TSTP Solution File: SWC322-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC322-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 05:13:00 EDT 2024
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 380
% Syntax : Number of formulae : 759 ( 213 unt; 0 def)
% Number of atoms : 2175 ( 297 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2560 (1144 ~;1202 |; 0 &)
% ( 214 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 235 ( 233 usr; 215 prp; 0-2 aty)
% Number of functors : 55 ( 55 usr; 9 con; 0-2 aty)
% Number of variables : 635 ( 635 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1863,plain,
$false,
inference(avatar_sat_refutation,[],[f249,f254,f263,f268,f274,f280,f287,f292,f299,f304,f311,f316,f323,f324,f334,f339,f344,f349,f354,f359,f364,f369,f374,f379,f383,f387,f391,f395,f399,f403,f407,f411,f415,f419,f423,f427,f431,f435,f439,f443,f447,f451,f455,f459,f463,f467,f471,f475,f479,f483,f487,f491,f495,f499,f503,f507,f511,f515,f519,f523,f528,f532,f536,f540,f544,f548,f552,f556,f561,f567,f571,f575,f579,f583,f587,f588,f590,f591,f596,f601,f602,f609,f630,f636,f641,f645,f649,f653,f657,f662,f666,f670,f676,f682,f688,f692,f696,f701,f705,f710,f714,f719,f724,f728,f733,f737,f742,f746,f751,f758,f794,f799,f836,f841,f878,f883,f890,f895,f899,f905,f912,f918,f925,f931,f938,f942,f953,f957,f961,f965,f969,f973,f977,f981,f985,f989,f994,f998,f1003,f1007,f1011,f1015,f1019,f1023,f1028,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1074,f1099,f1136,f1140,f1145,f1183,f1188,f1226,f1232,f1238,f1245,f1249,f1255,f1260,f1283,f1287,f1292,f1298,f1304,f1308,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1347,f1384,f1389,f1431,f1435,f1439,f1443,f1447,f1451,f1455,f1496,f1501,f1507,f1512,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1600,f1605,f1643,f1663,f1667,f1694,f1698,f1702,f1706,f1710,f1730,f1736,f1741,f1745,f1845,f1857,f1858,f1862]) ).
fof(f1862,plain,
( spl0_15
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1860,f256,f331]) ).
fof(f331,plain,
( spl0_15
<=> ssList(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f256,plain,
( spl0_3
<=> nil = sk3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1860,plain,
( ssList(sk6)
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f1859]) ).
fof(f1859,plain,
( sk3 != sk3
| ssList(sk6)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f206,f257]) ).
fof(f257,plain,
( nil = sk3
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f206,plain,
( ssList(sk6)
| nil != sk3 ),
inference(definition_unfolding,[],[f199,f191]) ).
fof(f191,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f199,axiom,
( ssList(sk6)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f1858,plain,
( spl0_214
| ~ spl0_3
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f1849,f376,f256,f1854]) ).
fof(f1854,plain,
( spl0_214
<=> sk3 = app(cons(sk5,sk3),sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f376,plain,
( spl0_24
<=> sk3 = app(cons(sk5,nil),sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1849,plain,
( sk3 = app(cons(sk5,sk3),sk6)
| ~ spl0_3
| ~ spl0_24 ),
inference(forward_demodulation,[],[f377,f257]) ).
fof(f377,plain,
( sk3 = app(cons(sk5,nil),sk6)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f1857,plain,
( ~ spl0_214
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1848,f256,f1854]) ).
fof(f1848,plain,
( sk3 != app(cons(sk5,sk3),sk6)
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f1847]) ).
fof(f1847,plain,
( sk3 != sk3
| sk3 != app(cons(sk5,sk3),sk6)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f243,f257]) ).
fof(f243,plain,
( nil != sk3
| sk3 != app(cons(sk5,sk3),sk6) ),
inference(inner_rewriting,[],[f208]) ).
fof(f208,plain,
( nil != sk3
| sk3 != app(cons(sk5,nil),sk6) ),
inference(definition_unfolding,[],[f201,f191,f191]) ).
fof(f201,axiom,
( nil != sk1
| sk1 != app(cons(sk5,nil),sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f1845,plain,
( ~ spl0_78
| ~ spl0_3
| spl0_23 ),
inference(avatar_split_clause,[],[f619,f371,f256,f633]) ).
fof(f633,plain,
( spl0_78
<=> sk3 = app(sk6,cons(sk5,sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f371,plain,
( spl0_23
<=> sk3 = app(sk6,cons(sk5,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f619,plain,
( sk3 != app(sk6,cons(sk5,sk3))
| ~ spl0_3
| spl0_23 ),
inference(superposition,[],[f372,f257]) ).
fof(f372,plain,
( sk3 != app(sk6,cons(sk5,nil))
| spl0_23 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f1745,plain,
spl0_213,
inference(avatar_split_clause,[],[f161,f1743]) ).
fof(f1743,plain,
( spl0_213
<=> ! [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_213])]) ).
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(f1741,plain,
( spl0_212
| ~ spl0_3
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1737,f1734,f256,f1739]) ).
fof(f1739,plain,
( spl0_212
<=> ! [X0,X1] :
( sk3 = X1
| ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1734,plain,
( spl0_211
<=> ! [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_211])]) ).
fof(f1737,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) )
| ~ spl0_3
| ~ spl0_211 ),
inference(forward_demodulation,[],[f1735,f257]) ).
fof(f1735,plain,
( ! [X0,X1] :
( ~ strictorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ lt(X0,hd(X1))
| strictorderedP(cons(X0,X1)) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f1734]) ).
fof(f1736,plain,
spl0_211,
inference(avatar_split_clause,[],[f160,f1734]) ).
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(f1730,plain,
( spl0_210
| ~ spl0_3
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1711,f1708,f256,f1728]) ).
fof(f1728,plain,
( spl0_210
<=> ! [X0,X1] :
( sk3 = X1
| ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1708,plain,
( spl0_209
<=> ! [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_209])]) ).
fof(f1711,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) )
| ~ spl0_3
| ~ spl0_209 ),
inference(forward_demodulation,[],[f1709,f257]) ).
fof(f1709,plain,
( ! [X0,X1] :
( ~ totalorderedP(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ leq(X0,hd(X1))
| totalorderedP(cons(X0,X1)) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1708]) ).
fof(f1710,plain,
spl0_209,
inference(avatar_split_clause,[],[f159,f1708]) ).
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(f1706,plain,
spl0_208,
inference(avatar_split_clause,[],[f158,f1704]) ).
fof(f1704,plain,
( spl0_208
<=> ! [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_208])]) ).
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(f1702,plain,
spl0_207,
inference(avatar_split_clause,[],[f157,f1700]) ).
fof(f1700,plain,
( spl0_207
<=> ! [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_207])]) ).
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(f1698,plain,
spl0_206,
inference(avatar_split_clause,[],[f149,f1696]) ).
fof(f1696,plain,
( spl0_206
<=> ! [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_206])]) ).
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(f1694,plain,
spl0_205,
inference(avatar_split_clause,[],[f142,f1692]) ).
fof(f1692,plain,
( spl0_205
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| app(skaf80(X0),cons(skaf78(X0),cons(skaf79(X0),skaf81(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
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(f1667,plain,
spl0_204,
inference(avatar_split_clause,[],[f236,f1665]) ).
fof(f1665,plain,
( spl0_204
<=> ! [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_204])]) ).
fof(f236,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(duplicate_literal_removal,[],[f229]) ).
fof(f229,plain,
! [X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| frontsegP(cons(X3,X0),cons(X3,X1)) ),
inference(equality_resolution,[],[f178]) ).
fof(f178,axiom,
! [X2,X3,X0,X1] :
( ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| X2 != X3
| ~ frontsegP(X0,X1)
| frontsegP(cons(X2,X0),cons(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause178) ).
fof(f1663,plain,
spl0_203,
inference(avatar_split_clause,[],[f151,f1661]) ).
fof(f1661,plain,
( spl0_203
<=> ! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X2
| app(X0,X1) != app(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
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(f1643,plain,
spl0_202,
inference(avatar_split_clause,[],[f150,f1641]) ).
fof(f1641,plain,
( spl0_202
<=> ! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| X1 = X2
| app(X0,X1) != app(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
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(f1605,plain,
( spl0_201
| ~ spl0_3
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1601,f1598,f256,f1603]) ).
fof(f1603,plain,
( spl0_201
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| tl(app(X1,X0)) = app(tl(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1598,plain,
( spl0_200
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1601,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ spl0_3
| ~ spl0_200 ),
inference(forward_demodulation,[],[f1599,f257]) ).
fof(f1599,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| tl(app(X1,X0)) = app(tl(X1),X0) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f1600,plain,
spl0_200,
inference(avatar_split_clause,[],[f133,f1598]) ).
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(f1553,plain,
spl0_199,
inference(avatar_split_clause,[],[f156,f1551]) ).
fof(f1551,plain,
( spl0_199
<=> ! [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_199])]) ).
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(f1549,plain,
spl0_198,
inference(avatar_split_clause,[],[f155,f1547]) ).
fof(f1547,plain,
( spl0_198
<=> ! [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_198])]) ).
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(f1545,plain,
spl0_197,
inference(avatar_split_clause,[],[f154,f1543]) ).
fof(f1543,plain,
( spl0_197
<=> ! [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_197])]) ).
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(f1541,plain,
spl0_196,
inference(avatar_split_clause,[],[f153,f1539]) ).
fof(f1539,plain,
( spl0_196
<=> ! [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_196])]) ).
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(f1537,plain,
spl0_195,
inference(avatar_split_clause,[],[f152,f1535]) ).
fof(f1535,plain,
( spl0_195
<=> ! [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_195])]) ).
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(f1533,plain,
spl0_194,
inference(avatar_split_clause,[],[f148,f1531]) ).
fof(f1531,plain,
( spl0_194
<=> ! [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_194])]) ).
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(f1529,plain,
spl0_193,
inference(avatar_split_clause,[],[f147,f1527]) ).
fof(f1527,plain,
( spl0_193
<=> ! [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_193])]) ).
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(f1525,plain,
spl0_192,
inference(avatar_split_clause,[],[f146,f1523]) ).
fof(f1523,plain,
( spl0_192
<=> ! [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_192])]) ).
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(f1512,plain,
( spl0_191
| ~ spl0_3
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1508,f1505,f256,f1510]) ).
fof(f1510,plain,
( spl0_191
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1505,plain,
( spl0_190
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1508,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) )
| ~ spl0_3
| ~ spl0_190 ),
inference(forward_demodulation,[],[f1506,f257]) ).
fof(f1506,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| leq(X0,hd(X1)) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1505]) ).
fof(f1507,plain,
spl0_190,
inference(avatar_split_clause,[],[f135,f1505]) ).
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(f1501,plain,
( spl0_189
| ~ spl0_3
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1497,f1494,f256,f1499]) ).
fof(f1499,plain,
( spl0_189
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1494,plain,
( spl0_188
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1497,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) )
| ~ spl0_3
| ~ spl0_188 ),
inference(forward_demodulation,[],[f1495,f257]) ).
fof(f1495,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| lt(X0,hd(X1)) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1494]) ).
fof(f1496,plain,
spl0_188,
inference(avatar_split_clause,[],[f134,f1494]) ).
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(f1455,plain,
spl0_187,
inference(avatar_split_clause,[],[f141,f1453]) ).
fof(f1453,plain,
( spl0_187
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1)
| memberP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
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(f1451,plain,
spl0_186,
inference(avatar_split_clause,[],[f140,f1449]) ).
fof(f1449,plain,
( spl0_186
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
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(f1447,plain,
spl0_185,
inference(avatar_split_clause,[],[f139,f1445]) ).
fof(f1445,plain,
( spl0_185
<=> ! [X2,X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1)
| memberP(cons(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
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(f1443,plain,
spl0_184,
inference(avatar_split_clause,[],[f137,f1441]) ).
fof(f1441,plain,
( spl0_184
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f137,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| frontsegP(app(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause137) ).
fof(f1439,plain,
spl0_183,
inference(avatar_split_clause,[],[f136,f1437]) ).
fof(f1437,plain,
( spl0_183
<=> ! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f136,axiom,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| rearsegP(app(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause136) ).
fof(f1435,plain,
spl0_182,
inference(avatar_split_clause,[],[f132,f1433]) ).
fof(f1433,plain,
( spl0_182
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f132,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| app(X1,skaf45(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
fof(f1431,plain,
spl0_181,
inference(avatar_split_clause,[],[f131,f1429]) ).
fof(f1429,plain,
( spl0_181
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f131,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause131) ).
fof(f1389,plain,
( spl0_180
| ~ spl0_3
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1385,f1382,f256,f1387]) ).
fof(f1387,plain,
( spl0_180
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| hd(app(X1,X0)) = hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1382,plain,
( spl0_179
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1385,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| hd(app(X1,X0)) = hd(X1) )
| ~ spl0_3
| ~ spl0_179 ),
inference(forward_demodulation,[],[f1383,f257]) ).
fof(f1383,plain,
( ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X1
| hd(app(X1,X0)) = hd(X1) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1382]) ).
fof(f1384,plain,
spl0_179,
inference(avatar_split_clause,[],[f123,f1382]) ).
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(f1347,plain,
( spl0_178
| ~ spl0_15
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f872,f839,f331,f1344]) ).
fof(f1344,plain,
( spl0_178
<=> sk6 = app(sk3,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f839,plain,
( spl0_109
<=> ! [X0] :
( app(sk3,X0) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f872,plain,
( sk6 = app(sk3,sk6)
| ~ spl0_15
| ~ spl0_109 ),
inference(resolution,[],[f840,f333]) ).
fof(f333,plain,
( ssList(sk6)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f840,plain,
( ! [X0] :
( ~ ssList(X0)
| app(sk3,X0) = X0 )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f1338,plain,
spl0_177,
inference(avatar_split_clause,[],[f223,f1336]) ).
fof(f1336,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f223,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| frontsegP(X2,X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
fof(f1334,plain,
spl0_176,
inference(avatar_split_clause,[],[f222,f1332]) ).
fof(f1332,plain,
( spl0_176
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f222,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ),
inference(equality_resolution,[],[f143]) ).
fof(f143,axiom,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X2,X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause143) ).
fof(f1330,plain,
spl0_175,
inference(avatar_split_clause,[],[f130,f1328]) ).
fof(f1328,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
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(f1326,plain,
spl0_174,
inference(avatar_split_clause,[],[f129,f1324]) ).
fof(f1324,plain,
( spl0_174
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
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(f1322,plain,
spl0_173,
inference(avatar_split_clause,[],[f128,f1320]) ).
fof(f1320,plain,
( spl0_173
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f128,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause128) ).
fof(f1318,plain,
spl0_172,
inference(avatar_split_clause,[],[f127,f1316]) ).
fof(f1316,plain,
( spl0_172
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f127,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
fof(f1314,plain,
spl0_171,
inference(avatar_split_clause,[],[f126,f1312]) ).
fof(f1312,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f126,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause126) ).
fof(f1308,plain,
( spl0_170
| ~ spl0_3
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1299,f1296,f256,f1306]) ).
fof(f1306,plain,
( spl0_170
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| ~ totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1296,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1299,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| ~ totalorderedP(cons(X0,X1)) )
| ~ spl0_3
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1297,f257]) ).
fof(f1297,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1)) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f1304,plain,
( spl0_169
| ~ spl0_3
| ~ spl0_19
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f831,f797,f351,f256,f1301]) ).
fof(f1301,plain,
( spl0_169
<=> sk3 = app(sk3,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f351,plain,
( spl0_19
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f797,plain,
( spl0_107
<=> ! [X0] :
( app(X0,sk3) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f831,plain,
( sk3 = app(sk3,sk3)
| ~ spl0_3
| ~ spl0_19
| ~ spl0_107 ),
inference(forward_demodulation,[],[f800,f257]) ).
fof(f800,plain,
( nil = app(nil,sk3)
| ~ spl0_19
| ~ spl0_107 ),
inference(resolution,[],[f798,f353]) ).
fof(f353,plain,
( ssList(nil)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f798,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,sk3) = X0 )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f797]) ).
fof(f1298,plain,
spl0_168,
inference(avatar_split_clause,[],[f125,f1296]) ).
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(f1292,plain,
( spl0_167
| ~ spl0_3
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1288,f1285,f256,f1290]) ).
fof(f1290,plain,
( spl0_167
<=> ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| ~ strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1285,plain,
( spl0_166
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1288,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| ~ strictorderedP(cons(X0,X1)) )
| ~ spl0_3
| ~ spl0_166 ),
inference(forward_demodulation,[],[f1286,f257]) ).
fof(f1286,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1)) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f1287,plain,
spl0_166,
inference(avatar_split_clause,[],[f124,f1285]) ).
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(f1283,plain,
spl0_165,
inference(avatar_split_clause,[],[f122,f1281]) ).
fof(f1281,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1)
| X0 = X1
| lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
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(f1260,plain,
( spl0_164
| ~ spl0_3
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1256,f1253,f256,f1258]) ).
fof(f1258,plain,
( spl0_164
<=> ! [X0,X1] :
( cons(X0,X1) = app(cons(X0,sk3),X1)
| ~ ssItem(X0)
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1253,plain,
( spl0_163
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1256,plain,
( ! [X0,X1] :
( cons(X0,X1) = app(cons(X0,sk3),X1)
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl0_3
| ~ spl0_163 ),
inference(forward_demodulation,[],[f1254,f257]) ).
fof(f1254,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f1255,plain,
spl0_163,
inference(avatar_split_clause,[],[f120,f1253]) ).
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(f1249,plain,
( spl0_162
| ~ spl0_3
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1240,f1236,f256,f1247]) ).
fof(f1247,plain,
( spl0_162
<=> ! [X0,X1] :
( app(X0,X1) != sk3
| sk3 = X1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1236,plain,
( spl0_160
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1240,plain,
( ! [X0,X1] :
( app(X0,X1) != sk3
| sk3 = X1
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_160 ),
inference(forward_demodulation,[],[f1239,f257]) ).
fof(f1239,plain,
( ! [X0,X1] :
( sk3 = X1
| ~ ssList(X1)
| ~ ssList(X0)
| nil != app(X0,X1) )
| ~ spl0_3
| ~ spl0_160 ),
inference(forward_demodulation,[],[f1237,f257]) ).
fof(f1237,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f1245,plain,
( spl0_161
| ~ spl0_15
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f830,f797,f331,f1242]) ).
fof(f1242,plain,
( spl0_161
<=> sk6 = app(sk6,sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f830,plain,
( sk6 = app(sk6,sk3)
| ~ spl0_15
| ~ spl0_107 ),
inference(resolution,[],[f798,f333]) ).
fof(f1238,plain,
spl0_160,
inference(avatar_split_clause,[],[f119,f1236]) ).
fof(f119,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X1
| nil != app(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause119) ).
fof(f1232,plain,
( spl0_159
| ~ spl0_3
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1228,f1224,f256,f1230]) ).
fof(f1230,plain,
( spl0_159
<=> ! [X0,X1] :
( app(X0,X1) != sk3
| sk3 = X0
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1224,plain,
( spl0_158
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1228,plain,
( ! [X0,X1] :
( app(X0,X1) != sk3
| sk3 = X0
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_158 ),
inference(forward_demodulation,[],[f1227,f257]) ).
fof(f1227,plain,
( ! [X0,X1] :
( sk3 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| nil != app(X0,X1) )
| ~ spl0_3
| ~ spl0_158 ),
inference(forward_demodulation,[],[f1225,f257]) ).
fof(f1225,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f1226,plain,
spl0_158,
inference(avatar_split_clause,[],[f118,f1224]) ).
fof(f118,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| nil = X0
| nil != app(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause118) ).
fof(f1188,plain,
( spl0_157
| ~ spl0_3
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1184,f1181,f256,f1186]) ).
fof(f1186,plain,
( spl0_157
<=> ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| cons(skaf83(X0),skaf82(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1181,plain,
( spl0_156
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1184,plain,
( ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ spl0_3
| ~ spl0_156 ),
inference(forward_demodulation,[],[f1182,f257]) ).
fof(f1182,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f1183,plain,
spl0_156,
inference(avatar_split_clause,[],[f109,f1181]) ).
fof(f109,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause109) ).
fof(f1145,plain,
( spl0_155
| ~ spl0_3
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1141,f1138,f256,f1143]) ).
fof(f1143,plain,
( spl0_155
<=> ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1138,plain,
( spl0_154
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1141,plain,
( ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl0_3
| ~ spl0_154 ),
inference(forward_demodulation,[],[f1139,f257]) ).
fof(f1139,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f1140,plain,
spl0_154,
inference(avatar_split_clause,[],[f104,f1138]) ).
fof(f104,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
fof(f1136,plain,
( spl0_153
| ~ spl0_3
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f678,f585,f256,f1134]) ).
fof(f1134,plain,
( spl0_153
<=> ! [X0] :
( frontsegP(X0,sk3)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f585,plain,
( spl0_75
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f678,plain,
( ! [X0] :
( frontsegP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_75 ),
inference(superposition,[],[f586,f257]) ).
fof(f586,plain,
( ! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f1099,plain,
( spl0_152
| ~ spl0_3
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f677,f577,f256,f1097]) ).
fof(f1097,plain,
( spl0_152
<=> ! [X0] :
( rearsegP(X0,sk3)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f577,plain,
( spl0_73
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f677,plain,
( ! [X0] :
( rearsegP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_73 ),
inference(superposition,[],[f578,f257]) ).
fof(f578,plain,
( ! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f1074,plain,
( spl0_151
| ~ spl0_3
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1070,f1066,f256,f1072]) ).
fof(f1072,plain,
( spl0_151
<=> ! [X0] :
( singletonP(cons(X0,sk3))
| ~ ssList(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1066,plain,
( spl0_150
<=> ! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1070,plain,
( ! [X0] :
( singletonP(cons(X0,sk3))
| ~ ssList(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_150 ),
inference(forward_demodulation,[],[f1069,f257]) ).
fof(f1069,plain,
( ! [X0] :
( ~ ssList(cons(X0,sk3))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) )
| ~ spl0_3
| ~ spl0_150 ),
inference(forward_demodulation,[],[f1067,f257]) ).
fof(f1067,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f1068,plain,
spl0_150,
inference(avatar_split_clause,[],[f217,f1066]) ).
fof(f217,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| singletonP(cons(X0,nil)) ),
inference(equality_resolution,[],[f116]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| singletonP(X1)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause116) ).
fof(f1064,plain,
spl0_149,
inference(avatar_split_clause,[],[f114,f1062]) ).
fof(f1062,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f114,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
fof(f1060,plain,
spl0_148,
inference(avatar_split_clause,[],[f110,f1058]) ).
fof(f1058,plain,
( spl0_148
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f110,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
fof(f1056,plain,
spl0_147,
inference(avatar_split_clause,[],[f108,f1054]) ).
fof(f1054,plain,
( spl0_147
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f108,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,X1)
| geq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause108) ).
fof(f1052,plain,
spl0_146,
inference(avatar_split_clause,[],[f107,f1050]) ).
fof(f1050,plain,
( spl0_146
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f107,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X0,X1)
| leq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause107) ).
fof(f1048,plain,
spl0_145,
inference(avatar_split_clause,[],[f106,f1046]) ).
fof(f1046,plain,
( spl0_145
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f106,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause106) ).
fof(f1044,plain,
spl0_144,
inference(avatar_split_clause,[],[f105,f1042]) ).
fof(f1042,plain,
( spl0_144
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X0,X1)
| lt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause105) ).
fof(f1040,plain,
( spl0_143
| ~ spl0_3
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f671,f569,f256,f1038]) ).
fof(f1038,plain,
( spl0_143
<=> ! [X0] :
( segmentP(X0,sk3)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f569,plain,
( spl0_71
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f671,plain,
( ! [X0] :
( segmentP(X0,sk3)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_71 ),
inference(superposition,[],[f570,f257]) ).
fof(f570,plain,
( ! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f1036,plain,
spl0_142,
inference(avatar_split_clause,[],[f103,f1034]) ).
fof(f1034,plain,
( spl0_142
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f103,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1)
| leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause103) ).
fof(f1032,plain,
spl0_141,
inference(avatar_split_clause,[],[f102,f1030]) ).
fof(f1030,plain,
( spl0_141
<=> ! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f102,axiom,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause102) ).
fof(f1028,plain,
( spl0_140
| ~ spl0_3
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1024,f1021,f256,f1026]) ).
fof(f1026,plain,
( spl0_140
<=> ! [X0] :
( cons(skaf44(X0),sk3) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1021,plain,
( spl0_139
<=> ! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1024,plain,
( ! [X0] :
( cons(skaf44(X0),sk3) = X0
| ~ singletonP(X0)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_139 ),
inference(forward_demodulation,[],[f1022,f257]) ).
fof(f1022,plain,
( ! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1023,plain,
spl0_139,
inference(avatar_split_clause,[],[f101,f1021]) ).
fof(f101,axiom,
! [X0] :
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(skaf44(X0),nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause101) ).
fof(f1019,plain,
spl0_138,
inference(avatar_split_clause,[],[f100,f1017]) ).
fof(f1017,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f100,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1
| neq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f1015,plain,
spl0_137,
inference(avatar_split_clause,[],[f97,f1013]) ).
fof(f1013,plain,
( spl0_137
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| hd(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause97) ).
fof(f1011,plain,
spl0_136,
inference(avatar_split_clause,[],[f96,f1009]) ).
fof(f1009,plain,
( spl0_136
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f96,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| tl(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause96) ).
fof(f1007,plain,
spl0_135,
inference(avatar_split_clause,[],[f238,f1005]) ).
fof(f1005,plain,
( spl0_135
<=> ! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f238,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f221,plain,
! [X2,X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
fof(f1003,plain,
( spl0_134
| ~ spl0_15
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f789,f756,f331,f1000]) ).
fof(f1000,plain,
( spl0_134
<=> duplicatefreeP(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f756,plain,
( spl0_105
<=> ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f789,plain,
( duplicatefreeP(sk6)
| ~ spl0_15
| ~ spl0_105 ),
inference(resolution,[],[f757,f333]) ).
fof(f757,plain,
( ! [X0] :
( ~ ssList(X0)
| duplicatefreeP(X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f998,plain,
spl0_133,
inference(avatar_split_clause,[],[f99,f996]) ).
fof(f996,plain,
( spl0_133
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f99,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
fof(f994,plain,
( spl0_132
| ~ spl0_3
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f990,f987,f256,f992]) ).
fof(f992,plain,
( spl0_132
<=> ! [X0,X1] :
( cons(X0,X1) != sk3
| ~ ssItem(X0)
| ~ ssList(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f987,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f990,plain,
( ! [X0,X1] :
( cons(X0,X1) != sk3
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl0_3
| ~ spl0_131 ),
inference(forward_demodulation,[],[f988,f257]) ).
fof(f988,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f989,plain,
spl0_131,
inference(avatar_split_clause,[],[f98,f987]) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| nil != cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f985,plain,
spl0_130,
inference(avatar_split_clause,[],[f95,f983]) ).
fof(f983,plain,
( spl0_130
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f95,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf54(X0),skaf55(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause95) ).
fof(f981,plain,
spl0_129,
inference(avatar_split_clause,[],[f94,f979]) ).
fof(f979,plain,
( spl0_129
<=> ! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f94,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderP(X0)
| ~ leq(skaf55(X0),skaf54(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause94) ).
fof(f977,plain,
spl0_128,
inference(avatar_split_clause,[],[f93,f975]) ).
fof(f975,plain,
( spl0_128
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f93,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf59(X0),skaf60(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause93) ).
fof(f973,plain,
spl0_127,
inference(avatar_split_clause,[],[f92,f971]) ).
fof(f971,plain,
( spl0_127
<=> ! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f92,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderP(X0)
| ~ lt(skaf60(X0),skaf59(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause92) ).
fof(f969,plain,
spl0_126,
inference(avatar_split_clause,[],[f91,f967]) ).
fof(f967,plain,
( spl0_126
<=> ! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f91,axiom,
! [X0] :
( ~ ssList(X0)
| totalorderedP(X0)
| ~ leq(skaf64(X0),skaf65(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause91) ).
fof(f965,plain,
spl0_125,
inference(avatar_split_clause,[],[f90,f963]) ).
fof(f963,plain,
( spl0_125
<=> ! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f90,axiom,
! [X0] :
( ~ ssList(X0)
| strictorderedP(X0)
| ~ lt(skaf69(X0),skaf70(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause90) ).
fof(f961,plain,
spl0_124,
inference(avatar_split_clause,[],[f89,f959]) ).
fof(f959,plain,
( spl0_124
<=> ! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f89,axiom,
! [X0] :
( ~ ssList(X0)
| equalelemsP(X0)
| skaf79(X0) != skaf78(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause89) ).
fof(f957,plain,
spl0_123,
inference(avatar_split_clause,[],[f88,f955]) ).
fof(f955,plain,
( spl0_123
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f88,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf49(X0),skaf50(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause88) ).
fof(f953,plain,
spl0_122,
inference(avatar_split_clause,[],[f87,f951]) ).
fof(f951,plain,
( spl0_122
<=> ! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f87,axiom,
! [X0] :
( ~ ssList(X0)
| cyclefreeP(X0)
| leq(skaf50(X0),skaf49(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause87) ).
fof(f942,plain,
spl0_121,
inference(avatar_split_clause,[],[f86,f940]) ).
fof(f940,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f86,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f938,plain,
spl0_120,
inference(avatar_split_clause,[],[f85,f936]) ).
fof(f936,plain,
( spl0_120
<=> ! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f931,plain,
( spl0_119
| ~ spl0_3
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f927,f923,f256,f929]) ).
fof(f929,plain,
( spl0_119
<=> ! [X0] :
( sk3 = X0
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f923,plain,
( spl0_118
<=> ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f927,plain,
( ! [X0] :
( sk3 = X0
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_118 ),
inference(forward_demodulation,[],[f926,f257]) ).
fof(f926,plain,
( ! [X0] :
( ~ frontsegP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_3
| ~ spl0_118 ),
inference(forward_demodulation,[],[f924,f257]) ).
fof(f924,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f925,plain,
spl0_118,
inference(avatar_split_clause,[],[f84,f923]) ).
fof(f84,axiom,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause84) ).
fof(f918,plain,
( spl0_117
| ~ spl0_3
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f914,f910,f256,f916]) ).
fof(f916,plain,
( spl0_117
<=> ! [X0] :
( sk3 = X0
| ~ rearsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f910,plain,
( spl0_116
<=> ! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f914,plain,
( ! [X0] :
( sk3 = X0
| ~ rearsegP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_116 ),
inference(forward_demodulation,[],[f913,f257]) ).
fof(f913,plain,
( ! [X0] :
( ~ rearsegP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_3
| ~ spl0_116 ),
inference(forward_demodulation,[],[f911,f257]) ).
fof(f911,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f912,plain,
spl0_116,
inference(avatar_split_clause,[],[f82,f910]) ).
fof(f82,axiom,
! [X0] :
( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
fof(f905,plain,
( spl0_115
| ~ spl0_3
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f901,f897,f256,f903]) ).
fof(f903,plain,
( spl0_115
<=> ! [X0] :
( sk3 = X0
| ~ segmentP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f897,plain,
( spl0_114
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f901,plain,
( ! [X0] :
( sk3 = X0
| ~ segmentP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_114 ),
inference(forward_demodulation,[],[f900,f257]) ).
fof(f900,plain,
( ! [X0] :
( ~ segmentP(sk3,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl0_3
| ~ spl0_114 ),
inference(forward_demodulation,[],[f898,f257]) ).
fof(f898,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f899,plain,
spl0_114,
inference(avatar_split_clause,[],[f80,f897]) ).
fof(f80,axiom,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause80) ).
fof(f895,plain,
( spl0_113
| ~ spl0_3
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f891,f888,f256,f893]) ).
fof(f893,plain,
( spl0_113
<=> ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssItem(hd(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f888,plain,
( spl0_112
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f891,plain,
( ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssItem(hd(X0)) )
| ~ spl0_3
| ~ spl0_112 ),
inference(forward_demodulation,[],[f889,f257]) ).
fof(f889,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f890,plain,
spl0_112,
inference(avatar_split_clause,[],[f78,f888]) ).
fof(f78,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
fof(f883,plain,
( spl0_111
| ~ spl0_3
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f879,f876,f256,f881]) ).
fof(f881,plain,
( spl0_111
<=> ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssList(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f876,plain,
( spl0_110
<=> ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f879,plain,
( ! [X0] :
( sk3 = X0
| ~ ssList(X0)
| ssList(tl(X0)) )
| ~ spl0_3
| ~ spl0_110 ),
inference(forward_demodulation,[],[f877,f257]) ).
fof(f877,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f878,plain,
spl0_110,
inference(avatar_split_clause,[],[f77,f876]) ).
fof(f77,axiom,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
fof(f841,plain,
( spl0_109
| ~ spl0_3
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f837,f834,f256,f839]) ).
fof(f834,plain,
( spl0_108
<=> ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f837,plain,
( ! [X0] :
( app(sk3,X0) = X0
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_108 ),
inference(forward_demodulation,[],[f835,f257]) ).
fof(f835,plain,
( ! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f834]) ).
fof(f836,plain,
spl0_108,
inference(avatar_split_clause,[],[f74,f834]) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f799,plain,
( spl0_107
| ~ spl0_3
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f795,f792,f256,f797]) ).
fof(f792,plain,
( spl0_106
<=> ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f795,plain,
( ! [X0] :
( app(X0,sk3) = X0
| ~ ssList(X0) )
| ~ spl0_3
| ~ spl0_106 ),
inference(forward_demodulation,[],[f793,f257]) ).
fof(f793,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f794,plain,
spl0_106,
inference(avatar_split_clause,[],[f73,f792]) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause73) ).
fof(f758,plain,
( spl0_104
| spl0_105 ),
inference(avatar_split_clause,[],[f72,f756,f753]) ).
fof(f753,plain,
( spl0_104
<=> ! [X1] : ssItem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ ssList(X0)
| duplicatefreeP(X0)
| ssItem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause72) ).
fof(f751,plain,
( spl0_103
| ~ spl0_3
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f747,f744,f256,f749]) ).
fof(f749,plain,
( spl0_103
<=> ! [X0] :
( cyclefreeP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f744,plain,
( spl0_102
<=> ! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f747,plain,
( ! [X0] :
( cyclefreeP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_102 ),
inference(forward_demodulation,[],[f745,f257]) ).
fof(f745,plain,
( ! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f746,plain,
spl0_102,
inference(avatar_split_clause,[],[f70,f744]) ).
fof(f70,axiom,
! [X0] :
( ~ ssItem(X0)
| cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
fof(f742,plain,
( spl0_101
| ~ spl0_3
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f738,f735,f256,f740]) ).
fof(f740,plain,
( spl0_101
<=> ! [X0] :
( totalorderP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f735,plain,
( spl0_100
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f738,plain,
( ! [X0] :
( totalorderP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_100 ),
inference(forward_demodulation,[],[f736,f257]) ).
fof(f736,plain,
( ! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f737,plain,
spl0_100,
inference(avatar_split_clause,[],[f69,f735]) ).
fof(f69,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
fof(f733,plain,
( spl0_99
| ~ spl0_3
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f729,f726,f256,f731]) ).
fof(f731,plain,
( spl0_99
<=> ! [X0] :
( strictorderP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f726,plain,
( spl0_98
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f729,plain,
( ! [X0] :
( strictorderP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_98 ),
inference(forward_demodulation,[],[f727,f257]) ).
fof(f727,plain,
( ! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f726]) ).
fof(f728,plain,
spl0_98,
inference(avatar_split_clause,[],[f68,f726]) ).
fof(f68,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
fof(f724,plain,
( ~ spl0_97
| ~ spl0_3
| spl0_22 ),
inference(avatar_split_clause,[],[f618,f366,f256,f721]) ).
fof(f721,plain,
( spl0_97
<=> singletonP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f366,plain,
( spl0_22
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f618,plain,
( ~ singletonP(sk3)
| ~ spl0_3
| spl0_22 ),
inference(superposition,[],[f368,f257]) ).
fof(f368,plain,
( ~ singletonP(nil)
| spl0_22 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f719,plain,
( spl0_96
| ~ spl0_3
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f715,f712,f256,f717]) ).
fof(f717,plain,
( spl0_96
<=> ! [X0] :
( totalorderedP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f712,plain,
( spl0_95
<=> ! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f715,plain,
( ! [X0] :
( totalorderedP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_95 ),
inference(forward_demodulation,[],[f713,f257]) ).
fof(f713,plain,
( ! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f714,plain,
spl0_95,
inference(avatar_split_clause,[],[f67,f712]) ).
fof(f67,axiom,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
fof(f710,plain,
( spl0_94
| ~ spl0_3
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f706,f703,f256,f708]) ).
fof(f708,plain,
( spl0_94
<=> ! [X0] :
( strictorderedP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f703,plain,
( spl0_93
<=> ! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f706,plain,
( ! [X0] :
( strictorderedP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_93 ),
inference(forward_demodulation,[],[f704,f257]) ).
fof(f704,plain,
( ! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f705,plain,
spl0_93,
inference(avatar_split_clause,[],[f66,f703]) ).
fof(f66,axiom,
! [X0] :
( ~ ssItem(X0)
| strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
fof(f701,plain,
( spl0_92
| ~ spl0_3
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f697,f694,f256,f699]) ).
fof(f699,plain,
( spl0_92
<=> ! [X0] :
( duplicatefreeP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f694,plain,
( spl0_91
<=> ! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f697,plain,
( ! [X0] :
( duplicatefreeP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_91 ),
inference(forward_demodulation,[],[f695,f257]) ).
fof(f695,plain,
( ! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f696,plain,
spl0_91,
inference(avatar_split_clause,[],[f65,f694]) ).
fof(f65,axiom,
! [X0] :
( ~ ssItem(X0)
| duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
fof(f692,plain,
( spl0_90
| ~ spl0_3
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f683,f680,f256,f690]) ).
fof(f690,plain,
( spl0_90
<=> ! [X0] :
( equalelemsP(cons(X0,sk3))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f680,plain,
( spl0_88
<=> ! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f683,plain,
( ! [X0] :
( equalelemsP(cons(X0,sk3))
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_88 ),
inference(forward_demodulation,[],[f681,f257]) ).
fof(f681,plain,
( ! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f688,plain,
( spl0_89
| ~ spl0_3
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f616,f346,f256,f685]) ).
fof(f685,plain,
( spl0_89
<=> cyclefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f346,plain,
( spl0_18
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f616,plain,
( cyclefreeP(sk3)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f348,f257]) ).
fof(f348,plain,
( cyclefreeP(nil)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f682,plain,
spl0_88,
inference(avatar_split_clause,[],[f64,f680]) ).
fof(f64,axiom,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
fof(f676,plain,
( spl0_87
| ~ spl0_3
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f615,f341,f256,f673]) ).
fof(f673,plain,
( spl0_87
<=> totalorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f341,plain,
( spl0_17
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f615,plain,
( totalorderP(sk3)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f343,f257]) ).
fof(f343,plain,
( totalorderP(nil)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f670,plain,
spl0_86,
inference(avatar_split_clause,[],[f241,f668]) ).
fof(f668,plain,
( spl0_86
<=> ! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f241,plain,
! [X1] :
( ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f215,plain,
! [X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
fof(f666,plain,
spl0_85,
inference(avatar_split_clause,[],[f239,f664]) ).
fof(f664,plain,
( spl0_85
<=> ! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f239,plain,
! [X1] :
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f220,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f115]) ).
fof(f115,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f662,plain,
( spl0_84
| ~ spl0_3
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f658,f655,f256,f660]) ).
fof(f660,plain,
( spl0_84
<=> ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f655,plain,
( spl0_83
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f658,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_3
| ~ spl0_83 ),
inference(forward_demodulation,[],[f656,f257]) ).
fof(f656,plain,
( ! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f657,plain,
spl0_83,
inference(avatar_split_clause,[],[f71,f655]) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f653,plain,
spl0_82,
inference(avatar_split_clause,[],[f63,f651]) ).
fof(f651,plain,
( spl0_82
<=> ! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f63,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
fof(f649,plain,
spl0_81,
inference(avatar_split_clause,[],[f62,f647]) ).
fof(f647,plain,
( spl0_81
<=> ! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f62,axiom,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause62) ).
fof(f645,plain,
spl0_80,
inference(avatar_split_clause,[],[f61,f643]) ).
fof(f643,plain,
( spl0_80
<=> ! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f61,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause61) ).
fof(f641,plain,
( spl0_79
| ~ spl0_3
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f614,f336,f256,f638]) ).
fof(f638,plain,
( spl0_79
<=> strictorderP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f336,plain,
( spl0_16
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f614,plain,
( strictorderP(sk3)
| ~ spl0_3
| ~ spl0_16 ),
inference(superposition,[],[f338,f257]) ).
fof(f338,plain,
( strictorderP(nil)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f636,plain,
( spl0_78
| ~ spl0_6
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f631,f627,f271,f633]) ).
fof(f271,plain,
( spl0_6
<=> sk3 = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f627,plain,
( spl0_77
<=> sk4 = app(sk6,cons(sk5,sk3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f631,plain,
( sk3 = app(sk6,cons(sk5,sk3))
| ~ spl0_6
| ~ spl0_77 ),
inference(forward_demodulation,[],[f629,f273]) ).
fof(f273,plain,
( sk3 = sk4
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f629,plain,
( sk4 = app(sk6,cons(sk5,sk3))
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f630,plain,
( spl0_77
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f244,f256,f627]) ).
fof(f244,plain,
( nil != sk3
| sk4 = app(sk6,cons(sk5,sk3)) ),
inference(inner_rewriting,[],[f209]) ).
fof(f209,plain,
( nil != sk3
| sk4 = app(sk6,cons(sk5,nil)) ),
inference(definition_unfolding,[],[f200,f191,f190]) ).
fof(f190,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f200,axiom,
( nil != sk1
| sk2 = app(sk6,cons(sk5,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f609,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f607,f271,f265,f256]) ).
fof(f265,plain,
( spl0_5
<=> nil = sk4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f607,plain,
( nil = sk3
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f267,f273]) ).
fof(f267,plain,
( nil = sk4
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f602,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f207,f331,f265]) ).
fof(f207,plain,
( ssList(sk6)
| nil = sk4 ),
inference(definition_unfolding,[],[f196,f190]) ).
fof(f196,axiom,
( ssList(sk6)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f601,plain,
( spl0_24
| ~ spl0_4
| ~ spl0_15
| ~ spl0_68
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f600,f593,f554,f331,f260,f376]) ).
fof(f260,plain,
( spl0_4
<=> ssItem(sk5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f554,plain,
( spl0_68
<=> ! [X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| sk4 != app(X7,cons(X6,nil))
| sk3 = app(cons(X6,nil),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f593,plain,
( spl0_76
<=> sk4 = app(sk6,cons(sk5,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f600,plain,
( ~ ssList(sk6)
| ~ ssItem(sk5)
| sk3 = app(cons(sk5,nil),sk6)
| ~ spl0_68
| ~ spl0_76 ),
inference(trivial_inequality_removal,[],[f599]) ).
fof(f599,plain,
( sk4 != sk4
| ~ ssList(sk6)
| ~ ssItem(sk5)
| sk3 = app(cons(sk5,nil),sk6)
| ~ spl0_68
| ~ spl0_76 ),
inference(superposition,[],[f555,f595]) ).
fof(f595,plain,
( sk4 = app(sk6,cons(sk5,nil))
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f555,plain,
( ! [X6,X7] :
( sk4 != app(X7,cons(X6,nil))
| ~ ssList(X7)
| ~ ssItem(X6)
| sk3 = app(cons(X6,nil),X7) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f596,plain,
( spl0_76
| spl0_5 ),
inference(avatar_split_clause,[],[f211,f265,f593]) ).
fof(f211,plain,
( nil = sk4
| sk4 = app(sk6,cons(sk5,nil)) ),
inference(definition_unfolding,[],[f197,f190,f190]) ).
fof(f197,axiom,
( nil = sk2
| sk2 = app(sk6,cons(sk5,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f591,plain,
( ~ spl0_24
| spl0_5 ),
inference(avatar_split_clause,[],[f210,f265,f376]) ).
fof(f210,plain,
( nil = sk4
| sk3 != app(cons(sk5,nil),sk6) ),
inference(definition_unfolding,[],[f198,f190,f191]) ).
fof(f198,axiom,
( nil = sk2
| sk1 != app(cons(sk5,nil),sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f590,plain,
( spl0_5
| spl0_6
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f589,f371,f271,f265]) ).
fof(f589,plain,
( sk3 = sk4
| nil = sk4
| ~ spl0_23 ),
inference(forward_demodulation,[],[f211,f373]) ).
fof(f373,plain,
( sk3 = app(sk6,cons(sk5,nil))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f588,plain,
( spl0_24
| ~ spl0_15
| ~ spl0_4
| ~ spl0_23
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f563,f559,f371,f260,f331,f376]) ).
fof(f559,plain,
( spl0_69
<=> ! [X6,X7] :
( sk3 != app(X7,cons(X6,nil))
| ~ ssItem(X6)
| ~ ssList(X7)
| sk3 = app(cons(X6,nil),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f563,plain,
( ~ ssItem(sk5)
| ~ ssList(sk6)
| sk3 = app(cons(sk5,nil),sk6)
| ~ spl0_23
| ~ spl0_69 ),
inference(trivial_inequality_removal,[],[f562]) ).
fof(f562,plain,
( sk3 != sk3
| ~ ssItem(sk5)
| ~ ssList(sk6)
| sk3 = app(cons(sk5,nil),sk6)
| ~ spl0_23
| ~ spl0_69 ),
inference(superposition,[],[f560,f373]) ).
fof(f560,plain,
( ! [X6,X7] :
( sk3 != app(X7,cons(X6,nil))
| ~ ssItem(X6)
| ~ ssList(X7)
| sk3 = app(cons(X6,nil),X7) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f587,plain,
spl0_75,
inference(avatar_split_clause,[],[f60,f585]) ).
fof(f60,axiom,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
fof(f583,plain,
spl0_74,
inference(avatar_split_clause,[],[f59,f581]) ).
fof(f581,plain,
( spl0_74
<=> ! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f59,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
fof(f579,plain,
spl0_73,
inference(avatar_split_clause,[],[f58,f577]) ).
fof(f58,axiom,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
fof(f575,plain,
spl0_72,
inference(avatar_split_clause,[],[f57,f573]) ).
fof(f573,plain,
( spl0_72
<=> ! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f57,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
fof(f571,plain,
spl0_71,
inference(avatar_split_clause,[],[f56,f569]) ).
fof(f56,axiom,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
fof(f567,plain,
spl0_70,
inference(avatar_split_clause,[],[f55,f565]) ).
fof(f565,plain,
( spl0_70
<=> ! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f55,axiom,
! [X0] :
( ~ ssItem(X0)
| geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
fof(f561,plain,
( spl0_69
| ~ spl0_6
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f557,f554,f271,f559]) ).
fof(f557,plain,
( ! [X6,X7] :
( sk3 != app(X7,cons(X6,nil))
| ~ ssItem(X6)
| ~ ssList(X7)
| sk3 = app(cons(X6,nil),X7) )
| ~ spl0_6
| ~ spl0_68 ),
inference(forward_demodulation,[],[f555,f273]) ).
fof(f556,plain,
spl0_68,
inference(avatar_split_clause,[],[f192,f554]) ).
fof(f192,axiom,
! [X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X7)
| sk4 != app(X7,cons(X6,nil))
| sk3 = app(cons(X6,nil),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f552,plain,
spl0_67,
inference(avatar_split_clause,[],[f53,f550]) ).
fof(f550,plain,
( spl0_67
<=> ! [X0,X1] : ssList(skaf42(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f53,axiom,
! [X0,X1] : ssList(skaf42(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
fof(f548,plain,
spl0_66,
inference(avatar_split_clause,[],[f52,f546]) ).
fof(f546,plain,
( spl0_66
<=> ! [X0,X1] : ssList(skaf43(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f52,axiom,
! [X0,X1] : ssList(skaf43(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
fof(f544,plain,
spl0_65,
inference(avatar_split_clause,[],[f51,f542]) ).
fof(f542,plain,
( spl0_65
<=> ! [X0,X1] : ssList(skaf45(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
fof(f540,plain,
spl0_64,
inference(avatar_split_clause,[],[f50,f538]) ).
fof(f538,plain,
( spl0_64
<=> ! [X0,X1] : ssList(skaf46(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
fof(f536,plain,
spl0_63,
inference(avatar_split_clause,[],[f49,f534]) ).
fof(f534,plain,
( spl0_63
<=> ! [X0,X1] : ssList(skaf47(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f49,axiom,
! [X0,X1] : ssList(skaf47(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
fof(f532,plain,
spl0_62,
inference(avatar_split_clause,[],[f48,f530]) ).
fof(f530,plain,
( spl0_62
<=> ! [X0,X1] : ssList(skaf48(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f48,axiom,
! [X0,X1] : ssList(skaf48(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
fof(f528,plain,
~ spl0_61,
inference(avatar_split_clause,[],[f54,f525]) ).
fof(f525,plain,
( spl0_61
<=> skac3 = skac2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f54,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
fof(f523,plain,
spl0_60,
inference(avatar_split_clause,[],[f47,f521]) ).
fof(f521,plain,
( spl0_60
<=> ! [X0] : ssItem(skaf44(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
fof(f519,plain,
spl0_59,
inference(avatar_split_clause,[],[f46,f517]) ).
fof(f517,plain,
( spl0_59
<=> ! [X0] : ssItem(skaf49(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f46,axiom,
! [X0] : ssItem(skaf49(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
fof(f515,plain,
spl0_58,
inference(avatar_split_clause,[],[f45,f513]) ).
fof(f513,plain,
( spl0_58
<=> ! [X0] : ssItem(skaf50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f45,axiom,
! [X0] : ssItem(skaf50(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
fof(f511,plain,
spl0_57,
inference(avatar_split_clause,[],[f44,f509]) ).
fof(f509,plain,
( spl0_57
<=> ! [X0] : ssList(skaf51(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f44,axiom,
! [X0] : ssList(skaf51(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
fof(f507,plain,
spl0_56,
inference(avatar_split_clause,[],[f43,f505]) ).
fof(f505,plain,
( spl0_56
<=> ! [X0] : ssList(skaf52(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f43,axiom,
! [X0] : ssList(skaf52(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
fof(f503,plain,
spl0_55,
inference(avatar_split_clause,[],[f42,f501]) ).
fof(f501,plain,
( spl0_55
<=> ! [X0] : ssList(skaf53(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f42,axiom,
! [X0] : ssList(skaf53(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
fof(f499,plain,
spl0_54,
inference(avatar_split_clause,[],[f41,f497]) ).
fof(f497,plain,
( spl0_54
<=> ! [X0] : ssItem(skaf54(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f41,axiom,
! [X0] : ssItem(skaf54(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
fof(f495,plain,
spl0_53,
inference(avatar_split_clause,[],[f40,f493]) ).
fof(f493,plain,
( spl0_53
<=> ! [X0] : ssItem(skaf55(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f40,axiom,
! [X0] : ssItem(skaf55(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
fof(f491,plain,
spl0_52,
inference(avatar_split_clause,[],[f39,f489]) ).
fof(f489,plain,
( spl0_52
<=> ! [X0] : ssList(skaf56(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f39,axiom,
! [X0] : ssList(skaf56(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
fof(f487,plain,
spl0_51,
inference(avatar_split_clause,[],[f38,f485]) ).
fof(f485,plain,
( spl0_51
<=> ! [X0] : ssList(skaf57(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f38,axiom,
! [X0] : ssList(skaf57(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
fof(f483,plain,
spl0_50,
inference(avatar_split_clause,[],[f37,f481]) ).
fof(f481,plain,
( spl0_50
<=> ! [X0] : ssList(skaf58(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f37,axiom,
! [X0] : ssList(skaf58(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
fof(f479,plain,
spl0_49,
inference(avatar_split_clause,[],[f36,f477]) ).
fof(f477,plain,
( spl0_49
<=> ! [X0] : ssItem(skaf59(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f36,axiom,
! [X0] : ssItem(skaf59(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
fof(f475,plain,
spl0_48,
inference(avatar_split_clause,[],[f35,f473]) ).
fof(f473,plain,
( spl0_48
<=> ! [X0] : ssItem(skaf60(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f35,axiom,
! [X0] : ssItem(skaf60(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
fof(f471,plain,
spl0_47,
inference(avatar_split_clause,[],[f34,f469]) ).
fof(f469,plain,
( spl0_47
<=> ! [X0] : ssList(skaf61(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f34,axiom,
! [X0] : ssList(skaf61(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
fof(f467,plain,
spl0_46,
inference(avatar_split_clause,[],[f33,f465]) ).
fof(f465,plain,
( spl0_46
<=> ! [X0] : ssList(skaf62(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f33,axiom,
! [X0] : ssList(skaf62(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
fof(f463,plain,
spl0_45,
inference(avatar_split_clause,[],[f32,f461]) ).
fof(f461,plain,
( spl0_45
<=> ! [X0] : ssList(skaf63(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f32,axiom,
! [X0] : ssList(skaf63(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
fof(f459,plain,
spl0_44,
inference(avatar_split_clause,[],[f31,f457]) ).
fof(f457,plain,
( spl0_44
<=> ! [X0] : ssItem(skaf64(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f31,axiom,
! [X0] : ssItem(skaf64(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
fof(f455,plain,
spl0_43,
inference(avatar_split_clause,[],[f30,f453]) ).
fof(f453,plain,
( spl0_43
<=> ! [X0] : ssItem(skaf65(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f30,axiom,
! [X0] : ssItem(skaf65(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
fof(f451,plain,
spl0_42,
inference(avatar_split_clause,[],[f29,f449]) ).
fof(f449,plain,
( spl0_42
<=> ! [X0] : ssList(skaf66(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f29,axiom,
! [X0] : ssList(skaf66(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
fof(f447,plain,
spl0_41,
inference(avatar_split_clause,[],[f28,f445]) ).
fof(f445,plain,
( spl0_41
<=> ! [X0] : ssList(skaf67(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f28,axiom,
! [X0] : ssList(skaf67(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
fof(f443,plain,
spl0_40,
inference(avatar_split_clause,[],[f27,f441]) ).
fof(f441,plain,
( spl0_40
<=> ! [X0] : ssList(skaf68(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f27,axiom,
! [X0] : ssList(skaf68(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
fof(f439,plain,
spl0_39,
inference(avatar_split_clause,[],[f26,f437]) ).
fof(f437,plain,
( spl0_39
<=> ! [X0] : ssItem(skaf69(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f26,axiom,
! [X0] : ssItem(skaf69(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
fof(f435,plain,
spl0_38,
inference(avatar_split_clause,[],[f25,f433]) ).
fof(f433,plain,
( spl0_38
<=> ! [X0] : ssItem(skaf70(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f25,axiom,
! [X0] : ssItem(skaf70(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
fof(f431,plain,
spl0_37,
inference(avatar_split_clause,[],[f24,f429]) ).
fof(f429,plain,
( spl0_37
<=> ! [X0] : ssList(skaf71(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f24,axiom,
! [X0] : ssList(skaf71(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
fof(f427,plain,
spl0_36,
inference(avatar_split_clause,[],[f23,f425]) ).
fof(f425,plain,
( spl0_36
<=> ! [X0] : ssList(skaf72(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f23,axiom,
! [X0] : ssList(skaf72(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
fof(f423,plain,
spl0_35,
inference(avatar_split_clause,[],[f22,f421]) ).
fof(f421,plain,
( spl0_35
<=> ! [X0] : ssList(skaf73(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f22,axiom,
! [X0] : ssList(skaf73(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
fof(f419,plain,
spl0_34,
inference(avatar_split_clause,[],[f21,f417]) ).
fof(f417,plain,
( spl0_34
<=> ! [X0] : ssItem(skaf74(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f21,axiom,
! [X0] : ssItem(skaf74(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
fof(f415,plain,
spl0_33,
inference(avatar_split_clause,[],[f20,f413]) ).
fof(f413,plain,
( spl0_33
<=> ! [X0] : ssList(skaf75(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f20,axiom,
! [X0] : ssList(skaf75(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
fof(f411,plain,
spl0_32,
inference(avatar_split_clause,[],[f19,f409]) ).
fof(f409,plain,
( spl0_32
<=> ! [X0] : ssList(skaf76(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f19,axiom,
! [X0] : ssList(skaf76(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
fof(f407,plain,
spl0_31,
inference(avatar_split_clause,[],[f18,f405]) ).
fof(f405,plain,
( spl0_31
<=> ! [X0] : ssList(skaf77(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f18,axiom,
! [X0] : ssList(skaf77(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
fof(f403,plain,
spl0_30,
inference(avatar_split_clause,[],[f17,f401]) ).
fof(f401,plain,
( spl0_30
<=> ! [X0] : ssItem(skaf78(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f17,axiom,
! [X0] : ssItem(skaf78(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
fof(f399,plain,
spl0_29,
inference(avatar_split_clause,[],[f16,f397]) ).
fof(f397,plain,
( spl0_29
<=> ! [X0] : ssItem(skaf79(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f16,axiom,
! [X0] : ssItem(skaf79(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
fof(f395,plain,
spl0_28,
inference(avatar_split_clause,[],[f15,f393]) ).
fof(f393,plain,
( spl0_28
<=> ! [X0] : ssList(skaf80(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f15,axiom,
! [X0] : ssList(skaf80(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
fof(f391,plain,
spl0_27,
inference(avatar_split_clause,[],[f14,f389]) ).
fof(f389,plain,
( spl0_27
<=> ! [X0] : ssList(skaf81(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f14,axiom,
! [X0] : ssList(skaf81(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
fof(f387,plain,
spl0_26,
inference(avatar_split_clause,[],[f13,f385]) ).
fof(f385,plain,
( spl0_26
<=> ! [X0] : ssList(skaf82(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
fof(f383,plain,
spl0_25,
inference(avatar_split_clause,[],[f12,f381]) ).
fof(f381,plain,
( spl0_25
<=> ! [X0] : ssItem(skaf83(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
fof(f379,plain,
( ~ spl0_24
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f327,f271,f256,f376]) ).
fof(f327,plain,
( nil = sk3
| sk3 != app(cons(sk5,nil),sk6)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f210,f273]) ).
fof(f374,plain,
( spl0_3
| spl0_23
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f326,f271,f371,f256]) ).
fof(f326,plain,
( sk3 = app(sk6,cons(sk5,nil))
| nil = sk3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f325,f273]) ).
fof(f325,plain,
( nil = sk3
| sk4 = app(sk6,cons(sk5,nil))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f211,f273]) ).
fof(f369,plain,
~ spl0_22,
inference(avatar_split_clause,[],[f11,f366]) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
fof(f364,plain,
spl0_21,
inference(avatar_split_clause,[],[f10,f361]) ).
fof(f361,plain,
( spl0_21
<=> ssItem(skac2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
fof(f359,plain,
spl0_20,
inference(avatar_split_clause,[],[f9,f356]) ).
fof(f356,plain,
( spl0_20
<=> ssItem(skac3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
fof(f354,plain,
spl0_19,
inference(avatar_split_clause,[],[f8,f351]) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f349,plain,
spl0_18,
inference(avatar_split_clause,[],[f7,f346]) ).
fof(f7,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
fof(f344,plain,
spl0_17,
inference(avatar_split_clause,[],[f6,f341]) ).
fof(f6,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
fof(f339,plain,
spl0_16,
inference(avatar_split_clause,[],[f5,f336]) ).
fof(f5,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
fof(f334,plain,
( spl0_15
| spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f328,f271,f256,f331]) ).
fof(f328,plain,
( nil = sk3
| ssList(sk6)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f207,f273]) ).
fof(f324,plain,
( ~ spl0_6
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f269,f265,f256,f271]) ).
fof(f269,plain,
( sk3 != sk4
| spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f258,f267]) ).
fof(f258,plain,
( nil != sk3
| spl0_3 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f323,plain,
( spl0_14
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f318,f313,f271,f265,f320]) ).
fof(f320,plain,
( spl0_14
<=> totalorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f313,plain,
( spl0_13
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f318,plain,
( totalorderedP(sk3)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f317,f273]) ).
fof(f317,plain,
( totalorderedP(sk4)
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f315,f267]) ).
fof(f315,plain,
( totalorderedP(nil)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,plain,
spl0_13,
inference(avatar_split_clause,[],[f4,f313]) ).
fof(f4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
fof(f311,plain,
( spl0_12
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f306,f301,f271,f265,f308]) ).
fof(f308,plain,
( spl0_12
<=> strictorderedP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f301,plain,
( spl0_11
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f306,plain,
( strictorderedP(sk3)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f305,f273]) ).
fof(f305,plain,
( strictorderedP(sk4)
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f303,f267]) ).
fof(f303,plain,
( strictorderedP(nil)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f304,plain,
spl0_11,
inference(avatar_split_clause,[],[f3,f301]) ).
fof(f3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
fof(f299,plain,
( spl0_10
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f294,f289,f271,f265,f296]) ).
fof(f296,plain,
( spl0_10
<=> duplicatefreeP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f289,plain,
( spl0_9
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f294,plain,
( duplicatefreeP(sk3)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f293,f273]) ).
fof(f293,plain,
( duplicatefreeP(sk4)
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f291,f267]) ).
fof(f291,plain,
( duplicatefreeP(nil)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f292,plain,
spl0_9,
inference(avatar_split_clause,[],[f2,f289]) ).
fof(f2,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
fof(f287,plain,
( spl0_8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f282,f277,f271,f265,f284]) ).
fof(f284,plain,
( spl0_8
<=> equalelemsP(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f277,plain,
( spl0_7
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f282,plain,
( equalelemsP(sk3)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f281,f273]) ).
fof(f281,plain,
( equalelemsP(sk4)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f279,f267]) ).
fof(f279,plain,
( equalelemsP(nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f280,plain,
spl0_7,
inference(avatar_split_clause,[],[f1,f277]) ).
fof(f1,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
fof(f274,plain,
( spl0_6
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f242,f265,f271]) ).
fof(f242,plain,
( nil != sk4
| sk3 = sk4 ),
inference(inner_rewriting,[],[f193]) ).
fof(f193,axiom,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f268,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f205,f260,f265]) ).
fof(f205,plain,
( ssItem(sk5)
| nil = sk4 ),
inference(definition_unfolding,[],[f194,f190]) ).
fof(f194,axiom,
( ssItem(sk5)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f263,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f204,f260,f256]) ).
fof(f204,plain,
( ssItem(sk5)
| nil != sk3 ),
inference(definition_unfolding,[],[f195,f191]) ).
fof(f195,axiom,
( ssItem(sk5)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f254,plain,
spl0_2,
inference(avatar_split_clause,[],[f189,f251]) ).
fof(f251,plain,
( spl0_2
<=> ssList(sk4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
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(f246,plain,
( spl0_1
<=> ssList(sk3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f188,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC322-1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 03:55:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (26522)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.36 % (26525)WARNING: value z3 for option sas not known
% 0.19/0.36 % (26525)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)
% 0.19/0.36 % (26524)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.36 % (26528)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)
% 0.19/0.36 % (26527)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)
% 0.19/0.36 % (26526)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.37 % (26529)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)
% 0.19/0.37 % (26523)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.38 TRYING [1]
% 0.19/0.38 TRYING [2]
% 0.19/0.39 TRYING [3]
% 0.19/0.40 % (26527)First to succeed.
% 0.19/0.41 % (26527)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26522"
% 0.19/0.41 % (26527)Refutation found. Thanks to Tanya!
% 0.19/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.42 % (26527)------------------------------
% 0.19/0.42 % (26527)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.42 % (26527)Termination reason: Refutation
% 0.19/0.42
% 0.19/0.42 % (26527)Memory used [KB]: 1870
% 0.19/0.42 % (26527)Time elapsed: 0.046 s
% 0.19/0.42 % (26527)Instructions burned: 83 (million)
% 0.19/0.42 % (26522)Success in time 0.067 s
%------------------------------------------------------------------------------