TSTP Solution File: SWC381+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC381+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 : n004.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 05:14:05 EDT 2024
% Result : Theorem 0.20s 0.46s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 184
% Syntax : Number of formulae : 1258 ( 60 unt; 0 def)
% Number of atoms : 5029 (1281 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 5966 (2195 ~;2624 |; 760 &)
% ( 93 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 57 ( 55 usr; 17 prp; 0-4 aty)
% Number of functors : 57 ( 57 usr; 7 con; 0-2 aty)
% Number of variables : 2241 (1907 !; 334 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1822,plain,
$false,
inference(avatar_sat_refutation,[],[f682,f739,f801,f804,f896,f1146,f1150,f1156,f1505,f1509,f1524,f1528,f1562,f1651,f1655,f1677,f1681,f1821]) ).
fof(f1821,plain,
( ~ spl72_2
| ~ spl72_3 ),
inference(avatar_contradiction_clause,[],[f1820]) ).
fof(f1820,plain,
( $false
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1819,f1363]) ).
fof(f1363,plain,
( memberP(sK22,hd(sK21))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1361,f740]) ).
fof(f740,plain,
( sP0(sK22,sK21)
| ~ spl72_2 ),
inference(resolution,[],[f386,f681]) ).
fof(f681,plain,
( sP1(sK21,sK22,sK22,sK21)
| ~ spl72_2 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f679,plain,
( spl72_2
<=> sP1(sK21,sK22,sK22,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_2])]) ).
fof(f386,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1,X2,X3)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2,X3] :
( ( sP0(X1,X0)
& ! [X4] :
( ~ memberP(X2,X4)
| cons(X4,nil) != X3
| ~ ssItem(X4) )
& neq(X2,nil) )
| ~ sP1(X0,X1,X2,X3) ),
inference(rectify,[],[f254]) ).
fof(f254,plain,
! [X2,X3,X1,X0] :
( ( sP0(X3,X2)
& ! [X5] :
( ~ memberP(X1,X5)
| cons(X5,nil) != X0
| ~ ssItem(X5) )
& neq(X1,nil) )
| ~ sP1(X2,X3,X1,X0) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X2,X3,X1,X0] :
( ( sP0(X3,X2)
& ! [X5] :
( ~ memberP(X1,X5)
| cons(X5,nil) != X0
| ~ ssItem(X5) )
& neq(X1,nil) )
| ~ sP1(X2,X3,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f1361,plain,
( memberP(sK22,hd(sK21))
| ~ sP0(sK22,sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f389,f1317]) ).
fof(f1317,plain,
( sK20(sK22,sK21) = hd(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(forward_demodulation,[],[f1296,f1161]) ).
fof(f1161,plain,
( sK21 = cons(sK20(sK22,sK21),nil)
| ~ spl72_2 ),
inference(resolution,[],[f740,f388]) ).
fof(f388,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK20(X0,X1),nil) = X1 ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1] :
( ( memberP(X0,sK20(X0,X1))
& cons(sK20(X0,X1),nil) = X1
& ssItem(sK20(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f257,f258]) ).
fof(f258,plain,
! [X0,X1] :
( ? [X2] :
( memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
=> ( memberP(X0,sK20(X0,X1))
& cons(sK20(X0,X1),nil) = X1
& ssItem(sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
! [X0,X1] :
( ? [X2] :
( memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f256]) ).
fof(f256,plain,
! [X3,X2] :
( ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP0(X3,X2) ),
inference(nnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X3,X2] :
( ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP0(X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1296,plain,
( sK20(sK22,sK21) = hd(cons(sK20(sK22,sK21),nil))
| ~ spl72_3 ),
inference(resolution,[],[f1020,f795]) ).
fof(f795,plain,
( ssItem(sK20(sK22,sK21))
| ~ spl72_3 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f794,plain,
( spl72_3
<=> ssItem(sK20(sK22,sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_3])]) ).
fof(f1020,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 ),
inference(resolution,[],[f572,f406]) ).
fof(f406,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f572,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f389,plain,
! [X0,X1] :
( memberP(X0,sK20(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f1819,plain,
( ~ memberP(sK22,hd(sK21))
| ~ spl72_2
| ~ spl72_3 ),
inference(resolution,[],[f1739,f681]) ).
fof(f1739,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0,X1,X2,sK21)
| ~ memberP(X2,hd(sK21)) )
| ~ spl72_2
| ~ spl72_3 ),
inference(forward_demodulation,[],[f1738,f1317]) ).
fof(f1738,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0,X1,X2,sK21)
| ~ memberP(X2,sK20(sK22,sK21)) )
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1734,f795]) ).
fof(f1734,plain,
( ! [X2,X0,X1] :
( ~ sP1(X0,X1,X2,sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ memberP(X2,sK20(sK22,sK21)) )
| ~ spl72_2 ),
inference(superposition,[],[f615,f1161]) ).
fof(f615,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2,cons(X4,nil))
| ~ ssItem(X4)
| ~ memberP(X2,X4) ),
inference(equality_resolution,[],[f385]) ).
fof(f385,plain,
! [X2,X3,X0,X1,X4] :
( ~ memberP(X2,X4)
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1681,plain,
( spl72_6
| spl72_15 ),
inference(avatar_contradiction_clause,[],[f1680]) ).
fof(f1680,plain,
( $false
| spl72_6
| spl72_15 ),
inference(subsumption_resolution,[],[f1679,f391]) ).
fof(f391,plain,
ssList(sK22),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
( ( ( ~ neq(sK24,nil)
& neq(sK22,nil) )
| sP1(sK23,sK24,sK22,sK21) )
& sK21 = sK23
& sK22 = sK24
& ssList(sK24)
& ssList(sK23)
& ssList(sK22)
& ssList(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24])],[f226,f263,f262,f261,f260]) ).
fof(f260,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP1(X2,X3,X1,X0) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP1(X2,X3,X1,sK21) )
& sK21 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f261,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP1(X2,X3,X1,sK21) )
& sK21 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK22,nil) )
| sP1(X2,X3,sK22,sK21) )
& sK21 = X2
& sK22 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f262,plain,
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK22,nil) )
| sP1(X2,X3,sK22,sK21) )
& sK21 = X2
& sK22 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK22,nil) )
| sP1(sK23,X3,sK22,sK21) )
& sK21 = sK23
& sK22 = X3
& ssList(X3) )
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f263,plain,
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK22,nil) )
| sP1(sK23,X3,sK22,sK21) )
& sK21 = sK23
& sK22 = X3
& ssList(X3) )
=> ( ( ( ~ neq(sK24,nil)
& neq(sK22,nil) )
| sP1(sK23,sK24,sK22,sK21) )
& sK21 = sK23
& sK22 = sK24
& ssList(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP1(X2,X3,X1,X0) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f100,f225,f224]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
& ! [X5] :
( ~ memberP(X1,X5)
| cons(X5,nil) != X0
| ~ ssItem(X5) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
& ! [X5] :
( ~ memberP(X1,X5)
| cons(X5,nil) != X0
| ~ ssItem(X5) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) )
| ? [X5] :
( memberP(X1,X5)
& cons(X5,nil) = X0
& ssItem(X5) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| cons(X5,nil) != X2 ) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f1679,plain,
( ~ ssList(sK22)
| spl72_6
| spl72_15 ),
inference(subsumption_resolution,[],[f1678,f894]) ).
fof(f894,plain,
( nil != sK22
| spl72_6 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f893,plain,
( spl72_6
<=> nil = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl72_6])]) ).
fof(f1678,plain,
( nil = sK22
| ~ ssList(sK22)
| spl72_15 ),
inference(resolution,[],[f1672,f473]) ).
fof(f473,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f1672,plain,
( ~ ssItem(hd(sK22))
| spl72_15 ),
inference(avatar_component_clause,[],[f1670]) ).
fof(f1670,plain,
( spl72_15
<=> ssItem(hd(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_15])]) ).
fof(f1677,plain,
( ~ spl72_15
| ~ spl72_16
| spl72_6 ),
inference(avatar_split_clause,[],[f1642,f893,f1674,f1670]) ).
fof(f1674,plain,
( spl72_16
<=> sK22 = tl(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_16])]) ).
fof(f1642,plain,
( sK22 != tl(sK22)
| ~ ssItem(hd(sK22))
| spl72_6 ),
inference(subsumption_resolution,[],[f1641,f391]) ).
fof(f1641,plain,
( sK22 != tl(sK22)
| ~ ssItem(hd(sK22))
| ~ ssList(sK22)
| spl72_6 ),
inference(inner_rewriting,[],[f1639]) ).
fof(f1639,plain,
( sK22 != tl(sK22)
| ~ ssItem(hd(sK22))
| ~ ssList(tl(sK22))
| spl72_6 ),
inference(superposition,[],[f570,f1609]) ).
fof(f1609,plain,
( sK22 = cons(hd(sK22),tl(sK22))
| spl72_6 ),
inference(global_subsumption,[],[f615,f397,f396,f419,f421,f422,f431,f648,f432,f433,f434,f435,f436,f439,f437,f646,f441,f440,f461,f460,f459,f490,f625,f501,f645,f512,f628,f524,f629,f536,f630,f548,f631,f559,f632,f633,f634,f635,f573,f636,f576,f579,f580,f581,f582,f583,f584,f638,f588,f639,f592,f640,f595,f643,f598,f597,f600,f602,f601,f603,f604,f605,f606,f607,f608,f609,f610,f611,f390,f391,f392,f393,f398,f399,f400,f401,f402,f403,f404,f405,f406,f612,f613,f394,f395,f614,f620,f622,f650,f651,f652,f492,f503,f515,f527,f539,f550,f561,f407,f408,f409,f410,f462,f463,f464,f465,f466,f467,f486,f487,f488,f489,f496,f497,f498,f499,f500,f507,f508,f509,f510,f511,f519,f520,f521,f522,f523,f531,f532,f533,f534,f535,f543,f544,f545,f546,f547,f554,f555,f556,f557,f558,f644,f649,f653,f411,f412,f413,f414,f415,f416,f417,f483,f493,f504,f516,f528,f540,f541,f551,f552,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f387,f450,f458,f468,f708,f709,f684,f685,f469,f735,f736,f711,f712,f480,f491,f502,f513,f514,f525,f526,f537,f538,f549,f560,f384,f386,f389,f742,f446,f454,f470,f745,f746,f471,f473,f474,f747,f748,f476,f478,f749,f750,f562,f564,f566,f568,f766,f767,f578,f768,f769,f569,f570,f647,f688,f388,f418,f420,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f423,f699,f700,f701,f702,f813,f703,f814,f704,f815,f705,f816,f706,f817,f707,f818,f715,f716,f424,f821,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f426,f728,f729,f827,f730,f828,f731,f829,f732,f830,f733,f831,f734,f832,f427,f428,f430,f443,f444,f447,f451,f452,f455,f847,f848,f849,f477,f880,f851,f853,f886,f858,f859,f860,f861,f862,f863,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f855,f479,f928,f899,f901,f936,f906,f907,f908,f909,f910,f911,f912,f913,f914,f915,f916,f917,f918,f919,f920,f921,f922,f923,f924,f925,f926,f927,f930,f481,f571,f939,f940,f942,f969,f970,f947,f948,f949,f950,f951,f952,f953,f954,f955,f956,f957,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f943,f971,f974,f975,f976,f991,f992,f944,f995,f996,f998,f999,f1000,f1015,f572,f1018,f1019,f1021,f1048,f1049,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f1034,f1035,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1016,f1022,f1051,f1052,f1054,f1055,f1056,f1071,f1073,f1074,f1072,f1076,f1077,f1023,f1079,f1080,f1082,f1083,f1084,f1099,f1101,f1102,f1100,f1104,f1105,f586,f977,f978,f979,f980,f981,f982,f983,f984,f985,f624,f1115,f1152,f902,f1153,f854,f574,f1200,f1201,f1202,f1203,f1204,f1205,f986,f987,f1214,f988,f1215,f575,f1216,f1217,f1218,f1219,f1220,f1221,f989,f1222,f990,f1223,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f587,f1224,f1225,f1226,f1227,f1228,f1229,f1010,f1011,f1230,f1012,f1231,f1013,f1232,f1014,f1233,f1057,f1058,f1059,f1060,f1061,f1062,f590,f1234,f1235,f1236,f1237,f1238,f1239,f1063,f1064,f1065,f1066,f1067,f1240,f1068,f1241,f1069,f1242,f1070,f1243,f1085,f1086,f1087,f591,f1244,f1245,f1246,f1247,f1248,f1249,f1088,f1089,f1090,f1091,f1092,f1093,f1094,f1095,f1250,f1096,f1251,f1097,f1252,f1098,f1253,f594,f1254,f1255,f1256,f1257,f1258,f1259,f941,f1266,f1267,f1269,f1270,f1271,f1273,f1274,f1275,f1276,f1277,f1278,f1279,f1280,f1281,f1282,f1283,f1284,f1285,f1286,f1287,f1288,f1020,f1294,f1295,f1297,f1298,f1299,f1301,f1302,f1303,f1304,f1305,f1306,f1307,f1308,f1309,f1310,f1311,f1312,f1313,f1314,f449,f1336,f1339,f1340,f1343,f1344,f457,f1386,f1387,f1390,f1391,f1315,f1409,f1410,f1411,f1412,f1316,f1414,f1415,f1416,f1417,f972,f472,f1466,f1431,f1433,f1474,f1438,f1439,f1440,f1441,f1442,f1443,f1444,f1445,f1446,f1447,f1448,f1449,f1450,f1451,f1452,f1453,f1454,f1455,f1456,f1457,f1458,f1459,f1460,f1461,f1462,f1463,f1464,f1465,f1468,f1487,f1488,f1489,f1490,f1493,f1494,f1496,f903,f1566,f1533,f1567,f1435,f1568,f1530,f1569,f894,f475,f1606,f1571,f1573,f1575]) ).
fof(f1575,plain,
( nil = sK22
| sK22 = cons(hd(sK22),tl(sK22)) ),
inference(resolution,[],[f475,f391]) ).
fof(f1573,plain,
! [X0] :
( nil = tl(X0)
| tl(X0) = cons(hd(tl(X0)),tl(tl(X0)))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f475,f474]) ).
fof(f1571,plain,
! [X0,X1] :
( nil = app(X0,X1)
| app(X0,X1) = cons(hd(app(X0,X1)),tl(app(X0,X1)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f475,f578]) ).
fof(f1606,plain,
! [X0,X1] :
( cons(X0,X1) = cons(hd(cons(X0,X1)),tl(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f1570,f569]) ).
fof(f1570,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| cons(X0,X1) = cons(hd(cons(X0,X1)),tl(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f475,f568]) ).
fof(f475,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f1569,plain,
( sK22 = cons(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(global_subsumption,[],[f615,f397,f396,f419,f421,f422,f431,f648,f432,f433,f434,f435,f436,f439,f437,f646,f441,f440,f461,f460,f459,f475,f490,f625,f501,f645,f512,f628,f524,f629,f536,f630,f548,f631,f559,f632,f633,f634,f635,f573,f636,f576,f579,f580,f581,f582,f583,f584,f638,f588,f639,f592,f640,f595,f643,f598,f597,f600,f602,f601,f603,f604,f605,f606,f607,f608,f609,f610,f611,f390,f391,f392,f393,f398,f399,f400,f401,f402,f403,f404,f405,f406,f612,f613,f394,f395,f614,f620,f622,f650,f651,f652,f492,f503,f515,f527,f539,f550,f561,f407,f408,f409,f410,f462,f463,f464,f465,f466,f467,f486,f487,f488,f489,f496,f497,f498,f499,f500,f507,f508,f509,f510,f511,f519,f520,f521,f522,f523,f531,f532,f533,f534,f535,f543,f544,f545,f546,f547,f554,f555,f556,f557,f558,f644,f649,f653,f411,f412,f413,f414,f415,f416,f417,f483,f493,f504,f516,f528,f540,f541,f551,f552,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f387,f450,f458,f468,f708,f709,f684,f685,f469,f735,f736,f711,f712,f480,f491,f502,f513,f514,f525,f526,f537,f538,f549,f560,f384,f386,f389,f742,f446,f454,f470,f745,f746,f471,f473,f474,f747,f748,f476,f478,f749,f750,f562,f564,f566,f568,f766,f767,f578,f768,f769,f569,f570,f647,f688,f388,f418,f420,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f423,f699,f700,f701,f702,f813,f703,f814,f704,f815,f705,f816,f706,f817,f707,f818,f715,f716,f424,f821,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f426,f728,f729,f827,f730,f828,f731,f829,f732,f830,f733,f831,f734,f832,f427,f428,f430,f443,f444,f447,f451,f452,f455,f847,f848,f849,f477,f880,f851,f853,f886,f858,f859,f860,f861,f862,f863,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f855,f894,f479,f928,f899,f901,f936,f906,f907,f908,f909,f910,f911,f912,f913,f914,f915,f916,f917,f918,f919,f920,f921,f922,f923,f924,f925,f926,f927,f930,f481,f571,f939,f940,f942,f969,f970,f947,f948,f949,f950,f951,f952,f953,f954,f955,f956,f957,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f943,f971,f974,f975,f976,f991,f992,f944,f995,f996,f998,f999,f1000,f1015,f572,f1018,f1019,f1021,f1048,f1049,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f1034,f1035,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1016,f1022,f1051,f1052,f1054,f1055,f1056,f1071,f1073,f1074,f1072,f1076,f1077,f1023,f1079,f1080,f1082,f1083,f1084,f1099,f1101,f1102,f1100,f1104,f1105,f586,f977,f978,f979,f980,f981,f982,f983,f984,f985,f624,f1115,f1152,f902,f1153,f854,f574,f1200,f1201,f1202,f1203,f1204,f1205,f986,f987,f1214,f988,f1215,f575,f1216,f1217,f1218,f1219,f1220,f1221,f989,f1222,f990,f1223,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f587,f1224,f1225,f1226,f1227,f1228,f1229,f1010,f1011,f1230,f1012,f1231,f1013,f1232,f1014,f1233,f1057,f1058,f1059,f1060,f1061,f1062,f590,f1234,f1235,f1236,f1237,f1238,f1239,f1063,f1064,f1065,f1066,f1067,f1240,f1068,f1241,f1069,f1242,f1070,f1243,f1085,f1086,f1087,f591,f1244,f1245,f1246,f1247,f1248,f1249,f1088,f1089,f1090,f1091,f1092,f1093,f1094,f1095,f1250,f1096,f1251,f1097,f1252,f1098,f1253,f594,f1254,f1255,f1256,f1257,f1258,f1259,f941,f1266,f1267,f1269,f1270,f1271,f1273,f1274,f1275,f1276,f1277,f1278,f1279,f1280,f1281,f1282,f1283,f1284,f1285,f1286,f1287,f1288,f1020,f1294,f1295,f1297,f1298,f1299,f1301,f1302,f1303,f1304,f1305,f1306,f1307,f1308,f1309,f1310,f1311,f1312,f1313,f1314,f449,f1336,f1339,f1340,f1343,f1344,f457,f1386,f1387,f1390,f1391,f1315,f1409,f1410,f1411,f1412,f1316,f1414,f1415,f1416,f1417,f972,f472,f1466,f1431,f1433,f1474,f1438,f1439,f1440,f1441,f1442,f1443,f1444,f1445,f1446,f1447,f1448,f1449,f1450,f1451,f1452,f1453,f1454,f1455,f1456,f1457,f1458,f1459,f1460,f1461,f1462,f1463,f1464,f1465,f1468,f1487,f1488,f1489,f1490,f1493,f1494,f1496,f903,f1566,f1533,f1567,f1435,f1568,f1530]) ).
fof(f1530,plain,
( sK22 = cons(sK26(sK22),sK25(sK22))
| nil = sK22 ),
inference(forward_demodulation,[],[f1472,f394]) ).
fof(f1472,plain,
( nil = sK22
| sK24 = cons(sK26(sK24),sK25(sK24)) ),
inference(forward_demodulation,[],[f1437,f394]) ).
fof(f1437,plain,
( nil = sK24
| sK24 = cons(sK26(sK24),sK25(sK24)) ),
inference(resolution,[],[f472,f393]) ).
fof(f1568,plain,
( sK22 = cons(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(global_subsumption,[],[f615,f397,f396,f419,f421,f422,f431,f648,f432,f433,f434,f435,f436,f439,f437,f646,f441,f440,f461,f460,f459,f475,f490,f625,f501,f645,f512,f628,f524,f629,f536,f630,f548,f631,f559,f632,f633,f634,f635,f573,f636,f576,f579,f580,f581,f582,f583,f584,f638,f588,f639,f592,f640,f595,f643,f598,f597,f600,f602,f601,f603,f604,f605,f606,f607,f608,f609,f610,f611,f390,f391,f392,f393,f398,f399,f400,f401,f402,f403,f404,f405,f406,f612,f613,f394,f395,f614,f620,f622,f650,f651,f652,f492,f503,f515,f527,f539,f550,f561,f407,f408,f409,f410,f462,f463,f464,f465,f466,f467,f486,f487,f488,f489,f496,f497,f498,f499,f500,f507,f508,f509,f510,f511,f519,f520,f521,f522,f523,f531,f532,f533,f534,f535,f543,f544,f545,f546,f547,f554,f555,f556,f557,f558,f644,f649,f653,f411,f412,f413,f414,f415,f416,f417,f483,f493,f504,f516,f528,f540,f541,f551,f552,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f387,f450,f458,f468,f708,f709,f684,f685,f469,f735,f736,f711,f712,f480,f491,f502,f513,f514,f525,f526,f537,f538,f549,f560,f384,f386,f389,f742,f446,f454,f470,f745,f746,f471,f473,f474,f747,f748,f476,f478,f749,f750,f562,f564,f566,f568,f766,f767,f578,f768,f769,f569,f570,f647,f688,f388,f418,f420,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f423,f699,f700,f701,f702,f813,f703,f814,f704,f815,f705,f816,f706,f817,f707,f818,f715,f716,f424,f821,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f426,f728,f729,f827,f730,f828,f731,f829,f732,f830,f733,f831,f734,f832,f427,f428,f430,f443,f444,f447,f451,f452,f455,f847,f848,f849,f477,f880,f851,f853,f886,f858,f859,f860,f861,f862,f863,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f855,f894,f479,f928,f899,f901,f936,f906,f907,f908,f909,f910,f911,f912,f913,f914,f915,f916,f917,f918,f919,f920,f921,f922,f923,f924,f925,f926,f927,f930,f481,f571,f939,f940,f942,f969,f970,f947,f948,f949,f950,f951,f952,f953,f954,f955,f956,f957,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f943,f971,f974,f975,f976,f991,f992,f944,f995,f996,f998,f999,f1000,f1015,f572,f1018,f1019,f1021,f1048,f1049,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f1034,f1035,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1016,f1022,f1051,f1052,f1054,f1055,f1056,f1071,f1073,f1074,f1072,f1076,f1077,f1023,f1079,f1080,f1082,f1083,f1084,f1099,f1101,f1102,f1100,f1104,f1105,f586,f977,f978,f979,f980,f981,f982,f983,f984,f985,f624,f1115,f1152,f902,f1153,f854,f574,f1200,f1201,f1202,f1203,f1204,f1205,f986,f987,f1214,f988,f1215,f575,f1216,f1217,f1218,f1219,f1220,f1221,f989,f1222,f990,f1223,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f587,f1224,f1225,f1226,f1227,f1228,f1229,f1010,f1011,f1230,f1012,f1231,f1013,f1232,f1014,f1233,f1057,f1058,f1059,f1060,f1061,f1062,f590,f1234,f1235,f1236,f1237,f1238,f1239,f1063,f1064,f1065,f1066,f1067,f1240,f1068,f1241,f1069,f1242,f1070,f1243,f1085,f1086,f1087,f591,f1244,f1245,f1246,f1247,f1248,f1249,f1088,f1089,f1090,f1091,f1092,f1093,f1094,f1095,f1250,f1096,f1251,f1097,f1252,f1098,f1253,f594,f1254,f1255,f1256,f1257,f1258,f1259,f941,f1266,f1267,f1269,f1270,f1271,f1273,f1274,f1275,f1276,f1277,f1278,f1279,f1280,f1281,f1282,f1283,f1284,f1285,f1286,f1287,f1288,f1020,f1294,f1295,f1297,f1298,f1299,f1301,f1302,f1303,f1304,f1305,f1306,f1307,f1308,f1309,f1310,f1311,f1312,f1313,f1314,f449,f1336,f1339,f1340,f1343,f1344,f457,f1386,f1387,f1390,f1391,f1315,f1409,f1410,f1411,f1412,f1316,f1414,f1415,f1416,f1417,f972,f472,f1466,f1431,f1433,f1474,f1438,f1439,f1440,f1441,f1442,f1443,f1444,f1445,f1446,f1447,f1448,f1449,f1450,f1451,f1452,f1453,f1454,f1455,f1456,f1457,f1458,f1459,f1460,f1461,f1462,f1463,f1464,f1465,f1468,f1487,f1488,f1489,f1490,f1493,f1494,f1496,f1530,f903,f1566,f1533,f1567,f1435]) ).
fof(f1435,plain,
( nil = sK22
| sK22 = cons(sK26(sK22),sK25(sK22)) ),
inference(resolution,[],[f472,f391]) ).
fof(f1567,plain,
( tl(sK22) = sK28(sK22)
| spl72_6 ),
inference(global_subsumption,[],[f615,f397,f396,f419,f421,f422,f431,f648,f432,f433,f434,f435,f436,f439,f437,f646,f441,f440,f461,f460,f459,f475,f490,f625,f501,f645,f512,f628,f524,f629,f536,f630,f548,f631,f559,f632,f633,f634,f635,f573,f636,f576,f579,f580,f581,f582,f583,f584,f638,f588,f639,f592,f640,f595,f643,f598,f597,f600,f602,f601,f603,f604,f605,f606,f607,f608,f609,f610,f611,f390,f391,f392,f393,f398,f399,f400,f401,f402,f403,f404,f405,f406,f612,f613,f394,f395,f614,f620,f622,f650,f651,f652,f492,f503,f515,f527,f539,f550,f561,f407,f408,f409,f410,f462,f463,f464,f465,f466,f467,f486,f487,f488,f489,f496,f497,f498,f499,f500,f507,f508,f509,f510,f511,f519,f520,f521,f522,f523,f531,f532,f533,f534,f535,f543,f544,f545,f546,f547,f554,f555,f556,f557,f558,f644,f649,f653,f411,f412,f413,f414,f415,f416,f417,f483,f493,f504,f516,f528,f540,f541,f551,f552,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f387,f450,f458,f468,f708,f709,f684,f685,f469,f735,f736,f711,f712,f480,f491,f502,f513,f514,f525,f526,f537,f538,f549,f560,f384,f386,f389,f742,f446,f454,f470,f745,f746,f471,f473,f474,f747,f748,f476,f478,f749,f750,f562,f564,f566,f568,f766,f767,f578,f768,f769,f569,f570,f647,f688,f388,f418,f420,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f423,f699,f700,f701,f702,f813,f703,f814,f704,f815,f705,f816,f706,f817,f707,f818,f715,f716,f424,f821,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f426,f728,f729,f827,f730,f828,f731,f829,f732,f830,f733,f831,f734,f832,f427,f428,f430,f443,f444,f447,f451,f452,f455,f847,f848,f849,f477,f880,f851,f853,f886,f858,f859,f860,f861,f862,f863,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f855,f894,f479,f928,f899,f901,f936,f906,f907,f908,f909,f910,f911,f912,f913,f914,f915,f916,f917,f918,f919,f920,f921,f922,f923,f924,f925,f926,f927,f930,f481,f571,f939,f940,f942,f969,f970,f947,f948,f949,f950,f951,f952,f953,f954,f955,f956,f957,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f943,f971,f974,f975,f976,f991,f992,f944,f995,f996,f998,f999,f1000,f1015,f572,f1018,f1019,f1021,f1048,f1049,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f1034,f1035,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1016,f1022,f1051,f1052,f1054,f1055,f1056,f1071,f1073,f1074,f1072,f1076,f1077,f1023,f1079,f1080,f1082,f1083,f1084,f1099,f1101,f1102,f1100,f1104,f1105,f586,f977,f978,f979,f980,f981,f982,f983,f984,f985,f624,f1115,f1152,f902,f1153,f854,f574,f1200,f1201,f1202,f1203,f1204,f1205,f986,f987,f1214,f988,f1215,f575,f1216,f1217,f1218,f1219,f1220,f1221,f989,f1222,f990,f1223,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f587,f1224,f1225,f1226,f1227,f1228,f1229,f1010,f1011,f1230,f1012,f1231,f1013,f1232,f1014,f1233,f1057,f1058,f1059,f1060,f1061,f1062,f590,f1234,f1235,f1236,f1237,f1238,f1239,f1063,f1064,f1065,f1066,f1067,f1240,f1068,f1241,f1069,f1242,f1070,f1243,f1085,f1086,f1087,f591,f1244,f1245,f1246,f1247,f1248,f1249,f1088,f1089,f1090,f1091,f1092,f1093,f1094,f1095,f1250,f1096,f1251,f1097,f1252,f1098,f1253,f594,f1254,f1255,f1256,f1257,f1258,f1259,f941,f1266,f1267,f1269,f1270,f1271,f1273,f1274,f1275,f1276,f1277,f1278,f1279,f1280,f1281,f1282,f1283,f1284,f1285,f1286,f1287,f1288,f1020,f1294,f1295,f1297,f1298,f1299,f1301,f1302,f1303,f1304,f1305,f1306,f1307,f1308,f1309,f1310,f1311,f1312,f1313,f1314,f449,f1336,f1339,f1340,f1343,f1344,f457,f1386,f1387,f1390,f1391,f1315,f1409,f1410,f1411,f1412,f1316,f1414,f1415,f1416,f1417,f972,f472,f1466,f1431,f1433,f1474,f1438,f1439,f1440,f1441,f1442,f1443,f1444,f1445,f1446,f1447,f1448,f1449,f1450,f1451,f1452,f1453,f1454,f1455,f1456,f1457,f1458,f1459,f1460,f1461,f1462,f1463,f1464,f1465,f1468,f1487,f1488,f1489,f1490,f1493,f1494,f1496,f1530,f1435,f903,f1566,f1533]) ).
fof(f1533,plain,
( tl(sK22) = sK28(sK22)
| nil = sK22 ),
inference(forward_demodulation,[],[f934,f394]) ).
fof(f934,plain,
( nil = sK22
| tl(sK24) = sK28(sK24) ),
inference(forward_demodulation,[],[f905,f394]) ).
fof(f905,plain,
( nil = sK24
| tl(sK24) = sK28(sK24) ),
inference(resolution,[],[f479,f393]) ).
fof(f1566,plain,
( tl(sK22) = sK28(sK22)
| spl72_6 ),
inference(global_subsumption,[],[f615,f397,f396,f419,f421,f422,f431,f648,f432,f433,f434,f435,f436,f439,f437,f646,f441,f440,f461,f460,f459,f475,f490,f625,f501,f645,f512,f628,f524,f629,f536,f630,f548,f631,f559,f632,f633,f634,f635,f573,f636,f576,f579,f580,f581,f582,f583,f584,f638,f588,f639,f592,f640,f595,f643,f598,f597,f600,f602,f601,f603,f604,f605,f606,f607,f608,f609,f610,f611,f390,f391,f392,f393,f398,f399,f400,f401,f402,f403,f404,f405,f406,f612,f613,f394,f395,f614,f620,f622,f650,f651,f652,f492,f503,f515,f527,f539,f550,f561,f407,f408,f409,f410,f462,f463,f464,f465,f466,f467,f486,f487,f488,f489,f496,f497,f498,f499,f500,f507,f508,f509,f510,f511,f519,f520,f521,f522,f523,f531,f532,f533,f534,f535,f543,f544,f545,f546,f547,f554,f555,f556,f557,f558,f644,f649,f653,f411,f412,f413,f414,f415,f416,f417,f483,f493,f504,f516,f528,f540,f541,f551,f552,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f387,f450,f458,f468,f708,f709,f684,f685,f469,f735,f736,f711,f712,f480,f491,f502,f513,f514,f525,f526,f537,f538,f549,f560,f384,f386,f389,f742,f446,f454,f470,f745,f746,f471,f473,f474,f747,f748,f476,f478,f749,f750,f562,f564,f566,f568,f766,f767,f578,f768,f769,f569,f570,f647,f688,f388,f418,f420,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f423,f699,f700,f701,f702,f813,f703,f814,f704,f815,f705,f816,f706,f817,f707,f818,f715,f716,f424,f821,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f426,f728,f729,f827,f730,f828,f731,f829,f732,f830,f733,f831,f734,f832,f427,f428,f430,f443,f444,f447,f451,f452,f455,f847,f848,f849,f477,f880,f851,f853,f886,f858,f859,f860,f861,f862,f863,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f855,f894,f479,f928,f899,f901,f936,f906,f907,f908,f909,f910,f911,f912,f913,f914,f915,f916,f917,f918,f919,f920,f921,f922,f923,f924,f925,f926,f927,f930,f481,f571,f939,f940,f942,f969,f970,f947,f948,f949,f950,f951,f952,f953,f954,f955,f956,f957,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f943,f971,f974,f975,f976,f991,f992,f944,f995,f996,f998,f999,f1000,f1015,f572,f1018,f1019,f1021,f1048,f1049,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f1034,f1035,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1016,f1022,f1051,f1052,f1054,f1055,f1056,f1071,f1073,f1074,f1072,f1076,f1077,f1023,f1079,f1080,f1082,f1083,f1084,f1099,f1101,f1102,f1100,f1104,f1105,f586,f977,f978,f979,f980,f981,f982,f983,f984,f985,f624,f1115,f1152,f902,f1153,f854,f574,f1200,f1201,f1202,f1203,f1204,f1205,f986,f987,f1214,f988,f1215,f575,f1216,f1217,f1218,f1219,f1220,f1221,f989,f1222,f990,f1223,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f587,f1224,f1225,f1226,f1227,f1228,f1229,f1010,f1011,f1230,f1012,f1231,f1013,f1232,f1014,f1233,f1057,f1058,f1059,f1060,f1061,f1062,f590,f1234,f1235,f1236,f1237,f1238,f1239,f1063,f1064,f1065,f1066,f1067,f1240,f1068,f1241,f1069,f1242,f1070,f1243,f1085,f1086,f1087,f591,f1244,f1245,f1246,f1247,f1248,f1249,f1088,f1089,f1090,f1091,f1092,f1093,f1094,f1095,f1250,f1096,f1251,f1097,f1252,f1098,f1253,f594,f1254,f1255,f1256,f1257,f1258,f1259,f941,f1266,f1267,f1269,f1270,f1271,f1273,f1274,f1275,f1276,f1277,f1278,f1279,f1280,f1281,f1282,f1283,f1284,f1285,f1286,f1287,f1288,f1020,f1294,f1295,f1297,f1298,f1299,f1301,f1302,f1303,f1304,f1305,f1306,f1307,f1308,f1309,f1310,f1311,f1312,f1313,f1314,f449,f1336,f1339,f1340,f1343,f1344,f457,f1386,f1387,f1390,f1391,f1315,f1409,f1410,f1411,f1412,f1316,f1414,f1415,f1416,f1417,f972,f472,f1466,f1431,f1433,f1474,f1438,f1439,f1440,f1441,f1442,f1443,f1444,f1445,f1446,f1447,f1448,f1449,f1450,f1451,f1452,f1453,f1454,f1455,f1456,f1457,f1458,f1459,f1460,f1461,f1462,f1463,f1464,f1465,f1468,f1487,f1488,f1489,f1490,f1493,f1494,f1496,f1530,f1435,f1533,f903]) ).
fof(f903,plain,
( nil = sK22
| tl(sK22) = sK28(sK22) ),
inference(resolution,[],[f479,f391]) ).
fof(f1496,plain,
( sK22 != sK25(sK22)
| ~ ssItem(sK26(sK22))
| spl72_6 ),
inference(subsumption_resolution,[],[f1495,f391]) ).
fof(f1495,plain,
( sK22 != sK25(sK22)
| ~ ssItem(sK26(sK22))
| ~ ssList(sK22)
| spl72_6 ),
inference(inner_rewriting,[],[f1493]) ).
fof(f1494,plain,
( memberP(sK22,sK26(sK22))
| ~ ssList(sK25(sK22))
| ~ ssItem(sK26(sK22))
| spl72_6 ),
inference(superposition,[],[f647,f1468]) ).
fof(f1493,plain,
( sK22 != sK25(sK22)
| ~ ssItem(sK26(sK22))
| ~ ssList(sK25(sK22))
| spl72_6 ),
inference(superposition,[],[f570,f1468]) ).
fof(f1490,plain,
( strictorderedP(sK22)
| ~ sP4(sK25(sK22),sK26(sK22))
| ~ sP5(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(superposition,[],[f452,f1468]) ).
fof(f1489,plain,
( ~ strictorderedP(sK22)
| sP4(sK25(sK22),sK26(sK22))
| ~ sP5(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(superposition,[],[f451,f1468]) ).
fof(f1488,plain,
( totalorderedP(sK22)
| ~ sP2(sK25(sK22),sK26(sK22))
| ~ sP3(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(superposition,[],[f444,f1468]) ).
fof(f1487,plain,
( ~ totalorderedP(sK22)
| sP2(sK25(sK22),sK26(sK22))
| ~ sP3(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(superposition,[],[f443,f1468]) ).
fof(f1468,plain,
( sK22 = cons(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(subsumption_resolution,[],[f1435,f894]) ).
fof(f1465,plain,
! [X0,X1] :
( nil = sK69(X0,X1)
| sK69(X0,X1) = cons(sK26(sK69(X0,X1)),sK25(sK69(X0,X1)))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f472,f594]) ).
fof(f1464,plain,
! [X0,X1] :
( nil = sK68(X0,X1)
| sK68(X0,X1) = cons(sK26(sK68(X0,X1)),sK25(sK68(X0,X1)))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f472,f591]) ).
fof(f1463,plain,
! [X0,X1] :
( nil = sK67(X0,X1)
| sK67(X0,X1) = cons(sK26(sK67(X0,X1)),sK25(sK67(X0,X1)))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f472,f590]) ).
fof(f1462,plain,
! [X0,X1] :
( nil = sK66(X0,X1)
| sK66(X0,X1) = cons(sK26(sK66(X0,X1)),sK25(sK66(X0,X1)))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f472,f587]) ).
fof(f1461,plain,
! [X0,X1] :
( nil = sK65(X0,X1)
| sK65(X0,X1) = cons(sK26(sK65(X0,X1)),sK25(sK65(X0,X1)))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f472,f575]) ).
fof(f1460,plain,
! [X0,X1] :
( nil = sK64(X0,X1)
| sK64(X0,X1) = cons(sK26(sK64(X0,X1)),sK25(sK64(X0,X1)))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f472,f574]) ).
fof(f1459,plain,
! [X0] :
( nil = sK63(X0)
| sK63(X0) = cons(sK26(sK63(X0)),sK25(sK63(X0)))
| sP18(X0) ),
inference(resolution,[],[f472,f558]) ).
fof(f1458,plain,
! [X0] :
( nil = sK62(X0)
| sK62(X0) = cons(sK26(sK62(X0)),sK25(sK62(X0)))
| sP18(X0) ),
inference(resolution,[],[f472,f557]) ).
fof(f1457,plain,
! [X0] :
( nil = sK61(X0)
| sK61(X0) = cons(sK26(sK61(X0)),sK25(sK61(X0)))
| sP18(X0) ),
inference(resolution,[],[f472,f556]) ).
fof(f1456,plain,
! [X0] :
( nil = sK58(X0)
| sK58(X0) = cons(sK26(sK58(X0)),sK25(sK58(X0)))
| sP16(X0) ),
inference(resolution,[],[f472,f547]) ).
fof(f1455,plain,
! [X0] :
( nil = sK57(X0)
| sK57(X0) = cons(sK26(sK57(X0)),sK25(sK57(X0)))
| sP16(X0) ),
inference(resolution,[],[f472,f546]) ).
fof(f1454,plain,
! [X0] :
( nil = sK56(X0)
| sK56(X0) = cons(sK26(sK56(X0)),sK25(sK56(X0)))
| sP16(X0) ),
inference(resolution,[],[f472,f545]) ).
fof(f1453,plain,
! [X0] :
( nil = sK53(X0)
| sK53(X0) = cons(sK26(sK53(X0)),sK25(sK53(X0)))
| sP14(X0) ),
inference(resolution,[],[f472,f535]) ).
fof(f1452,plain,
! [X0] :
( nil = sK52(X0)
| sK52(X0) = cons(sK26(sK52(X0)),sK25(sK52(X0)))
| sP14(X0) ),
inference(resolution,[],[f472,f534]) ).
fof(f1451,plain,
! [X0] :
( nil = sK51(X0)
| sK51(X0) = cons(sK26(sK51(X0)),sK25(sK51(X0)))
| sP14(X0) ),
inference(resolution,[],[f472,f533]) ).
fof(f1450,plain,
! [X0] :
( nil = sK48(X0)
| sK48(X0) = cons(sK26(sK48(X0)),sK25(sK48(X0)))
| sP12(X0) ),
inference(resolution,[],[f472,f523]) ).
fof(f1449,plain,
! [X0] :
( nil = sK47(X0)
| sK47(X0) = cons(sK26(sK47(X0)),sK25(sK47(X0)))
| sP12(X0) ),
inference(resolution,[],[f472,f522]) ).
fof(f1448,plain,
! [X0] :
( nil = sK46(X0)
| sK46(X0) = cons(sK26(sK46(X0)),sK25(sK46(X0)))
| sP12(X0) ),
inference(resolution,[],[f472,f521]) ).
fof(f1447,plain,
! [X0] :
( nil = sK43(X0)
| sK43(X0) = cons(sK26(sK43(X0)),sK25(sK43(X0)))
| sP10(X0) ),
inference(resolution,[],[f472,f511]) ).
fof(f1446,plain,
! [X0] :
( nil = sK42(X0)
| sK42(X0) = cons(sK26(sK42(X0)),sK25(sK42(X0)))
| sP10(X0) ),
inference(resolution,[],[f472,f510]) ).
fof(f1445,plain,
! [X0] :
( nil = sK41(X0)
| sK41(X0) = cons(sK26(sK41(X0)),sK25(sK41(X0)))
| sP10(X0) ),
inference(resolution,[],[f472,f509]) ).
fof(f1444,plain,
! [X0] :
( nil = sK38(X0)
| sK38(X0) = cons(sK26(sK38(X0)),sK25(sK38(X0)))
| sP8(X0) ),
inference(resolution,[],[f472,f500]) ).
fof(f1443,plain,
! [X0] :
( nil = sK37(X0)
| sK37(X0) = cons(sK26(sK37(X0)),sK25(sK37(X0)))
| sP8(X0) ),
inference(resolution,[],[f472,f499]) ).
fof(f1442,plain,
! [X0] :
( nil = sK36(X0)
| sK36(X0) = cons(sK26(sK36(X0)),sK25(sK36(X0)))
| sP8(X0) ),
inference(resolution,[],[f472,f498]) ).
fof(f1441,plain,
! [X0] :
( nil = sK33(X0)
| sK33(X0) = cons(sK26(sK33(X0)),sK25(sK33(X0)))
| sP6(X0) ),
inference(resolution,[],[f472,f489]) ).
fof(f1440,plain,
! [X0] :
( nil = sK32(X0)
| sK32(X0) = cons(sK26(sK32(X0)),sK25(sK32(X0)))
| sP6(X0) ),
inference(resolution,[],[f472,f488]) ).
fof(f1439,plain,
! [X0] :
( nil = sK28(X0)
| sK28(X0) = cons(sK26(sK28(X0)),sK25(sK28(X0)))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f472,f478]) ).
fof(f1438,plain,
! [X0] :
( nil = sK25(X0)
| sK25(X0) = cons(sK26(sK25(X0)),sK25(sK25(X0)))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f472,f470]) ).
fof(f1474,plain,
( sK22 = cons(sK26(sK22),sK25(sK22))
| spl72_6 ),
inference(forward_demodulation,[],[f1473,f394]) ).
fof(f1473,plain,
( sK24 = cons(sK26(sK24),sK25(sK24))
| spl72_6 ),
inference(subsumption_resolution,[],[f1472,f894]) ).
fof(f1433,plain,
! [X0] :
( nil = tl(X0)
| tl(X0) = cons(sK26(tl(X0)),sK25(tl(X0)))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f472,f474]) ).
fof(f1431,plain,
! [X0,X1] :
( nil = app(X0,X1)
| app(X0,X1) = cons(sK26(app(X0,X1)),sK25(app(X0,X1)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f472,f578]) ).
fof(f1466,plain,
! [X0,X1] :
( cons(X0,X1) = cons(sK26(cons(X0,X1)),sK25(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f1430,f569]) ).
fof(f1430,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| cons(X0,X1) = cons(sK26(cons(X0,X1)),sK25(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f472,f568]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK26(X0),sK25(X0)) = X0 ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(X0))
& ssList(sK25(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f150,f285,f284]) ).
fof(f284,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
& ssList(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f285,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
=> ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f972,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21 = tl(cons(sK20(X0,X1),sK21)) ),
inference(resolution,[],[f943,f387]) ).
fof(f1417,plain,
! [X0] :
( leq(X0,sK71)
| nil = cons(sK71,nil)
| ~ sP2(cons(sK71,nil),X0) ),
inference(superposition,[],[f447,f1316]) ).
fof(f1416,plain,
! [X0] :
( lt(X0,sK71)
| nil = cons(sK71,nil)
| ~ sP4(cons(sK71,nil),X0) ),
inference(superposition,[],[f455,f1316]) ).
fof(f1415,plain,
! [X0] :
( ~ leq(X0,sK71)
| sP2(cons(sK71,nil),X0)
| ~ totalorderedP(cons(sK71,nil))
| nil = cons(sK71,nil) ),
inference(superposition,[],[f449,f1316]) ).
fof(f1414,plain,
! [X0] :
( ~ lt(X0,sK71)
| sP4(cons(sK71,nil),X0)
| ~ strictorderedP(cons(sK71,nil))
| nil = cons(sK71,nil) ),
inference(superposition,[],[f457,f1316]) ).
fof(f1316,plain,
sK71 = hd(cons(sK71,nil)),
inference(resolution,[],[f1020,f613]) ).
fof(f1412,plain,
! [X0] :
( leq(X0,sK70)
| nil = cons(sK70,nil)
| ~ sP2(cons(sK70,nil),X0) ),
inference(superposition,[],[f447,f1315]) ).
fof(f1411,plain,
! [X0] :
( lt(X0,sK70)
| nil = cons(sK70,nil)
| ~ sP4(cons(sK70,nil),X0) ),
inference(superposition,[],[f455,f1315]) ).
fof(f1410,plain,
! [X0] :
( ~ leq(X0,sK70)
| sP2(cons(sK70,nil),X0)
| ~ totalorderedP(cons(sK70,nil))
| nil = cons(sK70,nil) ),
inference(superposition,[],[f449,f1315]) ).
fof(f1409,plain,
! [X0] :
( ~ lt(X0,sK70)
| sP4(cons(sK70,nil),X0)
| ~ strictorderedP(cons(sK70,nil))
| nil = cons(sK70,nil) ),
inference(superposition,[],[f457,f1315]) ).
fof(f1315,plain,
sK70 = hd(cons(sK70,nil)),
inference(resolution,[],[f1020,f612]) ).
fof(f1391,plain,
! [X0] :
( ~ lt(X0,sK71)
| sP4(cons(sK71,sK22),X0)
| ~ strictorderedP(cons(sK71,sK22))
| nil = cons(sK71,sK22) ),
inference(superposition,[],[f457,f1100]) ).
fof(f1390,plain,
! [X0] :
( ~ lt(X0,sK70)
| sP4(cons(sK70,sK22),X0)
| ~ strictorderedP(cons(sK70,sK22))
| nil = cons(sK70,sK22) ),
inference(superposition,[],[f457,f1099]) ).
fof(f1387,plain,
! [X0] :
( ~ lt(X0,sK71)
| sP4(cons(sK71,sK21),X0)
| ~ strictorderedP(cons(sK71,sK21))
| nil = cons(sK71,sK21) ),
inference(superposition,[],[f457,f1072]) ).
fof(f1386,plain,
! [X0] :
( ~ lt(X0,sK70)
| sP4(cons(sK70,sK21),X0)
| ~ strictorderedP(cons(sK70,sK21))
| nil = cons(sK70,sK21) ),
inference(superposition,[],[f457,f1071]) ).
fof(f457,plain,
! [X0,X1] :
( ~ lt(X1,hd(X0))
| sP4(X0,X1)
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f280]) ).
fof(f280,plain,
! [X1,X0] :
( ( sP4(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP4(X1,X0) ) ),
inference(flattening,[],[f279]) ).
fof(f279,plain,
! [X1,X0] :
( ( sP4(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP4(X1,X0) ) ),
inference(nnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X1,X0] :
( sP4(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f1344,plain,
! [X0] :
( ~ leq(X0,sK71)
| sP2(cons(sK71,sK22),X0)
| ~ totalorderedP(cons(sK71,sK22))
| nil = cons(sK71,sK22) ),
inference(superposition,[],[f449,f1100]) ).
fof(f1343,plain,
! [X0] :
( ~ leq(X0,sK70)
| sP2(cons(sK70,sK22),X0)
| ~ totalorderedP(cons(sK70,sK22))
| nil = cons(sK70,sK22) ),
inference(superposition,[],[f449,f1099]) ).
fof(f1340,plain,
! [X0] :
( ~ leq(X0,sK71)
| sP2(cons(sK71,sK21),X0)
| ~ totalorderedP(cons(sK71,sK21))
| nil = cons(sK71,sK21) ),
inference(superposition,[],[f449,f1072]) ).
fof(f1339,plain,
! [X0] :
( ~ leq(X0,sK70)
| sP2(cons(sK70,sK21),X0)
| ~ totalorderedP(cons(sK70,sK21))
| nil = cons(sK70,sK21) ),
inference(superposition,[],[f449,f1071]) ).
fof(f1336,plain,
! [X0] :
( sP2(X0,hd(X0))
| ~ totalorderedP(X0)
| nil = X0
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f449,f410]) ).
fof(f449,plain,
! [X0,X1] :
( ~ leq(X1,hd(X0))
| sP2(X0,X1)
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f276]) ).
fof(f276,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f275]) ).
fof(f275,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1314,plain,
! [X0] :
( sK60(X0) = hd(cons(sK60(X0),nil))
| sP18(X0) ),
inference(resolution,[],[f1020,f555]) ).
fof(f1313,plain,
! [X0] :
( sK59(X0) = hd(cons(sK59(X0),nil))
| sP18(X0) ),
inference(resolution,[],[f1020,f554]) ).
fof(f1312,plain,
! [X0] :
( sK55(X0) = hd(cons(sK55(X0),nil))
| sP16(X0) ),
inference(resolution,[],[f1020,f544]) ).
fof(f1311,plain,
! [X0] :
( sK54(X0) = hd(cons(sK54(X0),nil))
| sP16(X0) ),
inference(resolution,[],[f1020,f543]) ).
fof(f1310,plain,
! [X0] :
( sK50(X0) = hd(cons(sK50(X0),nil))
| sP14(X0) ),
inference(resolution,[],[f1020,f532]) ).
fof(f1309,plain,
! [X0] :
( sK49(X0) = hd(cons(sK49(X0),nil))
| sP14(X0) ),
inference(resolution,[],[f1020,f531]) ).
fof(f1308,plain,
! [X0] :
( sK45(X0) = hd(cons(sK45(X0),nil))
| sP12(X0) ),
inference(resolution,[],[f1020,f520]) ).
fof(f1307,plain,
! [X0] :
( sK44(X0) = hd(cons(sK44(X0),nil))
| sP12(X0) ),
inference(resolution,[],[f1020,f519]) ).
fof(f1306,plain,
! [X0] :
( sK40(X0) = hd(cons(sK40(X0),nil))
| sP10(X0) ),
inference(resolution,[],[f1020,f508]) ).
fof(f1305,plain,
! [X0] :
( sK39(X0) = hd(cons(sK39(X0),nil))
| sP10(X0) ),
inference(resolution,[],[f1020,f507]) ).
fof(f1304,plain,
! [X0] :
( sK35(X0) = hd(cons(sK35(X0),nil))
| sP8(X0) ),
inference(resolution,[],[f1020,f497]) ).
fof(f1303,plain,
! [X0] :
( sK34(X0) = hd(cons(sK34(X0),nil))
| sP8(X0) ),
inference(resolution,[],[f1020,f496]) ).
fof(f1302,plain,
! [X0] :
( sK31(X0) = hd(cons(sK31(X0),nil))
| sP6(X0) ),
inference(resolution,[],[f1020,f487]) ).
fof(f1301,plain,
! [X0] :
( sK30(X0) = hd(cons(sK30(X0),nil))
| sP6(X0) ),
inference(resolution,[],[f1020,f486]) ).
fof(f1299,plain,
! [X0] :
( sK29(X0) = hd(cons(sK29(X0),nil))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1020,f480]) ).
fof(f1298,plain,
! [X0] :
( sK27(X0) = hd(cons(sK27(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1020,f476]) ).
fof(f1297,plain,
! [X0] :
( sK26(X0) = hd(cons(sK26(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1020,f471]) ).
fof(f1295,plain,
! [X0,X1] :
( sK20(X0,X1) = hd(cons(sK20(X0,X1),nil))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f1020,f387]) ).
fof(f1294,plain,
! [X0] :
( hd(X0) = hd(cons(hd(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1020,f473]) ).
fof(f1288,plain,
nil = tl(cons(sK71,nil)),
inference(resolution,[],[f941,f613]) ).
fof(f1287,plain,
nil = tl(cons(sK70,nil)),
inference(resolution,[],[f941,f612]) ).
fof(f1286,plain,
! [X0] :
( nil = tl(cons(sK60(X0),nil))
| sP18(X0) ),
inference(resolution,[],[f941,f555]) ).
fof(f1285,plain,
! [X0] :
( nil = tl(cons(sK59(X0),nil))
| sP18(X0) ),
inference(resolution,[],[f941,f554]) ).
fof(f1284,plain,
! [X0] :
( nil = tl(cons(sK55(X0),nil))
| sP16(X0) ),
inference(resolution,[],[f941,f544]) ).
fof(f1283,plain,
! [X0] :
( nil = tl(cons(sK54(X0),nil))
| sP16(X0) ),
inference(resolution,[],[f941,f543]) ).
fof(f1282,plain,
! [X0] :
( nil = tl(cons(sK50(X0),nil))
| sP14(X0) ),
inference(resolution,[],[f941,f532]) ).
fof(f1281,plain,
! [X0] :
( nil = tl(cons(sK49(X0),nil))
| sP14(X0) ),
inference(resolution,[],[f941,f531]) ).
fof(f1280,plain,
! [X0] :
( nil = tl(cons(sK45(X0),nil))
| sP12(X0) ),
inference(resolution,[],[f941,f520]) ).
fof(f1279,plain,
! [X0] :
( nil = tl(cons(sK44(X0),nil))
| sP12(X0) ),
inference(resolution,[],[f941,f519]) ).
fof(f1278,plain,
! [X0] :
( nil = tl(cons(sK40(X0),nil))
| sP10(X0) ),
inference(resolution,[],[f941,f508]) ).
fof(f1277,plain,
! [X0] :
( nil = tl(cons(sK39(X0),nil))
| sP10(X0) ),
inference(resolution,[],[f941,f507]) ).
fof(f1276,plain,
! [X0] :
( nil = tl(cons(sK35(X0),nil))
| sP8(X0) ),
inference(resolution,[],[f941,f497]) ).
fof(f1275,plain,
! [X0] :
( nil = tl(cons(sK34(X0),nil))
| sP8(X0) ),
inference(resolution,[],[f941,f496]) ).
fof(f1274,plain,
! [X0] :
( nil = tl(cons(sK31(X0),nil))
| sP6(X0) ),
inference(resolution,[],[f941,f487]) ).
fof(f1273,plain,
! [X0] :
( nil = tl(cons(sK30(X0),nil))
| sP6(X0) ),
inference(resolution,[],[f941,f486]) ).
fof(f1271,plain,
! [X0] :
( nil = tl(cons(sK29(X0),nil))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f941,f480]) ).
fof(f1270,plain,
! [X0] :
( nil = tl(cons(sK27(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f941,f476]) ).
fof(f1269,plain,
! [X0] :
( nil = tl(cons(sK26(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f941,f471]) ).
fof(f1267,plain,
! [X0,X1] :
( nil = tl(cons(sK20(X0,X1),nil))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f941,f387]) ).
fof(f1266,plain,
! [X0] :
( nil = tl(cons(hd(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f941,f473]) ).
fof(f941,plain,
! [X0] :
( ~ ssItem(X0)
| nil = tl(cons(X0,nil)) ),
inference(resolution,[],[f571,f406]) ).
fof(f1259,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK69(X0,X1) = app(sK69(X0,X1),nil) ),
inference(resolution,[],[f594,f468]) ).
fof(f1258,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK69(X0,X1) = app(nil,sK69(X0,X1)) ),
inference(resolution,[],[f594,f469]) ).
fof(f1257,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK69(X0,X1)
| hd(sK69(X0,X1)) = sK27(sK69(X0,X1)) ),
inference(resolution,[],[f594,f477]) ).
fof(f1256,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK69(X0,X1)
| tl(sK69(X0,X1)) = sK28(sK69(X0,X1)) ),
inference(resolution,[],[f594,f479]) ).
fof(f1255,plain,
! [X2,X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sK69(X0,X1) = tl(cons(X2,sK69(X0,X1))) ),
inference(resolution,[],[f594,f571]) ).
fof(f1254,plain,
! [X2,X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| hd(cons(X2,sK69(X0,X1))) = X2 ),
inference(resolution,[],[f594,f572]) ).
fof(f594,plain,
! [X0,X1] :
( ssList(sK69(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f376,f377]) ).
fof(f377,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f376,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f375]) ).
fof(f375,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f1253,plain,
! [X0] :
( sK60(X0) = hd(cons(sK60(X0),sK22))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1098,f664]) ).
fof(f1098,plain,
! [X0] :
( sP18(X0)
| sK60(X0) = hd(cons(sK60(X0),sK22)) ),
inference(resolution,[],[f1023,f555]) ).
fof(f1252,plain,
! [X0] :
( sK59(X0) = hd(cons(sK59(X0),sK22))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1097,f664]) ).
fof(f1097,plain,
! [X0] :
( sP18(X0)
| sK59(X0) = hd(cons(sK59(X0),sK22)) ),
inference(resolution,[],[f1023,f554]) ).
fof(f1251,plain,
! [X0] :
( sK55(X0) = hd(cons(sK55(X0),sK22))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1096,f662]) ).
fof(f1096,plain,
! [X0] :
( sP16(X0)
| sK55(X0) = hd(cons(sK55(X0),sK22)) ),
inference(resolution,[],[f1023,f544]) ).
fof(f1250,plain,
! [X0] :
( sK54(X0) = hd(cons(sK54(X0),sK22))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1095,f662]) ).
fof(f1095,plain,
! [X0] :
( sP16(X0)
| sK54(X0) = hd(cons(sK54(X0),sK22)) ),
inference(resolution,[],[f1023,f543]) ).
fof(f1094,plain,
! [X0] :
( sP14(X0)
| sK50(X0) = hd(cons(sK50(X0),sK22)) ),
inference(resolution,[],[f1023,f532]) ).
fof(f1093,plain,
! [X0] :
( sP14(X0)
| sK49(X0) = hd(cons(sK49(X0),sK22)) ),
inference(resolution,[],[f1023,f531]) ).
fof(f1092,plain,
! [X0] :
( sP12(X0)
| sK45(X0) = hd(cons(sK45(X0),sK22)) ),
inference(resolution,[],[f1023,f520]) ).
fof(f1091,plain,
! [X0] :
( sP12(X0)
| sK44(X0) = hd(cons(sK44(X0),sK22)) ),
inference(resolution,[],[f1023,f519]) ).
fof(f1090,plain,
! [X0] :
( sP10(X0)
| sK40(X0) = hd(cons(sK40(X0),sK22)) ),
inference(resolution,[],[f1023,f508]) ).
fof(f1089,plain,
! [X0] :
( sP10(X0)
| sK39(X0) = hd(cons(sK39(X0),sK22)) ),
inference(resolution,[],[f1023,f507]) ).
fof(f1088,plain,
! [X0] :
( sP8(X0)
| sK35(X0) = hd(cons(sK35(X0),sK22)) ),
inference(resolution,[],[f1023,f497]) ).
fof(f1249,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK68(X0,X1) = app(sK68(X0,X1),nil) ),
inference(resolution,[],[f591,f468]) ).
fof(f1248,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK68(X0,X1) = app(nil,sK68(X0,X1)) ),
inference(resolution,[],[f591,f469]) ).
fof(f1247,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK68(X0,X1)
| hd(sK68(X0,X1)) = sK27(sK68(X0,X1)) ),
inference(resolution,[],[f591,f477]) ).
fof(f1246,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK68(X0,X1)
| tl(sK68(X0,X1)) = sK28(sK68(X0,X1)) ),
inference(resolution,[],[f591,f479]) ).
fof(f1245,plain,
! [X2,X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sK68(X0,X1) = tl(cons(X2,sK68(X0,X1))) ),
inference(resolution,[],[f591,f571]) ).
fof(f1244,plain,
! [X2,X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| hd(cons(X2,sK68(X0,X1))) = X2 ),
inference(resolution,[],[f591,f572]) ).
fof(f591,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f374,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1))
& ssList(sK67(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f371,f373,f372]) ).
fof(f372,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f373,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f371,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f370]) ).
fof(f370,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f1087,plain,
! [X0] :
( sP8(X0)
| sK34(X0) = hd(cons(sK34(X0),sK22)) ),
inference(resolution,[],[f1023,f496]) ).
fof(f1086,plain,
! [X0] :
( sP6(X0)
| sK31(X0) = hd(cons(sK31(X0),sK22)) ),
inference(resolution,[],[f1023,f487]) ).
fof(f1085,plain,
! [X0] :
( sP6(X0)
| sK30(X0) = hd(cons(sK30(X0),sK22)) ),
inference(resolution,[],[f1023,f486]) ).
fof(f1243,plain,
! [X0] :
( sK60(X0) = hd(cons(sK60(X0),sK21))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1070,f664]) ).
fof(f1070,plain,
! [X0] :
( sP18(X0)
| sK60(X0) = hd(cons(sK60(X0),sK21)) ),
inference(resolution,[],[f1022,f555]) ).
fof(f1242,plain,
! [X0] :
( sK59(X0) = hd(cons(sK59(X0),sK21))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1069,f664]) ).
fof(f1069,plain,
! [X0] :
( sP18(X0)
| sK59(X0) = hd(cons(sK59(X0),sK21)) ),
inference(resolution,[],[f1022,f554]) ).
fof(f1241,plain,
! [X0] :
( sK55(X0) = hd(cons(sK55(X0),sK21))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1068,f662]) ).
fof(f1068,plain,
! [X0] :
( sP16(X0)
| sK55(X0) = hd(cons(sK55(X0),sK21)) ),
inference(resolution,[],[f1022,f544]) ).
fof(f1240,plain,
! [X0] :
( sK54(X0) = hd(cons(sK54(X0),sK21))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1067,f662]) ).
fof(f1067,plain,
! [X0] :
( sP16(X0)
| sK54(X0) = hd(cons(sK54(X0),sK21)) ),
inference(resolution,[],[f1022,f543]) ).
fof(f1066,plain,
! [X0] :
( sP14(X0)
| sK50(X0) = hd(cons(sK50(X0),sK21)) ),
inference(resolution,[],[f1022,f532]) ).
fof(f1065,plain,
! [X0] :
( sP14(X0)
| sK49(X0) = hd(cons(sK49(X0),sK21)) ),
inference(resolution,[],[f1022,f531]) ).
fof(f1064,plain,
! [X0] :
( sP12(X0)
| sK45(X0) = hd(cons(sK45(X0),sK21)) ),
inference(resolution,[],[f1022,f520]) ).
fof(f1063,plain,
! [X0] :
( sP12(X0)
| sK44(X0) = hd(cons(sK44(X0),sK21)) ),
inference(resolution,[],[f1022,f519]) ).
fof(f1239,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK67(X0,X1) = app(sK67(X0,X1),nil) ),
inference(resolution,[],[f590,f468]) ).
fof(f1238,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK67(X0,X1) = app(nil,sK67(X0,X1)) ),
inference(resolution,[],[f590,f469]) ).
fof(f1237,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK67(X0,X1)
| hd(sK67(X0,X1)) = sK27(sK67(X0,X1)) ),
inference(resolution,[],[f590,f477]) ).
fof(f1236,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK67(X0,X1)
| tl(sK67(X0,X1)) = sK28(sK67(X0,X1)) ),
inference(resolution,[],[f590,f479]) ).
fof(f1235,plain,
! [X2,X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sK67(X0,X1) = tl(cons(X2,sK67(X0,X1))) ),
inference(resolution,[],[f590,f571]) ).
fof(f1234,plain,
! [X2,X0,X1] :
( ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| hd(cons(X2,sK67(X0,X1))) = X2 ),
inference(resolution,[],[f590,f572]) ).
fof(f590,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f1062,plain,
! [X0] :
( sP10(X0)
| sK40(X0) = hd(cons(sK40(X0),sK21)) ),
inference(resolution,[],[f1022,f508]) ).
fof(f1061,plain,
! [X0] :
( sP10(X0)
| sK39(X0) = hd(cons(sK39(X0),sK21)) ),
inference(resolution,[],[f1022,f507]) ).
fof(f1060,plain,
! [X0] :
( sP8(X0)
| sK35(X0) = hd(cons(sK35(X0),sK21)) ),
inference(resolution,[],[f1022,f497]) ).
fof(f1059,plain,
! [X0] :
( sP8(X0)
| sK34(X0) = hd(cons(sK34(X0),sK21)) ),
inference(resolution,[],[f1022,f496]) ).
fof(f1058,plain,
! [X0] :
( sP6(X0)
| sK31(X0) = hd(cons(sK31(X0),sK21)) ),
inference(resolution,[],[f1022,f487]) ).
fof(f1057,plain,
! [X0] :
( sP6(X0)
| sK30(X0) = hd(cons(sK30(X0),sK21)) ),
inference(resolution,[],[f1022,f486]) ).
fof(f1233,plain,
! [X0] :
( sK22 = tl(cons(sK60(X0),sK22))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1014,f664]) ).
fof(f1014,plain,
! [X0] :
( sP18(X0)
| sK22 = tl(cons(sK60(X0),sK22)) ),
inference(resolution,[],[f944,f555]) ).
fof(f1232,plain,
! [X0] :
( sK22 = tl(cons(sK59(X0),sK22))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1013,f664]) ).
fof(f1013,plain,
! [X0] :
( sP18(X0)
| sK22 = tl(cons(sK59(X0),sK22)) ),
inference(resolution,[],[f944,f554]) ).
fof(f1231,plain,
! [X0] :
( sK22 = tl(cons(sK55(X0),sK22))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1012,f662]) ).
fof(f1012,plain,
! [X0] :
( sP16(X0)
| sK22 = tl(cons(sK55(X0),sK22)) ),
inference(resolution,[],[f944,f544]) ).
fof(f1230,plain,
! [X0] :
( sK22 = tl(cons(sK54(X0),sK22))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1011,f662]) ).
fof(f1011,plain,
! [X0] :
( sP16(X0)
| sK22 = tl(cons(sK54(X0),sK22)) ),
inference(resolution,[],[f944,f543]) ).
fof(f1010,plain,
! [X0] :
( sP14(X0)
| sK22 = tl(cons(sK50(X0),sK22)) ),
inference(resolution,[],[f944,f532]) ).
fof(f1229,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK66(X0,X1) = app(sK66(X0,X1),nil) ),
inference(resolution,[],[f587,f468]) ).
fof(f1228,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| sK66(X0,X1) = app(nil,sK66(X0,X1)) ),
inference(resolution,[],[f587,f469]) ).
fof(f1227,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK66(X0,X1)
| hd(sK66(X0,X1)) = sK27(sK66(X0,X1)) ),
inference(resolution,[],[f587,f477]) ).
fof(f1226,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = sK66(X0,X1)
| tl(sK66(X0,X1)) = sK28(sK66(X0,X1)) ),
inference(resolution,[],[f587,f479]) ).
fof(f1225,plain,
! [X2,X0,X1] :
( ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sK66(X0,X1) = tl(cons(X2,sK66(X0,X1))) ),
inference(resolution,[],[f587,f571]) ).
fof(f1224,plain,
! [X2,X0,X1] :
( ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| hd(cons(X2,sK66(X0,X1))) = X2 ),
inference(resolution,[],[f587,f572]) ).
fof(f587,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f367,f368]) ).
fof(f368,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f1009,plain,
! [X0] :
( sP14(X0)
| sK22 = tl(cons(sK49(X0),sK22)) ),
inference(resolution,[],[f944,f531]) ).
fof(f1008,plain,
! [X0] :
( sP12(X0)
| sK22 = tl(cons(sK45(X0),sK22)) ),
inference(resolution,[],[f944,f520]) ).
fof(f1007,plain,
! [X0] :
( sP12(X0)
| sK22 = tl(cons(sK44(X0),sK22)) ),
inference(resolution,[],[f944,f519]) ).
fof(f1006,plain,
! [X0] :
( sP10(X0)
| sK22 = tl(cons(sK40(X0),sK22)) ),
inference(resolution,[],[f944,f508]) ).
fof(f1005,plain,
! [X0] :
( sP10(X0)
| sK22 = tl(cons(sK39(X0),sK22)) ),
inference(resolution,[],[f944,f507]) ).
fof(f1004,plain,
! [X0] :
( sP8(X0)
| sK22 = tl(cons(sK35(X0),sK22)) ),
inference(resolution,[],[f944,f497]) ).
fof(f1003,plain,
! [X0] :
( sP8(X0)
| sK22 = tl(cons(sK34(X0),sK22)) ),
inference(resolution,[],[f944,f496]) ).
fof(f1002,plain,
! [X0] :
( sP6(X0)
| sK22 = tl(cons(sK31(X0),sK22)) ),
inference(resolution,[],[f944,f487]) ).
fof(f1001,plain,
! [X0] :
( sP6(X0)
| sK22 = tl(cons(sK30(X0),sK22)) ),
inference(resolution,[],[f944,f486]) ).
fof(f1223,plain,
! [X0] :
( sK21 = tl(cons(sK60(X0),sK21))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f990,f664]) ).
fof(f990,plain,
! [X0] :
( sP18(X0)
| sK21 = tl(cons(sK60(X0),sK21)) ),
inference(resolution,[],[f943,f555]) ).
fof(f1222,plain,
! [X0] :
( sK21 = tl(cons(sK59(X0),sK21))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f989,f664]) ).
fof(f989,plain,
! [X0] :
( sP18(X0)
| sK21 = tl(cons(sK59(X0),sK21)) ),
inference(resolution,[],[f943,f554]) ).
fof(f1221,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| sK65(X0,X1) = app(sK65(X0,X1),nil) ),
inference(resolution,[],[f575,f468]) ).
fof(f1220,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| sK65(X0,X1) = app(nil,sK65(X0,X1)) ),
inference(resolution,[],[f575,f469]) ).
fof(f1219,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| nil = sK65(X0,X1)
| hd(sK65(X0,X1)) = sK27(sK65(X0,X1)) ),
inference(resolution,[],[f575,f477]) ).
fof(f1218,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| nil = sK65(X0,X1)
| tl(sK65(X0,X1)) = sK28(sK65(X0,X1)) ),
inference(resolution,[],[f575,f479]) ).
fof(f1217,plain,
! [X2,X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sK65(X0,X1) = tl(cons(X2,sK65(X0,X1))) ),
inference(resolution,[],[f575,f571]) ).
fof(f1216,plain,
! [X2,X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| hd(cons(X2,sK65(X0,X1))) = X2 ),
inference(resolution,[],[f575,f572]) ).
fof(f575,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f364]) ).
fof(f364,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK64(X0,X1),cons(X1,sK65(X0,X1))) = X0
& ssList(sK65(X0,X1))
& ssList(sK64(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f361,f363,f362]) ).
fof(f362,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK64(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f363,plain,
! [X0,X1] :
( ? [X5] :
( app(sK64(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK64(X0,X1),cons(X1,sK65(X0,X1))) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f360]) ).
fof(f360,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f1215,plain,
! [X0] :
( sK21 = tl(cons(sK55(X0),sK21))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f988,f662]) ).
fof(f988,plain,
! [X0] :
( sP16(X0)
| sK21 = tl(cons(sK55(X0),sK21)) ),
inference(resolution,[],[f943,f544]) ).
fof(f1214,plain,
! [X0] :
( sK21 = tl(cons(sK54(X0),sK21))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f987,f662]) ).
fof(f987,plain,
! [X0] :
( sP16(X0)
| sK21 = tl(cons(sK54(X0),sK21)) ),
inference(resolution,[],[f943,f543]) ).
fof(f986,plain,
! [X0] :
( sP14(X0)
| sK21 = tl(cons(sK50(X0),sK21)) ),
inference(resolution,[],[f943,f532]) ).
fof(f1205,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| sK64(X0,X1) = app(sK64(X0,X1),nil) ),
inference(resolution,[],[f574,f468]) ).
fof(f1204,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| sK64(X0,X1) = app(nil,sK64(X0,X1)) ),
inference(resolution,[],[f574,f469]) ).
fof(f1203,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| nil = sK64(X0,X1)
| hd(sK64(X0,X1)) = sK27(sK64(X0,X1)) ),
inference(resolution,[],[f574,f477]) ).
fof(f1202,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| nil = sK64(X0,X1)
| tl(sK64(X0,X1)) = sK28(sK64(X0,X1)) ),
inference(resolution,[],[f574,f479]) ).
fof(f1201,plain,
! [X2,X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sK64(X0,X1) = tl(cons(X2,sK64(X0,X1))) ),
inference(resolution,[],[f574,f571]) ).
fof(f1200,plain,
! [X2,X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| hd(cons(X2,sK64(X0,X1))) = X2 ),
inference(resolution,[],[f574,f572]) ).
fof(f574,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f364]) ).
fof(f854,plain,
( nil = sK21
| hd(sK21) = sK27(sK21) ),
inference(resolution,[],[f477,f390]) ).
fof(f1153,plain,
( hd(sK21) = sK27(sK21)
| nil = sK21 ),
inference(forward_demodulation,[],[f882,f395]) ).
fof(f882,plain,
( nil = sK21
| hd(sK23) = sK27(sK23) ),
inference(forward_demodulation,[],[f856,f395]) ).
fof(f856,plain,
( nil = sK23
| hd(sK23) = sK27(sK23) ),
inference(resolution,[],[f477,f392]) ).
fof(f902,plain,
( nil = sK21
| tl(sK21) = sK28(sK21) ),
inference(resolution,[],[f479,f390]) ).
fof(f1152,plain,
( tl(sK21) = sK28(sK21)
| nil = sK21 ),
inference(forward_demodulation,[],[f931,f395]) ).
fof(f931,plain,
( nil = sK21
| tl(sK23) = sK28(sK23) ),
inference(forward_demodulation,[],[f904,f395]) ).
fof(f904,plain,
( nil = sK23
| tl(sK23) = sK28(sK23) ),
inference(resolution,[],[f479,f392]) ).
fof(f1115,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| cons(X0,nil) = cons(sK29(cons(X0,nil)),nil) ),
inference(duplicate_literal_removal,[],[f1113]) ).
fof(f1113,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| cons(X0,nil) = cons(sK29(cons(X0,nil)),nil)
| ~ ssList(cons(X0,nil)) ),
inference(resolution,[],[f624,f481]) ).
fof(f624,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f482]) ).
fof(f482,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f292,f293]) ).
fof(f293,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f291]) ).
fof(f291,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f985,plain,
! [X0] :
( sP14(X0)
| sK21 = tl(cons(sK49(X0),sK21)) ),
inference(resolution,[],[f943,f531]) ).
fof(f984,plain,
! [X0] :
( sP12(X0)
| sK21 = tl(cons(sK45(X0),sK21)) ),
inference(resolution,[],[f943,f520]) ).
fof(f983,plain,
! [X0] :
( sP12(X0)
| sK21 = tl(cons(sK44(X0),sK21)) ),
inference(resolution,[],[f943,f519]) ).
fof(f982,plain,
! [X0] :
( sP10(X0)
| sK21 = tl(cons(sK40(X0),sK21)) ),
inference(resolution,[],[f943,f508]) ).
fof(f981,plain,
! [X0] :
( sP10(X0)
| sK21 = tl(cons(sK39(X0),sK21)) ),
inference(resolution,[],[f943,f507]) ).
fof(f980,plain,
! [X0] :
( sP8(X0)
| sK21 = tl(cons(sK35(X0),sK21)) ),
inference(resolution,[],[f943,f497]) ).
fof(f979,plain,
! [X0] :
( sP8(X0)
| sK21 = tl(cons(sK34(X0),sK21)) ),
inference(resolution,[],[f943,f496]) ).
fof(f978,plain,
! [X0] :
( sP6(X0)
| sK21 = tl(cons(sK31(X0),sK21)) ),
inference(resolution,[],[f943,f487]) ).
fof(f977,plain,
! [X0] :
( sP6(X0)
| sK21 = tl(cons(sK30(X0),sK21)) ),
inference(resolution,[],[f943,f486]) ).
fof(f586,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f1105,plain,
! [X0] :
( leq(X0,sK71)
| nil = cons(sK71,sK22)
| ~ sP2(cons(sK71,sK22),X0) ),
inference(superposition,[],[f447,f1100]) ).
fof(f1104,plain,
! [X0] :
( lt(X0,sK71)
| nil = cons(sK71,sK22)
| ~ sP4(cons(sK71,sK22),X0) ),
inference(superposition,[],[f455,f1100]) ).
fof(f1100,plain,
sK71 = hd(cons(sK71,sK22)),
inference(resolution,[],[f1023,f613]) ).
fof(f1102,plain,
! [X0] :
( leq(X0,sK70)
| nil = cons(sK70,sK22)
| ~ sP2(cons(sK70,sK22),X0) ),
inference(superposition,[],[f447,f1099]) ).
fof(f1101,plain,
! [X0] :
( lt(X0,sK70)
| nil = cons(sK70,sK22)
| ~ sP4(cons(sK70,sK22),X0) ),
inference(superposition,[],[f455,f1099]) ).
fof(f1099,plain,
sK70 = hd(cons(sK70,sK22)),
inference(resolution,[],[f1023,f612]) ).
fof(f1084,plain,
! [X0] :
( sK29(X0) = hd(cons(sK29(X0),sK22))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1023,f480]) ).
fof(f1083,plain,
! [X0] :
( sK27(X0) = hd(cons(sK27(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1023,f476]) ).
fof(f1082,plain,
! [X0] :
( sK26(X0) = hd(cons(sK26(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1023,f471]) ).
fof(f1080,plain,
! [X0,X1] :
( sK20(X0,X1) = hd(cons(sK20(X0,X1),sK22))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f1023,f387]) ).
fof(f1079,plain,
! [X0] :
( hd(X0) = hd(cons(hd(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1023,f473]) ).
fof(f1023,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22)) = X0 ),
inference(resolution,[],[f572,f391]) ).
fof(f1077,plain,
! [X0] :
( leq(X0,sK71)
| nil = cons(sK71,sK21)
| ~ sP2(cons(sK71,sK21),X0) ),
inference(superposition,[],[f447,f1072]) ).
fof(f1076,plain,
! [X0] :
( lt(X0,sK71)
| nil = cons(sK71,sK21)
| ~ sP4(cons(sK71,sK21),X0) ),
inference(superposition,[],[f455,f1072]) ).
fof(f1072,plain,
sK71 = hd(cons(sK71,sK21)),
inference(resolution,[],[f1022,f613]) ).
fof(f1074,plain,
! [X0] :
( leq(X0,sK70)
| nil = cons(sK70,sK21)
| ~ sP2(cons(sK70,sK21),X0) ),
inference(superposition,[],[f447,f1071]) ).
fof(f1073,plain,
! [X0] :
( lt(X0,sK70)
| nil = cons(sK70,sK21)
| ~ sP4(cons(sK70,sK21),X0) ),
inference(superposition,[],[f455,f1071]) ).
fof(f1071,plain,
sK70 = hd(cons(sK70,sK21)),
inference(resolution,[],[f1022,f612]) ).
fof(f1056,plain,
! [X0] :
( sK29(X0) = hd(cons(sK29(X0),sK21))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f1022,f480]) ).
fof(f1055,plain,
! [X0] :
( sK27(X0) = hd(cons(sK27(X0),sK21))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1022,f476]) ).
fof(f1054,plain,
! [X0] :
( sK26(X0) = hd(cons(sK26(X0),sK21))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1022,f471]) ).
fof(f1052,plain,
! [X0,X1] :
( sK20(X0,X1) = hd(cons(sK20(X0,X1),sK21))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f1022,f387]) ).
fof(f1051,plain,
! [X0] :
( hd(X0) = hd(cons(hd(X0),sK21))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f1022,f473]) ).
fof(f1022,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 ),
inference(resolution,[],[f572,f390]) ).
fof(f1016,plain,
sK22 = tl(cons(sK71,sK22)),
inference(resolution,[],[f944,f613]) ).
fof(f1047,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK63(X1))) = X0
| sP18(X1) ),
inference(resolution,[],[f572,f558]) ).
fof(f1046,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK62(X1))) = X0
| sP18(X1) ),
inference(resolution,[],[f572,f557]) ).
fof(f1045,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK61(X1))) = X0
| sP18(X1) ),
inference(resolution,[],[f572,f556]) ).
fof(f1044,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK58(X1))) = X0
| sP16(X1) ),
inference(resolution,[],[f572,f547]) ).
fof(f1043,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK57(X1))) = X0
| sP16(X1) ),
inference(resolution,[],[f572,f546]) ).
fof(f1042,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK56(X1))) = X0
| sP16(X1) ),
inference(resolution,[],[f572,f545]) ).
fof(f1041,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK53(X1))) = X0
| sP14(X1) ),
inference(resolution,[],[f572,f535]) ).
fof(f1040,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK52(X1))) = X0
| sP14(X1) ),
inference(resolution,[],[f572,f534]) ).
fof(f1039,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK51(X1))) = X0
| sP14(X1) ),
inference(resolution,[],[f572,f533]) ).
fof(f1038,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK48(X1))) = X0
| sP12(X1) ),
inference(resolution,[],[f572,f523]) ).
fof(f1037,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK47(X1))) = X0
| sP12(X1) ),
inference(resolution,[],[f572,f522]) ).
fof(f1036,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK46(X1))) = X0
| sP12(X1) ),
inference(resolution,[],[f572,f521]) ).
fof(f1035,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK43(X1))) = X0
| sP10(X1) ),
inference(resolution,[],[f572,f511]) ).
fof(f1034,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK42(X1))) = X0
| sP10(X1) ),
inference(resolution,[],[f572,f510]) ).
fof(f1033,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK41(X1))) = X0
| sP10(X1) ),
inference(resolution,[],[f572,f509]) ).
fof(f1032,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK38(X1))) = X0
| sP8(X1) ),
inference(resolution,[],[f572,f500]) ).
fof(f1031,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK37(X1))) = X0
| sP8(X1) ),
inference(resolution,[],[f572,f499]) ).
fof(f1030,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK36(X1))) = X0
| sP8(X1) ),
inference(resolution,[],[f572,f498]) ).
fof(f1029,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK33(X1))) = X0
| sP6(X1) ),
inference(resolution,[],[f572,f489]) ).
fof(f1028,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK32(X1))) = X0
| sP6(X1) ),
inference(resolution,[],[f572,f488]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK28(X1))) = X0
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f572,f478]) ).
fof(f1026,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK25(X1))) = X0
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f572,f470]) ).
fof(f1049,plain,
! [X0] :
( hd(cons(X0,sK22)) = X0
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f1025,f394]) ).
fof(f1025,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK24)) = X0 ),
inference(resolution,[],[f572,f393]) ).
fof(f1048,plain,
! [X0] :
( hd(cons(X0,sK21)) = X0
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f1024,f395]) ).
fof(f1024,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK23)) = X0 ),
inference(resolution,[],[f572,f392]) ).
fof(f1021,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,tl(X1))) = X0
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f572,f474]) ).
fof(f1019,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,app(X1,X2))) = X0
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(resolution,[],[f572,f578]) ).
fof(f1018,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,cons(X1,X2))) = X0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(resolution,[],[f572,f568]) ).
fof(f1015,plain,
sK22 = tl(cons(sK70,sK22)),
inference(resolution,[],[f944,f612]) ).
fof(f1000,plain,
! [X0] :
( sK22 = tl(cons(sK29(X0),sK22))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f944,f480]) ).
fof(f999,plain,
! [X0] :
( sK22 = tl(cons(sK27(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f944,f476]) ).
fof(f998,plain,
! [X0] :
( sK22 = tl(cons(sK26(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f944,f471]) ).
fof(f996,plain,
! [X0,X1] :
( sK22 = tl(cons(sK20(X0,X1),sK22))
| ~ sP0(X0,X1) ),
inference(resolution,[],[f944,f387]) ).
fof(f995,plain,
! [X0] :
( sK22 = tl(cons(hd(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f944,f473]) ).
fof(f944,plain,
! [X0] :
( ~ ssItem(X0)
| sK22 = tl(cons(X0,sK22)) ),
inference(resolution,[],[f571,f391]) ).
fof(f992,plain,
sK21 = tl(cons(sK71,sK21)),
inference(resolution,[],[f943,f613]) ).
fof(f991,plain,
sK21 = tl(cons(sK70,sK21)),
inference(resolution,[],[f943,f612]) ).
fof(f976,plain,
! [X0] :
( sK21 = tl(cons(sK29(X0),sK21))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f943,f480]) ).
fof(f975,plain,
! [X0] :
( sK21 = tl(cons(sK27(X0),sK21))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f943,f476]) ).
fof(f974,plain,
! [X0] :
( sK21 = tl(cons(sK26(X0),sK21))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f943,f471]) ).
fof(f971,plain,
! [X0] :
( sK21 = tl(cons(hd(X0),sK21))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f943,f473]) ).
fof(f943,plain,
! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) ),
inference(resolution,[],[f571,f390]) ).
fof(f968,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK63(X1) = tl(cons(X0,sK63(X1)))
| sP18(X1) ),
inference(resolution,[],[f571,f558]) ).
fof(f967,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK62(X1) = tl(cons(X0,sK62(X1)))
| sP18(X1) ),
inference(resolution,[],[f571,f557]) ).
fof(f966,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK61(X1) = tl(cons(X0,sK61(X1)))
| sP18(X1) ),
inference(resolution,[],[f571,f556]) ).
fof(f965,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK58(X1) = tl(cons(X0,sK58(X1)))
| sP16(X1) ),
inference(resolution,[],[f571,f547]) ).
fof(f964,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK57(X1) = tl(cons(X0,sK57(X1)))
| sP16(X1) ),
inference(resolution,[],[f571,f546]) ).
fof(f963,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK56(X1) = tl(cons(X0,sK56(X1)))
| sP16(X1) ),
inference(resolution,[],[f571,f545]) ).
fof(f962,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK53(X1) = tl(cons(X0,sK53(X1)))
| sP14(X1) ),
inference(resolution,[],[f571,f535]) ).
fof(f961,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK52(X1) = tl(cons(X0,sK52(X1)))
| sP14(X1) ),
inference(resolution,[],[f571,f534]) ).
fof(f960,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK51(X1) = tl(cons(X0,sK51(X1)))
| sP14(X1) ),
inference(resolution,[],[f571,f533]) ).
fof(f959,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK48(X1) = tl(cons(X0,sK48(X1)))
| sP12(X1) ),
inference(resolution,[],[f571,f523]) ).
fof(f958,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK47(X1) = tl(cons(X0,sK47(X1)))
| sP12(X1) ),
inference(resolution,[],[f571,f522]) ).
fof(f957,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK46(X1) = tl(cons(X0,sK46(X1)))
| sP12(X1) ),
inference(resolution,[],[f571,f521]) ).
fof(f956,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK43(X1) = tl(cons(X0,sK43(X1)))
| sP10(X1) ),
inference(resolution,[],[f571,f511]) ).
fof(f955,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK42(X1) = tl(cons(X0,sK42(X1)))
| sP10(X1) ),
inference(resolution,[],[f571,f510]) ).
fof(f954,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK41(X1) = tl(cons(X0,sK41(X1)))
| sP10(X1) ),
inference(resolution,[],[f571,f509]) ).
fof(f953,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK38(X1) = tl(cons(X0,sK38(X1)))
| sP8(X1) ),
inference(resolution,[],[f571,f500]) ).
fof(f952,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK37(X1) = tl(cons(X0,sK37(X1)))
| sP8(X1) ),
inference(resolution,[],[f571,f499]) ).
fof(f951,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK36(X1) = tl(cons(X0,sK36(X1)))
| sP8(X1) ),
inference(resolution,[],[f571,f498]) ).
fof(f950,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK33(X1) = tl(cons(X0,sK33(X1)))
| sP6(X1) ),
inference(resolution,[],[f571,f489]) ).
fof(f949,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK32(X1) = tl(cons(X0,sK32(X1)))
| sP6(X1) ),
inference(resolution,[],[f571,f488]) ).
fof(f948,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK28(X1) = tl(cons(X0,sK28(X1)))
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f571,f478]) ).
fof(f947,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK25(X1) = tl(cons(X0,sK25(X1)))
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f571,f470]) ).
fof(f970,plain,
! [X0] :
( sK22 = tl(cons(X0,sK22))
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f946,f394]) ).
fof(f946,plain,
! [X0] :
( ~ ssItem(X0)
| sK24 = tl(cons(X0,sK24)) ),
inference(resolution,[],[f571,f393]) ).
fof(f969,plain,
! [X0] :
( sK21 = tl(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f945,f395]) ).
fof(f945,plain,
! [X0] :
( ~ ssItem(X0)
| sK23 = tl(cons(X0,sK23)) ),
inference(resolution,[],[f571,f392]) ).
fof(f942,plain,
! [X0,X1] :
( ~ ssItem(X0)
| tl(X1) = tl(cons(X0,tl(X1)))
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f571,f474]) ).
fof(f940,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| app(X1,X2) = tl(cons(X0,app(X1,X2)))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(resolution,[],[f571,f578]) ).
fof(f939,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| cons(X1,X2) = tl(cons(X0,cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(resolution,[],[f571,f568]) ).
fof(f571,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f481,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK29(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f930,plain,
( tl(sK22) = sK28(sK22)
| spl72_6 ),
inference(subsumption_resolution,[],[f903,f894]) ).
fof(f927,plain,
! [X0] :
( nil = sK63(X0)
| tl(sK63(X0)) = sK28(sK63(X0))
| sP18(X0) ),
inference(resolution,[],[f479,f558]) ).
fof(f926,plain,
! [X0] :
( nil = sK62(X0)
| tl(sK62(X0)) = sK28(sK62(X0))
| sP18(X0) ),
inference(resolution,[],[f479,f557]) ).
fof(f925,plain,
! [X0] :
( nil = sK61(X0)
| tl(sK61(X0)) = sK28(sK61(X0))
| sP18(X0) ),
inference(resolution,[],[f479,f556]) ).
fof(f924,plain,
! [X0] :
( nil = sK58(X0)
| tl(sK58(X0)) = sK28(sK58(X0))
| sP16(X0) ),
inference(resolution,[],[f479,f547]) ).
fof(f923,plain,
! [X0] :
( nil = sK57(X0)
| tl(sK57(X0)) = sK28(sK57(X0))
| sP16(X0) ),
inference(resolution,[],[f479,f546]) ).
fof(f922,plain,
! [X0] :
( nil = sK56(X0)
| tl(sK56(X0)) = sK28(sK56(X0))
| sP16(X0) ),
inference(resolution,[],[f479,f545]) ).
fof(f921,plain,
! [X0] :
( nil = sK53(X0)
| tl(sK53(X0)) = sK28(sK53(X0))
| sP14(X0) ),
inference(resolution,[],[f479,f535]) ).
fof(f920,plain,
! [X0] :
( nil = sK52(X0)
| tl(sK52(X0)) = sK28(sK52(X0))
| sP14(X0) ),
inference(resolution,[],[f479,f534]) ).
fof(f919,plain,
! [X0] :
( nil = sK51(X0)
| tl(sK51(X0)) = sK28(sK51(X0))
| sP14(X0) ),
inference(resolution,[],[f479,f533]) ).
fof(f918,plain,
! [X0] :
( nil = sK48(X0)
| tl(sK48(X0)) = sK28(sK48(X0))
| sP12(X0) ),
inference(resolution,[],[f479,f523]) ).
fof(f917,plain,
! [X0] :
( nil = sK47(X0)
| tl(sK47(X0)) = sK28(sK47(X0))
| sP12(X0) ),
inference(resolution,[],[f479,f522]) ).
fof(f916,plain,
! [X0] :
( nil = sK46(X0)
| tl(sK46(X0)) = sK28(sK46(X0))
| sP12(X0) ),
inference(resolution,[],[f479,f521]) ).
fof(f915,plain,
! [X0] :
( nil = sK43(X0)
| tl(sK43(X0)) = sK28(sK43(X0))
| sP10(X0) ),
inference(resolution,[],[f479,f511]) ).
fof(f914,plain,
! [X0] :
( nil = sK42(X0)
| tl(sK42(X0)) = sK28(sK42(X0))
| sP10(X0) ),
inference(resolution,[],[f479,f510]) ).
fof(f913,plain,
! [X0] :
( nil = sK41(X0)
| tl(sK41(X0)) = sK28(sK41(X0))
| sP10(X0) ),
inference(resolution,[],[f479,f509]) ).
fof(f912,plain,
! [X0] :
( nil = sK38(X0)
| tl(sK38(X0)) = sK28(sK38(X0))
| sP8(X0) ),
inference(resolution,[],[f479,f500]) ).
fof(f911,plain,
! [X0] :
( nil = sK37(X0)
| tl(sK37(X0)) = sK28(sK37(X0))
| sP8(X0) ),
inference(resolution,[],[f479,f499]) ).
fof(f910,plain,
! [X0] :
( nil = sK36(X0)
| tl(sK36(X0)) = sK28(sK36(X0))
| sP8(X0) ),
inference(resolution,[],[f479,f498]) ).
fof(f909,plain,
! [X0] :
( nil = sK33(X0)
| tl(sK33(X0)) = sK28(sK33(X0))
| sP6(X0) ),
inference(resolution,[],[f479,f489]) ).
fof(f908,plain,
! [X0] :
( nil = sK32(X0)
| tl(sK32(X0)) = sK28(sK32(X0))
| sP6(X0) ),
inference(resolution,[],[f479,f488]) ).
fof(f907,plain,
! [X0] :
( nil = sK28(X0)
| tl(sK28(X0)) = sK28(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f479,f478]) ).
fof(f906,plain,
! [X0] :
( nil = sK25(X0)
| tl(sK25(X0)) = sK28(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f479,f470]) ).
fof(f936,plain,
( tl(sK22) = sK28(sK22)
| spl72_6 ),
inference(forward_demodulation,[],[f935,f394]) ).
fof(f935,plain,
( tl(sK24) = sK28(sK24)
| spl72_6 ),
inference(subsumption_resolution,[],[f934,f894]) ).
fof(f901,plain,
! [X0] :
( nil = tl(X0)
| tl(tl(X0)) = sK28(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f479,f474]) ).
fof(f899,plain,
! [X0,X1] :
( nil = app(X0,X1)
| tl(app(X0,X1)) = sK28(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f479,f578]) ).
fof(f928,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = sK28(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f898,f569]) ).
fof(f898,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| tl(cons(X0,X1)) = sK28(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f479,f568]) ).
fof(f479,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK28(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ( tl(X0) = sK28(X0)
& ssList(sK28(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f160,f289]) ).
fof(f289,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK28(X0)
& ssList(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f855,plain,
( nil = sK22
| hd(sK22) = sK27(sK22) ),
inference(resolution,[],[f477,f391]) ).
fof(f879,plain,
! [X0] :
( nil = sK63(X0)
| hd(sK63(X0)) = sK27(sK63(X0))
| sP18(X0) ),
inference(resolution,[],[f477,f558]) ).
fof(f878,plain,
! [X0] :
( nil = sK62(X0)
| hd(sK62(X0)) = sK27(sK62(X0))
| sP18(X0) ),
inference(resolution,[],[f477,f557]) ).
fof(f877,plain,
! [X0] :
( nil = sK61(X0)
| hd(sK61(X0)) = sK27(sK61(X0))
| sP18(X0) ),
inference(resolution,[],[f477,f556]) ).
fof(f876,plain,
! [X0] :
( nil = sK58(X0)
| hd(sK58(X0)) = sK27(sK58(X0))
| sP16(X0) ),
inference(resolution,[],[f477,f547]) ).
fof(f875,plain,
! [X0] :
( nil = sK57(X0)
| hd(sK57(X0)) = sK27(sK57(X0))
| sP16(X0) ),
inference(resolution,[],[f477,f546]) ).
fof(f874,plain,
! [X0] :
( nil = sK56(X0)
| hd(sK56(X0)) = sK27(sK56(X0))
| sP16(X0) ),
inference(resolution,[],[f477,f545]) ).
fof(f873,plain,
! [X0] :
( nil = sK53(X0)
| hd(sK53(X0)) = sK27(sK53(X0))
| sP14(X0) ),
inference(resolution,[],[f477,f535]) ).
fof(f872,plain,
! [X0] :
( nil = sK52(X0)
| hd(sK52(X0)) = sK27(sK52(X0))
| sP14(X0) ),
inference(resolution,[],[f477,f534]) ).
fof(f871,plain,
! [X0] :
( nil = sK51(X0)
| hd(sK51(X0)) = sK27(sK51(X0))
| sP14(X0) ),
inference(resolution,[],[f477,f533]) ).
fof(f870,plain,
! [X0] :
( nil = sK48(X0)
| hd(sK48(X0)) = sK27(sK48(X0))
| sP12(X0) ),
inference(resolution,[],[f477,f523]) ).
fof(f869,plain,
! [X0] :
( nil = sK47(X0)
| hd(sK47(X0)) = sK27(sK47(X0))
| sP12(X0) ),
inference(resolution,[],[f477,f522]) ).
fof(f868,plain,
! [X0] :
( nil = sK46(X0)
| hd(sK46(X0)) = sK27(sK46(X0))
| sP12(X0) ),
inference(resolution,[],[f477,f521]) ).
fof(f867,plain,
! [X0] :
( nil = sK43(X0)
| hd(sK43(X0)) = sK27(sK43(X0))
| sP10(X0) ),
inference(resolution,[],[f477,f511]) ).
fof(f866,plain,
! [X0] :
( nil = sK42(X0)
| hd(sK42(X0)) = sK27(sK42(X0))
| sP10(X0) ),
inference(resolution,[],[f477,f510]) ).
fof(f865,plain,
! [X0] :
( nil = sK41(X0)
| hd(sK41(X0)) = sK27(sK41(X0))
| sP10(X0) ),
inference(resolution,[],[f477,f509]) ).
fof(f864,plain,
! [X0] :
( nil = sK38(X0)
| hd(sK38(X0)) = sK27(sK38(X0))
| sP8(X0) ),
inference(resolution,[],[f477,f500]) ).
fof(f863,plain,
! [X0] :
( nil = sK37(X0)
| hd(sK37(X0)) = sK27(sK37(X0))
| sP8(X0) ),
inference(resolution,[],[f477,f499]) ).
fof(f862,plain,
! [X0] :
( nil = sK36(X0)
| hd(sK36(X0)) = sK27(sK36(X0))
| sP8(X0) ),
inference(resolution,[],[f477,f498]) ).
fof(f861,plain,
! [X0] :
( nil = sK33(X0)
| hd(sK33(X0)) = sK27(sK33(X0))
| sP6(X0) ),
inference(resolution,[],[f477,f489]) ).
fof(f860,plain,
! [X0] :
( nil = sK32(X0)
| hd(sK32(X0)) = sK27(sK32(X0))
| sP6(X0) ),
inference(resolution,[],[f477,f488]) ).
fof(f859,plain,
! [X0] :
( nil = sK28(X0)
| hd(sK28(X0)) = sK27(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f477,f478]) ).
fof(f858,plain,
! [X0] :
( nil = sK25(X0)
| hd(sK25(X0)) = sK27(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f477,f470]) ).
fof(f886,plain,
( hd(sK22) = sK27(sK22)
| nil = sK22 ),
inference(forward_demodulation,[],[f885,f394]) ).
fof(f885,plain,
( nil = sK22
| hd(sK24) = sK27(sK24) ),
inference(forward_demodulation,[],[f857,f394]) ).
fof(f857,plain,
( nil = sK24
| hd(sK24) = sK27(sK24) ),
inference(resolution,[],[f477,f393]) ).
fof(f853,plain,
! [X0] :
( nil = tl(X0)
| hd(tl(X0)) = sK27(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f477,f474]) ).
fof(f851,plain,
! [X0,X1] :
( nil = app(X0,X1)
| hd(app(X0,X1)) = sK27(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f477,f578]) ).
fof(f880,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = sK27(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f850,f569]) ).
fof(f850,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| hd(cons(X0,X1)) = sK27(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f477,f568]) ).
fof(f477,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK27(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ( hd(X0) = sK27(X0)
& ssItem(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f158,f287]) ).
fof(f287,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK27(X0)
& ssItem(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f849,plain,
! [X0,X1] :
( nil = X0
| ~ sP4(X0,X1)
| ~ lt(hd(X0),X1)
| ~ ssItem(X1)
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f455,f420]) ).
fof(f848,plain,
! [X0,X1] :
( nil = X0
| ~ sP4(X0,X1)
| leq(X1,hd(X0))
| ~ ssItem(hd(X0))
| ~ ssItem(X1) ),
inference(resolution,[],[f455,f430]) ).
fof(f847,plain,
! [X0] :
( nil = X0
| ~ sP4(X0,hd(X0))
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f455,f408]) ).
fof(f455,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f281]) ).
fof(f452,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP4(X1,X0) )
| ~ sP5(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f451,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP4(X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
fof(f447,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f277]) ).
fof(f444,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f443,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f430,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f428,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( geq(X0,X1)
<=> leq(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( geq(X0,X1)
<=> leq(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
fof(f427,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f832,plain,
! [X0] :
( sK63(X0) = app(nil,sK63(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f734,f664]) ).
fof(f734,plain,
! [X0] :
( sP18(X0)
| sK63(X0) = app(nil,sK63(X0)) ),
inference(resolution,[],[f469,f558]) ).
fof(f831,plain,
! [X0] :
( sK62(X0) = app(nil,sK62(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f733,f664]) ).
fof(f733,plain,
! [X0] :
( sP18(X0)
| sK62(X0) = app(nil,sK62(X0)) ),
inference(resolution,[],[f469,f557]) ).
fof(f830,plain,
! [X0] :
( sK61(X0) = app(nil,sK61(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f732,f664]) ).
fof(f732,plain,
! [X0] :
( sP18(X0)
| sK61(X0) = app(nil,sK61(X0)) ),
inference(resolution,[],[f469,f556]) ).
fof(f829,plain,
! [X0] :
( sK58(X0) = app(nil,sK58(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f731,f662]) ).
fof(f731,plain,
! [X0] :
( sP16(X0)
| sK58(X0) = app(nil,sK58(X0)) ),
inference(resolution,[],[f469,f547]) ).
fof(f828,plain,
! [X0] :
( sK57(X0) = app(nil,sK57(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f730,f662]) ).
fof(f730,plain,
! [X0] :
( sP16(X0)
| sK57(X0) = app(nil,sK57(X0)) ),
inference(resolution,[],[f469,f546]) ).
fof(f827,plain,
! [X0] :
( sK56(X0) = app(nil,sK56(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f729,f662]) ).
fof(f729,plain,
! [X0] :
( sP16(X0)
| sK56(X0) = app(nil,sK56(X0)) ),
inference(resolution,[],[f469,f545]) ).
fof(f728,plain,
! [X0] :
( sP14(X0)
| sK53(X0) = app(nil,sK53(X0)) ),
inference(resolution,[],[f469,f535]) ).
fof(f426,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f727,plain,
! [X0] :
( sP14(X0)
| sK52(X0) = app(nil,sK52(X0)) ),
inference(resolution,[],[f469,f534]) ).
fof(f726,plain,
! [X0] :
( sP14(X0)
| sK51(X0) = app(nil,sK51(X0)) ),
inference(resolution,[],[f469,f533]) ).
fof(f725,plain,
! [X0] :
( sP12(X0)
| sK48(X0) = app(nil,sK48(X0)) ),
inference(resolution,[],[f469,f523]) ).
fof(f724,plain,
! [X0] :
( sP12(X0)
| sK47(X0) = app(nil,sK47(X0)) ),
inference(resolution,[],[f469,f522]) ).
fof(f723,plain,
! [X0] :
( sP12(X0)
| sK46(X0) = app(nil,sK46(X0)) ),
inference(resolution,[],[f469,f521]) ).
fof(f722,plain,
! [X0] :
( sP10(X0)
| sK43(X0) = app(nil,sK43(X0)) ),
inference(resolution,[],[f469,f511]) ).
fof(f721,plain,
! [X0] :
( sP10(X0)
| sK42(X0) = app(nil,sK42(X0)) ),
inference(resolution,[],[f469,f510]) ).
fof(f720,plain,
! [X0] :
( sP10(X0)
| sK41(X0) = app(nil,sK41(X0)) ),
inference(resolution,[],[f469,f509]) ).
fof(f719,plain,
! [X0] :
( sP8(X0)
| sK38(X0) = app(nil,sK38(X0)) ),
inference(resolution,[],[f469,f500]) ).
fof(f718,plain,
! [X0] :
( sP8(X0)
| sK37(X0) = app(nil,sK37(X0)) ),
inference(resolution,[],[f469,f499]) ).
fof(f717,plain,
! [X0] :
( sP8(X0)
| sK36(X0) = app(nil,sK36(X0)) ),
inference(resolution,[],[f469,f498]) ).
fof(f821,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X0,X1) ),
inference(duplicate_literal_removal,[],[f820]) ).
fof(f820,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[],[f424,f418]) ).
fof(f424,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
fof(f716,plain,
! [X0] :
( sP6(X0)
| sK33(X0) = app(nil,sK33(X0)) ),
inference(resolution,[],[f469,f489]) ).
fof(f715,plain,
! [X0] :
( sP6(X0)
| sK32(X0) = app(nil,sK32(X0)) ),
inference(resolution,[],[f469,f488]) ).
fof(f818,plain,
! [X0] :
( sK63(X0) = app(sK63(X0),nil)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f707,f664]) ).
fof(f707,plain,
! [X0] :
( sP18(X0)
| sK63(X0) = app(sK63(X0),nil) ),
inference(resolution,[],[f468,f558]) ).
fof(f817,plain,
! [X0] :
( sK62(X0) = app(sK62(X0),nil)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f706,f664]) ).
fof(f706,plain,
! [X0] :
( sP18(X0)
| sK62(X0) = app(sK62(X0),nil) ),
inference(resolution,[],[f468,f557]) ).
fof(f816,plain,
! [X0] :
( sK61(X0) = app(sK61(X0),nil)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f705,f664]) ).
fof(f705,plain,
! [X0] :
( sP18(X0)
| sK61(X0) = app(sK61(X0),nil) ),
inference(resolution,[],[f468,f556]) ).
fof(f815,plain,
! [X0] :
( sK58(X0) = app(sK58(X0),nil)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f704,f662]) ).
fof(f704,plain,
! [X0] :
( sP16(X0)
| sK58(X0) = app(sK58(X0),nil) ),
inference(resolution,[],[f468,f547]) ).
fof(f814,plain,
! [X0] :
( sK57(X0) = app(sK57(X0),nil)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f703,f662]) ).
fof(f703,plain,
! [X0] :
( sP16(X0)
| sK57(X0) = app(sK57(X0),nil) ),
inference(resolution,[],[f468,f546]) ).
fof(f813,plain,
! [X0] :
( sK56(X0) = app(sK56(X0),nil)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f702,f662]) ).
fof(f702,plain,
! [X0] :
( sP16(X0)
| sK56(X0) = app(sK56(X0),nil) ),
inference(resolution,[],[f468,f545]) ).
fof(f701,plain,
! [X0] :
( sP14(X0)
| sK53(X0) = app(sK53(X0),nil) ),
inference(resolution,[],[f468,f535]) ).
fof(f700,plain,
! [X0] :
( sP14(X0)
| sK52(X0) = app(sK52(X0),nil) ),
inference(resolution,[],[f468,f534]) ).
fof(f699,plain,
! [X0] :
( sP14(X0)
| sK51(X0) = app(sK51(X0),nil) ),
inference(resolution,[],[f468,f533]) ).
fof(f423,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f698,plain,
! [X0] :
( sP12(X0)
| sK48(X0) = app(sK48(X0),nil) ),
inference(resolution,[],[f468,f523]) ).
fof(f697,plain,
! [X0] :
( sP12(X0)
| sK47(X0) = app(sK47(X0),nil) ),
inference(resolution,[],[f468,f522]) ).
fof(f696,plain,
! [X0] :
( sP12(X0)
| sK46(X0) = app(sK46(X0),nil) ),
inference(resolution,[],[f468,f521]) ).
fof(f695,plain,
! [X0] :
( sP10(X0)
| sK43(X0) = app(sK43(X0),nil) ),
inference(resolution,[],[f468,f511]) ).
fof(f694,plain,
! [X0] :
( sP10(X0)
| sK42(X0) = app(sK42(X0),nil) ),
inference(resolution,[],[f468,f510]) ).
fof(f693,plain,
! [X0] :
( sP10(X0)
| sK41(X0) = app(sK41(X0),nil) ),
inference(resolution,[],[f468,f509]) ).
fof(f692,plain,
! [X0] :
( sP8(X0)
| sK38(X0) = app(sK38(X0),nil) ),
inference(resolution,[],[f468,f500]) ).
fof(f691,plain,
! [X0] :
( sP8(X0)
| sK37(X0) = app(sK37(X0),nil) ),
inference(resolution,[],[f468,f499]) ).
fof(f690,plain,
! [X0] :
( sP8(X0)
| sK36(X0) = app(sK36(X0),nil) ),
inference(resolution,[],[f468,f498]) ).
fof(f689,plain,
! [X0] :
( sP6(X0)
| sK33(X0) = app(sK33(X0),nil) ),
inference(resolution,[],[f468,f489]) ).
fof(f420,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
=> ~ lt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f418,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
=> ~ gt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax94) ).
fof(f688,plain,
! [X0] :
( sP6(X0)
| sK32(X0) = app(sK32(X0),nil) ),
inference(resolution,[],[f468,f488]) ).
fof(f647,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f618]) ).
fof(f618,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f438]) ).
fof(f438,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f569,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f769,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(app(X1,X0),nil) ),
inference(resolution,[],[f578,f468]) ).
fof(f768,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(nil,app(X1,X0)) ),
inference(resolution,[],[f578,f469]) ).
fof(f578,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f767,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,X1),nil) ),
inference(resolution,[],[f568,f468]) ).
fof(f766,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(nil,cons(X0,X1)) ),
inference(resolution,[],[f568,f469]) ).
fof(f568,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f566,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f564,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f562,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f750,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK28(X0) = app(sK28(X0),nil) ),
inference(resolution,[],[f478,f468]) ).
fof(f749,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK28(X0) = app(nil,sK28(X0)) ),
inference(resolution,[],[f478,f469]) ).
fof(f478,plain,
! [X0] :
( ssList(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f476,plain,
! [X0] :
( ssItem(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f748,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(tl(X0),nil) ),
inference(resolution,[],[f474,f468]) ).
fof(f747,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(nil,tl(X0)) ),
inference(resolution,[],[f474,f469]) ).
fof(f474,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f471,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f746,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK25(X0) = app(sK25(X0),nil) ),
inference(resolution,[],[f470,f468]) ).
fof(f745,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK25(X0) = app(nil,sK25(X0)) ),
inference(resolution,[],[f470,f469]) ).
fof(f470,plain,
! [X0] :
( ssList(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f454,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f446,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f742,plain,
! [X0] : ~ sP0(nil,X0),
inference(subsumption_resolution,[],[f741,f387]) ).
fof(f741,plain,
! [X0] :
( ~ sP0(nil,X0)
| ~ ssItem(sK20(nil,X0)) ),
inference(resolution,[],[f389,f407]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( ~ sP1(X0,X1,X2,X3)
| neq(X2,nil) ),
inference(cnf_transformation,[],[f255]) ).
fof(f560,plain,
! [X0] :
( ~ lt(sK59(X0),sK60(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ( sP18(X0)
| ( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0
& ssList(sK63(X0))
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssItem(sK60(X0))
& ssItem(sK59(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP18(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62,sK63])],[f350,f355,f354,f353,f352,f351]) ).
fof(f351,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),X2)
& app(app(X3,cons(sK59(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),X2)
& app(app(X3,cons(sK59(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(X3,cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(X3,cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0
& ssList(sK63(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0] :
( ( sP18(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP18(X0) ) ),
inference(rectify,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ( sP18(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP18(X0) ) ),
inference(nnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0] :
( sP18(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f549,plain,
! [X0] :
( ~ leq(sK54(X0),sK55(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( sP16(X0)
| ( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0))
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssItem(sK55(X0))
& ssItem(sK54(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56,sK57,sK58])],[f341,f346,f345,f344,f343,f342]) ).
fof(f342,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP16(X0) ) ),
inference(rectify,[],[f340]) ).
fof(f340,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP16(X0) ) ),
inference(nnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( sP16(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f538,plain,
! [X0] :
( leq(sK50(X0),sK49(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( sP14(X0)
| ( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0))
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssItem(sK50(X0))
& ssItem(sK49(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52,sK53])],[f332,f337,f336,f335,f334,f333]) ).
fof(f333,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK49(X0))
& leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK49(X0))
& leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f337,plain,
! [X0] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f332,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(rectify,[],[f331]) ).
fof(f331,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP14(X0) ) ),
inference(nnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( sP14(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f537,plain,
! [X0] :
( leq(sK49(X0),sK50(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f526,plain,
! [X0] :
( ~ lt(sK45(X0),sK44(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f329,plain,
! [X0] :
( ( sP12(X0)
| ( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0))
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssItem(sK45(X0))
& ssItem(sK44(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46,sK47,sK48])],[f323,f328,f327,f326,f325,f324]) ).
fof(f324,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK44(X0))
& ~ lt(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK44(X0))
& ~ lt(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f328,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f323,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(rectify,[],[f322]) ).
fof(f322,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP12(X0) ) ),
inference(nnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0] :
( sP12(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f525,plain,
! [X0] :
( ~ lt(sK44(X0),sK45(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f514,plain,
! [X0] :
( ~ leq(sK40(X0),sK39(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0] :
( ( sP10(X0)
| ( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0))
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssItem(sK40(X0))
& ssItem(sK39(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40,sK41,sK42,sK43])],[f314,f319,f318,f317,f316,f315]) ).
fof(f315,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK39(X0))
& ~ leq(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK39(X0))
& ~ leq(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f319,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f314,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(rectify,[],[f313]) ).
fof(f313,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP10(X0) ) ),
inference(nnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] :
( sP10(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f513,plain,
! [X0] :
( ~ leq(sK39(X0),sK40(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f502,plain,
! [X0] :
( sP8(X0)
| sK34(X0) = sK35(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ( sP8(X0)
| ( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0))
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssItem(sK35(X0))
& ssItem(sK34(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37,sK38])],[f305,f310,f309,f308,f307,f306]) ).
fof(f306,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = X2
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = X2
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f310,plain,
! [X0] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
=> ( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f305,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(rectify,[],[f304]) ).
fof(f304,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( sP8(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f491,plain,
! [X0] :
( sK30(X0) != sK31(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ( sP6(X0)
| ( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0
& ssList(sK33(X0))
& ssList(sK32(X0))
& ssItem(sK31(X0))
& ssItem(sK30(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33])],[f297,f301,f300,f299,f298]) ).
fof(f298,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != X2
& app(X3,cons(sK30(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != X2
& app(X3,cons(sK30(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(X3,cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f300,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(X3,cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f301,plain,
! [X0] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
=> ( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f297,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP6(X0) ) ),
inference(rectify,[],[f296]) ).
fof(f296,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0] :
( sP6(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f480,plain,
! [X0] :
( ssItem(sK29(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f712,plain,
sK22 = app(nil,sK22),
inference(resolution,[],[f469,f391]) ).
fof(f711,plain,
sK21 = app(nil,sK21),
inference(resolution,[],[f469,f390]) ).
fof(f736,plain,
sK22 = app(nil,sK22),
inference(forward_demodulation,[],[f714,f394]) ).
fof(f714,plain,
sK24 = app(nil,sK24),
inference(resolution,[],[f469,f393]) ).
fof(f735,plain,
sK21 = app(nil,sK21),
inference(forward_demodulation,[],[f713,f395]) ).
fof(f713,plain,
sK23 = app(nil,sK23),
inference(resolution,[],[f469,f392]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f685,plain,
sK22 = app(sK22,nil),
inference(resolution,[],[f468,f391]) ).
fof(f684,plain,
sK21 = app(sK21,nil),
inference(resolution,[],[f468,f390]) ).
fof(f709,plain,
sK22 = app(sK22,nil),
inference(forward_demodulation,[],[f687,f394]) ).
fof(f687,plain,
sK24 = app(sK24,nil),
inference(resolution,[],[f468,f393]) ).
fof(f708,plain,
sK21 = app(sK21,nil),
inference(forward_demodulation,[],[f686,f395]) ).
fof(f686,plain,
sK23 = app(sK23,nil),
inference(resolution,[],[f468,f392]) ).
fof(f468,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f458,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( sP5(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f139,f231,f230]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
fof(f450,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f228,f227]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
fof(f387,plain,
! [X0,X1] :
( ssItem(sK20(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f666,plain,
( sP1(sK21,sK22,sK22,sK21)
| neq(sK22,nil) ),
inference(forward_demodulation,[],[f665,f395]) ).
fof(f665,plain,
( sP1(sK23,sK22,sK22,sK21)
| neq(sK22,nil) ),
inference(forward_demodulation,[],[f396,f394]) ).
fof(f673,plain,
( sP1(sK21,sK22,sK22,sK21)
| ~ neq(sK22,nil) ),
inference(forward_demodulation,[],[f672,f395]) ).
fof(f672,plain,
( sP1(sK23,sK22,sK22,sK21)
| ~ neq(sK22,nil) ),
inference(forward_demodulation,[],[f671,f394]) ).
fof(f671,plain,
( ~ neq(sK22,nil)
| sP1(sK23,sK24,sK22,sK21) ),
inference(forward_demodulation,[],[f397,f394]) ).
fof(f664,plain,
! [X0] :
( ~ sP18(X0)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f552,f561]) ).
fof(f663,plain,
! [X0] :
( sP18(X0)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f551,f561]) ).
fof(f662,plain,
! [X0] :
( ~ sP16(X0)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f541,f550]) ).
fof(f661,plain,
! [X0] :
( sP16(X0)
| ~ totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f540,f550]) ).
fof(f660,plain,
! [X0] :
( sP14(X0)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f528,f539]) ).
fof(f659,plain,
! [X0] :
( sP12(X0)
| ~ strictorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f516,f527]) ).
fof(f658,plain,
! [X0] :
( sP10(X0)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f504,f515]) ).
fof(f657,plain,
! [X0] :
( sP8(X0)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f493,f503]) ).
fof(f656,plain,
! [X0] :
( sP6(X0)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f483,f492]) ).
fof(f552,plain,
! [X0] :
( ~ sP19(X0)
| ~ sP18(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP18(X0) )
& ( sP18(X0)
| ~ strictorderedP(X0) ) )
| ~ sP19(X0) ),
inference(nnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP18(X0) )
| ~ sP19(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f551,plain,
! [X0] :
( ~ sP19(X0)
| ~ strictorderedP(X0)
| sP18(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f541,plain,
! [X0] :
( ~ sP17(X0)
| ~ sP16(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f339,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ totalorderedP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP16(X0) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f540,plain,
! [X0] :
( ~ sP17(X0)
| ~ totalorderedP(X0)
| sP16(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f528,plain,
! [X0] :
( ~ sP15(X0)
| ~ cyclefreeP(X0)
| sP14(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f330,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP14(X0) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f516,plain,
! [X0] :
( ~ sP13(X0)
| ~ strictorderP(X0)
| sP12(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f321,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP12(X0) )
& ( sP12(X0)
| ~ strictorderP(X0) ) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP12(X0) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f504,plain,
! [X0] :
( ~ sP11(X0)
| ~ totalorderP(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f312,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP10(X0) )
& ( sP10(X0)
| ~ totalorderP(X0) ) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP10(X0) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f493,plain,
! [X0] :
( ~ sP9(X0)
| ~ duplicatefreeP(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP8(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f483,plain,
! [X0] :
( ~ sP7(X0)
| ~ equalelemsP(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ equalelemsP(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f417,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f416,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f415,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
fof(f414,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
fof(f413,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
fof(f412,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
fof(f411,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
fof(f653,plain,
nil = app(nil,nil),
inference(global_subsumption,[],[f386,f615,f384,f389,f388,f387,f397,f396,f395,f394,f393,f392,f391,f390,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f424,f423,f426,f649,f428,f427,f431,f430,f648,f432,f433,f434,f435,f436,f439,f647,f437,f646,f441,f440,f444,f443,f449,f620,f447,f446,f450,f452,f451,f457,f622,f455,f454,f458,f461,f460,f459,f462,f463,f464,f465,f466,f467,f468,f469,f472,f471,f470,f473,f474,f475,f477,f476,f479,f478,f624,f481,f480,f483,f491,f490,f489,f488,f487,f486,f625,f492,f493,f502,f501,f500,f499,f498,f497,f496,f645,f503,f504,f514,f513,f512,f511,f510,f509,f508,f507,f628,f515,f516,f526,f525,f524,f523,f522,f521,f520,f519,f629,f527,f528,f538,f537,f536,f535,f534,f533,f532,f531,f630,f539,f541,f540,f549,f548,f547,f546,f545,f544,f543,f631,f550,f552,f551,f560,f559,f558,f557,f556,f555,f554,f632,f561,f633,f650,f562,f634,f651,f564,f635,f652,f566,f568,f569,f570,f571,f572,f573,f636,f576,f575,f574,f578,f579,f580,f581,f582,f583,f584,f586,f644,f638,f588,f587,f639,f592,f591,f590,f640,f595,f594,f643]) ).
fof(f649,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f616,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f425]) ).
fof(f425,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f644,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f637]) ).
fof(f637,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f585]) ).
fof(f585,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f558,plain,
! [X0] :
( ssList(sK63(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f557,plain,
! [X0] :
( ssList(sK62(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f556,plain,
! [X0] :
( ssList(sK61(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f555,plain,
! [X0] :
( ssItem(sK60(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f554,plain,
! [X0] :
( ssItem(sK59(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f547,plain,
! [X0] :
( ssList(sK58(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f546,plain,
! [X0] :
( ssList(sK57(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f545,plain,
! [X0] :
( ssList(sK56(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f544,plain,
! [X0] :
( ssItem(sK55(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f543,plain,
! [X0] :
( ssItem(sK54(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f535,plain,
! [X0] :
( ssList(sK53(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f534,plain,
! [X0] :
( ssList(sK52(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f533,plain,
! [X0] :
( ssList(sK51(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f532,plain,
! [X0] :
( ssItem(sK50(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f531,plain,
! [X0] :
( ssItem(sK49(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f523,plain,
! [X0] :
( ssList(sK48(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f522,plain,
! [X0] :
( ssList(sK47(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f521,plain,
! [X0] :
( ssList(sK46(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f520,plain,
! [X0] :
( ssItem(sK45(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f519,plain,
! [X0] :
( ssItem(sK44(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f511,plain,
! [X0] :
( ssList(sK43(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f510,plain,
! [X0] :
( ssList(sK42(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f509,plain,
! [X0] :
( ssList(sK41(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f508,plain,
! [X0] :
( ssItem(sK40(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f507,plain,
! [X0] :
( ssItem(sK39(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f500,plain,
! [X0] :
( ssList(sK38(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f499,plain,
! [X0] :
( ssList(sK37(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f498,plain,
! [X0] :
( ssList(sK36(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f497,plain,
! [X0] :
( ssItem(sK35(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f496,plain,
! [X0] :
( ssItem(sK34(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f489,plain,
! [X0] :
( ssList(sK33(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f488,plain,
! [X0] :
( ssList(sK32(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f487,plain,
! [X0] :
( ssItem(sK31(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f486,plain,
! [X0] :
( ssItem(sK30(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f467,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f466,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f465,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f464,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f463,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f462,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f410,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
fof(f409,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax89) ).
fof(f408,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax90) ).
fof(f407,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f561,plain,
! [X0] :
( sP19(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f253]) ).
fof(f253,plain,
! [X0] :
( sP19(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f175,f252,f251]) ).
fof(f175,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
fof(f550,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f173,f249,f248]) ).
fof(f173,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
fof(f539,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f171,f246,f245]) ).
fof(f171,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f527,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f169,f243,f242]) ).
fof(f169,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( lt(X2,X1)
| lt(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
fof(f515,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f167,f240,f239]) ).
fof(f167,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( leq(X2,X1)
| leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
fof(f503,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f165,f237,f236]) ).
fof(f165,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
fof(f492,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f163,f234,f233]) ).
fof(f163,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ssList(X0)
=> ( equalelemsP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(X3,cons(X1,cons(X2,X4))) = X0
=> X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f652,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f386,f615,f384,f389,f388,f387,f397,f396,f395,f394,f393,f392,f391,f390,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f424,f423,f426,f649,f428,f427,f431,f430,f648,f432,f433,f434,f435,f436,f439,f647,f437,f646,f441,f440,f444,f443,f449,f620,f447,f446,f450,f452,f451,f457,f622,f455,f454,f458,f461,f460,f459,f462,f463,f464,f465,f466,f467,f468,f469,f472,f471,f470,f473,f474,f475,f477,f476,f479,f478,f624,f481,f480,f483,f491,f490,f489,f488,f487,f486,f625,f492,f493,f502,f501,f500,f499,f498,f497,f496,f645,f503,f504,f514,f513,f512,f511,f510,f509,f508,f507,f628,f515,f516,f526,f525,f524,f523,f522,f521,f520,f519,f629,f527,f528,f538,f537,f536,f535,f534,f533,f532,f531,f630,f539,f541,f540,f549,f548,f547,f546,f545,f544,f543,f631,f550,f552,f551,f560,f559,f558,f557,f556,f555,f554,f632,f561,f633,f650,f562,f634,f651,f564,f635]) ).
fof(f651,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f386,f615,f384,f389,f388,f387,f397,f396,f395,f394,f393,f392,f391,f390,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f424,f423,f426,f649,f428,f427,f431,f430,f648,f432,f433,f434,f435,f436,f439,f647,f437,f646,f441,f440,f444,f443,f449,f620,f447,f446,f450,f452,f451,f457,f622,f455,f454,f458,f461,f460,f459,f462,f463,f464,f465,f466,f467,f468,f469,f472,f471,f470,f473,f474,f475,f477,f476,f479,f478,f624,f481,f480,f483,f491,f490,f489,f488,f487,f486,f625,f492,f493,f502,f501,f500,f499,f498,f497,f496,f645,f503,f504,f514,f513,f512,f511,f510,f509,f508,f507,f628,f515,f516,f526,f525,f524,f523,f522,f521,f520,f519,f629,f527,f528,f538,f537,f536,f535,f534,f533,f532,f531,f630,f539,f541,f540,f549,f548,f547,f546,f545,f544,f543,f631,f550,f552,f551,f560,f559,f558,f557,f556,f555,f554,f632,f561,f633,f650,f562,f634]) ).
fof(f650,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f386,f615,f384,f389,f388,f387,f397,f396,f395,f394,f393,f392,f391,f390,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f424,f423,f426,f649,f428,f427,f431,f430,f648,f432,f433,f434,f435,f436,f439,f647,f437,f646,f441,f440,f444,f443,f449,f620,f447,f446,f450,f452,f451,f457,f622,f455,f454,f458,f461,f460,f459,f462,f463,f464,f465,f466,f467,f468,f469,f472,f471,f470,f473,f474,f475,f477,f476,f479,f478,f624,f481,f480,f483,f491,f490,f489,f488,f487,f486,f625,f492,f493,f502,f501,f500,f499,f498,f497,f496,f645,f503,f504,f514,f513,f512,f511,f510,f509,f508,f507,f628,f515,f516,f526,f525,f524,f523,f522,f521,f520,f519,f629,f527,f528,f538,f537,f536,f535,f534,f533,f532,f531,f630,f539,f541,f540,f549,f548,f547,f546,f545,f544,f543,f631,f550,f552,f551,f560,f559,f558,f557,f556,f555,f554,f632,f561,f633]) ).
fof(f622,plain,
! [X1] : sP4(nil,X1),
inference(equality_resolution,[],[f456]) ).
fof(f456,plain,
! [X0,X1] :
( sP4(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f281]) ).
fof(f620,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f448]) ).
fof(f448,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f277]) ).
fof(f614,plain,
sK70 != sK71,
inference(cnf_transformation,[],[f383]) ).
fof(f383,plain,
( sK70 != sK71
& ssItem(sK71)
& ssItem(sK70) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f2,f382,f381]) ).
fof(f381,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK70 != X1
& ssItem(X1) )
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f382,plain,
( ? [X1] :
( sK70 != X1
& ssItem(X1) )
=> ( sK70 != sK71
& ssItem(sK71) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f395,plain,
sK21 = sK23,
inference(cnf_transformation,[],[f264]) ).
fof(f394,plain,
sK22 = sK24,
inference(cnf_transformation,[],[f264]) ).
fof(f613,plain,
ssItem(sK71),
inference(cnf_transformation,[],[f383]) ).
fof(f612,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f383]) ).
fof(f405,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f404,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
fof(f403,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
fof(f402,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
fof(f401,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
fof(f400,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
fof(f399,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
fof(f398,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f393,plain,
ssList(sK24),
inference(cnf_transformation,[],[f264]) ).
fof(f392,plain,
ssList(sK23),
inference(cnf_transformation,[],[f264]) ).
fof(f390,plain,
ssList(sK21),
inference(cnf_transformation,[],[f264]) ).
fof(f611,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f610,plain,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f609,plain,
! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
fof(f608,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f607,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax80) ).
fof(f606,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax79) ).
fof(f605,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f604,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
fof(f603,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f601,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X0 = X1
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
fof(f602,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f600,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f597,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f379]) ).
fof(f379,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f598,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f643,plain,
( nil = app(nil,nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f642]) ).
fof(f642,plain,
( nil = app(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f641]) ).
fof(f641,plain,
! [X1] :
( nil = app(nil,X1)
| nil != X1
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f599]) ).
fof(f599,plain,
! [X0,X1] :
( nil = app(X0,X1)
| nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f595,plain,
! [X0,X1] :
( app(X1,sK69(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f640,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f596]) ).
fof(f596,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f592,plain,
! [X0,X1] :
( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f639,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f593]) ).
fof(f593,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f374]) ).
fof(f588,plain,
! [X0,X1] :
( app(sK66(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f638,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f589]) ).
fof(f589,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f584,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f583,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
fof(f582,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f581,plain,
! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( tl(X0) = tl(X1)
& hd(X0) = hd(X1)
& nil != X0
& nil != X1 )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax77) ).
fof(f580,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
fof(f579,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax85) ).
fof(f576,plain,
! [X0,X1] :
( app(sK64(X0,X1),cons(X1,sK65(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f364]) ).
fof(f636,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f577]) ).
fof(f577,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f364]) ).
fof(f573,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f635,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f567]) ).
fof(f567,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f634,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f565]) ).
fof(f565,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f633,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f563]) ).
fof(f563,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f632,plain,
! [X10,X8,X6,X9,X7] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP18(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f553]) ).
fof(f553,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f559,plain,
! [X0] :
( sP18(X0)
| app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0 ),
inference(cnf_transformation,[],[f356]) ).
fof(f631,plain,
! [X10,X8,X6,X9,X7] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f542]) ).
fof(f542,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f548,plain,
! [X0] :
( sP16(X0)
| app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0 ),
inference(cnf_transformation,[],[f347]) ).
fof(f630,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f530]) ).
fof(f530,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f536,plain,
! [X0] :
( sP14(X0)
| app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0 ),
inference(cnf_transformation,[],[f338]) ).
fof(f629,plain,
! [X10,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f518]) ).
fof(f518,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f524,plain,
! [X0] :
( sP12(X0)
| app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0 ),
inference(cnf_transformation,[],[f329]) ).
fof(f628,plain,
! [X10,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f506]) ).
fof(f506,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f512,plain,
! [X0] :
( sP10(X0)
| app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0 ),
inference(cnf_transformation,[],[f320]) ).
fof(f645,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP8(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f627]) ).
fof(f627,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP8(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f626]) ).
fof(f626,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP8(X0) ),
inference(equality_resolution,[],[f495]) ).
fof(f495,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f501,plain,
! [X0] :
( sP8(X0)
| app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0 ),
inference(cnf_transformation,[],[f311]) ).
fof(f625,plain,
! [X8,X6,X7,X5] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP6(app(X7,cons(X5,cons(X6,X8)))) ),
inference(equality_resolution,[],[f485]) ).
fof(f485,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f490,plain,
! [X0] :
( sP6(X0)
| app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0 ),
inference(cnf_transformation,[],[f302]) ).
fof(f459,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f282]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f460,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f461,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f440,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f441,plain,
! [X2,X3,X0,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f646,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f619]) ).
fof(f619,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f437,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f439,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f436,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& lt(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
fof(f435,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
fof(f434,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
fof(f433,plain,
! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X0,X1) )
=> geq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
fof(f432,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax95) ).
fof(f648,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f617]) ).
fof(f617,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f429]) ).
fof(f429,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f431,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f422,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f421,plain,
! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( geq(X1,X0)
& geq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
fof(f419,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( leq(X0,X1)
=> ( lt(X0,X1)
| X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax92) ).
fof(f396,plain,
( neq(sK22,nil)
| sP1(sK23,sK24,sK22,sK21) ),
inference(cnf_transformation,[],[f264]) ).
fof(f397,plain,
( ~ neq(sK24,nil)
| sP1(sK23,sK24,sK22,sK21) ),
inference(cnf_transformation,[],[f264]) ).
fof(f570,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f1655,plain,
( spl72_6
| spl72_13 ),
inference(avatar_contradiction_clause,[],[f1654]) ).
fof(f1654,plain,
( $false
| spl72_6
| spl72_13 ),
inference(subsumption_resolution,[],[f1653,f391]) ).
fof(f1653,plain,
( ~ ssList(sK22)
| spl72_6
| spl72_13 ),
inference(subsumption_resolution,[],[f1652,f894]) ).
fof(f1652,plain,
( nil = sK22
| ~ ssList(sK22)
| spl72_13 ),
inference(resolution,[],[f1646,f470]) ).
fof(f1646,plain,
( ~ ssList(sK25(sK22))
| spl72_13 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f1644,plain,
( spl72_13
<=> ssList(sK25(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_13])]) ).
fof(f1651,plain,
( ~ spl72_13
| spl72_14
| spl72_6
| ~ spl72_11 ),
inference(avatar_split_clause,[],[f1632,f1517,f893,f1648,f1644]) ).
fof(f1648,plain,
( spl72_14
<=> memberP(sK22,sK26(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_14])]) ).
fof(f1517,plain,
( spl72_11
<=> ssItem(sK26(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_11])]) ).
fof(f1632,plain,
( memberP(sK22,sK26(sK22))
| ~ ssList(sK25(sK22))
| spl72_6
| ~ spl72_11 ),
inference(subsumption_resolution,[],[f1631,f1518]) ).
fof(f1518,plain,
( ssItem(sK26(sK22))
| ~ spl72_11 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f1631,plain,
( memberP(sK22,sK26(sK22))
| ~ ssList(sK25(sK22))
| ~ ssItem(sK26(sK22))
| spl72_6 ),
inference(superposition,[],[f647,f1568]) ).
fof(f1562,plain,
( ~ spl72_2
| ~ spl72_6 ),
inference(avatar_contradiction_clause,[],[f1561]) ).
fof(f1561,plain,
( $false
| ~ spl72_2
| ~ spl72_6 ),
inference(subsumption_resolution,[],[f1541,f742]) ).
fof(f1541,plain,
( sP0(nil,sK21)
| ~ spl72_2
| ~ spl72_6 ),
inference(superposition,[],[f740,f895]) ).
fof(f895,plain,
( nil = sK22
| ~ spl72_6 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f1528,plain,
( spl72_6
| spl72_11 ),
inference(avatar_contradiction_clause,[],[f1527]) ).
fof(f1527,plain,
( $false
| spl72_6
| spl72_11 ),
inference(subsumption_resolution,[],[f1526,f391]) ).
fof(f1526,plain,
( ~ ssList(sK22)
| spl72_6
| spl72_11 ),
inference(subsumption_resolution,[],[f1525,f894]) ).
fof(f1525,plain,
( nil = sK22
| ~ ssList(sK22)
| spl72_11 ),
inference(resolution,[],[f1519,f471]) ).
fof(f1519,plain,
( ~ ssItem(sK26(sK22))
| spl72_11 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f1524,plain,
( ~ spl72_11
| ~ spl72_12
| spl72_6 ),
inference(avatar_split_clause,[],[f1496,f893,f1521,f1517]) ).
fof(f1521,plain,
( spl72_12
<=> sK22 = sK25(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_12])]) ).
fof(f1509,plain,
( ~ spl72_2
| ~ spl72_3
| spl72_9 ),
inference(avatar_contradiction_clause,[],[f1508]) ).
fof(f1508,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| spl72_9 ),
inference(subsumption_resolution,[],[f1507,f390]) ).
fof(f1507,plain,
( ~ ssList(sK21)
| ~ spl72_2
| ~ spl72_3
| spl72_9 ),
inference(subsumption_resolution,[],[f1506,f811]) ).
fof(f811,plain,
( nil != sK21
| ~ spl72_2
| ~ spl72_3 ),
inference(global_subsumption,[],[f615,f397,f396,f419,f420,f421,f422,f424,f423,f426,f428,f427,f431,f430,f648,f432,f433,f434,f435,f436,f439,f437,f646,f441,f440,f444,f443,f449,f447,f452,f451,f457,f455,f461,f460,f459,f472,f475,f477,f479,f624,f481,f490,f625,f501,f645,f512,f628,f524,f629,f536,f630,f548,f631,f559,f632,f633,f634,f635,f571,f572,f573,f636,f576,f575,f574,f579,f580,f581,f582,f583,f584,f586,f638,f588,f587,f639,f592,f591,f590,f640,f595,f594,f643,f598,f597,f600,f602,f601,f603,f604,f605,f606,f607,f608,f609,f610,f611,f390,f391,f392,f393,f398,f399,f400,f401,f402,f403,f404,f405,f406,f612,f613,f394,f395,f614,f620,f622,f650,f651,f652,f492,f503,f515,f527,f539,f550,f561,f407,f408,f409,f410,f462,f463,f464,f465,f466,f467,f486,f487,f488,f489,f496,f497,f498,f499,f500,f507,f508,f509,f510,f511,f519,f520,f521,f522,f523,f531,f532,f533,f534,f535,f543,f544,f545,f546,f547,f554,f555,f556,f557,f558,f644,f649,f653,f411,f412,f413,f414,f415,f416,f417,f483,f493,f504,f516,f528,f540,f541,f551,f552,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f681,f387,f450,f458,f468,f708,f709,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f699,f700,f701,f702,f703,f704,f705,f706,f707,f684,f685,f469,f735,f736,f715,f716,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f728,f729,f730,f731,f732,f733,f734,f711,f712,f480,f491,f502,f513,f514,f525,f526,f537,f538,f549,f560,f384,f737,f386,f740,f389,f742,f446,f454,f470,f745,f746,f471,f473,f474,f747,f748,f476,f478,f749,f750,f562,f564,f566,f568,f766,f767,f578,f768,f769,f569,f570,f647,f688,f388,f776,f778,f779,f780,f781,f782,f783,f788,f789,f791,f792,f777,f795,f805,f806,f418,f807,f808,f809,f810,f790]) ).
fof(f790,plain,
( nil != sK21
| ~ ssItem(sK20(sK22,nil))
| ~ spl72_2 ),
inference(inner_rewriting,[],[f789]) ).
fof(f810,plain,
( totalorderedP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f783,f795]) ).
fof(f809,plain,
( strictorderedP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f782,f795]) ).
fof(f808,plain,
( strictorderP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f781,f795]) ).
fof(f807,plain,
( totalorderP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f780,f795]) ).
fof(f806,plain,
( cyclefreeP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f779,f795]) ).
fof(f805,plain,
( duplicatefreeP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f778,f795]) ).
fof(f777,plain,
( equalelemsP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f411,f776]) ).
fof(f792,plain,
( nil != sK21
| ~ ssItem(sK20(sK22,nil))
| ~ spl72_2 ),
inference(inner_rewriting,[],[f791]) ).
fof(f791,plain,
( nil != sK21
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f786,f406]) ).
fof(f786,plain,
( nil != sK21
| ~ ssItem(sK20(sK22,sK21))
| ~ ssList(nil)
| ~ spl72_2 ),
inference(superposition,[],[f569,f776]) ).
fof(f789,plain,
( nil != sK21
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f785,f406]) ).
fof(f785,plain,
( nil != sK21
| ~ ssItem(sK20(sK22,sK21))
| ~ ssList(nil)
| ~ spl72_2 ),
inference(superposition,[],[f570,f776]) ).
fof(f788,plain,
( memberP(sK21,sK20(sK22,sK21))
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f784,f406]) ).
fof(f784,plain,
( memberP(sK21,sK20(sK22,sK21))
| ~ ssList(nil)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f647,f776]) ).
fof(f783,plain,
( totalorderedP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f417,f776]) ).
fof(f782,plain,
( strictorderedP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f416,f776]) ).
fof(f781,plain,
( strictorderP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f415,f776]) ).
fof(f780,plain,
( totalorderP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f414,f776]) ).
fof(f779,plain,
( cyclefreeP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f413,f776]) ).
fof(f778,plain,
( duplicatefreeP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ spl72_2 ),
inference(superposition,[],[f412,f776]) ).
fof(f776,plain,
( sK21 = cons(sK20(sK22,sK21),nil)
| ~ spl72_2 ),
inference(resolution,[],[f388,f740]) ).
fof(f737,plain,
( neq(sK22,nil)
| ~ spl72_2 ),
inference(resolution,[],[f384,f681]) ).
fof(f1506,plain,
( nil = sK21
| ~ ssList(sK21)
| spl72_9 ),
inference(resolution,[],[f1500,f471]) ).
fof(f1500,plain,
( ~ ssItem(sK26(sK21))
| spl72_9 ),
inference(avatar_component_clause,[],[f1498]) ).
fof(f1498,plain,
( spl72_9
<=> ssItem(sK26(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_9])]) ).
fof(f1505,plain,
( ~ spl72_9
| ~ spl72_10
| ~ spl72_2
| ~ spl72_3 ),
inference(avatar_split_clause,[],[f1486,f794,f679,f1502,f1498]) ).
fof(f1502,plain,
( spl72_10
<=> sK21 = sK25(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_10])]) ).
fof(f1486,plain,
( sK21 != sK25(sK21)
| ~ ssItem(sK26(sK21))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1485,f390]) ).
fof(f1485,plain,
( sK21 != sK25(sK21)
| ~ ssItem(sK26(sK21))
| ~ ssList(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(inner_rewriting,[],[f1481]) ).
fof(f1481,plain,
( sK21 != sK25(sK21)
| ~ ssItem(sK26(sK21))
| ~ ssList(sK25(sK21))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f570,f1467]) ).
fof(f1467,plain,
( sK21 = cons(sK26(sK21),sK25(sK21))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1434,f811]) ).
fof(f1434,plain,
( nil = sK21
| sK21 = cons(sK26(sK21),sK25(sK21)) ),
inference(resolution,[],[f472,f390]) ).
fof(f1156,plain,
spl72_2,
inference(avatar_contradiction_clause,[],[f1155]) ).
fof(f1155,plain,
( $false
| spl72_2 ),
inference(global_subsumption,[],[f615,f397,f396,f419,f421,f422,f431,f648,f432,f433,f434,f435,f436,f439,f437,f646,f441,f440,f449,f457,f461,f460,f459,f472,f475,f490,f625,f501,f645,f512,f628,f524,f629,f536,f630,f548,f631,f559,f632,f633,f634,f635,f573,f636,f576,f575,f574,f579,f580,f581,f582,f583,f584,f638,f588,f587,f639,f592,f591,f590,f640,f595,f594,f643,f598,f597,f600,f602,f601,f603,f604,f605,f606,f607,f608,f609,f610,f611,f390,f391,f392,f393,f398,f399,f400,f401,f402,f403,f404,f405,f406,f612,f613,f394,f395,f614,f620,f622,f650,f651,f652,f492,f503,f515,f527,f539,f550,f561,f407,f408,f409,f410,f462,f463,f464,f465,f466,f467,f486,f487,f488,f489,f496,f497,f498,f499,f500,f507,f508,f509,f510,f511,f519,f520,f521,f522,f523,f531,f532,f533,f534,f535,f543,f544,f545,f546,f547,f554,f555,f556,f557,f558,f644,f649,f653,f411,f412,f413,f414,f415,f416,f417,f483,f493,f504,f516,f528,f540,f541,f551,f552,f656,f657,f658,f659,f660,f661,f662,f663,f664,f673,f666,f387,f450,f458,f468,f708,f709,f684,f685,f469,f735,f736,f711,f712,f480,f491,f502,f513,f514,f525,f526,f537,f538,f549,f560,f384,f386,f389,f742,f446,f454,f470,f745,f746,f471,f473,f474,f747,f748,f476,f478,f749,f750,f562,f564,f566,f568,f766,f767,f578,f768,f769,f569,f570,f647,f688,f388,f418,f420,f689,f690,f691,f692,f693,f694,f695,f696,f697,f698,f423,f699,f700,f701,f702,f813,f703,f814,f704,f815,f705,f816,f706,f817,f707,f818,f715,f716,f424,f821,f717,f718,f719,f720,f721,f722,f723,f724,f725,f726,f727,f426,f728,f729,f827,f730,f828,f731,f829,f732,f830,f733,f831,f734,f832,f427,f428,f430,f443,f444,f447,f451,f452,f455,f847,f848,f849,f477,f880,f851,f853,f886,f858,f859,f860,f861,f862,f863,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f855,f479,f928,f899,f901,f906,f907,f908,f909,f910,f911,f912,f913,f914,f915,f916,f917,f918,f919,f920,f921,f922,f923,f924,f925,f926,f927,f481,f571,f939,f940,f941,f942,f969,f970,f947,f948,f949,f950,f951,f952,f953,f954,f955,f956,f957,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f943,f971,f972,f974,f975,f976,f986,f987,f988,f989,f990,f991,f992,f944,f995,f996,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f1012,f1013,f1014,f1015,f572,f1018,f1019,f1020,f1021,f1048,f1049,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f1034,f1035,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1016,f1022,f1051,f1052,f1054,f1055,f1056,f1057,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1073,f1074,f1072,f1076,f1077,f1023,f1079,f1080,f1082,f1083,f1084,f1085,f1086,f1087,f1088,f1089,f1090,f1091,f1092,f1093,f1094,f1095,f1096,f1097,f1098,f1099,f1101,f1102,f1100,f1104,f1105,f586,f977,f978,f979,f980,f981,f982,f983,f984,f985,f624,f1115,f1152,f902,f1153,f854,f680]) ).
fof(f680,plain,
( ~ sP1(sK21,sK22,sK22,sK21)
| spl72_2 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f1150,plain,
( ~ spl72_2
| ~ spl72_3
| spl72_7 ),
inference(avatar_contradiction_clause,[],[f1149]) ).
fof(f1149,plain,
( $false
| ~ spl72_2
| ~ spl72_3
| spl72_7 ),
inference(subsumption_resolution,[],[f1148,f390]) ).
fof(f1148,plain,
( ~ ssList(sK21)
| ~ spl72_2
| ~ spl72_3
| spl72_7 ),
inference(subsumption_resolution,[],[f1147,f1118]) ).
fof(f1118,plain,
( singletonP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1117,f390]) ).
fof(f1117,plain,
( ~ ssList(sK21)
| singletonP(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(forward_demodulation,[],[f1116,f776]) ).
fof(f1116,plain,
( singletonP(sK21)
| ~ ssList(cons(sK20(sK22,sK21),nil))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1114,f795]) ).
fof(f1114,plain,
( singletonP(sK21)
| ~ ssItem(sK20(sK22,sK21))
| ~ ssList(cons(sK20(sK22,sK21),nil))
| ~ spl72_2 ),
inference(superposition,[],[f624,f776]) ).
fof(f1147,plain,
( ~ singletonP(sK21)
| ~ ssList(sK21)
| spl72_7 ),
inference(resolution,[],[f1141,f480]) ).
fof(f1141,plain,
( ~ ssItem(sK29(sK21))
| spl72_7 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1139,plain,
( spl72_7
<=> ssItem(sK29(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_7])]) ).
fof(f1146,plain,
( ~ spl72_7
| spl72_8
| ~ spl72_2
| ~ spl72_3 ),
inference(avatar_split_clause,[],[f1137,f794,f679,f1143,f1139]) ).
fof(f1143,plain,
( spl72_8
<=> memberP(sK21,sK29(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_8])]) ).
fof(f1137,plain,
( memberP(sK21,sK29(sK21))
| ~ ssItem(sK29(sK21))
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1136,f406]) ).
fof(f1136,plain,
( memberP(sK21,sK29(sK21))
| ~ ssList(nil)
| ~ ssItem(sK29(sK21))
| ~ spl72_2
| ~ spl72_3 ),
inference(superposition,[],[f647,f1120]) ).
fof(f1120,plain,
( sK21 = cons(sK29(sK21),nil)
| ~ spl72_2
| ~ spl72_3 ),
inference(subsumption_resolution,[],[f1119,f390]) ).
fof(f1119,plain,
( sK21 = cons(sK29(sK21),nil)
| ~ ssList(sK21)
| ~ spl72_2
| ~ spl72_3 ),
inference(resolution,[],[f1118,f481]) ).
fof(f896,plain,
( spl72_5
| spl72_6 ),
inference(avatar_split_clause,[],[f855,f893,f889]) ).
fof(f889,plain,
( spl72_5
<=> hd(sK22) = sK27(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_5])]) ).
fof(f804,plain,
( ~ spl72_2
| spl72_3 ),
inference(avatar_contradiction_clause,[],[f803]) ).
fof(f803,plain,
( $false
| ~ spl72_2
| spl72_3 ),
inference(subsumption_resolution,[],[f802,f740]) ).
fof(f802,plain,
( ~ sP0(sK22,sK21)
| spl72_3 ),
inference(resolution,[],[f796,f387]) ).
fof(f796,plain,
( ~ ssItem(sK20(sK22,sK21))
| spl72_3 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f801,plain,
( ~ spl72_3
| spl72_4
| ~ spl72_2 ),
inference(avatar_split_clause,[],[f777,f679,f798,f794]) ).
fof(f798,plain,
( spl72_4
<=> equalelemsP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_4])]) ).
fof(f739,plain,
( spl72_1
| ~ spl72_2 ),
inference(avatar_contradiction_clause,[],[f738]) ).
fof(f738,plain,
( $false
| spl72_1
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f737,f676]) ).
fof(f676,plain,
( ~ neq(sK22,nil)
| spl72_1 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f675,plain,
( spl72_1
<=> neq(sK22,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_1])]) ).
fof(f682,plain,
( spl72_1
| spl72_2 ),
inference(avatar_split_clause,[],[f666,f679,f675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC381+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 02:46:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (28553)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (28556)WARNING: value z3 for option sas not known
% 0.14/0.38 % (28556)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)
% 0.14/0.38 % (28555)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (28560)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)
% 0.14/0.38 % (28558)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)
% 0.14/0.38 % (28554)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (28557)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (28559)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)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 TRYING [2]
% 0.20/0.40 TRYING [1]
% 0.20/0.40 TRYING [2]
% 0.20/0.41 TRYING [3]
% 0.20/0.41 TRYING [3]
% 0.20/0.42 TRYING [3]
% 0.20/0.43 % (28556)First to succeed.
% 0.20/0.45 TRYING [4]
% 0.20/0.45 % (28556)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28553"
% 0.20/0.46 TRYING [4]
% 0.20/0.46 TRYING [4]
% 0.20/0.46 % (28556)Refutation found. Thanks to Tanya!
% 0.20/0.46 % SZS status Theorem for theBenchmark
% 0.20/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47 % (28556)------------------------------
% 0.20/0.47 % (28556)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.47 % (28556)Termination reason: Refutation
% 0.20/0.47
% 0.20/0.47 % (28556)Memory used [KB]: 2060
% 0.20/0.47 % (28556)Time elapsed: 0.074 s
% 0.20/0.47 % (28556)Instructions burned: 153 (million)
% 0.20/0.47 % (28553)Success in time 0.098 s
%------------------------------------------------------------------------------