TSTP Solution File: SWC106-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC106-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 Apr 30 15:53:53 EDT 2024
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 385
% Syntax : Number of formulae : 651 ( 236 unt; 0 def)
% Number of atoms : 1871 ( 186 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2209 ( 989 ~;1019 |; 0 &)
% ( 201 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 222 ( 220 usr; 202 prp; 0-2 aty)
% Number of functors : 55 ( 55 usr; 9 con; 0-2 aty)
% Number of variables : 680 ( 680 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1920,plain,
$false,
inference(avatar_sat_refutation,[],[f249,f254,f259,f264,f269,f274,f279,f284,f289,f294,f299,f304,f309,f314,f319,f324,f329,f338,f343,f349,f353,f357,f361,f365,f369,f373,f377,f381,f385,f389,f393,f397,f401,f405,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f449,f453,f457,f461,f465,f469,f473,f477,f481,f485,f489,f493,f498,f502,f506,f510,f514,f518,f522,f526,f530,f534,f538,f542,f546,f550,f554,f558,f562,f566,f570,f574,f578,f582,f586,f590,f594,f598,f605,f617,f621,f625,f691,f695,f699,f703,f707,f711,f735,f739,f743,f747,f752,f756,f760,f764,f768,f772,f776,f780,f784,f794,f798,f802,f806,f810,f814,f818,f822,f826,f830,f834,f838,f842,f846,f863,f876,f880,f884,f888,f964,f968,f972,f976,f980,f984,f989,f993,f997,f1001,f1005,f1009,f1048,f1052,f1056,f1060,f1065,f1069,f1073,f1077,f1081,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1174,f1179,f1183,f1187,f1223,f1227,f1231,f1235,f1287,f1291,f1295,f1299,f1303,f1307,f1311,f1315,f1389,f1405,f1409,f1413,f1417,f1421,f1425,f1430,f1434,f1478,f1482,f1487,f1503,f1507,f1511,f1515,f1519,f1523,f1596,f1736,f1742,f1749,f1757,f1761,f1765,f1775,f1779,f1783,f1905,f1911,f1916,f1918,f1919]) ).
fof(f1919,plain,
( ~ spl0_5
| ~ spl0_1
| ~ spl0_2
| spl0_19
| ~ spl0_21
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1040,f1003,f346,f335,f251,f246,f266]) ).
fof(f266,plain,
( spl0_5
<=> ssList(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f246,plain,
( spl0_1
<=> ssList(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f251,plain,
( spl0_2
<=> ssList(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f335,plain,
( spl0_19
<=> rearsegP(sk4,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f346,plain,
( spl0_21
<=> sk4 = app(sk6,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1003,plain,
( spl0_137
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1040,plain,
( rearsegP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ spl0_21
| ~ spl0_137 ),
inference(superposition,[],[f1004,f348]) ).
fof(f348,plain,
( sk4 = app(sk6,sk3)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f1004,plain,
( ! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1918,plain,
( ~ spl0_1
| spl0_200
| ~ spl0_14
| spl0_18
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f849,f804,f331,f311,f1908,f246]) ).
fof(f1908,plain,
( spl0_200
<=> nil = sk3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f311,plain,
( spl0_14
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f331,plain,
( spl0_18
<=> neq(sk3,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f804,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f849,plain,
( ~ ssList(nil)
| nil = sk3
| ~ ssList(sk3)
| spl0_18
| ~ spl0_111 ),
inference(resolution,[],[f805,f333]) ).
fof(f333,plain,
( ~ neq(sk3,nil)
| spl0_18 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f805,plain,
( ! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X0)
| X0 = X1
| ~ ssList(X1) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f1916,plain,
( ~ spl0_4
| ~ spl0_14
| spl0_201
| ~ spl0_6
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f789,f782,f271,f1913,f311,f261]) ).
fof(f261,plain,
( spl0_4
<=> ssItem(sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1913,plain,
( spl0_201
<=> memberP(sk3,sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f271,plain,
( spl0_6
<=> sk3 = cons(sk5,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f782,plain,
( spl0_107
<=> ! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f789,plain,
( memberP(sk3,sk5)
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_107 ),
inference(superposition,[],[f783,f273]) ).
fof(f273,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f783,plain,
( ! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f1911,plain,
( ~ spl0_4
| ~ spl0_1
| ~ spl0_200
| ~ spl0_6
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f786,f774,f271,f1908,f246,f261]) ).
fof(f774,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f786,plain,
( nil != sk3
| ~ ssList(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_105 ),
inference(inner_rewriting,[],[f785]) ).
fof(f785,plain,
( nil != sk3
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_105 ),
inference(superposition,[],[f775,f273]) ).
fof(f775,plain,
( ! [X0,X1] :
( nil != cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f1905,plain,
( spl0_199
| ~ spl0_4
| ~ spl0_1
| ~ spl0_6
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f871,f844,f271,f246,f261,f1902]) ).
fof(f1902,plain,
( spl0_199
<=> singletonP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f844,plain,
( spl0_121
<=> ! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f871,plain,
( ~ ssList(sk3)
| ~ ssItem(sk5)
| singletonP(sk3)
| ~ spl0_6
| ~ spl0_121 ),
inference(superposition,[],[f845,f273]) ).
fof(f845,plain,
( ! [X0] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f1783,plain,
spl0_198,
inference(avatar_split_clause,[],[f237,f1781]) ).
fof(f1781,plain,
( spl0_198
<=> ! [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_198])]) ).
fof(f237,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(f1779,plain,
spl0_197,
inference(avatar_split_clause,[],[f236,f1777]) ).
fof(f1777,plain,
( spl0_197
<=> ! [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_197])]) ).
fof(f236,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(f1775,plain,
spl0_196,
inference(avatar_split_clause,[],[f235,f1773]) ).
fof(f1773,plain,
( spl0_196
<=> ! [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_196])]) ).
fof(f235,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(f1765,plain,
spl0_195,
inference(avatar_split_clause,[],[f234,f1763]) ).
fof(f1763,plain,
( spl0_195
<=> ! [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_195])]) ).
fof(f234,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(f1761,plain,
spl0_194,
inference(avatar_split_clause,[],[f233,f1759]) ).
fof(f1759,plain,
( spl0_194
<=> ! [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_194])]) ).
fof(f233,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(f1757,plain,
( spl0_193
| ~ spl0_5
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f687,f623,f266,f1754]) ).
fof(f1754,plain,
( spl0_193
<=> sk6 = app(nil,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f623,plain,
( spl0_88
<=> ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f687,plain,
( sk6 = app(nil,sk6)
| ~ spl0_5
| ~ spl0_88 ),
inference(resolution,[],[f624,f268]) ).
fof(f268,plain,
( ssList(sk6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f624,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f1749,plain,
spl0_192,
inference(avatar_split_clause,[],[f230,f1747]) ).
fof(f1747,plain,
( spl0_192
<=> ! [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_192])]) ).
fof(f230,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(f1742,plain,
spl0_191,
inference(avatar_split_clause,[],[f232,f1740]) ).
fof(f1740,plain,
( spl0_191
<=> ! [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_191])]) ).
fof(f232,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(f1736,plain,
spl0_190,
inference(avatar_split_clause,[],[f177,f1734]) ).
fof(f1734,plain,
( spl0_190
<=> ! [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_190])]) ).
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(f1596,plain,
( spl0_189
| ~ spl0_2
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f686,f623,f251,f1593]) ).
fof(f1593,plain,
( spl0_189
<=> sk4 = app(nil,sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f686,plain,
( sk4 = app(nil,sk4)
| ~ spl0_2
| ~ spl0_88 ),
inference(resolution,[],[f624,f253]) ).
fof(f253,plain,
( ssList(sk4)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f1523,plain,
spl0_188,
inference(avatar_split_clause,[],[f167,f1521]) ).
fof(f1521,plain,
( spl0_188
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f167,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| app(app(skaf51(X0),cons(skaf49(X0),skaf52(X0))),cons(skaf50(X0),skaf53(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause167) ).
fof(f1519,plain,
spl0_187,
inference(avatar_split_clause,[],[f166,f1517]) ).
fof(f1517,plain,
( spl0_187
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f166,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| app(app(skaf56(X0),cons(skaf54(X0),skaf57(X0))),cons(skaf55(X0),skaf58(X0))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause166) ).
fof(f1515,plain,
spl0_186,
inference(avatar_split_clause,[],[f165,f1513]) ).
fof(f1513,plain,
( spl0_186
<=> ! [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_186])]) ).
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(f1511,plain,
spl0_185,
inference(avatar_split_clause,[],[f164,f1509]) ).
fof(f1509,plain,
( spl0_185
<=> ! [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_185])]) ).
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(f1507,plain,
spl0_184,
inference(avatar_split_clause,[],[f163,f1505]) ).
fof(f1505,plain,
( spl0_184
<=> ! [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_184])]) ).
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(f1503,plain,
spl0_183,
inference(avatar_split_clause,[],[f162,f1501]) ).
fof(f1501,plain,
( spl0_183
<=> ! [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_183])]) ).
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(f1487,plain,
( spl0_182
| ~ spl0_1
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f685,f623,f246,f1484]) ).
fof(f1484,plain,
( spl0_182
<=> sk3 = app(nil,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f685,plain,
( sk3 = app(nil,sk3)
| ~ spl0_1
| ~ spl0_88 ),
inference(resolution,[],[f624,f248]) ).
fof(f248,plain,
( ssList(sk3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f1482,plain,
spl0_181,
inference(avatar_split_clause,[],[f229,f1480]) ).
fof(f1480,plain,
( spl0_181
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f229,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(f1478,plain,
spl0_180,
inference(avatar_split_clause,[],[f228,f1476]) ).
fof(f1476,plain,
( spl0_180
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f228,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(f1434,plain,
spl0_179,
inference(avatar_split_clause,[],[f176,f1432]) ).
fof(f1432,plain,
( spl0_179
<=> ! [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_179])]) ).
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(f1430,plain,
( spl0_178
| ~ spl0_5
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f656,f619,f266,f1427]) ).
fof(f1427,plain,
( spl0_178
<=> sk6 = app(sk6,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f619,plain,
( spl0_87
<=> ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f656,plain,
( sk6 = app(sk6,nil)
| ~ spl0_5
| ~ spl0_87 ),
inference(resolution,[],[f620,f268]) ).
fof(f620,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f1425,plain,
spl0_177,
inference(avatar_split_clause,[],[f174,f1423]) ).
fof(f1423,plain,
( spl0_177
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| frontsegP(X1,X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f174,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| frontsegP(X1,X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause174) ).
fof(f1421,plain,
spl0_176,
inference(avatar_split_clause,[],[f172,f1419]) ).
fof(f1419,plain,
( spl0_176
<=> ! [X0,X3,X2,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X3,X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(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(f1417,plain,
spl0_175,
inference(avatar_split_clause,[],[f171,f1415]) ).
fof(f1415,plain,
( spl0_175
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3
| cons(X0,X1) != cons(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause171) ).
fof(f1413,plain,
spl0_174,
inference(avatar_split_clause,[],[f170,f1411]) ).
fof(f1411,plain,
( spl0_174
<=> ! [X0,X3,X2,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| cons(X0,X1) != cons(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f170,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause170) ).
fof(f1409,plain,
spl0_173,
inference(avatar_split_clause,[],[f169,f1407]) ).
fof(f1407,plain,
( spl0_173
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(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(f1405,plain,
spl0_172,
inference(avatar_split_clause,[],[f168,f1403]) ).
fof(f1403,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1)
| app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f168,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1)
| app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause168) ).
fof(f1389,plain,
( spl0_171
| ~ spl0_2
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f655,f619,f251,f1386]) ).
fof(f1386,plain,
( spl0_171
<=> sk4 = app(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f655,plain,
( sk4 = app(sk4,nil)
| ~ spl0_2
| ~ spl0_87 ),
inference(resolution,[],[f620,f253]) ).
fof(f1315,plain,
spl0_170,
inference(avatar_split_clause,[],[f161,f1313]) ).
fof(f1313,plain,
( spl0_170
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2)
| ~ memberP(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2)
| ~ memberP(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
fof(f1311,plain,
spl0_169,
inference(avatar_split_clause,[],[f160,f1309]) ).
fof(f1309,plain,
( spl0_169
<=> ! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f160,axiom,
! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause160) ).
fof(f1307,plain,
spl0_168,
inference(avatar_split_clause,[],[f159,f1305]) ).
fof(f1305,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f159,axiom,
! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause159) ).
fof(f1303,plain,
spl0_167,
inference(avatar_split_clause,[],[f158,f1301]) ).
fof(f1301,plain,
( spl0_167
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X1,X2)
| memberP(X0,X2)
| ~ memberP(app(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(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(f1299,plain,
spl0_166,
inference(avatar_split_clause,[],[f157,f1297]) ).
fof(f1297,plain,
( spl0_166
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f157,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause157) ).
fof(f1295,plain,
spl0_165,
inference(avatar_split_clause,[],[f149,f1293]) ).
fof(f1293,plain,
( spl0_165
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X2,X1),X0) = app(X2,app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(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(f1291,plain,
spl0_164,
inference(avatar_split_clause,[],[f142,f1289]) ).
fof(f1289,plain,
( spl0_164
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f142,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause142) ).
fof(f1287,plain,
( spl0_163
| ~ spl0_1
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f654,f619,f246,f1284]) ).
fof(f1284,plain,
( spl0_163
<=> sk3 = app(sk3,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f654,plain,
( sk3 = app(sk3,nil)
| ~ spl0_1
| ~ spl0_87 ),
inference(resolution,[],[f620,f248]) ).
fof(f1235,plain,
spl0_162,
inference(avatar_split_clause,[],[f238,f1233]) ).
fof(f1233,plain,
( spl0_162
<=> ! [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_162])]) ).
fof(f238,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f231,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(f1231,plain,
spl0_161,
inference(avatar_split_clause,[],[f151,f1229]) ).
fof(f1229,plain,
( spl0_161
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
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(f1227,plain,
spl0_160,
inference(avatar_split_clause,[],[f150,f1225]) ).
fof(f1225,plain,
( spl0_160
<=> ! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
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(f1223,plain,
spl0_159,
inference(avatar_split_clause,[],[f133,f1221]) ).
fof(f1221,plain,
( spl0_159
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
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(f1187,plain,
spl0_158,
inference(avatar_split_clause,[],[f156,f1185]) ).
fof(f1185,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f156,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause156) ).
fof(f1183,plain,
spl0_157,
inference(avatar_split_clause,[],[f155,f1181]) ).
fof(f1181,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| lt(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| lt(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause155) ).
fof(f1179,plain,
( ~ spl0_4
| spl0_156
| ~ spl0_6
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f612,f596,f271,f1176,f261]) ).
fof(f1176,plain,
( spl0_156
<=> cyclefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f596,plain,
( spl0_83
<=> ! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f612,plain,
( cyclefreeP(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_83 ),
inference(superposition,[],[f597,f273]) ).
fof(f597,plain,
( ! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f1174,plain,
spl0_155,
inference(avatar_split_clause,[],[f154,f1172]) ).
fof(f1172,plain,
( spl0_155
<=> ! [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_155])]) ).
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(f1170,plain,
spl0_154,
inference(avatar_split_clause,[],[f153,f1168]) ).
fof(f1168,plain,
( spl0_154
<=> ! [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_154])]) ).
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(f1166,plain,
spl0_153,
inference(avatar_split_clause,[],[f152,f1164]) ).
fof(f1164,plain,
( spl0_153
<=> ! [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_153])]) ).
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(f1162,plain,
spl0_152,
inference(avatar_split_clause,[],[f148,f1160]) ).
fof(f1160,plain,
( spl0_152
<=> ! [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_152])]) ).
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(f1158,plain,
spl0_151,
inference(avatar_split_clause,[],[f147,f1156]) ).
fof(f1156,plain,
( spl0_151
<=> ! [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_151])]) ).
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(f1154,plain,
spl0_150,
inference(avatar_split_clause,[],[f146,f1152]) ).
fof(f1152,plain,
( spl0_150
<=> ! [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_150])]) ).
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(f1150,plain,
spl0_149,
inference(avatar_split_clause,[],[f135,f1148]) ).
fof(f1148,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
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(f1146,plain,
spl0_148,
inference(avatar_split_clause,[],[f134,f1144]) ).
fof(f1144,plain,
( spl0_148
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
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(f1081,plain,
spl0_147,
inference(avatar_split_clause,[],[f141,f1079]) ).
fof(f1079,plain,
( spl0_147
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
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(f1077,plain,
spl0_146,
inference(avatar_split_clause,[],[f140,f1075]) ).
fof(f1075,plain,
( spl0_146
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
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(f1073,plain,
spl0_145,
inference(avatar_split_clause,[],[f139,f1071]) ).
fof(f1071,plain,
( spl0_145
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
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(f1069,plain,
spl0_144,
inference(avatar_split_clause,[],[f137,f1067]) ).
fof(f1067,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
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(f1065,plain,
( ~ spl0_4
| spl0_143
| ~ spl0_6
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f611,f592,f271,f1062,f261]) ).
fof(f1062,plain,
( spl0_143
<=> totalorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f592,plain,
( spl0_82
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f611,plain,
( totalorderP(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_82 ),
inference(superposition,[],[f593,f273]) ).
fof(f593,plain,
( ! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f1060,plain,
spl0_142,
inference(avatar_split_clause,[],[f136,f1058]) ).
fof(f1058,plain,
( spl0_142
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
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(f1056,plain,
spl0_141,
inference(avatar_split_clause,[],[f132,f1054]) ).
fof(f1054,plain,
( spl0_141
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
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(f1052,plain,
spl0_140,
inference(avatar_split_clause,[],[f131,f1050]) ).
fof(f1050,plain,
( spl0_140
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
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(f1048,plain,
spl0_139,
inference(avatar_split_clause,[],[f123,f1046]) ).
fof(f1046,plain,
( spl0_139
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
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(f1009,plain,
spl0_138,
inference(avatar_split_clause,[],[f225,f1007]) ).
fof(f1007,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f225,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(f1005,plain,
spl0_137,
inference(avatar_split_clause,[],[f224,f1003]) ).
fof(f224,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(f1001,plain,
spl0_136,
inference(avatar_split_clause,[],[f130,f999]) ).
fof(f999,plain,
( spl0_136
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
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(f997,plain,
spl0_135,
inference(avatar_split_clause,[],[f129,f995]) ).
fof(f995,plain,
( spl0_135
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
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(f993,plain,
spl0_134,
inference(avatar_split_clause,[],[f128,f991]) ).
fof(f991,plain,
( spl0_134
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
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(f989,plain,
( ~ spl0_4
| spl0_133
| ~ spl0_6
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f610,f588,f271,f986,f261]) ).
fof(f986,plain,
( spl0_133
<=> strictorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f588,plain,
( spl0_81
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f610,plain,
( strictorderP(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_81 ),
inference(superposition,[],[f589,f273]) ).
fof(f589,plain,
( ! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f984,plain,
spl0_132,
inference(avatar_split_clause,[],[f127,f982]) ).
fof(f982,plain,
( spl0_132
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
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(f980,plain,
spl0_131,
inference(avatar_split_clause,[],[f126,f978]) ).
fof(f978,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
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(f976,plain,
spl0_130,
inference(avatar_split_clause,[],[f125,f974]) ).
fof(f974,plain,
( spl0_130
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
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(f972,plain,
spl0_129,
inference(avatar_split_clause,[],[f124,f970]) ).
fof(f970,plain,
( spl0_129
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
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(f968,plain,
spl0_128,
inference(avatar_split_clause,[],[f122,f966]) ).
fof(f966,plain,
( spl0_128
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
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(f964,plain,
spl0_127,
inference(avatar_split_clause,[],[f120,f962]) ).
fof(f962,plain,
( spl0_127
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
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_126,
inference(avatar_split_clause,[],[f119,f886]) ).
fof(f886,plain,
( spl0_126
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
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_125,
inference(avatar_split_clause,[],[f118,f882]) ).
fof(f882,plain,
( spl0_125
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
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_124,
inference(avatar_split_clause,[],[f109,f878]) ).
fof(f878,plain,
( spl0_124
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
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_123,
inference(avatar_split_clause,[],[f104,f874]) ).
fof(f874,plain,
( spl0_123
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f104,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
fof(f863,plain,
( ~ spl0_4
| spl0_122
| ~ spl0_6
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f609,f584,f271,f860,f261]) ).
fof(f860,plain,
( spl0_122
<=> totalorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f584,plain,
( spl0_80
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f609,plain,
( totalorderedP(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_80 ),
inference(superposition,[],[f585,f273]) ).
fof(f585,plain,
( ! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f846,plain,
spl0_121,
inference(avatar_split_clause,[],[f219,f844]) ).
fof(f219,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(f842,plain,
spl0_120,
inference(avatar_split_clause,[],[f114,f840]) ).
fof(f840,plain,
( spl0_120
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f114,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
fof(f838,plain,
spl0_119,
inference(avatar_split_clause,[],[f110,f836]) ).
fof(f836,plain,
( spl0_119
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f110,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
fof(f834,plain,
spl0_118,
inference(avatar_split_clause,[],[f108,f832]) ).
fof(f832,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f108,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
fof(f830,plain,
spl0_117,
inference(avatar_split_clause,[],[f107,f828]) ).
fof(f828,plain,
( spl0_117
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f107,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
fof(f826,plain,
spl0_116,
inference(avatar_split_clause,[],[f106,f824]) ).
fof(f824,plain,
( spl0_116
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f106,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
fof(f822,plain,
spl0_115,
inference(avatar_split_clause,[],[f105,f820]) ).
fof(f820,plain,
( spl0_115
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
fof(f818,plain,
spl0_114,
inference(avatar_split_clause,[],[f103,f816]) ).
fof(f816,plain,
( spl0_114
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f103,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
fof(f814,plain,
spl0_113,
inference(avatar_split_clause,[],[f102,f812]) ).
fof(f812,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f102,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
fof(f810,plain,
spl0_112,
inference(avatar_split_clause,[],[f101,f808]) ).
fof(f808,plain,
( spl0_112
<=> ! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f101,axiom,
! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
fof(f806,plain,
spl0_111,
inference(avatar_split_clause,[],[f100,f804]) ).
fof(f100,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f802,plain,
spl0_110,
inference(avatar_split_clause,[],[f97,f800]) ).
fof(f800,plain,
( spl0_110
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
fof(f798,plain,
spl0_109,
inference(avatar_split_clause,[],[f96,f796]) ).
fof(f796,plain,
( spl0_109
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f96,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
fof(f794,plain,
( ~ spl0_4
| spl0_108
| ~ spl0_6
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f608,f580,f271,f791,f261]) ).
fof(f791,plain,
( spl0_108
<=> strictorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f580,plain,
( spl0_79
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f608,plain,
( strictorderedP(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_79 ),
inference(superposition,[],[f581,f273]) ).
fof(f581,plain,
( ! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f784,plain,
spl0_107,
inference(avatar_split_clause,[],[f240,f782]) ).
fof(f240,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(duplicate_literal_removal,[],[f223]) ).
fof(f223,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(f780,plain,
spl0_106,
inference(avatar_split_clause,[],[f99,f778]) ).
fof(f778,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f99,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
fof(f776,plain,
spl0_105,
inference(avatar_split_clause,[],[f98,f774]) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f772,plain,
spl0_104,
inference(avatar_split_clause,[],[f95,f770]) ).
fof(f770,plain,
( spl0_104
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f95,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
fof(f768,plain,
spl0_103,
inference(avatar_split_clause,[],[f94,f766]) ).
fof(f766,plain,
( spl0_103
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f94,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
fof(f764,plain,
spl0_102,
inference(avatar_split_clause,[],[f93,f762]) ).
fof(f762,plain,
( spl0_102
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f93,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
fof(f760,plain,
spl0_101,
inference(avatar_split_clause,[],[f92,f758]) ).
fof(f758,plain,
( spl0_101
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f92,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
fof(f756,plain,
spl0_100,
inference(avatar_split_clause,[],[f91,f754]) ).
fof(f754,plain,
( spl0_100
<=> ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f91,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
fof(f752,plain,
( ~ spl0_4
| spl0_99
| ~ spl0_6
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f607,f576,f271,f749,f261]) ).
fof(f749,plain,
( spl0_99
<=> duplicatefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f576,plain,
( spl0_78
<=> ! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f607,plain,
( duplicatefreeP(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_78 ),
inference(superposition,[],[f577,f273]) ).
fof(f577,plain,
( ! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f747,plain,
spl0_98,
inference(avatar_split_clause,[],[f90,f745]) ).
fof(f745,plain,
( spl0_98
<=> ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f90,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
fof(f743,plain,
spl0_97,
inference(avatar_split_clause,[],[f89,f741]) ).
fof(f741,plain,
( spl0_97
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f89,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
fof(f739,plain,
spl0_96,
inference(avatar_split_clause,[],[f88,f737]) ).
fof(f737,plain,
( spl0_96
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f88,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
fof(f735,plain,
spl0_95,
inference(avatar_split_clause,[],[f87,f733]) ).
fof(f733,plain,
( spl0_95
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f87,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
fof(f711,plain,
spl0_94,
inference(avatar_split_clause,[],[f86,f709]) ).
fof(f709,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f86,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f707,plain,
spl0_93,
inference(avatar_split_clause,[],[f85,f705]) ).
fof(f705,plain,
( spl0_93
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f703,plain,
spl0_92,
inference(avatar_split_clause,[],[f84,f701]) ).
fof(f701,plain,
( spl0_92
<=> ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f84,axiom,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
fof(f699,plain,
spl0_91,
inference(avatar_split_clause,[],[f82,f697]) ).
fof(f697,plain,
( spl0_91
<=> ! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f82,axiom,
! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
fof(f695,plain,
spl0_90,
inference(avatar_split_clause,[],[f80,f693]) ).
fof(f693,plain,
( spl0_90
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f80,axiom,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
fof(f691,plain,
spl0_89,
inference(avatar_split_clause,[],[f77,f689]) ).
fof(f689,plain,
( spl0_89
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f77,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
fof(f625,plain,
spl0_88,
inference(avatar_split_clause,[],[f74,f623]) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f621,plain,
spl0_87,
inference(avatar_split_clause,[],[f73,f619]) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f617,plain,
( ~ spl0_4
| spl0_86
| ~ spl0_6
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f606,f572,f271,f614,f261]) ).
fof(f614,plain,
( spl0_86
<=> equalelemsP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f572,plain,
( spl0_77
<=> ! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f606,plain,
( equalelemsP(sk3)
| ~ ssItem(sk5)
| ~ spl0_6
| ~ spl0_77 ),
inference(superposition,[],[f573,f273]) ).
fof(f573,plain,
( ! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f605,plain,
( spl0_84
| spl0_85 ),
inference(avatar_split_clause,[],[f72,f603,f600]) ).
fof(f600,plain,
( spl0_84
<=> ! [X1] : ssItem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f603,plain,
( spl0_85
<=> ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
fof(f598,plain,
spl0_83,
inference(avatar_split_clause,[],[f70,f596]) ).
fof(f70,axiom,
! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
fof(f594,plain,
spl0_82,
inference(avatar_split_clause,[],[f69,f592]) ).
fof(f69,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
fof(f590,plain,
spl0_81,
inference(avatar_split_clause,[],[f68,f588]) ).
fof(f68,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
fof(f586,plain,
spl0_80,
inference(avatar_split_clause,[],[f67,f584]) ).
fof(f67,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
fof(f582,plain,
spl0_79,
inference(avatar_split_clause,[],[f66,f580]) ).
fof(f66,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
fof(f578,plain,
spl0_78,
inference(avatar_split_clause,[],[f65,f576]) ).
fof(f65,axiom,
! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
fof(f574,plain,
spl0_77,
inference(avatar_split_clause,[],[f64,f572]) ).
fof(f64,axiom,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
fof(f570,plain,
spl0_76,
inference(avatar_split_clause,[],[f242,f568]) ).
fof(f568,plain,
( spl0_76
<=> ! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f242,plain,
! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f218,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(f566,plain,
spl0_75,
inference(avatar_split_clause,[],[f241,f564]) ).
fof(f564,plain,
( spl0_75
<=> ! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f241,plain,
! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f222,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(f562,plain,
spl0_74,
inference(avatar_split_clause,[],[f71,f560]) ).
fof(f560,plain,
( spl0_74
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f558,plain,
spl0_73,
inference(avatar_split_clause,[],[f63,f556]) ).
fof(f556,plain,
( spl0_73
<=> ! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f63,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
fof(f554,plain,
spl0_72,
inference(avatar_split_clause,[],[f62,f552]) ).
fof(f552,plain,
( spl0_72
<=> ! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f62,axiom,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
fof(f550,plain,
spl0_71,
inference(avatar_split_clause,[],[f61,f548]) ).
fof(f548,plain,
( spl0_71
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f61,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
fof(f546,plain,
spl0_70,
inference(avatar_split_clause,[],[f60,f544]) ).
fof(f544,plain,
( spl0_70
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f60,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
fof(f542,plain,
spl0_69,
inference(avatar_split_clause,[],[f59,f540]) ).
fof(f540,plain,
( spl0_69
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f59,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
fof(f538,plain,
spl0_68,
inference(avatar_split_clause,[],[f58,f536]) ).
fof(f536,plain,
( spl0_68
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f58,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
fof(f534,plain,
spl0_67,
inference(avatar_split_clause,[],[f57,f532]) ).
fof(f532,plain,
( spl0_67
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f57,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
fof(f530,plain,
spl0_66,
inference(avatar_split_clause,[],[f56,f528]) ).
fof(f528,plain,
( spl0_66
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f56,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
fof(f526,plain,
spl0_65,
inference(avatar_split_clause,[],[f55,f524]) ).
fof(f524,plain,
( spl0_65
<=> ! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f55,axiom,
! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
fof(f522,plain,
spl0_64,
inference(avatar_split_clause,[],[f53,f520]) ).
fof(f520,plain,
( spl0_64
<=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f53,axiom,
! [X0,X1] : ssList(skaf42(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
fof(f518,plain,
spl0_63,
inference(avatar_split_clause,[],[f52,f516]) ).
fof(f516,plain,
( spl0_63
<=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f52,axiom,
! [X0,X1] : ssList(skaf43(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
fof(f514,plain,
spl0_62,
inference(avatar_split_clause,[],[f51,f512]) ).
fof(f512,plain,
( spl0_62
<=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
fof(f510,plain,
spl0_61,
inference(avatar_split_clause,[],[f50,f508]) ).
fof(f508,plain,
( spl0_61
<=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
fof(f506,plain,
spl0_60,
inference(avatar_split_clause,[],[f49,f504]) ).
fof(f504,plain,
( spl0_60
<=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f49,axiom,
! [X0,X1] : ssList(skaf47(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
fof(f502,plain,
spl0_59,
inference(avatar_split_clause,[],[f48,f500]) ).
fof(f500,plain,
( spl0_59
<=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f48,axiom,
! [X0,X1] : ssList(skaf48(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
fof(f498,plain,
~ spl0_58,
inference(avatar_split_clause,[],[f54,f495]) ).
fof(f495,plain,
( spl0_58
<=> skac3 = skac2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f54,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
fof(f493,plain,
spl0_57,
inference(avatar_split_clause,[],[f47,f491]) ).
fof(f491,plain,
( spl0_57
<=> ! [X0] : ssItem(skaf44(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
fof(f489,plain,
spl0_56,
inference(avatar_split_clause,[],[f46,f487]) ).
fof(f487,plain,
( spl0_56
<=> ! [X0] : ssItem(skaf49(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f46,axiom,
! [X0] : ssItem(skaf49(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
fof(f485,plain,
spl0_55,
inference(avatar_split_clause,[],[f45,f483]) ).
fof(f483,plain,
( spl0_55
<=> ! [X0] : ssItem(skaf50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f45,axiom,
! [X0] : ssItem(skaf50(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
fof(f481,plain,
spl0_54,
inference(avatar_split_clause,[],[f44,f479]) ).
fof(f479,plain,
( spl0_54
<=> ! [X0] : ssList(skaf51(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f44,axiom,
! [X0] : ssList(skaf51(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
fof(f477,plain,
spl0_53,
inference(avatar_split_clause,[],[f43,f475]) ).
fof(f475,plain,
( spl0_53
<=> ! [X0] : ssList(skaf52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f43,axiom,
! [X0] : ssList(skaf52(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
fof(f473,plain,
spl0_52,
inference(avatar_split_clause,[],[f42,f471]) ).
fof(f471,plain,
( spl0_52
<=> ! [X0] : ssList(skaf53(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f42,axiom,
! [X0] : ssList(skaf53(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
fof(f469,plain,
spl0_51,
inference(avatar_split_clause,[],[f41,f467]) ).
fof(f467,plain,
( spl0_51
<=> ! [X0] : ssItem(skaf54(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f41,axiom,
! [X0] : ssItem(skaf54(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
fof(f465,plain,
spl0_50,
inference(avatar_split_clause,[],[f40,f463]) ).
fof(f463,plain,
( spl0_50
<=> ! [X0] : ssItem(skaf55(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f40,axiom,
! [X0] : ssItem(skaf55(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
fof(f461,plain,
spl0_49,
inference(avatar_split_clause,[],[f39,f459]) ).
fof(f459,plain,
( spl0_49
<=> ! [X0] : ssList(skaf56(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f39,axiom,
! [X0] : ssList(skaf56(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
fof(f457,plain,
spl0_48,
inference(avatar_split_clause,[],[f38,f455]) ).
fof(f455,plain,
( spl0_48
<=> ! [X0] : ssList(skaf57(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f38,axiom,
! [X0] : ssList(skaf57(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
fof(f453,plain,
spl0_47,
inference(avatar_split_clause,[],[f37,f451]) ).
fof(f451,plain,
( spl0_47
<=> ! [X0] : ssList(skaf58(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f37,axiom,
! [X0] : ssList(skaf58(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
fof(f449,plain,
spl0_46,
inference(avatar_split_clause,[],[f36,f447]) ).
fof(f447,plain,
( spl0_46
<=> ! [X0] : ssItem(skaf59(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f36,axiom,
! [X0] : ssItem(skaf59(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
fof(f445,plain,
spl0_45,
inference(avatar_split_clause,[],[f35,f443]) ).
fof(f443,plain,
( spl0_45
<=> ! [X0] : ssItem(skaf60(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f35,axiom,
! [X0] : ssItem(skaf60(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
fof(f441,plain,
spl0_44,
inference(avatar_split_clause,[],[f34,f439]) ).
fof(f439,plain,
( spl0_44
<=> ! [X0] : ssList(skaf61(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f34,axiom,
! [X0] : ssList(skaf61(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
fof(f437,plain,
spl0_43,
inference(avatar_split_clause,[],[f33,f435]) ).
fof(f435,plain,
( spl0_43
<=> ! [X0] : ssList(skaf62(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f33,axiom,
! [X0] : ssList(skaf62(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
fof(f433,plain,
spl0_42,
inference(avatar_split_clause,[],[f32,f431]) ).
fof(f431,plain,
( spl0_42
<=> ! [X0] : ssList(skaf63(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f32,axiom,
! [X0] : ssList(skaf63(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
fof(f429,plain,
spl0_41,
inference(avatar_split_clause,[],[f31,f427]) ).
fof(f427,plain,
( spl0_41
<=> ! [X0] : ssItem(skaf64(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f31,axiom,
! [X0] : ssItem(skaf64(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
fof(f425,plain,
spl0_40,
inference(avatar_split_clause,[],[f30,f423]) ).
fof(f423,plain,
( spl0_40
<=> ! [X0] : ssItem(skaf65(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f30,axiom,
! [X0] : ssItem(skaf65(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
fof(f421,plain,
spl0_39,
inference(avatar_split_clause,[],[f29,f419]) ).
fof(f419,plain,
( spl0_39
<=> ! [X0] : ssList(skaf66(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f29,axiom,
! [X0] : ssList(skaf66(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
fof(f417,plain,
spl0_38,
inference(avatar_split_clause,[],[f28,f415]) ).
fof(f415,plain,
( spl0_38
<=> ! [X0] : ssList(skaf67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f28,axiom,
! [X0] : ssList(skaf67(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
fof(f413,plain,
spl0_37,
inference(avatar_split_clause,[],[f27,f411]) ).
fof(f411,plain,
( spl0_37
<=> ! [X0] : ssList(skaf68(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f27,axiom,
! [X0] : ssList(skaf68(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
fof(f409,plain,
spl0_36,
inference(avatar_split_clause,[],[f26,f407]) ).
fof(f407,plain,
( spl0_36
<=> ! [X0] : ssItem(skaf69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f26,axiom,
! [X0] : ssItem(skaf69(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
fof(f405,plain,
spl0_35,
inference(avatar_split_clause,[],[f25,f403]) ).
fof(f403,plain,
( spl0_35
<=> ! [X0] : ssItem(skaf70(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f25,axiom,
! [X0] : ssItem(skaf70(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
fof(f401,plain,
spl0_34,
inference(avatar_split_clause,[],[f24,f399]) ).
fof(f399,plain,
( spl0_34
<=> ! [X0] : ssList(skaf71(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f24,axiom,
! [X0] : ssList(skaf71(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
fof(f397,plain,
spl0_33,
inference(avatar_split_clause,[],[f23,f395]) ).
fof(f395,plain,
( spl0_33
<=> ! [X0] : ssList(skaf72(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f23,axiom,
! [X0] : ssList(skaf72(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
fof(f393,plain,
spl0_32,
inference(avatar_split_clause,[],[f22,f391]) ).
fof(f391,plain,
( spl0_32
<=> ! [X0] : ssList(skaf73(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f22,axiom,
! [X0] : ssList(skaf73(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
fof(f389,plain,
spl0_31,
inference(avatar_split_clause,[],[f21,f387]) ).
fof(f387,plain,
( spl0_31
<=> ! [X0] : ssItem(skaf74(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f21,axiom,
! [X0] : ssItem(skaf74(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
fof(f385,plain,
spl0_30,
inference(avatar_split_clause,[],[f20,f383]) ).
fof(f383,plain,
( spl0_30
<=> ! [X0] : ssList(skaf75(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f20,axiom,
! [X0] : ssList(skaf75(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
fof(f381,plain,
spl0_29,
inference(avatar_split_clause,[],[f19,f379]) ).
fof(f379,plain,
( spl0_29
<=> ! [X0] : ssList(skaf76(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f19,axiom,
! [X0] : ssList(skaf76(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
fof(f377,plain,
spl0_28,
inference(avatar_split_clause,[],[f18,f375]) ).
fof(f375,plain,
( spl0_28
<=> ! [X0] : ssList(skaf77(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f18,axiom,
! [X0] : ssList(skaf77(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
fof(f373,plain,
spl0_27,
inference(avatar_split_clause,[],[f17,f371]) ).
fof(f371,plain,
( spl0_27
<=> ! [X0] : ssItem(skaf78(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f17,axiom,
! [X0] : ssItem(skaf78(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
fof(f369,plain,
spl0_26,
inference(avatar_split_clause,[],[f16,f367]) ).
fof(f367,plain,
( spl0_26
<=> ! [X0] : ssItem(skaf79(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f16,axiom,
! [X0] : ssItem(skaf79(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
fof(f365,plain,
spl0_25,
inference(avatar_split_clause,[],[f15,f363]) ).
fof(f363,plain,
( spl0_25
<=> ! [X0] : ssList(skaf80(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f15,axiom,
! [X0] : ssList(skaf80(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
fof(f361,plain,
spl0_24,
inference(avatar_split_clause,[],[f14,f359]) ).
fof(f359,plain,
( spl0_24
<=> ! [X0] : ssList(skaf81(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f14,axiom,
! [X0] : ssList(skaf81(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
fof(f357,plain,
spl0_23,
inference(avatar_split_clause,[],[f13,f355]) ).
fof(f355,plain,
( spl0_23
<=> ! [X0] : ssList(skaf82(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
fof(f353,plain,
spl0_22,
inference(avatar_split_clause,[],[f12,f351]) ).
fof(f351,plain,
( spl0_22
<=> ! [X0] : ssItem(skaf83(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
fof(f349,plain,
( spl0_21
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f344,f340,f271,f346]) ).
fof(f340,plain,
( spl0_20
<=> sk4 = app(sk6,cons(sk5,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f344,plain,
( sk4 = app(sk6,sk3)
| ~ spl0_6
| ~ spl0_20 ),
inference(forward_demodulation,[],[f342,f273]) ).
fof(f342,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f343,plain,
( spl0_20
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f202,f256,f340]) ).
fof(f256,plain,
( spl0_3
<=> neq(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f202,axiom,
( ~ neq(sk4,nil)
| sk4 = app(sk6,cons(sk5,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f338,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f212,f335,f331,f256]) ).
fof(f212,plain,
( ~ rearsegP(sk4,sk3)
| ~ neq(sk3,nil)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f203,f190,f191,f191]) ).
fof(f191,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f190,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f203,axiom,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f329,plain,
~ spl0_17,
inference(avatar_split_clause,[],[f11,f326]) ).
fof(f326,plain,
( spl0_17
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
fof(f324,plain,
spl0_16,
inference(avatar_split_clause,[],[f10,f321]) ).
fof(f321,plain,
( spl0_16
<=> ssItem(skac2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
fof(f319,plain,
spl0_15,
inference(avatar_split_clause,[],[f9,f316]) ).
fof(f316,plain,
( spl0_15
<=> ssItem(skac3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
fof(f314,plain,
spl0_14,
inference(avatar_split_clause,[],[f8,f311]) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f309,plain,
spl0_13,
inference(avatar_split_clause,[],[f7,f306]) ).
fof(f306,plain,
( spl0_13
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f7,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
fof(f304,plain,
spl0_12,
inference(avatar_split_clause,[],[f6,f301]) ).
fof(f301,plain,
( spl0_12
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f6,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
fof(f299,plain,
spl0_11,
inference(avatar_split_clause,[],[f5,f296]) ).
fof(f296,plain,
( spl0_11
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f5,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
fof(f294,plain,
spl0_10,
inference(avatar_split_clause,[],[f4,f291]) ).
fof(f291,plain,
( spl0_10
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
fof(f289,plain,
spl0_9,
inference(avatar_split_clause,[],[f3,f286]) ).
fof(f286,plain,
( spl0_9
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
fof(f284,plain,
spl0_8,
inference(avatar_split_clause,[],[f2,f281]) ).
fof(f281,plain,
( spl0_8
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f2,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
fof(f279,plain,
spl0_7,
inference(avatar_split_clause,[],[f1,f276]) ).
fof(f276,plain,
( spl0_7
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
fof(f274,plain,
( spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f201,f256,f271]) ).
fof(f201,axiom,
( ~ neq(sk4,nil)
| sk3 = cons(sk5,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f269,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f200,f266,f256]) ).
fof(f200,axiom,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f264,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f199,f261,f256]) ).
fof(f199,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f259,plain,
spl0_3,
inference(avatar_split_clause,[],[f244,f256]) ).
fof(f244,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f209,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(f254,plain,
spl0_2,
inference(avatar_split_clause,[],[f189,f251]) ).
fof(f189,axiom,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f249,plain,
spl0_1,
inference(avatar_split_clause,[],[f188,f246]) ).
fof(f188,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC106-1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 30 04:05:51 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (22005)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (22008)WARNING: value z3 for option sas not known
% 0.20/0.37 % (22009)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (22006)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (22010)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)
% 0.20/0.37 % (22011)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)
% 0.20/0.37 % (22007)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (22012)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)
% 0.20/0.37 % (22008)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)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.39 TRYING [3]
% 0.20/0.40 TRYING [1]
% 0.20/0.40 TRYING [2]
% 0.20/0.41 % (22010)First to succeed.
% 0.20/0.41 TRYING [3]
% 0.20/0.42 % (22010)Refutation found. Thanks to Tanya!
% 0.20/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43 % (22010)------------------------------
% 0.20/0.43 % (22010)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.43 % (22010)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (22010)Memory used [KB]: 2169
% 0.20/0.43 % (22010)Time elapsed: 0.055 s
% 0.20/0.43 % (22010)Instructions burned: 96 (million)
% 0.20/0.43 % (22010)------------------------------
% 0.20/0.43 % (22010)------------------------------
% 0.20/0.43 % (22005)Success in time 0.066 s
%------------------------------------------------------------------------------