[],[f168,f1461]) ).
fof(f1461,plain,
( spl0_170
<=> ! [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_170])]) ).
fof(f168,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1)
| app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause168) ).
fof(f1454,plain,
( ~ spl0_81
| spl0_164 ),
inference(avatar_contradiction_clause,[],[f1453]) ).
fof(f1453,plain,
( $false
| ~ spl0_81
| spl0_164 ),
inference(resolution,[],[f1353,f579]) ).
fof(f579,plain,
( ! [X1] : ssItem(X1)
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f578,plain,
( spl0_81
<=> ! [X1] : ssItem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1353,plain,
( ~ ssItem(hd(sk3))
| spl0_164 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f1351,plain,
( spl0_164
<=> ssItem(hd(sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1374,plain,
spl0_169,
inference(avatar_split_clause,[],[f161,f1372]) ).
fof(f1372,plain,
( spl0_169
<=> ! [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_169])]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2)
| ~ memberP(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
fof(f1370,plain,
spl0_168,
inference(avatar_split_clause,[],[f160,f1368]) ).
fof(f1368,plain,
( spl0_168
<=> ! [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_168])]) ).
fof(f160,axiom,
! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).
fof(f1366,plain,
spl0_167,
inference(avatar_split_clause,[],[f159,f1364]) ).
fof(f1364,plain,
( spl0_167
<=> ! [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_167])]) ).
fof(f159,axiom,
! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).
fof(f1362,plain,
spl0_166,
inference(avatar_split_clause,[],[f158,f1360]) ).
fof(f1360,plain,
( spl0_166
<=> ! [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_166])]) ).
fof(f158,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X1,X2)
| memberP(X0,X2)
| ~ memberP(app(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause158) ).
fof(f1358,plain,
( ~ spl0_164
| ~ spl0_2
| ~ spl0_165
| ~ spl0_103
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1263,f1176,f776,f1355,f245,f1351]) ).
fof(f1355,plain,
( spl0_165
<=> sk3 = tl(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f776,plain,
( spl0_103
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1176,plain,
( spl0_146
<=> sk3 = cons(hd(sk3),tl(sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1263,plain,
( sk3 != tl(sk3)
| ~ ssList(sk3)
| ~ ssItem(hd(sk3))
| ~ spl0_103
| ~ spl0_146 ),
inference(inner_rewriting,[],[f1256]) ).
fof(f1256,plain,
( sk3 != tl(sk3)
| ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ~ spl0_103
| ~ spl0_146 ),
inference(superposition,[],[f777,f1178]) ).
fof(f1178,plain,
( sk3 = cons(hd(sk3),tl(sk3))
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f777,plain,
( ! [X0,X1] :
( cons(X0,X1) != X1
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f1349,plain,
spl0_163,
inference(avatar_split_clause,[],[f157,f1347]) ).
fof(f1347,plain,
( spl0_163
<=> ! [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_163])]) ).
fof(f157,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).
fof(f1345,plain,
spl0_162,
inference(avatar_split_clause,[],[f149,f1343]) ).
fof(f149,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause149) ).
fof(f1341,plain,
spl0_161,
inference(avatar_split_clause,[],[f142,f1339]) ).
fof(f142,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
fof(f1275,plain,
spl0_160,
inference(avatar_split_clause,[],[f232,f1273]) ).
fof(f1273,plain,
( spl0_160
<=> ! [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_160])]) ).
fof(f232,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f225,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(equality_resolution,[],[f178]) ).
fof(f178,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| X2 != X3
| ~ frontsegP(X0,X1)
| frontsegP(cons(X2,X0),cons(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause178) ).
fof(f1271,plain,
spl0_159,
inference(avatar_split_clause,[],[f151,f1269]) ).
fof(f151,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
fof(f1267,plain,
spl0_158,
inference(avatar_split_clause,[],[f150,f1265]) ).
fof(f150,axiom,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause150) ).
fof(f1253,plain,
spl0_157,
inference(avatar_split_clause,[],[f133,f1251]) ).
fof(f133,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
fof(f1219,plain,
spl0_156,
inference(avatar_split_clause,[],[f156,f1217]) ).
fof(f1217,plain,
( spl0_156
<=> ! [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_156])]) ).
fof(f156,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).
fof(f1215,plain,
spl0_155,
inference(avatar_split_clause,[],[f155,f1213]) ).
fof(f1213,plain,
( spl0_155
<=> ! [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_155])]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| lt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).
fof(f1211,plain,
spl0_154,
inference(avatar_split_clause,[],[f154,f1209]) ).
fof(f1209,plain,
( spl0_154
<=> ! [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_154])]) ).
fof(f154,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| frontsegP(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause154) ).
fof(f1207,plain,
spl0_153,
inference(avatar_split_clause,[],[f153,f1205]) ).
fof(f1205,plain,
( spl0_153
<=> ! [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_153])]) ).
fof(f153,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| rearsegP(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause153) ).
fof(f1203,plain,
spl0_152,
inference(avatar_split_clause,[],[f152,f1201]) ).
fof(f1201,plain,
( spl0_152
<=> ! [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_152])]) ).
fof(f152,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause152) ).
fof(f1199,plain,
spl0_151,
inference(avatar_split_clause,[],[f148,f1197]) ).
fof(f1197,plain,
( spl0_151
<=> ! [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_151])]) ).
fof(f148,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| geq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause148) ).
fof(f1195,plain,
spl0_150,
inference(avatar_split_clause,[],[f147,f1193]) ).
fof(f1193,plain,
( spl0_150
<=> ! [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_150])]) ).
fof(f147,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| lt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause147) ).
fof(f1191,plain,
spl0_149,
inference(avatar_split_clause,[],[f146,f1189]) ).
fof(f1189,plain,
( spl0_149
<=> ! [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_149])]) ).
fof(f146,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause146) ).
fof(f1187,plain,
spl0_148,
inference(avatar_split_clause,[],[f135,f1185]) ).
fof(f1185,plain,
( spl0_148
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f135,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause135) ).
fof(f1183,plain,
( spl0_146
| spl0_147
| ~ spl0_2
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f920,f874,f245,f1180,f1176]) ).
fof(f920,plain,
( nil = sk3
| sk3 = cons(hd(sk3),tl(sk3))
| ~ spl0_2
| ~ spl0_122 ),
inference(resolution,[],[f875,f247]) ).
fof(f1174,plain,
spl0_145,
inference(avatar_split_clause,[],[f134,f1172]) ).
fof(f1172,plain,
( spl0_145
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f134,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause134) ).
fof(f1095,plain,
spl0_144,
inference(avatar_split_clause,[],[f141,f1093]) ).
fof(f141,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
fof(f1084,plain,
spl0_143,
inference(avatar_split_clause,[],[f140,f1082]) ).
fof(f1082,plain,
( spl0_143
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f140,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
fof(f1080,plain,
spl0_142,
inference(avatar_split_clause,[],[f139,f1078]) ).
fof(f1078,plain,
( spl0_142
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause139) ).
fof(f1076,plain,
spl0_141,
inference(avatar_split_clause,[],[f137,f1074]) ).
fof(f137,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
fof(f1072,plain,
spl0_140,
inference(avatar_split_clause,[],[f136,f1070]) ).
fof(f136,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
fof(f1068,plain,
spl0_139,
inference(avatar_split_clause,[],[f132,f1066]) ).
fof(f1066,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f132,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
fof(f1064,plain,
spl0_138,
inference(avatar_split_clause,[],[f131,f1062]) ).
fof(f1062,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f131,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
fof(f1060,plain,
spl0_137,
inference(avatar_split_clause,[],[f123,f1058]) ).
fof(f123,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
fof(f1008,plain,
spl0_136,
inference(avatar_split_clause,[],[f219,f1006]) ).
fof(f219,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| frontsegP(X2,X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
fof(f1004,plain,
spl0_135,
inference(avatar_split_clause,[],[f218,f1002]) ).
fof(f1002,plain,
( spl0_135
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f218,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ),
inference(equality_resolution,[],[f143]) ).
fof(f143,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X2,X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
fof(f997,plain,
spl0_134,
inference(avatar_split_clause,[],[f130,f995]) ).
fof(f995,plain,
( spl0_134
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f130,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause130) ).
fof(f993,plain,
spl0_133,
inference(avatar_split_clause,[],[f129,f991]) ).
fof(f991,plain,
( spl0_133
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f129,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause129) ).
fof(f989,plain,
spl0_132,
inference(avatar_split_clause,[],[f128,f987]) ).
fof(f987,plain,
( spl0_132
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f128,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
fof(f985,plain,
spl0_131,
inference(avatar_split_clause,[],[f127,f983]) ).
fof(f983,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f127,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
fof(f981,plain,
spl0_130,
inference(avatar_split_clause,[],[f126,f979]) ).
fof(f979,plain,
( spl0_130
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f126,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
fof(f977,plain,
spl0_129,
inference(avatar_split_clause,[],[f125,f975]) ).
fof(f975,plain,
( spl0_129
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause125) ).
fof(f973,plain,
spl0_128,
inference(avatar_split_clause,[],[f124,f971]) ).
fof(f971,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f124,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause124) ).
fof(f969,plain,
spl0_127,
inference(avatar_split_clause,[],[f122,f967]) ).
fof(f967,plain,
( spl0_127
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f122,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause122) ).
fof(f965,plain,
spl0_126,
inference(avatar_split_clause,[],[f120,f963]) ).
fof(f963,plain,
( spl0_126
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f120,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
fof(f888,plain,
spl0_125,
inference(avatar_split_clause,[],[f119,f886]) ).
fof(f886,plain,
( spl0_125
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f119,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
fof(f884,plain,
spl0_124,
inference(avatar_split_clause,[],[f118,f882]) ).
fof(f882,plain,
( spl0_124
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f118,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
fof(f880,plain,
spl0_123,
inference(avatar_split_clause,[],[f109,f878]) ).
fof(f109,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
fof(f876,plain,
spl0_122,
inference(avatar_split_clause,[],[f104,f874]) ).
fof(f104,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
fof(f870,plain,
( spl0_121
| ~ spl0_1
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f686,f624,f240,f867]) ).
fof(f867,plain,
( spl0_121
<=> sk4 = app(nil,sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f624,plain,
( spl0_85
<=> ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f686,plain,
( sk4 = app(nil,sk4)
| ~ spl0_1
| ~ spl0_85 ),
inference(resolution,[],[f625,f242]) ).
fof(f625,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f849,plain,
( spl0_120
| ~ spl0_2
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f685,f624,f245,f846]) ).
fof(f846,plain,
( spl0_120
<=> sk3 = app(nil,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f685,plain,
( sk3 = app(nil,sk3)
| ~ spl0_2
| ~ spl0_85 ),
inference(resolution,[],[f625,f247]) ).
fof(f844,plain,
spl0_119,
inference(avatar_split_clause,[],[f213,f842]) ).
fof(f842,plain,
( spl0_119
<=> ! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f213,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ),
inference(equality_resolution,[],[f116]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
fof(f840,plain,
spl0_118,
inference(avatar_split_clause,[],[f114,f838]) ).
fof(f838,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f114,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
fof(f836,plain,
spl0_117,
inference(avatar_split_clause,[],[f110,f834]) ).
fof(f834,plain,
( spl0_117
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f110,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
fof(f832,plain,
spl0_116,
inference(avatar_split_clause,[],[f108,f830]) ).
fof(f830,plain,
( spl0_116
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f108,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
fof(f828,plain,
spl0_115,
inference(avatar_split_clause,[],[f107,f826]) ).
fof(f826,plain,
( spl0_115
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f107,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
fof(f824,plain,
spl0_114,
inference(avatar_split_clause,[],[f106,f822]) ).
fof(f822,plain,
( spl0_114
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f106,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
fof(f820,plain,
spl0_113,
inference(avatar_split_clause,[],[f105,f818]) ).
fof(f818,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
fof(f816,plain,
spl0_112,
inference(avatar_split_clause,[],[f103,f814]) ).
fof(f814,plain,
( spl0_112
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f103,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
fof(f812,plain,
spl0_111,
inference(avatar_split_clause,[],[f102,f810]) ).
fof(f810,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f102,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
fof(f808,plain,
spl0_110,
inference(avatar_split_clause,[],[f101,f806]) ).
fof(f806,plain,
( spl0_110
<=> ! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f101,axiom,
! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
fof(f804,plain,
( spl0_109
| ~ spl0_1
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f656,f620,f240,f801]) ).
fof(f656,plain,
( sk4 = app(sk4,nil)
| ~ spl0_1
| ~ spl0_84 ),
inference(resolution,[],[f621,f242]) ).
fof(f799,plain,
spl0_108,
inference(avatar_split_clause,[],[f100,f797]) ).
fof(f797,plain,
( spl0_108
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f100,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f795,plain,
spl0_107,
inference(avatar_split_clause,[],[f97,f793]) ).
fof(f793,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
fof(f791,plain,
spl0_106,
inference(avatar_split_clause,[],[f96,f789]) ).
fof(f789,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f96,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
fof(f787,plain,
( spl0_105
| ~ spl0_2
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f655,f620,f245,f784]) ).
fof(f655,plain,
( sk3 = app(sk3,nil)
| ~ spl0_2
| ~ spl0_84 ),
inference(resolution,[],[f621,f247]) ).
fof(f782,plain,
spl0_104,
inference(avatar_split_clause,[],[f234,f780]) ).
fof(f780,plain,
( spl0_104
<=> ! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f234,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(duplicate_literal_removal,[],[f217]) ).
fof(f217,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
fof(f778,plain,
spl0_103,
inference(avatar_split_clause,[],[f99,f776]) ).
fof(f99,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
fof(f774,plain,
spl0_102,
inference(avatar_split_clause,[],[f98,f772]) ).
fof(f772,plain,
( spl0_102
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f770,plain,
spl0_101,
inference(avatar_split_clause,[],[f95,f768]) ).
fof(f768,plain,
( spl0_101
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f95,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
fof(f766,plain,
spl0_100,
inference(avatar_split_clause,[],[f94,f764]) ).
fof(f764,plain,
( spl0_100
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f94,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
fof(f762,plain,
spl0_99,
inference(avatar_split_clause,[],[f93,f760]) ).
fof(f760,plain,
( spl0_99
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f93,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
fof(f758,plain,
spl0_98,
inference(avatar_split_clause,[],[f92,f756]) ).
fof(f756,plain,
( spl0_98
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f92,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
fof(f754,plain,
spl0_97,
inference(avatar_split_clause,[],[f91,f752]) ).
fof(f752,plain,
( spl0_97
<=> ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f91,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
fof(f750,plain,
spl0_96,
inference(avatar_split_clause,[],[f90,f748]) ).
fof(f748,plain,
( spl0_96
<=> ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f90,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
fof(f746,plain,
spl0_95,
inference(avatar_split_clause,[],[f89,f744]) ).
fof(f744,plain,
( spl0_95
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f89,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
fof(f742,plain,
spl0_94,
inference(avatar_split_clause,[],[f88,f740]) ).
fof(f740,plain,
( spl0_94
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f88,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
fof(f738,plain,
spl0_93,
inference(avatar_split_clause,[],[f87,f736]) ).
fof(f736,plain,
( spl0_93
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f87,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
fof(f715,plain,
spl0_92,
inference(avatar_split_clause,[],[f86,f713]) ).
fof(f713,plain,
( spl0_92
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f86,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f711,plain,
spl0_91,
inference(avatar_split_clause,[],[f85,f709]) ).
fof(f709,plain,
( spl0_91
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f707,plain,
spl0_90,
inference(avatar_split_clause,[],[f84,f705]) ).
fof(f705,plain,
( spl0_90
<=> ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f84,axiom,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
fof(f703,plain,
spl0_89,
inference(avatar_split_clause,[],[f82,f701]) ).
fof(f701,plain,
( spl0_89
<=> ! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f82,axiom,
! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
fof(f699,plain,
spl0_88,
inference(avatar_split_clause,[],[f80,f697]) ).
fof(f697,plain,
( spl0_88
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f80,axiom,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
fof(f695,plain,
spl0_87,
inference(avatar_split_clause,[],[f77,f693]) ).
fof(f693,plain,
( spl0_87
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f77,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
fof(f691,plain,
( spl0_86
| ~ spl0_1
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f613,f581,f240,f688]) ).
fof(f581,plain,
( spl0_82
<=> ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f613,plain,
( duplicatefreeP(sk4)
| ~ spl0_1
| ~ spl0_82 ),
inference(resolution,[],[f582,f242]) ).
fof(f582,plain,
( ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f626,plain,
spl0_85,
inference(avatar_split_clause,[],[f74,f624]) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f622,plain,
spl0_84,
inference(avatar_split_clause,[],[f73,f620]) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f618,plain,
( spl0_83
| ~ spl0_2
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f612,f581,f245,f615]) ).
fof(f615,plain,
( spl0_83
<=> duplicatefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f612,plain,
( duplicatefreeP(sk3)
| ~ spl0_2
| ~ spl0_82 ),
inference(resolution,[],[f582,f247]) ).
fof(f583,plain,
( spl0_81
| spl0_82 ),
inference(avatar_split_clause,[],[f72,f581,f578]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
fof(f576,plain,
spl0_80,
inference(avatar_split_clause,[],[f70,f574]) ).
fof(f574,plain,
( spl0_80
<=> ! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f70,axiom,
! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
fof(f572,plain,
spl0_79,
inference(avatar_split_clause,[],[f69,f570]) ).
fof(f570,plain,
( spl0_79
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f69,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
fof(f568,plain,
spl0_78,
inference(avatar_split_clause,[],[f68,f566]) ).
fof(f566,plain,
( spl0_78
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f68,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
fof(f564,plain,
spl0_77,
inference(avatar_split_clause,[],[f67,f562]) ).
fof(f562,plain,
( spl0_77
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f67,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
fof(f560,plain,
spl0_76,
inference(avatar_split_clause,[],[f66,f558]) ).
fof(f558,plain,
( spl0_76
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f66,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
fof(f556,plain,
spl0_75,
inference(avatar_split_clause,[],[f65,f554]) ).
fof(f554,plain,
( spl0_75
<=> ! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f65,axiom,
! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
fof(f552,plain,
spl0_74,
inference(avatar_split_clause,[],[f64,f550]) ).
fof(f550,plain,
( spl0_74
<=> ! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f64,axiom,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
fof(f548,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_73
| ~ spl0_16
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f544,f541,f315,f546,f255,f245]) ).
fof(f255,plain,
( spl0_4
<=> ssItem(sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f541,plain,
( spl0_72
<=> ! [X6,X8,X7] :
( ~ ssItem(X6)
| sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssList(X8)
| ~ ssList(X7)
| sk3 != app(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f544,plain,
( ! [X0] :
( sk4 != app(sk4,X0)
| ~ ssItem(sk5)
| ~ ssList(X0)
| ~ ssList(sk3)
| sk3 != app(sk3,X0) )
| ~ spl0_16
| ~ spl0_72 ),
inference(superposition,[],[f542,f317]) ).
fof(f542,plain,
( ! [X8,X6,X7] :
( sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssItem(X6)
| ~ ssList(X8)
| ~ ssList(X7)
| sk3 != app(X7,X8) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f543,plain,
( ~ spl0_3
| spl0_72 ),
inference(avatar_split_clause,[],[f206,f541,f250]) ).
fof(f250,plain,
( spl0_3
<=> neq(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f206,plain,
! [X8,X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| ~ neq(sk4,nil)
| sk3 != app(X7,X8)
| sk4 != app(app(X7,cons(X6,nil)),X8) ),
inference(definition_unfolding,[],[f197,f191,f190]) ).
fof(f190,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f191,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f197,axiom,
! [X8,X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| ~ neq(sk4,nil)
| sk1 != app(X7,X8)
| sk2 != app(app(X7,cons(X6,nil)),X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f539,plain,
spl0_71,
inference(avatar_split_clause,[],[f237,f537]) ).
fof(f537,plain,
( spl0_71
<=> ! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f237,plain,
! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f211]) ).
fof(f211,plain,
! [X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
fof(f535,plain,
spl0_70,
inference(avatar_split_clause,[],[f235,f533]) ).
fof(f533,plain,
( spl0_70
<=> ! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f235,plain,
! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f216]) ).
fof(f216,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f115]) ).
fof(f115,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f531,plain,
spl0_69,
inference(avatar_split_clause,[],[f71,f529]) ).
fof(f529,plain,
( spl0_69
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f527,plain,
spl0_68,
inference(avatar_split_clause,[],[f63,f525]) ).
fof(f525,plain,
( spl0_68
<=> ! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f63,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
fof(f523,plain,
spl0_67,
inference(avatar_split_clause,[],[f62,f521]) ).
fof(f521,plain,
( spl0_67
<=> ! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f62,axiom,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
fof(f519,plain,
spl0_66,
inference(avatar_split_clause,[],[f61,f517]) ).
fof(f517,plain,
( spl0_66
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f61,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
fof(f515,plain,
spl0_65,
inference(avatar_split_clause,[],[f60,f513]) ).
fof(f513,plain,
( spl0_65
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f60,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
fof(f511,plain,
spl0_64,
inference(avatar_split_clause,[],[f59,f509]) ).
fof(f509,plain,
( spl0_64
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f59,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
fof(f507,plain,
spl0_63,
inference(avatar_split_clause,[],[f58,f505]) ).
fof(f505,plain,
( spl0_63
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f58,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
fof(f503,plain,
spl0_62,
inference(avatar_split_clause,[],[f57,f501]) ).
fof(f501,plain,
( spl0_62
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f57,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
fof(f499,plain,
spl0_61,
inference(avatar_split_clause,[],[f56,f497]) ).
fof(f497,plain,
( spl0_61
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f56,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
fof(f495,plain,
spl0_60,
inference(avatar_split_clause,[],[f55,f493]) ).
fof(f493,plain,
( spl0_60
<=> ! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f55,axiom,
! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
fof(f491,plain,
spl0_59,
inference(avatar_split_clause,[],[f53,f489]) ).
fof(f489,plain,
( spl0_59
<=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f53,axiom,
! [X0,X1] : ssList(skaf42(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
fof(f487,plain,
spl0_58,
inference(avatar_split_clause,[],[f52,f485]) ).
fof(f485,plain,
( spl0_58
<=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f52,axiom,
! [X0,X1] : ssList(skaf43(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
fof(f483,plain,
spl0_57,
inference(avatar_split_clause,[],[f51,f481]) ).
fof(f481,plain,
( spl0_57
<=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
fof(f479,plain,
spl0_56,
inference(avatar_split_clause,[],[f50,f477]) ).
fof(f477,plain,
( spl0_56
<=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
fof(f475,plain,
spl0_55,
inference(avatar_split_clause,[],[f49,f473]) ).
fof(f473,plain,
( spl0_55
<=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f49,axiom,
! [X0,X1] : ssList(skaf47(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
fof(f471,plain,
spl0_54,
inference(avatar_split_clause,[],[f48,f469]) ).
fof(f469,plain,
( spl0_54
<=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f48,axiom,
! [X0,X1] : ssList(skaf48(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
fof(f467,plain,
~ spl0_53,
inference(avatar_split_clause,[],[f54,f464]) ).
fof(f464,plain,
( spl0_53
<=> skac3 = skac2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f54,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
fof(f462,plain,
spl0_52,
inference(avatar_split_clause,[],[f47,f460]) ).
fof(f460,plain,
( spl0_52
<=> ! [X0] : ssItem(skaf44(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
fof(f458,plain,
spl0_51,
inference(avatar_split_clause,[],[f46,f456]) ).
fof(f456,plain,
( spl0_51
<=> ! [X0] : ssItem(skaf49(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f46,axiom,
! [X0] : ssItem(skaf49(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
fof(f454,plain,
spl0_50,
inference(avatar_split_clause,[],[f45,f452]) ).
fof(f452,plain,
( spl0_50
<=> ! [X0] : ssItem(skaf50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f45,axiom,
! [X0] : ssItem(skaf50(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
fof(f450,plain,
spl0_49,
inference(avatar_split_clause,[],[f44,f448]) ).
fof(f448,plain,
( spl0_49
<=> ! [X0] : ssList(skaf51(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f44,axiom,
! [X0] : ssList(skaf51(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
fof(f446,plain,
spl0_48,
inference(avatar_split_clause,[],[f43,f444]) ).
fof(f444,plain,
( spl0_48
<=> ! [X0] : ssList(skaf52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f43,axiom,
! [X0] : ssList(skaf52(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
fof(f442,plain,
spl0_47,
inference(avatar_split_clause,[],[f42,f440]) ).
fof(f440,plain,
( spl0_47
<=> ! [X0] : ssList(skaf53(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f42,axiom,
! [X0] : ssList(skaf53(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
fof(f438,plain,
spl0_46,
inference(avatar_split_clause,[],[f41,f436]) ).
fof(f436,plain,
( spl0_46
<=> ! [X0] : ssItem(skaf54(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f41,axiom,
! [X0] : ssItem(skaf54(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
fof(f434,plain,
spl0_45,
inference(avatar_split_clause,[],[f40,f432]) ).
fof(f432,plain,
( spl0_45
<=> ! [X0] : ssItem(skaf55(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f40,axiom,
! [X0] : ssItem(skaf55(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
fof(f430,plain,
spl0_44,
inference(avatar_split_clause,[],[f39,f428]) ).
fof(f428,plain,
( spl0_44
<=> ! [X0] : ssList(skaf56(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f39,axiom,
! [X0] : ssList(skaf56(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
fof(f426,plain,
spl0_43,
inference(avatar_split_clause,[],[f38,f424]) ).
fof(f424,plain,
( spl0_43
<=> ! [X0] : ssList(skaf57(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f38,axiom,
! [X0] : ssList(skaf57(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
fof(f422,plain,
spl0_42,
inference(avatar_split_clause,[],[f37,f420]) ).
fof(f420,plain,
( spl0_42
<=> ! [X0] : ssList(skaf58(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f37,axiom,
! [X0] : ssList(skaf58(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
fof(f418,plain,
spl0_41,
inference(avatar_split_clause,[],[f36,f416]) ).
fof(f416,plain,
( spl0_41
<=> ! [X0] : ssItem(skaf59(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f36,axiom,
! [X0] : ssItem(skaf59(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
fof(f414,plain,
spl0_40,
inference(avatar_split_clause,[],[f35,f412]) ).
fof(f412,plain,
( spl0_40
<=> ! [X0] : ssItem(skaf60(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f35,axiom,
! [X0] : ssItem(skaf60(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
fof(f410,plain,
spl0_39,
inference(avatar_split_clause,[],[f34,f408]) ).
fof(f408,plain,
( spl0_39
<=> ! [X0] : ssList(skaf61(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f34,axiom,
! [X0] : ssList(skaf61(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
fof(f406,plain,
spl0_38,
inference(avatar_split_clause,[],[f33,f404]) ).
fof(f404,plain,
( spl0_38
<=> ! [X0] : ssList(skaf62(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f33,axiom,
! [X0] : ssList(skaf62(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
fof(f402,plain,
spl0_37,
inference(avatar_split_clause,[],[f32,f400]) ).
fof(f400,plain,
( spl0_37
<=> ! [X0] : ssList(skaf63(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f32,axiom,
! [X0] : ssList(skaf63(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
fof(f398,plain,
spl0_36,
inference(avatar_split_clause,[],[f31,f396]) ).
fof(f396,plain,
( spl0_36
<=> ! [X0] : ssItem(skaf64(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f31,axiom,
! [X0] : ssItem(skaf64(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
fof(f394,plain,
spl0_35,
inference(avatar_split_clause,[],[f30,f392]) ).
fof(f392,plain,
( spl0_35
<=> ! [X0] : ssItem(skaf65(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f30,axiom,
! [X0] : ssItem(skaf65(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
fof(f390,plain,
spl0_34,
inference(avatar_split_clause,[],[f29,f388]) ).
fof(f388,plain,
( spl0_34
<=> ! [X0] : ssList(skaf66(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f29,axiom,
! [X0] : ssList(skaf66(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
fof(f386,plain,
spl0_33,
inference(avatar_split_clause,[],[f28,f384]) ).
fof(f384,plain,
( spl0_33
<=> ! [X0] : ssList(skaf67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f28,axiom,
! [X0] : ssList(skaf67(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
fof(f382,plain,
spl0_32,
inference(avatar_split_clause,[],[f27,f380]) ).
fof(f380,plain,
( spl0_32
<=> ! [X0] : ssList(skaf68(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f27,axiom,
! [X0] : ssList(skaf68(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
fof(f378,plain,
spl0_31,
inference(avatar_split_clause,[],[f26,f376]) ).
fof(f376,plain,
( spl0_31
<=> ! [X0] : ssItem(skaf69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f26,axiom,
! [X0] : ssItem(skaf69(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
fof(f374,plain,
spl0_30,
inference(avatar_split_clause,[],[f25,f372]) ).
fof(f372,plain,
( spl0_30
<=> ! [X0] : ssItem(skaf70(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f25,axiom,
! [X0] : ssItem(skaf70(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
fof(f370,plain,
spl0_29,
inference(avatar_split_clause,[],[f24,f368]) ).
fof(f368,plain,
( spl0_29
<=> ! [X0] : ssList(skaf71(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f24,axiom,
! [X0] : ssList(skaf71(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
fof(f366,plain,
spl0_28,
inference(avatar_split_clause,[],[f23,f364]) ).
fof(f364,plain,
( spl0_28
<=> ! [X0] : ssList(skaf72(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f23,axiom,
! [X0] : ssList(skaf72(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
fof(f362,plain,
spl0_27,
inference(avatar_split_clause,[],[f22,f360]) ).
fof(f360,plain,
( spl0_27
<=> ! [X0] : ssList(skaf73(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f22,axiom,
! [X0] : ssList(skaf73(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
fof(f358,plain,
spl0_26,
inference(avatar_split_clause,[],[f21,f356]) ).
fof(f356,plain,
( spl0_26
<=> ! [X0] : ssItem(skaf74(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f21,axiom,
! [X0] : ssItem(skaf74(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
fof(f354,plain,
spl0_25,
inference(avatar_split_clause,[],[f20,f352]) ).
fof(f352,plain,
( spl0_25
<=> ! [X0] : ssList(skaf75(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f20,axiom,
! [X0] : ssList(skaf75(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
fof(f350,plain,
spl0_24,
inference(avatar_split_clause,[],[f19,f348]) ).
fof(f348,plain,
( spl0_24
<=> ! [X0] : ssList(skaf76(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f19,axiom,
! [X0] : ssList(skaf76(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
fof(f346,plain,
spl0_23,
inference(avatar_split_clause,[],[f18,f344]) ).
fof(f344,plain,
( spl0_23
<=> ! [X0] : ssList(skaf77(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f18,axiom,
! [X0] : ssList(skaf77(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
fof(f342,plain,
spl0_22,
inference(avatar_split_clause,[],[f17,f340]) ).
fof(f340,plain,
( spl0_22
<=> ! [X0] : ssItem(skaf78(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f17,axiom,
! [X0] : ssItem(skaf78(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
fof(f338,plain,
spl0_21,
inference(avatar_split_clause,[],[f16,f336]) ).
fof(f336,plain,
( spl0_21
<=> ! [X0] : ssItem(skaf79(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f16,axiom,
! [X0] : ssItem(skaf79(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
fof(f334,plain,
spl0_20,
inference(avatar_split_clause,[],[f15,f332]) ).
fof(f332,plain,
( spl0_20
<=> ! [X0] : ssList(skaf80(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f15,axiom,
! [X0] : ssList(skaf80(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
fof(f330,plain,
spl0_19,
inference(avatar_split_clause,[],[f14,f328]) ).
fof(f328,plain,
( spl0_19
<=> ! [X0] : ssList(skaf81(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f14,axiom,
! [X0] : ssList(skaf81(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
fof(f326,plain,
spl0_18,
inference(avatar_split_clause,[],[f13,f324]) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
fof(f322,plain,
spl0_17,
inference(avatar_split_clause,[],[f12,f320]) ).
fof(f320,plain,
( spl0_17
<=> ! [X0] : ssItem(skaf83(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
fof(f318,plain,
( spl0_16
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f199,f250,f315]) ).
fof(f199,axiom,
( ~ neq(sk4,nil)
| sk4 = app(sk3,cons(sk5,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f313,plain,
~ spl0_15,
inference(avatar_split_clause,[],[f11,f310]) ).
fof(f310,plain,
( spl0_15
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
fof(f308,plain,
spl0_14,
inference(avatar_split_clause,[],[f10,f305]) ).
fof(f305,plain,
( spl0_14
<=> ssItem(skac2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
fof(f303,plain,
spl0_13,
inference(avatar_split_clause,[],[f9,f300]) ).
fof(f300,plain,
( spl0_13
<=> ssItem(skac3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
fof(f298,plain,
spl0_12,
inference(avatar_split_clause,[],[f8,f295]) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f293,plain,
spl0_11,
inference(avatar_split_clause,[],[f7,f290]) ).
fof(f290,plain,
( spl0_11
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f7,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
fof(f288,plain,
spl0_10,
inference(avatar_split_clause,[],[f6,f285]) ).
fof(f285,plain,
( spl0_10
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f6,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
fof(f283,plain,
spl0_9,
inference(avatar_split_clause,[],[f5,f280]) ).
fof(f280,plain,
( spl0_9
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f5,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
fof(f278,plain,
spl0_8,
inference(avatar_split_clause,[],[f4,f275]) ).
fof(f275,plain,
( spl0_8
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
fof(f273,plain,
spl0_7,
inference(avatar_split_clause,[],[f3,f270]) ).
fof(f3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
fof(f268,plain,
spl0_6,
inference(avatar_split_clause,[],[f2,f265]) ).
fof(f265,plain,
( spl0_6
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f2,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
fof(f263,plain,
spl0_5,
inference(avatar_split_clause,[],[f1,f260]) ).
fof(f1,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
fof(f258,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f198,f255,f250]) ).
fof(f198,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f253,plain,
spl0_3,
inference(avatar_split_clause,[],[f238,f250]) ).
fof(f238,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f204,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f192,f190,f190]) ).
fof(f192,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f248,plain,
spl0_2,
inference(avatar_split_clause,[],[f200,f245]) ).
fof(f200,plain,
ssList(sk3),
inference(definition_unfolding,[],[f186,f191]) ).
fof(f186,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
fof(f243,plain,
spl0_1,
inference(avatar_split_clause,[],[f189,f240]) ).
fof(f189,axiom,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC012-1 : TPTP v8.2.0. Released v2.4.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.38 % Computer : n021.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Sun May 19 03:12:23 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.15/0.39 % (30885)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.41 % (30888)WARNING: value z3 for option sas not known
% 0.15/0.41 % (30889)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.41 % (30886)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.41 % (30887)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.41 % (30890)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.41 % (30888)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)
% 0.15/0.41 % (30892)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.41 % (30891)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.42 TRYING [1]
% 0.15/0.42 TRYING [2]
% 0.25/0.44 TRYING [3]
% 0.25/0.47 TRYING [1]
% 0.25/0.47 TRYING [2]
% 0.25/0.48 TRYING [4]
% 0.25/0.49 % (30890)First to succeed.
% 0.25/0.50 % (30890)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30885"
% 0.25/0.50 % (30890)Refutation found. Thanks to Tanya!
% 0.25/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.51 % (30890)------------------------------
% 0.25/0.51 % (30890)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.25/0.51 % (30890)Termination reason: Refutation
% 0.25/0.51
% 0.25/0.51 % (30890)Memory used [KB]: 2636
% 0.25/0.51 % (30890)Time elapsed: 0.094 s
% 0.25/0.51 % (30890)Instructions burned: 158 (million)
% 0.25/0.51 % (30885)Success in time 0.118 s
%------------------------------------------------------------------------------