TSTP Solution File: SWC029+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC029+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:47:23 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 183
% Syntax : Number of formulae : 754 ( 34 unt; 0 def)
% Number of atoms : 3670 ( 780 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 4652 (1736 ~;1731 |; 800 &)
% ( 93 <=>; 292 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 17 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 9 con; 0-2 aty)
% Number of variables : 1625 (1280 !; 345 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1724,plain,
$false,
inference(avatar_sat_refutation,[],[f656,f666,f672,f676,f800,f1066,f1155,f1475,f1479,f1494,f1498,f1597,f1601,f1652,f1656,f1708,f1711,f1715,f1718,f1721]) ).
fof(f1721,plain,
( ~ spl71_1
| ~ spl71_16 ),
inference(avatar_contradiction_clause,[],[f1720]) ).
fof(f1720,plain,
( $false
| ~ spl71_1
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1719,f399]) ).
fof(f399,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f1719,plain,
( ~ ssList(nil)
| ~ spl71_1
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1702,f651]) ).
fof(f651,plain,
( ssItem(sK22)
| ~ spl71_1 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f649,plain,
( spl71_1
<=> ssItem(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_1])]) ).
fof(f1702,plain,
( ~ ssItem(sK22)
| ~ ssList(nil)
| ~ spl71_16 ),
inference(trivial_inequality_removal,[],[f1700]) ).
fof(f1700,plain,
( nil != nil
| ~ ssItem(sK22)
| ~ ssList(nil)
| ~ spl71_16 ),
inference(superposition,[],[f563,f1651]) ).
fof(f1651,plain,
( nil = cons(sK22,nil)
| ~ spl71_16 ),
inference(avatar_component_clause,[],[f1649]) ).
fof(f1649,plain,
( spl71_16
<=> nil = cons(sK22,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_16])]) ).
fof(f563,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,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/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f1718,plain,
( ~ spl71_1
| ~ spl71_16 ),
inference(avatar_contradiction_clause,[],[f1717]) ).
fof(f1717,plain,
( $false
| ~ spl71_1
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1716,f399]) ).
fof(f1716,plain,
( ~ ssList(nil)
| ~ spl71_1
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1703,f651]) ).
fof(f1703,plain,
( ~ ssItem(sK22)
| ~ ssList(nil)
| ~ spl71_16 ),
inference(trivial_inequality_removal,[],[f1699]) ).
fof(f1699,plain,
( nil != nil
| ~ ssItem(sK22)
| ~ ssList(nil)
| ~ spl71_16 ),
inference(superposition,[],[f562,f1651]) ).
fof(f562,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,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/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f1715,plain,
( ~ spl71_1
| ~ spl71_15
| ~ spl71_16 ),
inference(avatar_contradiction_clause,[],[f1714]) ).
fof(f1714,plain,
( $false
| ~ spl71_1
| ~ spl71_15
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1713,f1646]) ).
fof(f1646,plain,
( ssList(cons(sK22,nil))
| ~ spl71_15 ),
inference(avatar_component_clause,[],[f1645]) ).
fof(f1645,plain,
( spl71_15
<=> ssList(cons(sK22,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_15])]) ).
fof(f1713,plain,
( ~ ssList(cons(sK22,nil))
| ~ spl71_1
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1712,f651]) ).
fof(f1712,plain,
( ~ ssItem(sK22)
| ~ ssList(cons(sK22,nil))
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1693,f391]) ).
fof(f391,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f1693,plain,
( singletonP(nil)
| ~ ssItem(sK22)
| ~ ssList(cons(sK22,nil))
| ~ spl71_16 ),
inference(superposition,[],[f616,f1651]) ).
fof(f616,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f475]) ).
fof(f475,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f284,f285]) ).
fof(f285,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f284,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f283]) ).
fof(f283,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,[],[f160]) ).
fof(f160,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/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f1711,plain,
( ~ spl71_2
| spl71_3
| ~ spl71_8
| ~ spl71_16 ),
inference(avatar_contradiction_clause,[],[f1710]) ).
fof(f1710,plain,
( $false
| ~ spl71_2
| spl71_3
| ~ spl71_8
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1709,f660]) ).
fof(f660,plain,
( nil != sK19
| spl71_3 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f659,plain,
( spl71_3
<=> nil = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_3])]) ).
fof(f1709,plain,
( nil = sK19
| ~ spl71_2
| ~ spl71_8
| ~ spl71_16 ),
inference(forward_demodulation,[],[f1684,f643]) ).
fof(f643,plain,
nil = app(nil,nil),
inference(global_subsumption,[],[f390,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f376,f391,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f417,f419,f418,f421,f420,f424,f423,f639,f425,f426,f427,f428,f429,f432,f638,f430,f637,f434,f433,f437,f436,f442,f612,f440,f439,f443,f445,f444,f450,f614,f448,f447,f451,f454,f453,f452,f455,f456,f457,f458,f459,f460,f461,f462,f465,f464,f463,f466,f467,f468,f470,f469,f472,f471,f616,f474,f473,f476,f484,f483,f482,f481,f480,f479,f617,f485,f486,f495,f494,f493,f492,f491,f490,f489,f636,f496,f497,f507,f506,f505,f504,f503,f502,f501,f500,f620,f508,f509,f519,f518,f517,f516,f515,f514,f513,f512,f621,f520,f521,f531,f530,f529,f528,f527,f526,f525,f524,f622,f532,f534,f533,f542,f541,f540,f539,f538,f537,f536,f623,f543,f545,f544,f553,f552,f551,f550,f549,f548,f547,f624,f554,f625,f640,f555,f626,f641,f557,f627,f642,f559,f561,f562,f563,f564,f565,f566,f628,f569,f568,f567,f571,f572,f573,f574,f575,f576,f577,f579,f630,f581,f580,f631,f585,f584,f583,f632,f588,f587,f635]) ).
fof(f635,plain,
( nil = app(nil,nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f634]) ).
fof(f634,plain,
( nil = app(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f633]) ).
fof(f633,plain,
! [X1] :
( nil = app(nil,X1)
| nil != X1
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f592]) ).
fof(f592,plain,
! [X0,X1] :
( nil = app(X0,X1)
| nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,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,[],[f371]) ).
fof(f371,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,[],[f202]) ).
fof(f202,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/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f587,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f370]) ).
fof(f370,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f368,f369]) ).
fof(f369,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f368,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,[],[f367]) ).
fof(f367,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,[],[f201]) ).
fof(f201,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/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f588,plain,
! [X0,X1] :
( app(X1,sK68(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f370]) ).
fof(f632,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f589]) ).
fof(f589,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f370]) ).
fof(f583,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
& ssList(sK67(X0,X1))
& ssList(sK66(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f363,f365,f364]) ).
fof(f364,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK66(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f365,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK66(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f363,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,[],[f362]) ).
fof(f362,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,[],[f200]) ).
fof(f200,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/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f584,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f585,plain,
! [X0,X1] :
( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f631,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,[],[f586]) ).
fof(f586,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,[],[f366]) ).
fof(f580,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f359,f360]) ).
fof(f360,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f359,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,[],[f358]) ).
fof(f358,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,[],[f199]) ).
fof(f199,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/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f581,plain,
! [X0,X1] :
( app(sK65(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f630,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f582]) ).
fof(f582,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f579,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f198]) ).
fof(f198,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/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f577,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f196]) ).
fof(f196,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/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f576,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f194]) ).
fof(f194,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/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f575,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f192,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/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f574,plain,
! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f190]) ).
fof(f190,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/sandbox2/benchmark/theBenchmark.p',ax77) ).
fof(f573,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f188]) ).
fof(f188,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/sandbox2/benchmark/theBenchmark.p',ax86) ).
fof(f572,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f186]) ).
fof(f186,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/sandbox2/benchmark/theBenchmark.p',ax85) ).
fof(f571,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f185,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/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f567,plain,
! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1))
& ssList(sK63(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f353,f355,f354]) ).
fof(f354,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK63(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
! [X0,X1] :
( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f353,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,[],[f352]) ).
fof(f352,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,[],[f184]) ).
fof(f184,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/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f568,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f569,plain,
! [X0,X1] :
( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f628,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,[],[f570]) ).
fof(f570,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,[],[f356]) ).
fof(f566,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,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/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f565,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,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/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f564,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,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/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f561,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,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/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f559,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,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/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f642,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f390,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f376,f391,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f417,f419,f418,f421,f420,f424,f423,f639,f425,f426,f427,f428,f429,f432,f638,f430,f637,f434,f433,f437,f436,f442,f612,f440,f439,f443,f445,f444,f450,f614,f448,f447,f451,f454,f453,f452,f455,f456,f457,f458,f459,f460,f461,f462,f465,f464,f463,f466,f467,f468,f470,f469,f472,f471,f616,f474,f473,f476,f484,f483,f482,f481,f480,f479,f617,f485,f486,f495,f494,f493,f492,f491,f490,f489,f636,f496,f497,f507,f506,f505,f504,f503,f502,f501,f500,f620,f508,f509,f519,f518,f517,f516,f515,f514,f513,f512,f621,f520,f521,f531,f530,f529,f528,f527,f526,f525,f524,f622,f532,f534,f533,f542,f541,f540,f539,f538,f537,f536,f623,f543,f545,f544,f553,f552,f551,f550,f549,f548,f547,f624,f554,f625,f640,f555,f626,f641,f557,f627]) ).
fof(f627,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f560]) ).
fof(f560,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f557,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,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/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f641,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f390,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f376,f391,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f417,f419,f418,f421,f420,f424,f423,f639,f425,f426,f427,f428,f429,f432,f638,f430,f637,f434,f433,f437,f436,f442,f612,f440,f439,f443,f445,f444,f450,f614,f448,f447,f451,f454,f453,f452,f455,f456,f457,f458,f459,f460,f461,f462,f465,f464,f463,f466,f467,f468,f470,f469,f472,f471,f616,f474,f473,f476,f484,f483,f482,f481,f480,f479,f617,f485,f486,f495,f494,f493,f492,f491,f490,f489,f636,f496,f497,f507,f506,f505,f504,f503,f502,f501,f500,f620,f508,f509,f519,f518,f517,f516,f515,f514,f513,f512,f621,f520,f521,f531,f530,f529,f528,f527,f526,f525,f524,f622,f532,f534,f533,f542,f541,f540,f539,f538,f537,f536,f623,f543,f545,f544,f553,f552,f551,f550,f549,f548,f547,f624,f554,f625,f640,f555,f626]) ).
fof(f626,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f558]) ).
fof(f558,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f555,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f175]) ).
fof(f175,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/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f640,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f390,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f376,f391,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f417,f419,f418,f421,f420,f424,f423,f639,f425,f426,f427,f428,f429,f432,f638,f430,f637,f434,f433,f437,f436,f442,f612,f440,f439,f443,f445,f444,f450,f614,f448,f447,f451,f454,f453,f452,f455,f456,f457,f458,f459,f460,f461,f462,f465,f464,f463,f466,f467,f468,f470,f469,f472,f471,f616,f474,f473,f476,f484,f483,f482,f481,f480,f479,f617,f485,f486,f495,f494,f493,f492,f491,f490,f489,f636,f496,f497,f507,f506,f505,f504,f503,f502,f501,f500,f620,f508,f509,f519,f518,f517,f516,f515,f514,f513,f512,f621,f520,f521,f531,f530,f529,f528,f527,f526,f525,f524,f622,f532,f534,f533,f542,f541,f540,f539,f538,f537,f536,f623,f543,f545,f544,f553,f552,f551,f550,f549,f548,f547,f624,f554,f625]) ).
fof(f625,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f556]) ).
fof(f556,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f554,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f174,f248,f247]) ).
fof(f247,plain,
! [X0] :
( sP16(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,[sP16])]) ).
fof(f248,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP16(X0) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
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(flattening,[],[f173]) ).
fof(f173,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/sandbox2/benchmark/theBenchmark.p',ax12) ).
fof(f624,plain,
! [X10,X8,X6,X9,X7] :
( lt(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,[],[f546]) ).
fof(f546,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)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ( sP16(X0)
| ( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssList(sK60(X0))
& ssItem(sK59(X0))
& ssItem(sK58(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) )
| ~ sP16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61,sK62])],[f342,f347,f346,f345,f344,f343]) ).
fof(f343,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(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),X2)
& app(app(X3,cons(sK58(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(X3,cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),X4)),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK58(X0),sK59(X0))
& app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
! [X0] :
( ( sP16(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) )
| ~ sP16(X0) ) ),
inference(rectify,[],[f341]) ).
fof(f341,plain,
! [X0] :
( ( sP16(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) )
| ~ sP16(X0) ) ),
inference(nnf_transformation,[],[f247]) ).
fof(f547,plain,
! [X0] :
( ssItem(sK58(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f548,plain,
! [X0] :
( ssItem(sK59(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f549,plain,
! [X0] :
( ssList(sK60(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f550,plain,
! [X0] :
( ssList(sK61(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f551,plain,
! [X0] :
( ssList(sK62(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f552,plain,
! [X0] :
( sP16(X0)
| app(app(sK60(X0),cons(sK58(X0),sK61(X0))),cons(sK59(X0),sK62(X0))) = X0 ),
inference(cnf_transformation,[],[f348]) ).
fof(f553,plain,
! [X0] :
( ~ lt(sK58(X0),sK59(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f544,plain,
! [X0] :
( ~ sP17(X0)
| ~ strictorderedP(X0)
| sP16(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ strictorderedP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f248]) ).
fof(f545,plain,
! [X0] :
( ~ sP17(X0)
| ~ sP16(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f543,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f172,f245,f244]) ).
fof(f244,plain,
! [X0] :
( sP14(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,[sP14])]) ).
fof(f245,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP14(X0) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
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(flattening,[],[f171]) ).
fof(f171,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/sandbox2/benchmark/theBenchmark.p',ax11) ).
fof(f623,plain,
! [X10,X8,X6,X9,X7] :
( 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,[],[f535]) ).
fof(f535,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)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f339,plain,
! [X0] :
( ( sP14(X0)
| ( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssList(sK55(X0))
& ssItem(sK54(X0))
& ssItem(sK53(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) )
| ~ sP14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f333,f338,f337,f336,f335,f334]) ).
fof(f334,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(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),X2)
& app(app(X3,cons(sK53(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(X3,cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f337,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),X4)),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f338,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK53(X0),sK54(X0))
& app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f333,plain,
! [X0] :
( ( sP14(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) )
| ~ sP14(X0) ) ),
inference(rectify,[],[f332]) ).
fof(f332,plain,
! [X0] :
( ( sP14(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) )
| ~ sP14(X0) ) ),
inference(nnf_transformation,[],[f244]) ).
fof(f536,plain,
! [X0] :
( ssItem(sK53(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f537,plain,
! [X0] :
( ssItem(sK54(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f538,plain,
! [X0] :
( ssList(sK55(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f539,plain,
! [X0] :
( ssList(sK56(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f540,plain,
! [X0] :
( ssList(sK57(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f541,plain,
! [X0] :
( sP14(X0)
| app(app(sK55(X0),cons(sK53(X0),sK56(X0))),cons(sK54(X0),sK57(X0))) = X0 ),
inference(cnf_transformation,[],[f339]) ).
fof(f542,plain,
! [X0] :
( ~ leq(sK53(X0),sK54(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f533,plain,
! [X0] :
( ~ sP15(X0)
| ~ totalorderedP(X0)
| sP14(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ totalorderedP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f534,plain,
! [X0] :
( ~ sP15(X0)
| ~ sP14(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f532,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f170,f242,f241]) ).
fof(f241,plain,
! [X0] :
( sP12(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,[sP12])]) ).
fof(f242,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP12(X0) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
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(flattening,[],[f169]) ).
fof(f169,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/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f622,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(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,[],[f523]) ).
fof(f523,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)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f330,plain,
! [X0] :
( ( sP12(X0)
| ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssList(sK50(X0))
& ssItem(sK49(X0))
& ssItem(sK48(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) )
| ~ sP12(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51,sK52])],[f324,f329,f328,f327,f326,f325]) ).
fof(f325,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,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK48(X0))
& leq(sK48(X0),X2)
& app(app(X3,cons(sK48(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(X3,cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f328,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),X4)),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f329,plain,
! [X0] :
( ? [X5] :
( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK49(X0),sK48(X0))
& leq(sK48(X0),sK49(X0))
& app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
! [X0] :
( ( sP12(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) )
| ~ sP12(X0) ) ),
inference(rectify,[],[f323]) ).
fof(f323,plain,
! [X0] :
( ( sP12(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) )
| ~ sP12(X0) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f524,plain,
! [X0] :
( ssItem(sK48(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f525,plain,
! [X0] :
( ssItem(sK49(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f526,plain,
! [X0] :
( ssList(sK50(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f527,plain,
! [X0] :
( ssList(sK51(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f528,plain,
! [X0] :
( ssList(sK52(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f529,plain,
! [X0] :
( sP12(X0)
| app(app(sK50(X0),cons(sK48(X0),sK51(X0))),cons(sK49(X0),sK52(X0))) = X0 ),
inference(cnf_transformation,[],[f330]) ).
fof(f530,plain,
! [X0] :
( leq(sK48(X0),sK49(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f531,plain,
! [X0] :
( leq(sK49(X0),sK48(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f330]) ).
fof(f521,plain,
! [X0] :
( ~ sP13(X0)
| ~ cyclefreeP(X0)
| sP12(X0) ),
inference(cnf_transformation,[],[f322]) ).
fof(f322,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP12(X0) )
& ( sP12(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f242]) ).
fof(f520,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f168,f239,f238]) ).
fof(f238,plain,
! [X0] :
( sP10(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,[sP10])]) ).
fof(f239,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP10(X0) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
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(flattening,[],[f167]) ).
fof(f167,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/sandbox2/benchmark/theBenchmark.p',ax10) ).
fof(f621,plain,
! [X10,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(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,[],[f511]) ).
fof(f511,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)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f321,plain,
! [X0] :
( ( sP10(X0)
| ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssList(sK45(X0))
& ssItem(sK44(X0))
& ssItem(sK43(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) )
| ~ sP10(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45,sK46,sK47])],[f315,f320,f319,f318,f317,f316]) ).
fof(f316,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,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK43(X0))
& ~ lt(sK43(X0),X2)
& app(app(X3,cons(sK43(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(X3,cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f319,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),X4)),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK44(X0),sK43(X0))
& ~ lt(sK43(X0),sK44(X0))
& app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f315,plain,
! [X0] :
( ( sP10(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) )
| ~ sP10(X0) ) ),
inference(rectify,[],[f314]) ).
fof(f314,plain,
! [X0] :
( ( sP10(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) )
| ~ sP10(X0) ) ),
inference(nnf_transformation,[],[f238]) ).
fof(f512,plain,
! [X0] :
( ssItem(sK43(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f513,plain,
! [X0] :
( ssItem(sK44(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f514,plain,
! [X0] :
( ssList(sK45(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f515,plain,
! [X0] :
( ssList(sK46(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f516,plain,
! [X0] :
( ssList(sK47(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f517,plain,
! [X0] :
( sP10(X0)
| app(app(sK45(X0),cons(sK43(X0),sK46(X0))),cons(sK44(X0),sK47(X0))) = X0 ),
inference(cnf_transformation,[],[f321]) ).
fof(f518,plain,
! [X0] :
( ~ lt(sK43(X0),sK44(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f519,plain,
! [X0] :
( ~ lt(sK44(X0),sK43(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f321]) ).
fof(f509,plain,
! [X0] :
( ~ sP11(X0)
| ~ strictorderP(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP10(X0) )
& ( sP10(X0)
| ~ strictorderP(X0) ) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f239]) ).
fof(f508,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f166,f236,f235]) ).
fof(f235,plain,
! [X0] :
( sP8(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,[sP8])]) ).
fof(f236,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP8(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
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(flattening,[],[f165]) ).
fof(f165,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/sandbox2/benchmark/theBenchmark.p',ax9) ).
fof(f620,plain,
! [X10,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f499]) ).
fof(f499,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)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f312,plain,
! [X0] :
( ( sP8(X0)
| ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssList(sK40(X0))
& ssItem(sK39(X0))
& ssItem(sK38(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) )
| ~ sP8(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40,sK41,sK42])],[f306,f311,f310,f309,f308,f307]) ).
fof(f307,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,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK38(X0))
& ~ leq(sK38(X0),X2)
& app(app(X3,cons(sK38(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(X3,cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f310,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),X4)),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK39(X0),sK38(X0))
& ~ leq(sK38(X0),sK39(X0))
& app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f306,plain,
! [X0] :
( ( sP8(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) )
| ~ sP8(X0) ) ),
inference(rectify,[],[f305]) ).
fof(f305,plain,
! [X0] :
( ( sP8(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) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f235]) ).
fof(f500,plain,
! [X0] :
( ssItem(sK38(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f501,plain,
! [X0] :
( ssItem(sK39(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f502,plain,
! [X0] :
( ssList(sK40(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f503,plain,
! [X0] :
( ssList(sK41(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f504,plain,
! [X0] :
( ssList(sK42(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f505,plain,
! [X0] :
( sP8(X0)
| app(app(sK40(X0),cons(sK38(X0),sK41(X0))),cons(sK39(X0),sK42(X0))) = X0 ),
inference(cnf_transformation,[],[f312]) ).
fof(f506,plain,
! [X0] :
( ~ leq(sK38(X0),sK39(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f507,plain,
! [X0] :
( ~ leq(sK39(X0),sK38(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f497,plain,
! [X0] :
( ~ sP9(X0)
| ~ totalorderP(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f304]) ).
fof(f304,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ totalorderP(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f236]) ).
fof(f496,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f164,f233,f232]) ).
fof(f232,plain,
! [X0] :
( sP6(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,[sP6])]) ).
fof(f233,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
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(flattening,[],[f163]) ).
fof(f163,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/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(f636,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f619]) ).
fof(f619,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f618]) ).
fof(f618,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)
| ~ sP6(X0) ),
inference(equality_resolution,[],[f488]) ).
fof(f488,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)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0] :
( ( sP6(X0)
| ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssList(sK35(X0))
& ssItem(sK34(X0))
& ssItem(sK33(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) )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36,sK37])],[f297,f302,f301,f300,f299,f298]) ).
fof(f298,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] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = X2
& app(app(X3,cons(sK33(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f300,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(X3,cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f301,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),X4)),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f302,plain,
! [X0] :
( ? [X5] :
( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),X5)) = X0
& ssList(X5) )
=> ( sK33(X0) = sK34(X0)
& app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f297,plain,
! [X0] :
( ( sP6(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) )
| ~ sP6(X0) ) ),
inference(rectify,[],[f296]) ).
fof(f296,plain,
! [X0] :
( ( sP6(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) )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f489,plain,
! [X0] :
( ssItem(sK33(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f490,plain,
! [X0] :
( ssItem(sK34(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f491,plain,
! [X0] :
( ssList(sK35(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f492,plain,
! [X0] :
( ssList(sK36(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f493,plain,
! [X0] :
( ssList(sK37(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f494,plain,
! [X0] :
( sP6(X0)
| app(app(sK35(X0),cons(sK33(X0),sK36(X0))),cons(sK34(X0),sK37(X0))) = X0 ),
inference(cnf_transformation,[],[f303]) ).
fof(f495,plain,
! [X0] :
( sP6(X0)
| sK33(X0) = sK34(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f486,plain,
! [X0] :
( ~ sP7(X0)
| ~ duplicatefreeP(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f485,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f162,f230,f229]) ).
fof(f229,plain,
! [X0] :
( sP4(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,[sP4])]) ).
fof(f230,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
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(flattening,[],[f161]) ).
fof(f161,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/sandbox2/benchmark/theBenchmark.p',ax14) ).
fof(f617,plain,
! [X8,X6,X7,X5] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(app(X7,cons(X5,cons(X6,X8)))) ),
inference(equality_resolution,[],[f478]) ).
fof(f478,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ( sP4(X0)
| ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0))
& ssList(sK31(X0))
& ssItem(sK30(X0))
& ssItem(sK29(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f289,f293,f292,f291,f290]) ).
fof(f290,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] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f291,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != X2
& app(X3,cons(sK29(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(X3,cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
& ssList(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f293,plain,
! [X0] :
( ? [X4] :
( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),X4))) = X0
& ssList(X4) )
=> ( sK29(X0) != sK30(X0)
& app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f289,plain,
! [X0] :
( ( sP4(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) )
| ~ sP4(X0) ) ),
inference(rectify,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ( sP4(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) )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f479,plain,
! [X0] :
( ssItem(sK29(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f480,plain,
! [X0] :
( ssItem(sK30(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f481,plain,
! [X0] :
( ssList(sK31(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f482,plain,
! [X0] :
( ssList(sK32(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f483,plain,
! [X0] :
( sP4(X0)
| app(sK31(X0),cons(sK29(X0),cons(sK30(X0),sK32(X0)))) = X0 ),
inference(cnf_transformation,[],[f294]) ).
fof(f484,plain,
! [X0] :
( sK29(X0) != sK30(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f476,plain,
! [X0] :
( ~ sP5(X0)
| ~ equalelemsP(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ equalelemsP(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f230]) ).
fof(f473,plain,
! [X0] :
( ssItem(sK28(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f474,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK28(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f471,plain,
! [X0] :
( ssList(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0] :
( ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f159,f281]) ).
fof(f281,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f158]) ).
fof(f158,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/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK27(X0) ),
inference(cnf_transformation,[],[f282]) ).
fof(f469,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f157,f279]) ).
fof(f279,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f156]) ).
fof(f156,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/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK26(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f468,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f154]) ).
fof(f154,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/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f467,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f152]) ).
fof(f152,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/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f466,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f150]) ).
fof(f150,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/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f463,plain,
! [X0] :
( ssList(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0))
& ssList(sK24(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f149,f277,f276]) ).
fof(f276,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
& ssList(sK24(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f277,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
=> ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f148]) ).
fof(f148,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/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f464,plain,
! [X0] :
( ssItem(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f465,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK25(X0),sK24(X0)) = X0 ),
inference(cnf_transformation,[],[f278]) ).
fof(f462,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,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/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f461,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,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/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f460,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f459,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f458,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f457,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f456,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f455,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f452,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,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,[],[f274]) ).
fof(f274,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,[],[f139]) ).
fof(f139,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/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f453,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f454,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f451,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f227,f226]) ).
fof(f226,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f227,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f138,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/sandbox2/benchmark/theBenchmark.p',ax70) ).
fof(f447,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f272]) ).
fof(f272,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f271]) ).
fof(f271,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f226]) ).
fof(f448,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f614,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f449]) ).
fof(f449,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f273]) ).
fof(f450,plain,
! [X0,X1] :
( ~ lt(X1,hd(X0))
| sP2(X0,X1)
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f273]) ).
fof(f444,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f227]) ).
fof(f445,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f443,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0] :
( ! [X1] :
( sP1(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f137,f224,f223]) ).
fof(f223,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f224,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f137,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/sandbox2/benchmark/theBenchmark.p',ax67) ).
fof(f439,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f268]) ).
fof(f268,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f267]) ).
fof(f267,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f223]) ).
fof(f440,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f612,plain,
! [X1] : sP0(nil,X1),
inference(equality_resolution,[],[f441]) ).
fof(f441,plain,
! [X0,X1] :
( sP0(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f269]) ).
fof(f442,plain,
! [X0,X1] :
( ~ leq(X1,hd(X0))
| sP0(X0,X1)
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f269]) ).
fof(f436,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f224]) ).
fof(f437,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f266]) ).
fof(f433,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,[],[f265]) ).
fof(f265,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,[],[f264]) ).
fof(f264,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,[],[f136]) ).
fof(f136,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/sandbox2/benchmark/theBenchmark.p',ax44) ).
fof(f434,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,[],[f265]) ).
fof(f637,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f611]) ).
fof(f611,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,[],[f435]) ).
fof(f435,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,[],[f265]) ).
fof(f430,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,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,[],[f262]) ).
fof(f262,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,[],[f135]) ).
fof(f135,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/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f638,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f610]) ).
fof(f610,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f431]) ).
fof(f431,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f432,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f429,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f133]) ).
fof(f133,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/sandbox2/benchmark/theBenchmark.p',ax34) ).
fof(f428,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f131]) ).
fof(f131,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/sandbox2/benchmark/theBenchmark.p',ax91) ).
fof(f427,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f129]) ).
fof(f129,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/sandbox2/benchmark/theBenchmark.p',ax30) ).
fof(f426,plain,
! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f127]) ).
fof(f127,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/sandbox2/benchmark/theBenchmark.p',ax88) ).
fof(f425,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f125]) ).
fof(f125,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/sandbox2/benchmark/theBenchmark.p',ax95) ).
fof(f639,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f609]) ).
fof(f609,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f422]) ).
fof(f422,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,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,[],[f260]) ).
fof(f260,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,[],[f124]) ).
fof(f124,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/sandbox2/benchmark/theBenchmark.p',ax93) ).
fof(f423,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f424,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f420,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,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/sandbox2/benchmark/theBenchmark.p',ax32) ).
fof(f421,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f418,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,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/sandbox2/benchmark/theBenchmark.p',ax35) ).
fof(f419,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f417,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f121,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/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f415,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,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/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f414,plain,
! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f117]) ).
fof(f117,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/sandbox2/benchmark/theBenchmark.p',ax87) ).
fof(f413,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f115]) ).
fof(f115,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/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f412,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f113]) ).
fof(f113,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/sandbox2/benchmark/theBenchmark.p',ax92) ).
fof(f411,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f111]) ).
fof(f111,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/sandbox2/benchmark/theBenchmark.p',ax94) ).
fof(f410,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,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/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f409,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,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/sandbox2/benchmark/theBenchmark.p',ax68) ).
fof(f408,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,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/sandbox2/benchmark/theBenchmark.p',ax63) ).
fof(f407,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,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/sandbox2/benchmark/theBenchmark.p',ax61) ).
fof(f406,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(f405,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,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/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f404,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,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/sandbox2/benchmark/theBenchmark.p',ax73) ).
fof(f403,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f402,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
fof(f401,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
fof(f400,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f398,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f397,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f396,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f395,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f394,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f393,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f392,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f376,plain,
ssList(sK18),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
( ( ( nil != sK19
& nil = sK18 )
| ( nil != sK18
& nil = sK19 ) )
& ( ~ neq(sK21,nil)
| ( sK20 = app(sK23,cons(sK22,nil))
& sK21 = app(cons(sK22,nil),sK23)
& ssList(sK23)
& ssItem(sK22) ) )
& ( nil != sK21
| nil = sK20 )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23])],[f99,f255,f254,f253,f252,f251,f250]) ).
fof(f250,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != X1
& nil = sK18 )
| ( nil != sK18
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = X2 )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != X1
& nil = sK18 )
| ( nil != sK18
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = X2 )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil != sK19
& nil = sK18 )
| ( nil != sK18
& nil = sK19 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = X2 )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil != sK19
& nil = sK18 )
| ( nil != sK18
& nil = sK19 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = X2 )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil != sK19
& nil = sK18 )
| ( nil != sK18
& nil = sK19 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = sK20
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = sK20 )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X3] :
( ( ( nil != sK19
& nil = sK18 )
| ( nil != sK18
& nil = sK19 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = sK20
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = sK20 )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ( ( nil != sK19
& nil = sK18 )
| ( nil != sK18
& nil = sK19 ) )
& ( ~ neq(sK21,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = sK20
& app(cons(X4,nil),X5) = sK21
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != sK21
| nil = sK20 )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = sK20
& app(cons(X4,nil),X5) = sK21
& ssList(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( sK20 = app(X5,cons(sK22,nil))
& sK21 = app(cons(sK22,nil),X5)
& ssList(X5) )
& ssItem(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
( ? [X5] :
( sK20 = app(X5,cons(sK22,nil))
& sK21 = app(cons(sK22,nil),X5)
& ssList(X5) )
=> ( sK20 = app(sK23,cons(sK22,nil))
& sK21 = app(cons(sK22,nil),sK23)
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) )
& ssItem(X4) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3 ) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3 ) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f377,plain,
ssList(sK19),
inference(cnf_transformation,[],[f256]) ).
fof(f378,plain,
ssList(sK20),
inference(cnf_transformation,[],[f256]) ).
fof(f379,plain,
ssList(sK21),
inference(cnf_transformation,[],[f256]) ).
fof(f380,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f256]) ).
fof(f381,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f256]) ).
fof(f382,plain,
( nil != sK21
| nil = sK20 ),
inference(cnf_transformation,[],[f256]) ).
fof(f383,plain,
( ~ neq(sK21,nil)
| ssItem(sK22) ),
inference(cnf_transformation,[],[f256]) ).
fof(f384,plain,
( ~ neq(sK21,nil)
| ssList(sK23) ),
inference(cnf_transformation,[],[f256]) ).
fof(f385,plain,
( ~ neq(sK21,nil)
| sK21 = app(cons(sK22,nil),sK23) ),
inference(cnf_transformation,[],[f256]) ).
fof(f386,plain,
( ~ neq(sK21,nil)
| sK20 = app(sK23,cons(sK22,nil)) ),
inference(cnf_transformation,[],[f256]) ).
fof(f387,plain,
( nil = sK18
| nil = sK19 ),
inference(cnf_transformation,[],[f256]) ).
fof(f390,plain,
( nil != sK19
| nil != sK18 ),
inference(cnf_transformation,[],[f256]) ).
fof(f1684,plain,
( sK19 = app(nil,nil)
| ~ spl71_2
| ~ spl71_8
| ~ spl71_16 ),
inference(superposition,[],[f1516,f1651]) ).
fof(f1516,plain,
( sK19 = app(cons(sK22,nil),nil)
| ~ spl71_2
| ~ spl71_8 ),
inference(superposition,[],[f1157,f1154]) ).
fof(f1154,plain,
( nil = sK23
| ~ spl71_8 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1152,plain,
( spl71_8
<=> nil = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_8])]) ).
fof(f1157,plain,
( sK19 = app(cons(sK22,nil),sK23)
| ~ spl71_2 ),
inference(subsumption_resolution,[],[f1069,f654]) ).
fof(f654,plain,
( neq(sK19,nil)
| ~ spl71_2 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f653,plain,
( spl71_2
<=> neq(sK19,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_2])]) ).
fof(f1069,plain,
( sK19 = app(cons(sK22,nil),sK23)
| ~ neq(sK19,nil) ),
inference(forward_demodulation,[],[f751,f380]) ).
fof(f751,plain,
( ~ neq(sK19,nil)
| sK21 = app(cons(sK22,nil),sK23) ),
inference(forward_demodulation,[],[f385,f380]) ).
fof(f1708,plain,
( ~ spl71_2
| spl71_3
| ~ spl71_8
| ~ spl71_16 ),
inference(avatar_contradiction_clause,[],[f1707]) ).
fof(f1707,plain,
( $false
| ~ spl71_2
| spl71_3
| ~ spl71_8
| ~ spl71_16 ),
inference(subsumption_resolution,[],[f1706,f660]) ).
fof(f1706,plain,
( nil = sK19
| ~ spl71_2
| ~ spl71_8
| ~ spl71_16 ),
inference(forward_demodulation,[],[f1705,f643]) ).
fof(f1705,plain,
( sK19 = app(nil,nil)
| ~ spl71_2
| ~ spl71_8
| ~ spl71_16 ),
inference(forward_demodulation,[],[f1682,f1154]) ).
fof(f1682,plain,
( sK19 = app(nil,sK23)
| ~ spl71_2
| ~ spl71_16 ),
inference(superposition,[],[f1157,f1651]) ).
fof(f1656,plain,
( ~ spl71_1
| spl71_15 ),
inference(avatar_contradiction_clause,[],[f1655]) ).
fof(f1655,plain,
( $false
| ~ spl71_1
| spl71_15 ),
inference(subsumption_resolution,[],[f1654,f399]) ).
fof(f1654,plain,
( ~ ssList(nil)
| ~ spl71_1
| spl71_15 ),
inference(subsumption_resolution,[],[f1653,f651]) ).
fof(f1653,plain,
( ~ ssItem(sK22)
| ~ ssList(nil)
| spl71_15 ),
inference(resolution,[],[f1647,f561]) ).
fof(f1647,plain,
( ~ ssList(cons(sK22,nil))
| spl71_15 ),
inference(avatar_component_clause,[],[f1645]) ).
fof(f1652,plain,
( ~ spl71_15
| spl71_16
| ~ spl71_2
| ~ spl71_4 ),
inference(avatar_split_clause,[],[f1582,f663,f653,f1649,f1645]) ).
fof(f663,plain,
( spl71_4
<=> nil = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_4])]) ).
fof(f1582,plain,
( nil = cons(sK22,nil)
| ~ ssList(cons(sK22,nil))
| ~ spl71_2
| ~ spl71_4 ),
inference(subsumption_resolution,[],[f1581,f1074]) ).
fof(f1074,plain,
( ssList(sK23)
| ~ spl71_2 ),
inference(subsumption_resolution,[],[f647,f654]) ).
fof(f647,plain,
( ~ neq(sK19,nil)
| ssList(sK23) ),
inference(forward_demodulation,[],[f384,f380]) ).
fof(f1581,plain,
( nil = cons(sK22,nil)
| ~ ssList(cons(sK22,nil))
| ~ ssList(sK23)
| ~ spl71_2
| ~ spl71_4 ),
inference(trivial_inequality_removal,[],[f1574]) ).
fof(f1574,plain,
( nil != nil
| nil = cons(sK22,nil)
| ~ ssList(cons(sK22,nil))
| ~ ssList(sK23)
| ~ spl71_2
| ~ spl71_4 ),
inference(superposition,[],[f590,f1112]) ).
fof(f1112,plain,
( nil = app(sK23,cons(sK22,nil))
| ~ spl71_2
| ~ spl71_4 ),
inference(subsumption_resolution,[],[f1068,f654]) ).
fof(f1068,plain,
( nil = app(sK23,cons(sK22,nil))
| ~ neq(sK19,nil)
| ~ spl71_4 ),
inference(forward_demodulation,[],[f1067,f665]) ).
fof(f665,plain,
( nil = sK18
| ~ spl71_4 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f1067,plain,
( sK18 = app(sK23,cons(sK22,nil))
| ~ neq(sK19,nil) ),
inference(forward_demodulation,[],[f752,f381]) ).
fof(f752,plain,
( ~ neq(sK19,nil)
| sK20 = app(sK23,cons(sK22,nil)) ),
inference(forward_demodulation,[],[f386,f380]) ).
fof(f590,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f1601,plain,
( spl71_3
| spl71_13 ),
inference(avatar_contradiction_clause,[],[f1600]) ).
fof(f1600,plain,
( $false
| spl71_3
| spl71_13 ),
inference(subsumption_resolution,[],[f1599,f377]) ).
fof(f1599,plain,
( ~ ssList(sK19)
| spl71_3
| spl71_13 ),
inference(subsumption_resolution,[],[f1598,f660]) ).
fof(f1598,plain,
( nil = sK19
| ~ ssList(sK19)
| spl71_13 ),
inference(resolution,[],[f1592,f466]) ).
fof(f1592,plain,
( ~ ssItem(hd(sK19))
| spl71_13 ),
inference(avatar_component_clause,[],[f1590]) ).
fof(f1590,plain,
( spl71_13
<=> ssItem(hd(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_13])]) ).
fof(f1597,plain,
( ~ spl71_13
| ~ spl71_14
| spl71_3 ),
inference(avatar_split_clause,[],[f1573,f659,f1594,f1590]) ).
fof(f1594,plain,
( spl71_14
<=> sK19 = tl(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_14])]) ).
fof(f1573,plain,
( sK19 != tl(sK19)
| ~ ssItem(hd(sK19))
| spl71_3 ),
inference(subsumption_resolution,[],[f1572,f377]) ).
fof(f1572,plain,
( sK19 != tl(sK19)
| ~ ssItem(hd(sK19))
| ~ ssList(sK19)
| spl71_3 ),
inference(inner_rewriting,[],[f1570]) ).
fof(f1570,plain,
( sK19 != tl(sK19)
| ~ ssItem(hd(sK19))
| ~ ssList(tl(sK19))
| spl71_3 ),
inference(superposition,[],[f563,f1556]) ).
fof(f1556,plain,
( sK19 = cons(hd(sK19),tl(sK19))
| spl71_3 ),
inference(subsumption_resolution,[],[f1523,f660]) ).
fof(f1523,plain,
( nil = sK19
| sK19 = cons(hd(sK19),tl(sK19)) ),
inference(resolution,[],[f468,f377]) ).
fof(f1498,plain,
( ~ spl71_2
| spl71_8
| spl71_11 ),
inference(avatar_contradiction_clause,[],[f1497]) ).
fof(f1497,plain,
( $false
| ~ spl71_2
| spl71_8
| spl71_11 ),
inference(subsumption_resolution,[],[f1496,f1074]) ).
fof(f1496,plain,
( ~ ssList(sK23)
| spl71_8
| spl71_11 ),
inference(subsumption_resolution,[],[f1495,f1153]) ).
fof(f1153,plain,
( nil != sK23
| spl71_8 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1495,plain,
( nil = sK23
| ~ ssList(sK23)
| spl71_11 ),
inference(resolution,[],[f1489,f464]) ).
fof(f1489,plain,
( ~ ssItem(sK25(sK23))
| spl71_11 ),
inference(avatar_component_clause,[],[f1487]) ).
fof(f1487,plain,
( spl71_11
<=> ssItem(sK25(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_11])]) ).
fof(f1494,plain,
( ~ spl71_11
| ~ spl71_12
| ~ spl71_2
| spl71_8 ),
inference(avatar_split_clause,[],[f1466,f1152,f653,f1491,f1487]) ).
fof(f1491,plain,
( spl71_12
<=> sK23 = sK24(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_12])]) ).
fof(f1466,plain,
( sK23 != sK24(sK23)
| ~ ssItem(sK25(sK23))
| ~ spl71_2
| spl71_8 ),
inference(subsumption_resolution,[],[f1465,f1074]) ).
fof(f1465,plain,
( sK23 != sK24(sK23)
| ~ ssItem(sK25(sK23))
| ~ ssList(sK23)
| ~ spl71_2
| spl71_8 ),
inference(inner_rewriting,[],[f1463]) ).
fof(f1463,plain,
( sK23 != sK24(sK23)
| ~ ssItem(sK25(sK23))
| ~ ssList(sK24(sK23))
| ~ spl71_2
| spl71_8 ),
inference(superposition,[],[f563,f1446]) ).
fof(f1446,plain,
( sK23 = cons(sK25(sK23),sK24(sK23))
| ~ spl71_2
| spl71_8 ),
inference(subsumption_resolution,[],[f1411,f1153]) ).
fof(f1411,plain,
( nil = sK23
| sK23 = cons(sK25(sK23),sK24(sK23))
| ~ spl71_2 ),
inference(resolution,[],[f465,f1074]) ).
fof(f1479,plain,
( spl71_3
| spl71_9 ),
inference(avatar_contradiction_clause,[],[f1478]) ).
fof(f1478,plain,
( $false
| spl71_3
| spl71_9 ),
inference(subsumption_resolution,[],[f1477,f377]) ).
fof(f1477,plain,
( ~ ssList(sK19)
| spl71_3
| spl71_9 ),
inference(subsumption_resolution,[],[f1476,f660]) ).
fof(f1476,plain,
( nil = sK19
| ~ ssList(sK19)
| spl71_9 ),
inference(resolution,[],[f1470,f464]) ).
fof(f1470,plain,
( ~ ssItem(sK25(sK19))
| spl71_9 ),
inference(avatar_component_clause,[],[f1468]) ).
fof(f1468,plain,
( spl71_9
<=> ssItem(sK25(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_9])]) ).
fof(f1475,plain,
( ~ spl71_9
| ~ spl71_10
| spl71_3 ),
inference(avatar_split_clause,[],[f1456,f659,f1472,f1468]) ).
fof(f1472,plain,
( spl71_10
<=> sK19 = sK24(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_10])]) ).
fof(f1456,plain,
( sK19 != sK24(sK19)
| ~ ssItem(sK25(sK19))
| spl71_3 ),
inference(subsumption_resolution,[],[f1455,f377]) ).
fof(f1455,plain,
( sK19 != sK24(sK19)
| ~ ssItem(sK25(sK19))
| ~ ssList(sK19)
| spl71_3 ),
inference(inner_rewriting,[],[f1453]) ).
fof(f1453,plain,
( sK19 != sK24(sK19)
| ~ ssItem(sK25(sK19))
| ~ ssList(sK24(sK19))
| spl71_3 ),
inference(superposition,[],[f563,f1441]) ).
fof(f1441,plain,
( sK19 = cons(sK25(sK19),sK24(sK19))
| spl71_3 ),
inference(subsumption_resolution,[],[f1408,f660]) ).
fof(f1408,plain,
( nil = sK19
| sK19 = cons(sK25(sK19),sK24(sK19)) ),
inference(resolution,[],[f465,f377]) ).
fof(f1155,plain,
( spl71_7
| spl71_8
| ~ spl71_2 ),
inference(avatar_split_clause,[],[f1077,f653,f1152,f1148]) ).
fof(f1148,plain,
( spl71_7
<=> tl(sK23) = sK27(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_7])]) ).
fof(f1077,plain,
( nil = sK23
| tl(sK23) = sK27(sK23)
| ~ spl71_2 ),
inference(resolution,[],[f1074,f472]) ).
fof(f1066,plain,
( spl71_2
| spl71_3 ),
inference(avatar_contradiction_clause,[],[f1065]) ).
fof(f1065,plain,
( $false
| spl71_2
| spl71_3 ),
inference(subsumption_resolution,[],[f1064,f377]) ).
fof(f1064,plain,
( ~ ssList(sK19)
| spl71_2
| spl71_3 ),
inference(subsumption_resolution,[],[f1063,f399]) ).
fof(f1063,plain,
( ~ ssList(nil)
| ~ ssList(sK19)
| spl71_2
| spl71_3 ),
inference(subsumption_resolution,[],[f1062,f660]) ).
fof(f1062,plain,
( nil = sK19
| ~ ssList(nil)
| ~ ssList(sK19)
| spl71_2 ),
inference(resolution,[],[f579,f655]) ).
fof(f655,plain,
( ~ neq(sK19,nil)
| spl71_2 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f800,plain,
( ~ spl71_5
| ~ spl71_6
| spl71_2
| spl71_3 ),
inference(avatar_split_clause,[],[f791,f659,f653,f797,f793]) ).
fof(f793,plain,
( spl71_5
<=> ssItem(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_5])]) ).
fof(f797,plain,
( spl71_6
<=> ssItem(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_6])]) ).
fof(f791,plain,
( ~ ssItem(nil)
| ~ ssItem(sK19)
| spl71_2
| spl71_3 ),
inference(subsumption_resolution,[],[f790,f660]) ).
fof(f790,plain,
( nil = sK19
| ~ ssItem(nil)
| ~ ssItem(sK19)
| spl71_2 ),
inference(resolution,[],[f417,f655]) ).
fof(f676,plain,
( ~ spl71_3
| ~ spl71_4 ),
inference(avatar_contradiction_clause,[],[f675]) ).
fof(f675,plain,
( $false
| ~ spl71_3
| ~ spl71_4 ),
inference(global_subsumption,[],[f390,f386,f385,f384,f383,f382,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f417,f419,f418,f421,f420,f424,f423,f639,f425,f426,f427,f428,f429,f432,f638,f430,f637,f434,f433,f437,f436,f442,f440,f439,f443,f445,f444,f450,f448,f447,f451,f454,f453,f452,f455,f456,f457,f458,f459,f460,f461,f462,f465,f464,f463,f466,f467,f468,f470,f469,f472,f471,f616,f474,f473,f476,f484,f483,f482,f481,f480,f479,f617,f486,f495,f494,f493,f492,f491,f490,f489,f636,f497,f507,f506,f505,f504,f503,f502,f501,f500,f620,f509,f519,f518,f517,f516,f515,f514,f513,f512,f621,f521,f531,f530,f529,f528,f527,f526,f525,f524,f622,f534,f533,f542,f541,f540,f539,f538,f537,f536,f623,f545,f544,f553,f552,f551,f550,f549,f548,f547,f624,f625,f555,f626,f557,f627,f559,f561,f562,f563,f564,f565,f566,f628,f569,f568,f567,f571,f572,f573,f574,f575,f576,f577,f579,f630,f581,f580,f631,f585,f584,f583,f632,f588,f587,f635,f643,f591,f590,f593,f595,f594,f596,f597,f598,f599,f600,f601,f602,f603,f604,f376,f377,f378,f379,f391,f392,f393,f394,f395,f396,f397,f398,f399,f605,f606,f380,f381,f607,f612,f614,f640,f641,f642,f647,f646,f485,f496,f508,f520,f532,f543,f554,f387,f661,f657,f673,f674,f665]) ).
fof(f674,plain,
( nil != sK18
| ~ spl71_3 ),
inference(subsumption_resolution,[],[f390,f661]) ).
fof(f673,plain,
( nil != sK21
| ~ spl71_3 ),
inference(global_subsumption,[],[f390,f386,f385,f384,f383,f382,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f417,f419,f418,f421,f420,f424,f423,f639,f425,f426,f427,f428,f429,f432,f638,f430,f637,f434,f433,f437,f436,f442,f440,f439,f443,f445,f444,f450,f448,f447,f451,f454,f453,f452,f455,f456,f457,f458,f459,f460,f461,f462,f465,f464,f463,f466,f467,f468,f470,f469,f472,f471,f616,f474,f473,f476,f484,f483,f482,f481,f480,f479,f617,f486,f495,f494,f493,f492,f491,f490,f489,f636,f497,f507,f506,f505,f504,f503,f502,f501,f500,f620,f509,f519,f518,f517,f516,f515,f514,f513,f512,f621,f521,f531,f530,f529,f528,f527,f526,f525,f524,f622,f534,f533,f542,f541,f540,f539,f538,f537,f536,f623,f545,f544,f553,f552,f551,f550,f549,f548,f547,f624,f625,f555,f626,f557,f627,f559,f561,f562,f563,f564,f565,f566,f628,f569,f568,f567,f571,f572,f573,f574,f575,f576,f577,f579,f630,f581,f580,f631,f585,f584,f583,f632,f588,f587,f635,f643,f591,f590,f593,f595,f594,f596,f597,f598,f599,f600,f601,f602,f603,f604,f376,f377,f378,f379,f391,f392,f393,f394,f395,f396,f397,f398,f399,f605,f606,f380,f381,f607,f612,f614,f640,f641,f642,f647,f646,f485,f496,f508,f520,f532,f543,f554,f387,f661,f657]) ).
fof(f657,plain,
( nil = sK18
| nil != sK21 ),
inference(forward_demodulation,[],[f382,f381]) ).
fof(f661,plain,
( nil = sK19
| ~ spl71_3 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f646,plain,
( ~ neq(sK19,nil)
| ssItem(sK22) ),
inference(forward_demodulation,[],[f383,f380]) ).
fof(f607,plain,
sK69 != sK70,
inference(cnf_transformation,[],[f375]) ).
fof(f375,plain,
( sK69 != sK70
& ssItem(sK70)
& ssItem(sK69) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f2,f374,f373]) ).
fof(f373,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK69 != X1
& ssItem(X1) )
& ssItem(sK69) ) ),
introduced(choice_axiom,[]) ).
fof(f374,plain,
( ? [X1] :
( sK69 != X1
& ssItem(X1) )
=> ( sK69 != sK70
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f606,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f375]) ).
fof(f605,plain,
ssItem(sK69),
inference(cnf_transformation,[],[f375]) ).
fof(f604,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,[],[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(flattening,[],[f221]) ).
fof(f221,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/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f603,plain,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f219]) ).
fof(f219,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/sandbox2/benchmark/theBenchmark.p',ax40) ).
fof(f602,plain,
! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f217]) ).
fof(f217,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/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f601,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f215]) ).
fof(f215,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/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f600,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f213]) ).
fof(f213,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/sandbox2/benchmark/theBenchmark.p',ax80) ).
fof(f599,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f211]) ).
fof(f211,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/sandbox2/benchmark/theBenchmark.p',ax79) ).
fof(f598,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f209]) ).
fof(f209,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/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f597,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f207]) ).
fof(f207,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/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f596,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,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/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f594,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f204]) ).
fof(f204,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/sandbox2/benchmark/theBenchmark.p',ax19) ).
fof(f595,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f593,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f203,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/sandbox2/benchmark/theBenchmark.p',ax27) ).
fof(f591,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f672,plain,
( ~ spl71_3
| spl71_4 ),
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f671,plain,
( $false
| ~ spl71_3
| spl71_4 ),
inference(subsumption_resolution,[],[f670,f661]) ).
fof(f670,plain,
( nil != sK19
| spl71_4 ),
inference(superposition,[],[f669,f380]) ).
fof(f669,plain,
( nil != sK21
| spl71_4 ),
inference(subsumption_resolution,[],[f657,f664]) ).
fof(f664,plain,
( nil != sK18
| spl71_4 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f666,plain,
( spl71_3
| spl71_4 ),
inference(avatar_split_clause,[],[f387,f663,f659]) ).
fof(f656,plain,
( spl71_1
| ~ spl71_2 ),
inference(avatar_split_clause,[],[f646,f653,f649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC029+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34 % Computer : n009.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Apr 30 04:12:26 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.20/0.35 % (14363)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.36 % (14366)WARNING: value z3 for option sas not known
% 0.20/0.36 % (14366)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.37 % (14364)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (14367)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (14365)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (14368)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.37 % (14369)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.37 % (14370)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [1]
% 0.20/0.39 TRYING [2]
% 0.20/0.39 TRYING [2]
% 0.20/0.40 TRYING [3]
% 0.20/0.40 TRYING [3]
% 0.20/0.42 % (14366)First to succeed.
% 0.20/0.43 TRYING [1]
% 0.20/0.43 TRYING [2]
% 0.20/0.43 % (14366)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.44 % (14366)------------------------------
% 0.20/0.44 % (14366)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.44 % (14366)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (14366)Memory used [KB]: 2068
% 0.20/0.44 % (14366)Time elapsed: 0.069 s
% 0.20/0.44 % (14366)Instructions burned: 134 (million)
% 0.20/0.44 % (14366)------------------------------
% 0.20/0.44 % (14366)------------------------------
% 0.20/0.44 % (14363)Success in time 0.088 s
%------------------------------------------------------------------------------