TSTP Solution File: SWC373+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC373+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 05:13:40 EDT 2024
% Result : Theorem 2.03s 0.69s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 204
% Syntax : Number of formulae : 966 ( 55 unt; 0 def)
% Number of atoms : 3994 ( 666 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 4970 (1942 ~;1992 |; 680 &)
% ( 125 <=>; 231 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 96 ( 94 usr; 59 prp; 0-2 aty)
% Number of functors : 54 ( 54 usr; 7 con; 0-2 aty)
% Number of variables : 1399 (1090 !; 309 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7410,plain,
$false,
inference(avatar_sat_refutation,[],[f811,f819,f829,f874,f1484,f1488,f1503,f1507,f1587,f1591,f1606,f1610,f1717,f1721,f1817,f1821,f2196,f2290,f2294,f2357,f2361,f2667,f2698,f3083,f3088,f3280,f3285,f3460,f3465,f3557,f3635,f3689,f3939,f4377,f4381,f5107,f5112,f5280,f5284,f5921,f6053,f6057,f6070,f6202,f6207,f6411,f6459,f6462,f6466,f6475,f6478,f6642,f6690,f6693,f6697,f6706,f6709,f7409]) ).
fof(f7409,plain,
~ spl69_27,
inference(avatar_contradiction_clause,[],[f7408]) ).
fof(f7408,plain,
( $false
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f7407,f375]) ).
fof(f375,plain,
ssList(sK19),
inference(cnf_transformation,[],[f254]) ).
fof(f254,plain,
( ~ segmentP(sK19,sK18)
& rearsegP(sK21,sK20)
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f99,f253,f252,f251,f250]) ).
fof(f250,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ segmentP(X1,X0)
& rearsegP(X3,X2)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ segmentP(X1,sK18)
& rearsegP(X3,X2)
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ segmentP(X1,sK18)
& rearsegP(X3,X2)
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ~ segmentP(sK19,sK18)
& rearsegP(X3,X2)
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X2] :
( ? [X3] :
( ~ segmentP(sK19,sK18)
& rearsegP(X3,X2)
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ~ segmentP(sK19,sK18)
& rearsegP(X3,sK20)
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X3] :
( ~ segmentP(sK19,sK18)
& rearsegP(X3,sK20)
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ~ segmentP(sK19,sK18)
& rearsegP(sK21,sK20)
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ segmentP(X1,X0)
& rearsegP(X3,X2)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ segmentP(X1,X0)
& rearsegP(X3,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)
=> ( segmentP(X1,X0)
| ~ rearsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X1,X0)
| ~ rearsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f7407,plain,
( ~ ssList(sK19)
| ~ spl69_27 ),
inference(forward_demodulation,[],[f7406,f654]) ).
fof(f654,plain,
sK19 = app(sK19,nil),
inference(resolution,[],[f452,f375]) ).
fof(f452,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/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f7406,plain,
( ~ ssList(app(sK19,nil))
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f7405,f390]) ).
fof(f390,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f7405,plain,
( ~ ssList(app(sK19,nil))
| ~ ssList(nil)
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f7398,f381]) ).
fof(f381,plain,
~ segmentP(sK19,sK18),
inference(cnf_transformation,[],[f254]) ).
fof(f7398,plain,
( segmentP(sK19,sK18)
| ~ ssList(app(sK19,nil))
| ~ ssList(nil)
| ~ spl69_27 ),
inference(superposition,[],[f7324,f654]) ).
fof(f7324,plain,
( ! [X0] :
( segmentP(app(sK19,X0),sK18)
| ~ ssList(app(sK19,X0))
| ~ ssList(X0) )
| ~ spl69_27 ),
inference(forward_demodulation,[],[f7323,f3064]) ).
fof(f3064,plain,
sK19 = app(sK66(sK19,sK18),sK18),
inference(subsumption_resolution,[],[f3063,f375]) ).
fof(f3063,plain,
( sK19 = app(sK66(sK19,sK18),sK18)
| ~ ssList(sK19) ),
inference(subsumption_resolution,[],[f3047,f374]) ).
fof(f374,plain,
ssList(sK18),
inference(cnf_transformation,[],[f254]) ).
fof(f3047,plain,
( sK19 = app(sK66(sK19,sK18),sK18)
| ~ ssList(sK18)
| ~ ssList(sK19) ),
inference(resolution,[],[f579,f638]) ).
fof(f638,plain,
rearsegP(sK19,sK18),
inference(forward_demodulation,[],[f637,f378]) ).
fof(f378,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f254]) ).
fof(f637,plain,
rearsegP(sK21,sK18),
inference(forward_demodulation,[],[f380,f379]) ).
fof(f379,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f254]) ).
fof(f380,plain,
rearsegP(sK21,sK20),
inference(cnf_transformation,[],[f254]) ).
fof(f579,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK66(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f368,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f366,f367]) ).
fof(f367,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f366,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,[],[f365]) ).
fof(f365,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,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f7323,plain,
( ! [X0] :
( segmentP(app(sK19,X0),sK18)
| ~ ssList(X0)
| ~ ssList(app(app(sK66(sK19,sK18),sK18),X0)) )
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f7322,f374]) ).
fof(f7322,plain,
( ! [X0] :
( segmentP(app(sK19,X0),sK18)
| ~ ssList(X0)
| ~ ssList(sK18)
| ~ ssList(app(app(sK66(sK19,sK18),sK18),X0)) )
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f7209,f3077]) ).
fof(f3077,plain,
( ssList(sK66(sK19,sK18))
| ~ spl69_27 ),
inference(avatar_component_clause,[],[f3076]) ).
fof(f3076,plain,
( spl69_27
<=> ssList(sK66(sK19,sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_27])]) ).
fof(f7209,plain,
! [X0] :
( segmentP(app(sK19,X0),sK18)
| ~ ssList(X0)
| ~ ssList(sK66(sK19,sK18))
| ~ ssList(sK18)
| ~ ssList(app(app(sK66(sK19,sK18),sK18),X0)) ),
inference(superposition,[],[f622,f3064]) ).
fof(f622,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,[],[f577]) ).
fof(f577,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,[],[f364]) ).
fof(f364,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
& ssList(sK65(X0,X1))
& ssList(sK64(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f361,f363,f362]) ).
fof(f362,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK64(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f363,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK64(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f361,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,[],[f360]) ).
fof(f360,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/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f6709,plain,
~ spl69_57,
inference(avatar_contradiction_clause,[],[f6708]) ).
fof(f6708,plain,
( $false
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6707,f390]) ).
fof(f6707,plain,
( ~ ssList(nil)
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6686,f597]) ).
fof(f597,plain,
ssItem(sK68),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
( sK67 != sK68
& ssItem(sK68)
& ssItem(sK67) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f2,f372,f371]) ).
fof(f371,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK67 != X1
& ssItem(X1) )
& ssItem(sK67) ) ),
introduced(choice_axiom,[]) ).
fof(f372,plain,
( ? [X1] :
( sK67 != X1
& ssItem(X1) )
=> ( sK67 != sK68
& ssItem(sK68) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f6686,plain,
( ~ ssItem(sK68)
| ~ ssList(nil)
| ~ spl69_57 ),
inference(trivial_inequality_removal,[],[f6678]) ).
fof(f6678,plain,
( nil != nil
| ~ ssItem(sK68)
| ~ ssList(nil)
| ~ spl69_57 ),
inference(superposition,[],[f554,f6637]) ).
fof(f6637,plain,
( nil = cons(sK68,nil)
| ~ spl69_57 ),
inference(avatar_component_clause,[],[f6635]) ).
fof(f6635,plain,
( spl69_57
<=> nil = cons(sK68,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_57])]) ).
fof(f554,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/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f6706,plain,
~ spl69_57,
inference(avatar_contradiction_clause,[],[f6705]) ).
fof(f6705,plain,
( $false
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6704,f390]) ).
fof(f6704,plain,
( ~ ssList(nil)
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6687,f597]) ).
fof(f6687,plain,
( ~ ssItem(sK68)
| ~ ssList(nil)
| ~ spl69_57 ),
inference(trivial_inequality_removal,[],[f6677]) ).
fof(f6677,plain,
( nil != nil
| ~ ssItem(sK68)
| ~ ssList(nil)
| ~ spl69_57 ),
inference(superposition,[],[f553,f6637]) ).
fof(f553,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/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f6697,plain,
( ~ spl69_21
| ~ spl69_57 ),
inference(avatar_contradiction_clause,[],[f6696]) ).
fof(f6696,plain,
( $false
| ~ spl69_21
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6695,f2351]) ).
fof(f2351,plain,
( ssList(cons(sK68,nil))
| ~ spl69_21 ),
inference(avatar_component_clause,[],[f2350]) ).
fof(f2350,plain,
( spl69_21
<=> ssList(cons(sK68,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_21])]) ).
fof(f6695,plain,
( ~ ssList(cons(sK68,nil))
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6694,f597]) ).
fof(f6694,plain,
( ~ ssItem(sK68)
| ~ ssList(cons(sK68,nil))
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6665,f382]) ).
fof(f382,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f6665,plain,
( singletonP(nil)
| ~ ssItem(sK68)
| ~ ssList(cons(sK68,nil))
| ~ spl69_57 ),
inference(superposition,[],[f607,f6637]) ).
fof(f607,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f466]) ).
fof(f466,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK26(X0),nil) = X0
& ssItem(sK26(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f282,f283]) ).
fof(f283,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK26(X0),nil) = X0
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f282,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f281]) ).
fof(f281,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/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f6693,plain,
( spl69_38
| ~ spl69_57 ),
inference(avatar_contradiction_clause,[],[f6692]) ).
fof(f6692,plain,
( $false
| spl69_38
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6691,f3687]) ).
fof(f3687,plain,
( sK19 != cons(sK68,sK19)
| spl69_38 ),
inference(avatar_component_clause,[],[f3686]) ).
fof(f3686,plain,
( spl69_38
<=> sK19 = cons(sK68,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_38])]) ).
fof(f6691,plain,
( sK19 = cons(sK68,sK19)
| ~ spl69_57 ),
inference(forward_demodulation,[],[f6654,f681]) ).
fof(f681,plain,
sK19 = app(nil,sK19),
inference(resolution,[],[f453,f375]) ).
fof(f453,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/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f6654,plain,
( app(nil,sK19) = cons(sK68,sK19)
| ~ spl69_57 ),
inference(superposition,[],[f2818,f6637]) ).
fof(f2818,plain,
cons(sK68,sK19) = app(cons(sK68,nil),sK19),
inference(resolution,[],[f1987,f597]) ).
fof(f1987,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK19) = app(cons(X0,nil),sK19) ),
inference(resolution,[],[f557,f375]) ).
fof(f557,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),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/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f6690,plain,
( spl69_26
| ~ spl69_57 ),
inference(avatar_contradiction_clause,[],[f6689]) ).
fof(f6689,plain,
( $false
| spl69_26
| ~ spl69_57 ),
inference(subsumption_resolution,[],[f6688,f2696]) ).
fof(f2696,plain,
( sK18 != cons(sK68,sK18)
| spl69_26 ),
inference(avatar_component_clause,[],[f2695]) ).
fof(f2695,plain,
( spl69_26
<=> sK18 = cons(sK68,sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_26])]) ).
fof(f6688,plain,
( sK18 = cons(sK68,sK18)
| ~ spl69_57 ),
inference(forward_demodulation,[],[f6645,f680]) ).
fof(f680,plain,
sK18 = app(nil,sK18),
inference(resolution,[],[f453,f374]) ).
fof(f6645,plain,
( app(nil,sK18) = cons(sK68,sK18)
| ~ spl69_57 ),
inference(superposition,[],[f2272,f6637]) ).
fof(f2272,plain,
cons(sK68,sK18) = app(cons(sK68,nil),sK18),
inference(resolution,[],[f1986,f597]) ).
fof(f1986,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK18) = app(cons(X0,nil),sK18) ),
inference(resolution,[],[f557,f374]) ).
fof(f6642,plain,
( spl69_57
| spl69_58
| ~ spl69_21 ),
inference(avatar_split_clause,[],[f2377,f2350,f6639,f6635]) ).
fof(f6639,plain,
( spl69_58
<=> sK68 = sK24(cons(sK68,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_58])]) ).
fof(f2377,plain,
( sK68 = sK24(cons(sK68,nil))
| nil = cons(sK68,nil)
| ~ spl69_21 ),
inference(forward_demodulation,[],[f2366,f1123]) ).
fof(f1123,plain,
sK68 = hd(cons(sK68,nil)),
inference(resolution,[],[f958,f597]) ).
fof(f958,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 ),
inference(resolution,[],[f556,f390]) ).
fof(f556,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/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f2366,plain,
( nil = cons(sK68,nil)
| hd(cons(sK68,nil)) = sK24(cons(sK68,nil))
| ~ spl69_21 ),
inference(resolution,[],[f2351,f461]) ).
fof(f461,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK24(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ( hd(X0) = sK24(X0)
& ssItem(sK24(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f157,f277]) ).
fof(f277,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK24(X0)
& ssItem(sK24(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/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f6478,plain,
~ spl69_55,
inference(avatar_contradiction_clause,[],[f6477]) ).
fof(f6477,plain,
( $false
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6476,f390]) ).
fof(f6476,plain,
( ~ ssList(nil)
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6455,f596]) ).
fof(f596,plain,
ssItem(sK67),
inference(cnf_transformation,[],[f373]) ).
fof(f6455,plain,
( ~ ssItem(sK67)
| ~ ssList(nil)
| ~ spl69_55 ),
inference(trivial_inequality_removal,[],[f6447]) ).
fof(f6447,plain,
( nil != nil
| ~ ssItem(sK67)
| ~ ssList(nil)
| ~ spl69_55 ),
inference(superposition,[],[f554,f6406]) ).
fof(f6406,plain,
( nil = cons(sK67,nil)
| ~ spl69_55 ),
inference(avatar_component_clause,[],[f6404]) ).
fof(f6404,plain,
( spl69_55
<=> nil = cons(sK67,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_55])]) ).
fof(f6475,plain,
~ spl69_55,
inference(avatar_contradiction_clause,[],[f6474]) ).
fof(f6474,plain,
( $false
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6473,f390]) ).
fof(f6473,plain,
( ~ ssList(nil)
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6456,f596]) ).
fof(f6456,plain,
( ~ ssItem(sK67)
| ~ ssList(nil)
| ~ spl69_55 ),
inference(trivial_inequality_removal,[],[f6446]) ).
fof(f6446,plain,
( nil != nil
| ~ ssItem(sK67)
| ~ ssList(nil)
| ~ spl69_55 ),
inference(superposition,[],[f553,f6406]) ).
fof(f6466,plain,
( ~ spl69_19
| ~ spl69_55 ),
inference(avatar_contradiction_clause,[],[f6465]) ).
fof(f6465,plain,
( $false
| ~ spl69_19
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6464,f2284]) ).
fof(f2284,plain,
( ssList(cons(sK67,nil))
| ~ spl69_19 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f2283,plain,
( spl69_19
<=> ssList(cons(sK67,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_19])]) ).
fof(f6464,plain,
( ~ ssList(cons(sK67,nil))
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6463,f596]) ).
fof(f6463,plain,
( ~ ssItem(sK67)
| ~ ssList(cons(sK67,nil))
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6434,f382]) ).
fof(f6434,plain,
( singletonP(nil)
| ~ ssItem(sK67)
| ~ ssList(cons(sK67,nil))
| ~ spl69_55 ),
inference(superposition,[],[f607,f6406]) ).
fof(f6462,plain,
( spl69_36
| ~ spl69_55 ),
inference(avatar_contradiction_clause,[],[f6461]) ).
fof(f6461,plain,
( $false
| spl69_36
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6460,f3633]) ).
fof(f3633,plain,
( sK19 != cons(sK67,sK19)
| spl69_36 ),
inference(avatar_component_clause,[],[f3632]) ).
fof(f3632,plain,
( spl69_36
<=> sK19 = cons(sK67,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_36])]) ).
fof(f6460,plain,
( sK19 = cons(sK67,sK19)
| ~ spl69_55 ),
inference(forward_demodulation,[],[f6423,f681]) ).
fof(f6423,plain,
( app(nil,sK19) = cons(sK67,sK19)
| ~ spl69_55 ),
inference(superposition,[],[f2817,f6406]) ).
fof(f2817,plain,
cons(sK67,sK19) = app(cons(sK67,nil),sK19),
inference(resolution,[],[f1987,f596]) ).
fof(f6459,plain,
( spl69_24
| ~ spl69_55 ),
inference(avatar_contradiction_clause,[],[f6458]) ).
fof(f6458,plain,
( $false
| spl69_24
| ~ spl69_55 ),
inference(subsumption_resolution,[],[f6457,f2665]) ).
fof(f2665,plain,
( sK18 != cons(sK67,sK18)
| spl69_24 ),
inference(avatar_component_clause,[],[f2664]) ).
fof(f2664,plain,
( spl69_24
<=> sK18 = cons(sK67,sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_24])]) ).
fof(f6457,plain,
( sK18 = cons(sK67,sK18)
| ~ spl69_55 ),
inference(forward_demodulation,[],[f6414,f680]) ).
fof(f6414,plain,
( app(nil,sK18) = cons(sK67,sK18)
| ~ spl69_55 ),
inference(superposition,[],[f2271,f6406]) ).
fof(f2271,plain,
cons(sK67,sK18) = app(cons(sK67,nil),sK18),
inference(resolution,[],[f1986,f596]) ).
fof(f6411,plain,
( spl69_55
| spl69_56
| ~ spl69_19 ),
inference(avatar_split_clause,[],[f2310,f2283,f6408,f6404]) ).
fof(f6408,plain,
( spl69_56
<=> sK67 = sK24(cons(sK67,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_56])]) ).
fof(f2310,plain,
( sK67 = sK24(cons(sK67,nil))
| nil = cons(sK67,nil)
| ~ spl69_19 ),
inference(forward_demodulation,[],[f2299,f1122]) ).
fof(f1122,plain,
sK67 = hd(cons(sK67,nil)),
inference(resolution,[],[f958,f596]) ).
fof(f2299,plain,
( nil = cons(sK67,nil)
| hd(cons(sK67,nil)) = sK24(cons(sK67,nil))
| ~ spl69_19 ),
inference(resolution,[],[f2284,f461]) ).
fof(f6207,plain,
( spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51
| spl69_53 ),
inference(avatar_contradiction_clause,[],[f6206]) ).
fof(f6206,plain,
( $false
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51
| spl69_53 ),
inference(subsumption_resolution,[],[f6205,f375]) ).
fof(f6205,plain,
( ~ ssList(sK19)
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51
| spl69_53 ),
inference(subsumption_resolution,[],[f6204,f6123]) ).
fof(f6123,plain,
( singletonP(sK19)
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51 ),
inference(subsumption_resolution,[],[f6122,f5274]) ).
fof(f5274,plain,
( ssList(cons(hd(sK19),nil))
| ~ spl69_45 ),
inference(avatar_component_clause,[],[f5273]) ).
fof(f5273,plain,
( spl69_45
<=> ssList(cons(hd(sK19),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_45])]) ).
fof(f6122,plain,
( singletonP(sK19)
| ~ ssList(cons(hd(sK19),nil))
| spl69_4
| ~ spl69_11
| ~ spl69_51 ),
inference(subsumption_resolution,[],[f6098,f1600]) ).
fof(f1600,plain,
( ssItem(hd(sK19))
| ~ spl69_11 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f1599,plain,
( spl69_11
<=> ssItem(hd(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_11])]) ).
fof(f6098,plain,
( singletonP(sK19)
| ~ ssItem(hd(sK19))
| ~ ssList(cons(hd(sK19),nil))
| spl69_4
| ~ spl69_51 ),
inference(superposition,[],[f607,f6071]) ).
fof(f6071,plain,
( sK19 = cons(hd(sK19),nil)
| spl69_4
| ~ spl69_51 ),
inference(superposition,[],[f1552,f6065]) ).
fof(f6065,plain,
( nil = tl(sK19)
| ~ spl69_51 ),
inference(avatar_component_clause,[],[f6063]) ).
fof(f6063,plain,
( spl69_51
<=> nil = tl(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_51])]) ).
fof(f1552,plain,
( sK19 = cons(hd(sK19),tl(sK19))
| spl69_4 ),
inference(subsumption_resolution,[],[f1519,f827]) ).
fof(f827,plain,
( nil != sK19
| spl69_4 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f826,plain,
( spl69_4
<=> nil = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_4])]) ).
fof(f1519,plain,
( nil = sK19
| sK19 = cons(hd(sK19),tl(sK19)) ),
inference(resolution,[],[f459,f375]) ).
fof(f459,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/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f6204,plain,
( ~ singletonP(sK19)
| ~ ssList(sK19)
| spl69_53 ),
inference(resolution,[],[f6197,f464]) ).
fof(f464,plain,
! [X0] :
( ssItem(sK26(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f6197,plain,
( ~ ssItem(sK26(sK19))
| spl69_53 ),
inference(avatar_component_clause,[],[f6195]) ).
fof(f6195,plain,
( spl69_53
<=> ssItem(sK26(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_53])]) ).
fof(f6202,plain,
( ~ spl69_53
| spl69_54
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51 ),
inference(avatar_split_clause,[],[f6190,f6063,f5273,f1599,f826,f6199,f6195]) ).
fof(f6199,plain,
( spl69_54
<=> memberP(sK19,sK26(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_54])]) ).
fof(f6190,plain,
( memberP(sK19,sK26(sK19))
| ~ ssItem(sK26(sK19))
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51 ),
inference(subsumption_resolution,[],[f6180,f390]) ).
fof(f6180,plain,
( memberP(sK19,sK26(sK19))
| ~ ssList(nil)
| ~ ssItem(sK26(sK19))
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51 ),
inference(superposition,[],[f629,f6147]) ).
fof(f6147,plain,
( sK19 = cons(sK26(sK19),nil)
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51 ),
inference(subsumption_resolution,[],[f6144,f375]) ).
fof(f6144,plain,
( sK19 = cons(sK26(sK19),nil)
| ~ ssList(sK19)
| spl69_4
| ~ spl69_11
| ~ spl69_45
| ~ spl69_51 ),
inference(resolution,[],[f6123,f465]) ).
fof(f465,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK26(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f629,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f601]) ).
fof(f601,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f422]) ).
fof(f422,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,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,[],[f260]) ).
fof(f260,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/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f6070,plain,
( spl69_51
| spl69_52
| spl69_4
| ~ spl69_7
| ~ spl69_11
| ~ spl69_15 ),
inference(avatar_split_clause,[],[f4346,f1810,f1599,f1496,f826,f6067,f6063]) ).
fof(f6067,plain,
( spl69_52
<=> hd(tl(sK19)) = sK24(tl(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_52])]) ).
fof(f1496,plain,
( spl69_7
<=> ssItem(sK23(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_7])]) ).
fof(f1810,plain,
( spl69_15
<=> ssList(sK22(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_15])]) ).
fof(f4346,plain,
( hd(tl(sK19)) = sK24(tl(sK19))
| nil = tl(sK19)
| spl69_4
| ~ spl69_7
| ~ spl69_11
| ~ spl69_15 ),
inference(forward_demodulation,[],[f4345,f2091]) ).
fof(f2091,plain,
( tl(sK19) = sK22(sK19)
| spl69_4
| ~ spl69_7
| ~ spl69_11
| ~ spl69_15 ),
inference(forward_demodulation,[],[f2069,f1880]) ).
fof(f1880,plain,
( sK19 = cons(hd(sK19),sK22(sK19))
| spl69_4
| ~ spl69_7
| ~ spl69_15 ),
inference(superposition,[],[f1449,f1877]) ).
fof(f1877,plain,
( hd(sK19) = sK23(sK19)
| spl69_4
| ~ spl69_7
| ~ spl69_15 ),
inference(forward_demodulation,[],[f1857,f1449]) ).
fof(f1857,plain,
( sK23(sK19) = hd(cons(sK23(sK19),sK22(sK19)))
| ~ spl69_7
| ~ spl69_15 ),
inference(resolution,[],[f1829,f1497]) ).
fof(f1497,plain,
( ssItem(sK23(sK19))
| ~ spl69_7 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1829,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22(sK19))) = X0 )
| ~ spl69_15 ),
inference(resolution,[],[f1811,f556]) ).
fof(f1811,plain,
( ssList(sK22(sK19))
| ~ spl69_15 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f1449,plain,
( sK19 = cons(sK23(sK19),sK22(sK19))
| spl69_4 ),
inference(subsumption_resolution,[],[f1416,f827]) ).
fof(f1416,plain,
( nil = sK19
| sK19 = cons(sK23(sK19),sK22(sK19)) ),
inference(resolution,[],[f456,f375]) ).
fof(f456,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK23(X0),sK22(X0)) = X0 ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0] :
( ( cons(sK23(X0),sK22(X0)) = X0
& ssItem(sK23(X0))
& ssList(sK22(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f149,f275,f274]) ).
fof(f274,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK22(X0)) = X0
& ssItem(X2) )
& ssList(sK22(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f275,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK22(X0)) = X0
& ssItem(X2) )
=> ( cons(sK23(X0),sK22(X0)) = X0
& ssItem(sK23(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/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f2069,plain,
( sK22(sK19) = tl(cons(hd(sK19),sK22(sK19)))
| ~ spl69_11
| ~ spl69_15 ),
inference(resolution,[],[f1828,f1600]) ).
fof(f1828,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK22(sK19) = tl(cons(X0,sK22(sK19))) )
| ~ spl69_15 ),
inference(resolution,[],[f1811,f555]) ).
fof(f555,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/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f4345,plain,
( nil = tl(sK19)
| hd(sK22(sK19)) = sK24(sK22(sK19))
| spl69_4
| ~ spl69_7
| ~ spl69_11
| ~ spl69_15 ),
inference(forward_demodulation,[],[f1826,f2091]) ).
fof(f1826,plain,
( nil = sK22(sK19)
| hd(sK22(sK19)) = sK24(sK22(sK19))
| ~ spl69_15 ),
inference(resolution,[],[f1811,f461]) ).
fof(f6057,plain,
( spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47
| spl69_49 ),
inference(avatar_contradiction_clause,[],[f6056]) ).
fof(f6056,plain,
( $false
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47
| spl69_49 ),
inference(subsumption_resolution,[],[f6055,f374]) ).
fof(f6055,plain,
( ~ ssList(sK18)
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47
| spl69_49 ),
inference(subsumption_resolution,[],[f6054,f5974]) ).
fof(f5974,plain,
( singletonP(sK18)
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47 ),
inference(subsumption_resolution,[],[f5973,f4371]) ).
fof(f4371,plain,
( ssList(cons(hd(sK18),nil))
| ~ spl69_41 ),
inference(avatar_component_clause,[],[f4370]) ).
fof(f4370,plain,
( spl69_41
<=> ssList(cons(hd(sK18),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_41])]) ).
fof(f5973,plain,
( singletonP(sK18)
| ~ ssList(cons(hd(sK18),nil))
| spl69_2
| ~ spl69_9
| ~ spl69_47 ),
inference(subsumption_resolution,[],[f5949,f1581]) ).
fof(f1581,plain,
( ssItem(hd(sK18))
| ~ spl69_9 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1580,plain,
( spl69_9
<=> ssItem(hd(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_9])]) ).
fof(f5949,plain,
( singletonP(sK18)
| ~ ssItem(hd(sK18))
| ~ ssList(cons(hd(sK18),nil))
| spl69_2
| ~ spl69_47 ),
inference(superposition,[],[f607,f5922]) ).
fof(f5922,plain,
( sK18 = cons(hd(sK18),nil)
| spl69_2
| ~ spl69_47 ),
inference(superposition,[],[f1551,f5916]) ).
fof(f5916,plain,
( nil = tl(sK18)
| ~ spl69_47 ),
inference(avatar_component_clause,[],[f5914]) ).
fof(f5914,plain,
( spl69_47
<=> nil = tl(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_47])]) ).
fof(f1551,plain,
( sK18 = cons(hd(sK18),tl(sK18))
| spl69_2 ),
inference(subsumption_resolution,[],[f1518,f809]) ).
fof(f809,plain,
( nil != sK18
| spl69_2 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f808,plain,
( spl69_2
<=> nil = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_2])]) ).
fof(f1518,plain,
( nil = sK18
| sK18 = cons(hd(sK18),tl(sK18)) ),
inference(resolution,[],[f459,f374]) ).
fof(f6054,plain,
( ~ singletonP(sK18)
| ~ ssList(sK18)
| spl69_49 ),
inference(resolution,[],[f6048,f464]) ).
fof(f6048,plain,
( ~ ssItem(sK26(sK18))
| spl69_49 ),
inference(avatar_component_clause,[],[f6046]) ).
fof(f6046,plain,
( spl69_49
<=> ssItem(sK26(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_49])]) ).
fof(f6053,plain,
( ~ spl69_49
| spl69_50
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47 ),
inference(avatar_split_clause,[],[f6041,f5914,f4370,f1580,f808,f6050,f6046]) ).
fof(f6050,plain,
( spl69_50
<=> memberP(sK18,sK26(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_50])]) ).
fof(f6041,plain,
( memberP(sK18,sK26(sK18))
| ~ ssItem(sK26(sK18))
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47 ),
inference(subsumption_resolution,[],[f6031,f390]) ).
fof(f6031,plain,
( memberP(sK18,sK26(sK18))
| ~ ssList(nil)
| ~ ssItem(sK26(sK18))
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47 ),
inference(superposition,[],[f629,f5998]) ).
fof(f5998,plain,
( sK18 = cons(sK26(sK18),nil)
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47 ),
inference(subsumption_resolution,[],[f5995,f374]) ).
fof(f5995,plain,
( sK18 = cons(sK26(sK18),nil)
| ~ ssList(sK18)
| spl69_2
| ~ spl69_9
| ~ spl69_41
| ~ spl69_47 ),
inference(resolution,[],[f5974,f465]) ).
fof(f5921,plain,
( spl69_47
| spl69_48
| spl69_2
| ~ spl69_5
| ~ spl69_9
| ~ spl69_13 ),
inference(avatar_split_clause,[],[f3984,f1710,f1580,f1477,f808,f5918,f5914]) ).
fof(f5918,plain,
( spl69_48
<=> hd(tl(sK18)) = sK24(tl(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_48])]) ).
fof(f1477,plain,
( spl69_5
<=> ssItem(sK23(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).
fof(f1710,plain,
( spl69_13
<=> ssList(sK22(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_13])]) ).
fof(f3984,plain,
( hd(tl(sK18)) = sK24(tl(sK18))
| nil = tl(sK18)
| spl69_2
| ~ spl69_5
| ~ spl69_9
| ~ spl69_13 ),
inference(forward_demodulation,[],[f3983,f1936]) ).
fof(f1936,plain,
( tl(sK18) = sK22(sK18)
| spl69_2
| ~ spl69_5
| ~ spl69_9
| ~ spl69_13 ),
inference(forward_demodulation,[],[f1913,f1768]) ).
fof(f1768,plain,
( sK18 = cons(hd(sK18),sK22(sK18))
| spl69_2
| ~ spl69_5
| ~ spl69_13 ),
inference(superposition,[],[f1448,f1765]) ).
fof(f1765,plain,
( hd(sK18) = sK23(sK18)
| spl69_2
| ~ spl69_5
| ~ spl69_13 ),
inference(forward_demodulation,[],[f1745,f1448]) ).
fof(f1745,plain,
( sK23(sK18) = hd(cons(sK23(sK18),sK22(sK18)))
| ~ spl69_5
| ~ spl69_13 ),
inference(resolution,[],[f1729,f1478]) ).
fof(f1478,plain,
( ssItem(sK23(sK18))
| ~ spl69_5 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f1729,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22(sK18))) = X0 )
| ~ spl69_13 ),
inference(resolution,[],[f1711,f556]) ).
fof(f1711,plain,
( ssList(sK22(sK18))
| ~ spl69_13 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f1448,plain,
( sK18 = cons(sK23(sK18),sK22(sK18))
| spl69_2 ),
inference(subsumption_resolution,[],[f1415,f809]) ).
fof(f1415,plain,
( nil = sK18
| sK18 = cons(sK23(sK18),sK22(sK18)) ),
inference(resolution,[],[f456,f374]) ).
fof(f1913,plain,
( sK22(sK18) = tl(cons(hd(sK18),sK22(sK18)))
| ~ spl69_9
| ~ spl69_13 ),
inference(resolution,[],[f1728,f1581]) ).
fof(f1728,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK22(sK18) = tl(cons(X0,sK22(sK18))) )
| ~ spl69_13 ),
inference(resolution,[],[f1711,f555]) ).
fof(f3983,plain,
( nil = tl(sK18)
| hd(sK22(sK18)) = sK24(sK22(sK18))
| spl69_2
| ~ spl69_5
| ~ spl69_9
| ~ spl69_13 ),
inference(forward_demodulation,[],[f1726,f1936]) ).
fof(f1726,plain,
( nil = sK22(sK18)
| hd(sK22(sK18)) = sK24(sK22(sK18))
| ~ spl69_13 ),
inference(resolution,[],[f1711,f461]) ).
fof(f5284,plain,
( ~ spl69_11
| spl69_45 ),
inference(avatar_contradiction_clause,[],[f5283]) ).
fof(f5283,plain,
( $false
| ~ spl69_11
| spl69_45 ),
inference(subsumption_resolution,[],[f5282,f390]) ).
fof(f5282,plain,
( ~ ssList(nil)
| ~ spl69_11
| spl69_45 ),
inference(subsumption_resolution,[],[f5281,f1600]) ).
fof(f5281,plain,
( ~ ssItem(hd(sK19))
| ~ ssList(nil)
| spl69_45 ),
inference(resolution,[],[f5275,f552]) ).
fof(f552,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/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f5275,plain,
( ~ ssList(cons(hd(sK19),nil))
| spl69_45 ),
inference(avatar_component_clause,[],[f5273]) ).
fof(f5280,plain,
( ~ spl69_45
| spl69_46
| ~ spl69_11 ),
inference(avatar_split_clause,[],[f5259,f1599,f5277,f5273]) ).
fof(f5277,plain,
( spl69_46
<=> ssList(cons(hd(sK19),sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_46])]) ).
fof(f5259,plain,
( ssList(cons(hd(sK19),sK18))
| ~ ssList(cons(hd(sK19),nil))
| ~ spl69_11 ),
inference(subsumption_resolution,[],[f5245,f374]) ).
fof(f5245,plain,
( ssList(cons(hd(sK19),sK18))
| ~ ssList(sK18)
| ~ ssList(cons(hd(sK19),nil))
| ~ spl69_11 ),
inference(superposition,[],[f562,f2251]) ).
fof(f2251,plain,
( cons(hd(sK19),sK18) = app(cons(hd(sK19),nil),sK18)
| ~ spl69_11 ),
inference(resolution,[],[f1986,f1600]) ).
fof(f562,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/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f5112,plain,
spl69_43,
inference(avatar_contradiction_clause,[],[f5111]) ).
fof(f5111,plain,
( $false
| spl69_43 ),
inference(subsumption_resolution,[],[f5110,f390]) ).
fof(f5110,plain,
( ~ ssList(nil)
| spl69_43 ),
inference(subsumption_resolution,[],[f5109,f631]) ).
fof(f631,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f381,f380,f379,f378,f377,f376,f375,f374,f382,f383,f384,f385,f386,f387,f388,f389,f390,f391,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f410,f409,f412,f411,f415,f414,f630,f416,f417,f418,f419,f420,f423,f629,f421,f628,f425,f424,f428,f427,f433,f603,f431,f430,f434,f436,f435,f441,f605,f439,f438,f442,f445,f444,f443,f446,f447,f448,f449,f450,f451,f452,f453,f456,f455,f454,f457,f458,f459,f461,f460,f463,f462,f607,f465,f464,f467,f475,f474,f473,f472,f471,f470,f608,f476,f477,f486,f485,f484,f483,f482,f481,f480,f627,f487,f488,f498,f497,f496,f495,f494,f493,f492,f491,f611,f499,f500,f510,f509,f508,f507,f506,f505,f504,f503,f612,f511,f512,f522,f521,f520,f519,f518,f517,f516,f515,f613,f523,f525,f524,f533,f532,f531,f530,f529,f528,f527,f614,f534,f536,f535,f544,f543,f542,f541,f540,f539,f538,f615,f545,f616]) ).
fof(f616,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f545,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/sandbox/benchmark/theBenchmark.p',ax12) ).
fof(f615,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,[],[f537]) ).
fof(f537,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,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ( sP16(X0)
| ( ~ lt(sK56(X0),sK57(X0))
& app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),sK60(X0))) = X0
& ssList(sK60(X0))
& ssList(sK59(X0))
& ssList(sK58(X0))
& ssItem(sK57(X0))
& ssItem(sK56(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,[sK56,sK57,sK58,sK59,sK60])],[f340,f345,f344,f343,f342,f341]) ).
fof(f341,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(sK56(X0),X2)
& app(app(X3,cons(sK56(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK56(X0),X2)
& app(app(X3,cons(sK56(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK56(X0),sK57(X0))
& app(app(X3,cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK56(X0),sK57(X0))
& app(app(X3,cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK56(X0),sK57(X0))
& app(app(sK58(X0),cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK56(X0),sK57(X0))
& app(app(sK58(X0),cons(sK56(X0),X4)),cons(sK57(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK56(X0),sK57(X0))
& app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),X5)) = X0
& ssList(X5) )
& ssList(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK56(X0),sK57(X0))
& app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK56(X0),sK57(X0))
& app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),sK60(X0))) = X0
& ssList(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f340,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,[],[f339]) ).
fof(f339,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(f538,plain,
! [X0] :
( ssItem(sK56(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f539,plain,
! [X0] :
( ssItem(sK57(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f540,plain,
! [X0] :
( ssList(sK58(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f541,plain,
! [X0] :
( ssList(sK59(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f542,plain,
! [X0] :
( ssList(sK60(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f543,plain,
! [X0] :
( sP16(X0)
| app(app(sK58(X0),cons(sK56(X0),sK59(X0))),cons(sK57(X0),sK60(X0))) = X0 ),
inference(cnf_transformation,[],[f346]) ).
fof(f544,plain,
! [X0] :
( ~ lt(sK56(X0),sK57(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f535,plain,
! [X0] :
( ~ sP17(X0)
| ~ strictorderedP(X0)
| sP16(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ strictorderedP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f248]) ).
fof(f536,plain,
! [X0] :
( ~ sP17(X0)
| ~ sP16(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f338]) ).
fof(f534,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/sandbox/benchmark/theBenchmark.p',ax11) ).
fof(f614,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,[],[f526]) ).
fof(f526,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,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ( sP14(X0)
| ( ~ leq(sK51(X0),sK52(X0))
& app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),sK55(X0))) = X0
& ssList(sK55(X0))
& ssList(sK54(X0))
& ssList(sK53(X0))
& ssItem(sK52(X0))
& ssItem(sK51(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,[sK51,sK52,sK53,sK54,sK55])],[f331,f336,f335,f334,f333,f332]) ).
fof(f332,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(sK51(X0),X2)
& app(app(X3,cons(sK51(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f333,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK51(X0),X2)
& app(app(X3,cons(sK51(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK51(X0),sK52(X0))
& app(app(X3,cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK51(X0),sK52(X0))
& app(app(X3,cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK51(X0),sK52(X0))
& app(app(sK53(X0),cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK51(X0),sK52(X0))
& app(app(sK53(X0),cons(sK51(X0),X4)),cons(sK52(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK51(X0),sK52(X0))
& app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),X5)) = X0
& ssList(X5) )
& ssList(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK51(X0),sK52(X0))
& app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK51(X0),sK52(X0))
& app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),sK55(X0))) = X0
& ssList(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f331,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,[],[f330]) ).
fof(f330,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(f527,plain,
! [X0] :
( ssItem(sK51(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f528,plain,
! [X0] :
( ssItem(sK52(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f529,plain,
! [X0] :
( ssList(sK53(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f530,plain,
! [X0] :
( ssList(sK54(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f531,plain,
! [X0] :
( ssList(sK55(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f532,plain,
! [X0] :
( sP14(X0)
| app(app(sK53(X0),cons(sK51(X0),sK54(X0))),cons(sK52(X0),sK55(X0))) = X0 ),
inference(cnf_transformation,[],[f337]) ).
fof(f533,plain,
! [X0] :
( ~ leq(sK51(X0),sK52(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f524,plain,
! [X0] :
( ~ sP15(X0)
| ~ totalorderedP(X0)
| sP14(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f329,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ totalorderedP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f525,plain,
! [X0] :
( ~ sP15(X0)
| ~ sP14(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f523,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/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f613,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,[],[f514]) ).
fof(f514,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,[],[f328]) ).
fof(f328,plain,
! [X0] :
( ( sP12(X0)
| ( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),sK50(X0))) = X0
& ssList(sK50(X0))
& ssList(sK49(X0))
& ssList(sK48(X0))
& ssItem(sK47(X0))
& ssItem(sK46(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,[sK46,sK47,sK48,sK49,sK50])],[f322,f327,f326,f325,f324,f323]) ).
fof(f323,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,sK46(X0))
& leq(sK46(X0),X2)
& app(app(X3,cons(sK46(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK46(X0))
& leq(sK46(X0),X2)
& app(app(X3,cons(sK46(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(X3,cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(X3,cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(sK48(X0),cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(sK48(X0),cons(sK46(X0),X4)),cons(sK47(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),X5)) = X0
& ssList(X5) )
& ssList(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ? [X5] :
( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK47(X0),sK46(X0))
& leq(sK46(X0),sK47(X0))
& app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),sK50(X0))) = X0
& ssList(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f322,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,[],[f321]) ).
fof(f321,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(f515,plain,
! [X0] :
( ssItem(sK46(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f516,plain,
! [X0] :
( ssItem(sK47(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f517,plain,
! [X0] :
( ssList(sK48(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f518,plain,
! [X0] :
( ssList(sK49(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f519,plain,
! [X0] :
( ssList(sK50(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f520,plain,
! [X0] :
( sP12(X0)
| app(app(sK48(X0),cons(sK46(X0),sK49(X0))),cons(sK47(X0),sK50(X0))) = X0 ),
inference(cnf_transformation,[],[f328]) ).
fof(f521,plain,
! [X0] :
( leq(sK46(X0),sK47(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f522,plain,
! [X0] :
( leq(sK47(X0),sK46(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f512,plain,
! [X0] :
( ~ sP13(X0)
| ~ cyclefreeP(X0)
| sP12(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP12(X0) )
& ( sP12(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f242]) ).
fof(f511,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/sandbox/benchmark/theBenchmark.p',ax10) ).
fof(f612,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,[],[f502]) ).
fof(f502,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,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ( sP10(X0)
| ( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),sK45(X0))) = X0
& ssList(sK45(X0))
& ssList(sK44(X0))
& ssList(sK43(X0))
& ssItem(sK42(X0))
& ssItem(sK41(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,[sK41,sK42,sK43,sK44,sK45])],[f313,f318,f317,f316,f315,f314]) ).
fof(f314,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,sK41(X0))
& ~ lt(sK41(X0),X2)
& app(app(X3,cons(sK41(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f315,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK41(X0))
& ~ lt(sK41(X0),X2)
& app(app(X3,cons(sK41(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(X3,cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(X3,cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(sK43(X0),cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(sK43(X0),cons(sK41(X0),X4)),cons(sK42(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),X5)) = X0
& ssList(X5) )
& ssList(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK42(X0),sK41(X0))
& ~ lt(sK41(X0),sK42(X0))
& app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),sK45(X0))) = X0
& ssList(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f313,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,[],[f312]) ).
fof(f312,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(f503,plain,
! [X0] :
( ssItem(sK41(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f504,plain,
! [X0] :
( ssItem(sK42(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f505,plain,
! [X0] :
( ssList(sK43(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f506,plain,
! [X0] :
( ssList(sK44(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f507,plain,
! [X0] :
( ssList(sK45(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f508,plain,
! [X0] :
( sP10(X0)
| app(app(sK43(X0),cons(sK41(X0),sK44(X0))),cons(sK42(X0),sK45(X0))) = X0 ),
inference(cnf_transformation,[],[f319]) ).
fof(f509,plain,
! [X0] :
( ~ lt(sK41(X0),sK42(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f510,plain,
! [X0] :
( ~ lt(sK42(X0),sK41(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f500,plain,
! [X0] :
( ~ sP11(X0)
| ~ strictorderP(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP10(X0) )
& ( sP10(X0)
| ~ strictorderP(X0) ) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f239]) ).
fof(f499,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/sandbox/benchmark/theBenchmark.p',ax9) ).
fof(f611,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,[],[f490]) ).
fof(f490,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,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ( sP8(X0)
| ( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),sK40(X0))) = X0
& ssList(sK40(X0))
& ssList(sK39(X0))
& ssList(sK38(X0))
& ssItem(sK37(X0))
& ssItem(sK36(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,[sK36,sK37,sK38,sK39,sK40])],[f304,f309,f308,f307,f306,f305]) ).
fof(f305,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,sK36(X0))
& ~ leq(sK36(X0),X2)
& app(app(X3,cons(sK36(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f306,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK36(X0))
& ~ leq(sK36(X0),X2)
& app(app(X3,cons(sK36(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(X3,cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(X3,cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(sK38(X0),cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(sK38(X0),cons(sK36(X0),X4)),cons(sK37(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),X5)) = X0
& ssList(X5) )
& ssList(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK37(X0),sK36(X0))
& ~ leq(sK36(X0),sK37(X0))
& app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),sK40(X0))) = X0
& ssList(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f304,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,[],[f303]) ).
fof(f303,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(f491,plain,
! [X0] :
( ssItem(sK36(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f492,plain,
! [X0] :
( ssItem(sK37(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f493,plain,
! [X0] :
( ssList(sK38(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f494,plain,
! [X0] :
( ssList(sK39(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f495,plain,
! [X0] :
( ssList(sK40(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f496,plain,
! [X0] :
( sP8(X0)
| app(app(sK38(X0),cons(sK36(X0),sK39(X0))),cons(sK37(X0),sK40(X0))) = X0 ),
inference(cnf_transformation,[],[f310]) ).
fof(f497,plain,
! [X0] :
( ~ leq(sK36(X0),sK37(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f498,plain,
! [X0] :
( ~ leq(sK37(X0),sK36(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f488,plain,
! [X0] :
( ~ sP9(X0)
| ~ totalorderP(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ totalorderP(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f236]) ).
fof(f487,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/sandbox/benchmark/theBenchmark.p',ax13) ).
fof(f627,plain,
! [X10,X8,X9,X7] :
( ~ sP6(app(app(X8,cons(X7,X9)),cons(X7,X10)))
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssList(X10) ),
inference(duplicate_literal_removal,[],[f610]) ).
fof(f610,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,[],[f609]) ).
fof(f609,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,[],[f479]) ).
fof(f479,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,[],[f301]) ).
fof(f301,plain,
! [X0] :
( ( sP6(X0)
| ( sK31(X0) = sK32(X0)
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
& ssList(sK35(X0))
& ssList(sK34(X0))
& ssList(sK33(X0))
& ssItem(sK32(X0))
& ssItem(sK31(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,[sK31,sK32,sK33,sK34,sK35])],[f295,f300,f299,f298,f297,f296]) ).
fof(f296,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] :
( sK31(X0) = X2
& app(app(X3,cons(sK31(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f297,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK31(X0) = X2
& app(app(X3,cons(sK31(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK31(X0) = sK32(X0)
& app(app(X3,cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK31(X0) = sK32(X0)
& app(app(X3,cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK31(X0) = sK32(X0)
& app(app(sK33(X0),cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK31(X0) = sK32(X0)
& app(app(sK33(X0),cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK31(X0) = sK32(X0)
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f300,plain,
! [X0] :
( ? [X5] :
( sK31(X0) = sK32(X0)
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),X5)) = X0
& ssList(X5) )
=> ( sK31(X0) = sK32(X0)
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
& ssList(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f295,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,[],[f294]) ).
fof(f294,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(f480,plain,
! [X0] :
( ssItem(sK31(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f481,plain,
! [X0] :
( ssItem(sK32(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f482,plain,
! [X0] :
( ssList(sK33(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f483,plain,
! [X0] :
( ssList(sK34(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f484,plain,
! [X0] :
( ssList(sK35(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f485,plain,
! [X0] :
( sP6(X0)
| app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0 ),
inference(cnf_transformation,[],[f301]) ).
fof(f486,plain,
! [X0] :
( sP6(X0)
| sK31(X0) = sK32(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f477,plain,
! [X0] :
( ~ sP7(X0)
| ~ duplicatefreeP(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f476,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/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f608,plain,
! [X8,X6,X7,X5] :
( ~ sP4(app(X7,cons(X5,cons(X6,X8))))
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| X5 = X6 ),
inference(equality_resolution,[],[f469]) ).
fof(f469,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,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ( sP4(X0)
| ( sK27(X0) != sK28(X0)
& app(sK29(X0),cons(sK27(X0),cons(sK28(X0),sK30(X0)))) = X0
& ssList(sK30(X0))
& ssList(sK29(X0))
& ssItem(sK28(X0))
& ssItem(sK27(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,[sK27,sK28,sK29,sK30])],[f287,f291,f290,f289,f288]) ).
fof(f288,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] :
( sK27(X0) != X2
& app(X3,cons(sK27(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f289,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK27(X0) != X2
& app(X3,cons(sK27(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK27(X0) != sK28(X0)
& app(X3,cons(sK27(X0),cons(sK28(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f290,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK27(X0) != sK28(X0)
& app(X3,cons(sK27(X0),cons(sK28(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK27(X0) != sK28(X0)
& app(sK29(X0),cons(sK27(X0),cons(sK28(X0),X4))) = X0
& ssList(X4) )
& ssList(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f291,plain,
! [X0] :
( ? [X4] :
( sK27(X0) != sK28(X0)
& app(sK29(X0),cons(sK27(X0),cons(sK28(X0),X4))) = X0
& ssList(X4) )
=> ( sK27(X0) != sK28(X0)
& app(sK29(X0),cons(sK27(X0),cons(sK28(X0),sK30(X0)))) = X0
& ssList(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f287,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,[],[f286]) ).
fof(f286,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(f470,plain,
! [X0] :
( ssItem(sK27(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f471,plain,
! [X0] :
( ssItem(sK28(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f472,plain,
! [X0] :
( ssList(sK29(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f473,plain,
! [X0] :
( ssList(sK30(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f474,plain,
! [X0] :
( sP4(X0)
| app(sK29(X0),cons(sK27(X0),cons(sK28(X0),sK30(X0)))) = X0 ),
inference(cnf_transformation,[],[f292]) ).
fof(f475,plain,
! [X0] :
( sK27(X0) != sK28(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f467,plain,
! [X0] :
( ~ sP5(X0)
| ~ equalelemsP(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ equalelemsP(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f230]) ).
fof(f462,plain,
! [X0] :
( ssList(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ( tl(X0) = sK25(X0)
& ssList(sK25(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f159,f279]) ).
fof(f279,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK25(X0)
& ssList(sK25(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/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f463,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK25(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f460,plain,
! [X0] :
( ssItem(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f458,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/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f457,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/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f454,plain,
! [X0] :
( ssList(sK22(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f455,plain,
! [X0] :
( ssItem(sK23(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f451,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f450,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f449,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f448,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f447,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f446,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f443,plain,
! [X2,X0,X1] :
( ~ memberP(app(X1,X2),X0)
| memberP(X1,X0)
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,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,[],[f272]) ).
fof(f272,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/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f444,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f445,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f442,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/sandbox/benchmark/theBenchmark.p',ax70) ).
fof(f438,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,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,[],[f270]) ).
fof(f270,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,[],[f269]) ).
fof(f269,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(f439,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f605,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f440]) ).
fof(f440,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f271]) ).
fof(f441,plain,
! [X0,X1] :
( ~ lt(X1,hd(X0))
| sP2(X0,X1)
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f271]) ).
fof(f435,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f268]) ).
fof(f268,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(f436,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f268]) ).
fof(f434,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/sandbox/benchmark/theBenchmark.p',ax67) ).
fof(f430,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,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,[],[f266]) ).
fof(f266,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,[],[f265]) ).
fof(f265,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(f431,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f603,plain,
! [X1] : sP0(nil,X1),
inference(equality_resolution,[],[f432]) ).
fof(f432,plain,
! [X0,X1] :
( sP0(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f267]) ).
fof(f433,plain,
! [X0,X1] :
( ~ leq(X1,hd(X0))
| sP0(X0,X1)
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f267]) ).
fof(f427,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,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(f428,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f264]) ).
fof(f424,plain,
! [X2,X3,X0,X1] :
( ~ frontsegP(cons(X0,X2),cons(X1,X3))
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,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,[],[f262]) ).
fof(f262,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/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f425,plain,
! [X2,X3,X0,X1] :
( ~ frontsegP(cons(X0,X2),cons(X1,X3))
| frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f628,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f602]) ).
fof(f602,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,[],[f426]) ).
fof(f426,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,[],[f263]) ).
fof(f421,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| X0 = X1
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f423,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f420,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,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/sandbox/benchmark/theBenchmark.p',ax34) ).
fof(f419,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,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/sandbox/benchmark/theBenchmark.p',ax91) ).
fof(f418,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| leq(X0,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/sandbox/benchmark/theBenchmark.p',ax30) ).
fof(f417,plain,
! [X2,X0,X1] :
( ~ geq(X1,X2)
| geq(X0,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/sandbox/benchmark/theBenchmark.p',ax88) ).
fof(f416,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| gt(X0,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/sandbox/benchmark/theBenchmark.p',ax95) ).
fof(f630,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f600]) ).
fof(f600,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f413]) ).
fof(f413,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,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,[],[f258]) ).
fof(f258,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/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f414,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f415,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f411,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,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/sandbox/benchmark/theBenchmark.p',ax32) ).
fof(f412,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f257]) ).
fof(f409,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
fof(f410,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f256]) ).
fof(f406,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| X0 = X1
| ~ 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/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f405,plain,
! [X0,X1] :
( ~ geq(X1,X0)
| X0 = X1
| ~ 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/sandbox/benchmark/theBenchmark.p',ax87) ).
fof(f404,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/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f403,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/sandbox/benchmark/theBenchmark.p',ax92) ).
fof(f402,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/sandbox/benchmark/theBenchmark.p',ax94) ).
fof(f401,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/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f400,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/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f399,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
fof(f398,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax63) ).
fof(f397,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/sandbox/benchmark/theBenchmark.p',ax59) ).
fof(f396,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
fof(f395,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax71) ).
fof(f394,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/sandbox/benchmark/theBenchmark.p',ax31) ).
fof(f393,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/sandbox/benchmark/theBenchmark.p',ax89) ).
fof(f392,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/sandbox/benchmark/theBenchmark.p',ax90) ).
fof(f391,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/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f389,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
fof(f388,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f387,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
fof(f386,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
fof(f385,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
fof(f384,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
fof(f383,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
fof(f376,plain,
ssList(sK20),
inference(cnf_transformation,[],[f254]) ).
fof(f377,plain,
ssList(sK21),
inference(cnf_transformation,[],[f254]) ).
fof(f5109,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| spl69_43 ),
inference(duplicate_literal_removal,[],[f5108]) ).
fof(f5108,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl69_43 ),
inference(resolution,[],[f5102,f571]) ).
fof(f571,plain,
! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK63(X0,X1)) = X0
& ssList(sK63(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f357,f358]) ).
fof(f358,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK63(X0,X1)) = X0
& ssList(sK63(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f357,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,[],[f356]) ).
fof(f356,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,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f5102,plain,
( ~ ssList(sK63(nil,nil))
| spl69_43 ),
inference(avatar_component_clause,[],[f5100]) ).
fof(f5100,plain,
( spl69_43
<=> ssList(sK63(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_43])]) ).
fof(f5107,plain,
( ~ spl69_43
| spl69_44
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| ~ spl69_31 ),
inference(avatar_split_clause,[],[f5098,f3453,f3277,f3273,f3076,f5104,f5100]) ).
fof(f5104,plain,
( spl69_44
<=> nil = sK63(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_44])]) ).
fof(f3273,plain,
( spl69_29
<=> ssList(sK63(sK19,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_29])]) ).
fof(f3277,plain,
( spl69_30
<=> rearsegP(sK19,sK63(sK19,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_30])]) ).
fof(f3453,plain,
( spl69_31
<=> ssList(sK66(sK19,sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_31])]) ).
fof(f5098,plain,
( nil = sK63(nil,nil)
| ~ ssList(sK63(nil,nil))
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| ~ spl69_31 ),
inference(trivial_inequality_removal,[],[f5094]) ).
fof(f5094,plain,
( nil != nil
| nil = sK63(nil,nil)
| ~ ssList(sK63(nil,nil))
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| ~ spl69_31 ),
inference(superposition,[],[f4861,f2998]) ).
fof(f2998,plain,
nil = app(nil,sK63(nil,nil)),
inference(subsumption_resolution,[],[f2986,f390]) ).
fof(f2986,plain,
( nil = app(nil,sK63(nil,nil))
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f2985]) ).
fof(f2985,plain,
( nil = app(nil,sK63(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[],[f572,f631]) ).
fof(f572,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK63(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f4861,plain,
( ! [X0] :
( nil != app(nil,X0)
| nil = X0
| ~ ssList(X0) )
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| ~ spl69_31 ),
inference(forward_demodulation,[],[f4860,f4718]) ).
fof(f4718,plain,
( nil = sK66(sK19,sK19)
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| ~ spl69_31 ),
inference(subsumption_resolution,[],[f4717,f3454]) ).
fof(f3454,plain,
( ssList(sK66(sK19,sK19))
| ~ spl69_31 ),
inference(avatar_component_clause,[],[f3453]) ).
fof(f4717,plain,
( nil = sK66(sK19,sK19)
| ~ ssList(sK66(sK19,sK19))
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(trivial_inequality_removal,[],[f4716]) ).
fof(f4716,plain,
( sK19 != sK19
| nil = sK66(sK19,sK19)
| ~ ssList(sK66(sK19,sK19))
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(superposition,[],[f4575,f3400]) ).
fof(f3400,plain,
( sK19 = app(sK66(sK19,sK19),sK19)
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(subsumption_resolution,[],[f3399,f375]) ).
fof(f3399,plain,
( sK19 = app(sK66(sK19,sK19),sK19)
| ~ ssList(sK19)
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(duplicate_literal_removal,[],[f3396]) ).
fof(f3396,plain,
( sK19 = app(sK66(sK19,sK19),sK19)
| ~ ssList(sK19)
| ~ ssList(sK19)
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(resolution,[],[f3392,f579]) ).
fof(f3392,plain,
( rearsegP(sK19,sK19)
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(superposition,[],[f3279,f3384]) ).
fof(f3384,plain,
( sK19 = sK63(sK19,nil)
| ~ spl69_27
| ~ spl69_29 ),
inference(forward_demodulation,[],[f3370,f3261]) ).
fof(f3261,plain,
( sK19 = app(nil,sK63(sK19,nil))
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f3260,f375]) ).
fof(f3260,plain,
( sK19 = app(nil,sK63(sK19,nil))
| ~ ssList(sK19)
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f3258,f390]) ).
fof(f3258,plain,
( sK19 = app(nil,sK63(sK19,nil))
| ~ ssList(nil)
| ~ ssList(sK19)
| ~ spl69_27 ),
inference(resolution,[],[f3257,f572]) ).
fof(f3257,plain,
( frontsegP(sK19,nil)
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f3256,f3077]) ).
fof(f3256,plain,
( frontsegP(sK19,nil)
| ~ ssList(sK66(sK19,sK18))
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f3254,f390]) ).
fof(f3254,plain,
( frontsegP(sK19,nil)
| ~ ssList(nil)
| ~ ssList(sK66(sK19,sK18))
| ~ spl69_27 ),
inference(resolution,[],[f3214,f447]) ).
fof(f3214,plain,
( ! [X0] :
( ~ frontsegP(sK66(sK19,sK18),X0)
| frontsegP(sK19,X0)
| ~ ssList(X0) )
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f3213,f3077]) ).
fof(f3213,plain,
! [X0] :
( frontsegP(sK19,X0)
| ~ frontsegP(sK66(sK19,sK18),X0)
| ~ ssList(X0)
| ~ ssList(sK66(sK19,sK18)) ),
inference(subsumption_resolution,[],[f3177,f374]) ).
fof(f3177,plain,
! [X0] :
( frontsegP(sK19,X0)
| ~ frontsegP(sK66(sK19,sK18),X0)
| ~ ssList(sK18)
| ~ ssList(X0)
| ~ ssList(sK66(sK19,sK18)) ),
inference(superposition,[],[f588,f3064]) ).
fof(f588,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f3370,plain,
( sK63(sK19,nil) = app(nil,sK63(sK19,nil))
| ~ spl69_29 ),
inference(resolution,[],[f3274,f453]) ).
fof(f3274,plain,
( ssList(sK63(sK19,nil))
| ~ spl69_29 ),
inference(avatar_component_clause,[],[f3273]) ).
fof(f3279,plain,
( rearsegP(sK19,sK63(sK19,nil))
| ~ spl69_30 ),
inference(avatar_component_clause,[],[f3277]) ).
fof(f4575,plain,
! [X0] :
( sK19 != app(X0,sK19)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4574,f375]) ).
fof(f4574,plain,
! [X0] :
( sK19 != app(X0,sK19)
| nil = X0
| ~ ssList(sK19)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4462,f390]) ).
fof(f4462,plain,
! [X0] :
( sK19 != app(X0,sK19)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK19)
| ~ ssList(X0) ),
inference(superposition,[],[f590,f681]) ).
fof(f590,plain,
! [X2,X0,X1] :
( app(X2,X1) != app(X0,X1)
| X0 = X2
| ~ 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/sandbox/benchmark/theBenchmark.p',ax79) ).
fof(f4860,plain,
( ! [X0] :
( sK66(sK19,sK19) != app(sK66(sK19,sK19),X0)
| nil = X0
| ~ ssList(X0) )
| ~ spl69_31 ),
inference(subsumption_resolution,[],[f4859,f3454]) ).
fof(f4859,plain,
( ! [X0] :
( sK66(sK19,sK19) != app(sK66(sK19,sK19),X0)
| nil = X0
| ~ ssList(sK66(sK19,sK19))
| ~ ssList(X0) )
| ~ spl69_31 ),
inference(subsumption_resolution,[],[f4757,f390]) ).
fof(f4757,plain,
( ! [X0] :
( sK66(sK19,sK19) != app(sK66(sK19,sK19),X0)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK66(sK19,sK19))
| ~ ssList(X0) )
| ~ spl69_31 ),
inference(superposition,[],[f591,f3466]) ).
fof(f3466,plain,
( sK66(sK19,sK19) = app(sK66(sK19,sK19),nil)
| ~ spl69_31 ),
inference(resolution,[],[f3454,f452]) ).
fof(f591,plain,
! [X2,X0,X1] :
( app(X1,X2) != app(X1,X0)
| X0 = X2
| ~ 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/sandbox/benchmark/theBenchmark.p',ax80) ).
fof(f4381,plain,
( ~ spl69_9
| spl69_41 ),
inference(avatar_contradiction_clause,[],[f4380]) ).
fof(f4380,plain,
( $false
| ~ spl69_9
| spl69_41 ),
inference(subsumption_resolution,[],[f4379,f390]) ).
fof(f4379,plain,
( ~ ssList(nil)
| ~ spl69_9
| spl69_41 ),
inference(subsumption_resolution,[],[f4378,f1581]) ).
fof(f4378,plain,
( ~ ssItem(hd(sK18))
| ~ ssList(nil)
| spl69_41 ),
inference(resolution,[],[f4372,f552]) ).
fof(f4372,plain,
( ~ ssList(cons(hd(sK18),nil))
| spl69_41 ),
inference(avatar_component_clause,[],[f4370]) ).
fof(f4377,plain,
( ~ spl69_41
| spl69_42
| ~ spl69_9 ),
inference(avatar_split_clause,[],[f4360,f1580,f4374,f4370]) ).
fof(f4374,plain,
( spl69_42
<=> ssList(cons(hd(sK18),sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_42])]) ).
fof(f4360,plain,
( ssList(cons(hd(sK18),sK18))
| ~ ssList(cons(hd(sK18),nil))
| ~ spl69_9 ),
inference(subsumption_resolution,[],[f4351,f374]) ).
fof(f4351,plain,
( ssList(cons(hd(sK18),sK18))
| ~ ssList(sK18)
| ~ ssList(cons(hd(sK18),nil))
| ~ spl69_9 ),
inference(superposition,[],[f562,f2250]) ).
fof(f2250,plain,
( cons(hd(sK18),sK18) = app(cons(hd(sK18),nil),sK18)
| ~ spl69_9 ),
inference(resolution,[],[f1986,f1581]) ).
fof(f3939,plain,
( ~ spl69_39
| spl69_40
| ~ spl69_31
| ~ spl69_32 ),
inference(avatar_split_clause,[],[f3486,f3457,f3453,f3936,f3932]) ).
fof(f3932,plain,
( spl69_39
<=> frontsegP(sK66(sK19,sK19),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_39])]) ).
fof(f3936,plain,
( spl69_40
<=> sK19 = sK66(sK19,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_40])]) ).
fof(f3457,plain,
( spl69_32
<=> frontsegP(sK19,sK66(sK19,sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_32])]) ).
fof(f3486,plain,
( sK19 = sK66(sK19,sK19)
| ~ frontsegP(sK66(sK19,sK19),sK19)
| ~ spl69_31
| ~ spl69_32 ),
inference(subsumption_resolution,[],[f3485,f3454]) ).
fof(f3485,plain,
( sK19 = sK66(sK19,sK19)
| ~ frontsegP(sK66(sK19,sK19),sK19)
| ~ ssList(sK66(sK19,sK19))
| ~ spl69_32 ),
inference(subsumption_resolution,[],[f3482,f375]) ).
fof(f3482,plain,
( sK19 = sK66(sK19,sK19)
| ~ frontsegP(sK66(sK19,sK19),sK19)
| ~ ssList(sK19)
| ~ ssList(sK66(sK19,sK19))
| ~ spl69_32 ),
inference(resolution,[],[f3459,f566]) ).
fof(f566,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f3459,plain,
( frontsegP(sK19,sK66(sK19,sK19))
| ~ spl69_32 ),
inference(avatar_component_clause,[],[f3457]) ).
fof(f3689,plain,
( ~ spl69_37
| spl69_38
| ~ spl69_21 ),
inference(avatar_split_clause,[],[f2977,f2350,f3686,f3682]) ).
fof(f3682,plain,
( spl69_37
<=> rearsegP(sK19,cons(sK68,sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_37])]) ).
fof(f2977,plain,
( sK19 = cons(sK68,sK19)
| ~ rearsegP(sK19,cons(sK68,sK19))
| ~ spl69_21 ),
inference(subsumption_resolution,[],[f2976,f375]) ).
fof(f2976,plain,
( sK19 = cons(sK68,sK19)
| ~ rearsegP(sK19,cons(sK68,sK19))
| ~ ssList(sK19)
| ~ spl69_21 ),
inference(subsumption_resolution,[],[f2975,f2938]) ).
fof(f2938,plain,
( ssList(cons(sK68,sK19))
| ~ spl69_21 ),
inference(subsumption_resolution,[],[f2937,f2351]) ).
fof(f2937,plain,
( ssList(cons(sK68,sK19))
| ~ ssList(cons(sK68,nil)) ),
inference(subsumption_resolution,[],[f2928,f375]) ).
fof(f2928,plain,
( ssList(cons(sK68,sK19))
| ~ ssList(sK19)
| ~ ssList(cons(sK68,nil)) ),
inference(superposition,[],[f562,f2818]) ).
fof(f2975,plain,
( sK19 = cons(sK68,sK19)
| ~ rearsegP(sK19,cons(sK68,sK19))
| ~ ssList(cons(sK68,sK19))
| ~ ssList(sK19)
| ~ spl69_21 ),
inference(resolution,[],[f2948,f568]) ).
fof(f568,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f2948,plain,
( rearsegP(cons(sK68,sK19),sK19)
| ~ spl69_21 ),
inference(subsumption_resolution,[],[f2947,f375]) ).
fof(f2947,plain,
( rearsegP(cons(sK68,sK19),sK19)
| ~ ssList(sK19)
| ~ spl69_21 ),
inference(subsumption_resolution,[],[f2932,f2351]) ).
fof(f2932,plain,
( rearsegP(cons(sK68,sK19),sK19)
| ~ ssList(cons(sK68,nil))
| ~ ssList(sK19) ),
inference(superposition,[],[f2458,f2818]) ).
fof(f2458,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f623,f562]) ).
fof(f623,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f580]) ).
fof(f580,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f3635,plain,
( ~ spl69_35
| spl69_36
| ~ spl69_19 ),
inference(avatar_split_clause,[],[f2920,f2283,f3632,f3628]) ).
fof(f3628,plain,
( spl69_35
<=> rearsegP(sK19,cons(sK67,sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_35])]) ).
fof(f2920,plain,
( sK19 = cons(sK67,sK19)
| ~ rearsegP(sK19,cons(sK67,sK19))
| ~ spl69_19 ),
inference(subsumption_resolution,[],[f2919,f375]) ).
fof(f2919,plain,
( sK19 = cons(sK67,sK19)
| ~ rearsegP(sK19,cons(sK67,sK19))
| ~ ssList(sK19)
| ~ spl69_19 ),
inference(subsumption_resolution,[],[f2918,f2833]) ).
fof(f2833,plain,
( ssList(cons(sK67,sK19))
| ~ spl69_19 ),
inference(subsumption_resolution,[],[f2832,f2284]) ).
fof(f2832,plain,
( ssList(cons(sK67,sK19))
| ~ ssList(cons(sK67,nil)) ),
inference(subsumption_resolution,[],[f2823,f375]) ).
fof(f2823,plain,
( ssList(cons(sK67,sK19))
| ~ ssList(sK19)
| ~ ssList(cons(sK67,nil)) ),
inference(superposition,[],[f562,f2817]) ).
fof(f2918,plain,
( sK19 = cons(sK67,sK19)
| ~ rearsegP(sK19,cons(sK67,sK19))
| ~ ssList(cons(sK67,sK19))
| ~ ssList(sK19)
| ~ spl69_19 ),
inference(resolution,[],[f2843,f568]) ).
fof(f2843,plain,
( rearsegP(cons(sK67,sK19),sK19)
| ~ spl69_19 ),
inference(subsumption_resolution,[],[f2842,f375]) ).
fof(f2842,plain,
( rearsegP(cons(sK67,sK19),sK19)
| ~ ssList(sK19)
| ~ spl69_19 ),
inference(subsumption_resolution,[],[f2827,f2284]) ).
fof(f2827,plain,
( rearsegP(cons(sK67,sK19),sK19)
| ~ ssList(cons(sK67,nil))
| ~ ssList(sK19) ),
inference(superposition,[],[f2458,f2817]) ).
fof(f3557,plain,
( ~ spl69_33
| spl69_34
| ~ spl69_27
| ~ spl69_28 ),
inference(avatar_split_clause,[],[f3109,f3080,f3076,f3554,f3550]) ).
fof(f3550,plain,
( spl69_33
<=> frontsegP(sK66(sK19,sK18),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_33])]) ).
fof(f3554,plain,
( spl69_34
<=> sK19 = sK66(sK19,sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_34])]) ).
fof(f3080,plain,
( spl69_28
<=> frontsegP(sK19,sK66(sK19,sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_28])]) ).
fof(f3109,plain,
( sK19 = sK66(sK19,sK18)
| ~ frontsegP(sK66(sK19,sK18),sK19)
| ~ spl69_27
| ~ spl69_28 ),
inference(subsumption_resolution,[],[f3108,f3077]) ).
fof(f3108,plain,
( sK19 = sK66(sK19,sK18)
| ~ frontsegP(sK66(sK19,sK18),sK19)
| ~ ssList(sK66(sK19,sK18))
| ~ spl69_28 ),
inference(subsumption_resolution,[],[f3105,f375]) ).
fof(f3105,plain,
( sK19 = sK66(sK19,sK18)
| ~ frontsegP(sK66(sK19,sK18),sK19)
| ~ ssList(sK19)
| ~ ssList(sK66(sK19,sK18))
| ~ spl69_28 ),
inference(resolution,[],[f3082,f566]) ).
fof(f3082,plain,
( frontsegP(sK19,sK66(sK19,sK18))
| ~ spl69_28 ),
inference(avatar_component_clause,[],[f3080]) ).
fof(f3465,plain,
( ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| spl69_31 ),
inference(avatar_contradiction_clause,[],[f3464]) ).
fof(f3464,plain,
( $false
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| spl69_31 ),
inference(subsumption_resolution,[],[f3463,f375]) ).
fof(f3463,plain,
( ~ ssList(sK19)
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30
| spl69_31 ),
inference(subsumption_resolution,[],[f3462,f3392]) ).
fof(f3462,plain,
( ~ rearsegP(sK19,sK19)
| ~ ssList(sK19)
| spl69_31 ),
inference(duplicate_literal_removal,[],[f3461]) ).
fof(f3461,plain,
( ~ rearsegP(sK19,sK19)
| ~ ssList(sK19)
| ~ ssList(sK19)
| spl69_31 ),
inference(resolution,[],[f3455,f578]) ).
fof(f578,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f368]) ).
fof(f3455,plain,
( ~ ssList(sK66(sK19,sK19))
| spl69_31 ),
inference(avatar_component_clause,[],[f3453]) ).
fof(f3460,plain,
( ~ spl69_31
| spl69_32
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(avatar_split_clause,[],[f3412,f3277,f3273,f3076,f3457,f3453]) ).
fof(f3412,plain,
( frontsegP(sK19,sK66(sK19,sK19))
| ~ ssList(sK66(sK19,sK19))
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(subsumption_resolution,[],[f3408,f375]) ).
fof(f3408,plain,
( frontsegP(sK19,sK66(sK19,sK19))
| ~ ssList(sK19)
| ~ ssList(sK66(sK19,sK19))
| ~ spl69_27
| ~ spl69_29
| ~ spl69_30 ),
inference(superposition,[],[f2339,f3400]) ).
fof(f2339,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f621,f562]) ).
fof(f621,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f573]) ).
fof(f573,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f359]) ).
fof(f3285,plain,
( ~ spl69_27
| spl69_29 ),
inference(avatar_contradiction_clause,[],[f3284]) ).
fof(f3284,plain,
( $false
| ~ spl69_27
| spl69_29 ),
inference(subsumption_resolution,[],[f3283,f375]) ).
fof(f3283,plain,
( ~ ssList(sK19)
| ~ spl69_27
| spl69_29 ),
inference(subsumption_resolution,[],[f3282,f390]) ).
fof(f3282,plain,
( ~ ssList(nil)
| ~ ssList(sK19)
| ~ spl69_27
| spl69_29 ),
inference(subsumption_resolution,[],[f3281,f3257]) ).
fof(f3281,plain,
( ~ frontsegP(sK19,nil)
| ~ ssList(nil)
| ~ ssList(sK19)
| spl69_29 ),
inference(resolution,[],[f3275,f571]) ).
fof(f3275,plain,
( ~ ssList(sK63(sK19,nil))
| spl69_29 ),
inference(avatar_component_clause,[],[f3273]) ).
fof(f3280,plain,
( ~ spl69_29
| spl69_30
| ~ spl69_27 ),
inference(avatar_split_clause,[],[f3271,f3076,f3277,f3273]) ).
fof(f3271,plain,
( rearsegP(sK19,sK63(sK19,nil))
| ~ ssList(sK63(sK19,nil))
| ~ spl69_27 ),
inference(subsumption_resolution,[],[f3269,f390]) ).
fof(f3269,plain,
( rearsegP(sK19,sK63(sK19,nil))
| ~ ssList(nil)
| ~ ssList(sK63(sK19,nil))
| ~ spl69_27 ),
inference(superposition,[],[f2458,f3261]) ).
fof(f3088,plain,
spl69_27,
inference(avatar_contradiction_clause,[],[f3087]) ).
fof(f3087,plain,
( $false
| spl69_27 ),
inference(subsumption_resolution,[],[f3086,f375]) ).
fof(f3086,plain,
( ~ ssList(sK19)
| spl69_27 ),
inference(subsumption_resolution,[],[f3085,f374]) ).
fof(f3085,plain,
( ~ ssList(sK18)
| ~ ssList(sK19)
| spl69_27 ),
inference(subsumption_resolution,[],[f3084,f638]) ).
fof(f3084,plain,
( ~ rearsegP(sK19,sK18)
| ~ ssList(sK18)
| ~ ssList(sK19)
| spl69_27 ),
inference(resolution,[],[f3078,f578]) ).
fof(f3078,plain,
( ~ ssList(sK66(sK19,sK18))
| spl69_27 ),
inference(avatar_component_clause,[],[f3076]) ).
fof(f3083,plain,
( ~ spl69_27
| spl69_28 ),
inference(avatar_split_clause,[],[f3074,f3080,f3076]) ).
fof(f3074,plain,
( frontsegP(sK19,sK66(sK19,sK18))
| ~ ssList(sK66(sK19,sK18)) ),
inference(subsumption_resolution,[],[f3070,f374]) ).
fof(f3070,plain,
( frontsegP(sK19,sK66(sK19,sK18))
| ~ ssList(sK18)
| ~ ssList(sK66(sK19,sK18)) ),
inference(superposition,[],[f2339,f3064]) ).
fof(f2698,plain,
( ~ spl69_25
| spl69_26
| ~ spl69_21
| ~ spl69_22 ),
inference(avatar_split_clause,[],[f2576,f2354,f2350,f2695,f2691]) ).
fof(f2691,plain,
( spl69_25
<=> rearsegP(sK18,cons(sK68,sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_25])]) ).
fof(f2354,plain,
( spl69_22
<=> ssList(cons(sK68,sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_22])]) ).
fof(f2576,plain,
( sK18 = cons(sK68,sK18)
| ~ rearsegP(sK18,cons(sK68,sK18))
| ~ spl69_21
| ~ spl69_22 ),
inference(subsumption_resolution,[],[f2575,f374]) ).
fof(f2575,plain,
( sK18 = cons(sK68,sK18)
| ~ rearsegP(sK18,cons(sK68,sK18))
| ~ ssList(sK18)
| ~ spl69_21
| ~ spl69_22 ),
inference(subsumption_resolution,[],[f2574,f2356]) ).
fof(f2356,plain,
( ssList(cons(sK68,sK18))
| ~ spl69_22 ),
inference(avatar_component_clause,[],[f2354]) ).
fof(f2574,plain,
( sK18 = cons(sK68,sK18)
| ~ rearsegP(sK18,cons(sK68,sK18))
| ~ ssList(cons(sK68,sK18))
| ~ ssList(sK18)
| ~ spl69_21 ),
inference(resolution,[],[f2570,f568]) ).
fof(f2570,plain,
( rearsegP(cons(sK68,sK18),sK18)
| ~ spl69_21 ),
inference(subsumption_resolution,[],[f2569,f374]) ).
fof(f2569,plain,
( rearsegP(cons(sK68,sK18),sK18)
| ~ ssList(sK18)
| ~ spl69_21 ),
inference(subsumption_resolution,[],[f2560,f2351]) ).
fof(f2560,plain,
( rearsegP(cons(sK68,sK18),sK18)
| ~ ssList(cons(sK68,nil))
| ~ ssList(sK18) ),
inference(superposition,[],[f2458,f2272]) ).
fof(f2667,plain,
( ~ spl69_23
| spl69_24
| ~ spl69_19
| ~ spl69_20 ),
inference(avatar_split_clause,[],[f2573,f2287,f2283,f2664,f2660]) ).
fof(f2660,plain,
( spl69_23
<=> rearsegP(sK18,cons(sK67,sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_23])]) ).
fof(f2287,plain,
( spl69_20
<=> ssList(cons(sK67,sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_20])]) ).
fof(f2573,plain,
( sK18 = cons(sK67,sK18)
| ~ rearsegP(sK18,cons(sK67,sK18))
| ~ spl69_19
| ~ spl69_20 ),
inference(subsumption_resolution,[],[f2572,f374]) ).
fof(f2572,plain,
( sK18 = cons(sK67,sK18)
| ~ rearsegP(sK18,cons(sK67,sK18))
| ~ ssList(sK18)
| ~ spl69_19
| ~ spl69_20 ),
inference(subsumption_resolution,[],[f2571,f2289]) ).
fof(f2289,plain,
( ssList(cons(sK67,sK18))
| ~ spl69_20 ),
inference(avatar_component_clause,[],[f2287]) ).
fof(f2571,plain,
( sK18 = cons(sK67,sK18)
| ~ rearsegP(sK18,cons(sK67,sK18))
| ~ ssList(cons(sK67,sK18))
| ~ ssList(sK18)
| ~ spl69_19 ),
inference(resolution,[],[f2568,f568]) ).
fof(f2568,plain,
( rearsegP(cons(sK67,sK18),sK18)
| ~ spl69_19 ),
inference(subsumption_resolution,[],[f2567,f374]) ).
fof(f2567,plain,
( rearsegP(cons(sK67,sK18),sK18)
| ~ ssList(sK18)
| ~ spl69_19 ),
inference(subsumption_resolution,[],[f2559,f2284]) ).
fof(f2559,plain,
( rearsegP(cons(sK67,sK18),sK18)
| ~ ssList(cons(sK67,nil))
| ~ ssList(sK18) ),
inference(superposition,[],[f2458,f2271]) ).
fof(f2361,plain,
spl69_21,
inference(avatar_contradiction_clause,[],[f2360]) ).
fof(f2360,plain,
( $false
| spl69_21 ),
inference(subsumption_resolution,[],[f2359,f390]) ).
fof(f2359,plain,
( ~ ssList(nil)
| spl69_21 ),
inference(subsumption_resolution,[],[f2358,f597]) ).
fof(f2358,plain,
( ~ ssItem(sK68)
| ~ ssList(nil)
| spl69_21 ),
inference(resolution,[],[f2352,f552]) ).
fof(f2352,plain,
( ~ ssList(cons(sK68,nil))
| spl69_21 ),
inference(avatar_component_clause,[],[f2350]) ).
fof(f2357,plain,
( ~ spl69_21
| spl69_22 ),
inference(avatar_split_clause,[],[f2348,f2354,f2350]) ).
fof(f2348,plain,
( ssList(cons(sK68,sK18))
| ~ ssList(cons(sK68,nil)) ),
inference(subsumption_resolution,[],[f2344,f374]) ).
fof(f2344,plain,
( ssList(cons(sK68,sK18))
| ~ ssList(sK18)
| ~ ssList(cons(sK68,nil)) ),
inference(superposition,[],[f562,f2272]) ).
fof(f2294,plain,
spl69_19,
inference(avatar_contradiction_clause,[],[f2293]) ).
fof(f2293,plain,
( $false
| spl69_19 ),
inference(subsumption_resolution,[],[f2292,f390]) ).
fof(f2292,plain,
( ~ ssList(nil)
| spl69_19 ),
inference(subsumption_resolution,[],[f2291,f596]) ).
fof(f2291,plain,
( ~ ssItem(sK67)
| ~ ssList(nil)
| spl69_19 ),
inference(resolution,[],[f2285,f552]) ).
fof(f2285,plain,
( ~ ssList(cons(sK67,nil))
| spl69_19 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f2290,plain,
( ~ spl69_19
| spl69_20 ),
inference(avatar_split_clause,[],[f2281,f2287,f2283]) ).
fof(f2281,plain,
( ssList(cons(sK67,sK18))
| ~ ssList(cons(sK67,nil)) ),
inference(subsumption_resolution,[],[f2277,f374]) ).
fof(f2277,plain,
( ssList(cons(sK67,sK18))
| ~ ssList(sK18)
| ~ ssList(cons(sK67,nil)) ),
inference(superposition,[],[f562,f2271]) ).
fof(f2196,plain,
( ~ spl69_17
| spl69_18 ),
inference(avatar_split_clause,[],[f2187,f2193,f2189]) ).
fof(f2189,plain,
( spl69_17
<=> rearsegP(sK18,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_17])]) ).
fof(f2193,plain,
( spl69_18
<=> sK18 = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_18])]) ).
fof(f2187,plain,
( sK18 = sK19
| ~ rearsegP(sK18,sK19) ),
inference(subsumption_resolution,[],[f2186,f374]) ).
fof(f2186,plain,
( sK18 = sK19
| ~ rearsegP(sK18,sK19)
| ~ ssList(sK18) ),
inference(subsumption_resolution,[],[f2179,f375]) ).
fof(f2179,plain,
( sK18 = sK19
| ~ rearsegP(sK18,sK19)
| ~ ssList(sK19)
| ~ ssList(sK18) ),
inference(resolution,[],[f568,f638]) ).
fof(f1821,plain,
( spl69_4
| spl69_15 ),
inference(avatar_contradiction_clause,[],[f1820]) ).
fof(f1820,plain,
( $false
| spl69_4
| spl69_15 ),
inference(subsumption_resolution,[],[f1819,f375]) ).
fof(f1819,plain,
( ~ ssList(sK19)
| spl69_4
| spl69_15 ),
inference(subsumption_resolution,[],[f1818,f827]) ).
fof(f1818,plain,
( nil = sK19
| ~ ssList(sK19)
| spl69_15 ),
inference(resolution,[],[f1812,f454]) ).
fof(f1812,plain,
( ~ ssList(sK22(sK19))
| spl69_15 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f1817,plain,
( ~ spl69_15
| spl69_16
| spl69_4
| ~ spl69_7 ),
inference(avatar_split_clause,[],[f1808,f1496,f826,f1814,f1810]) ).
fof(f1814,plain,
( spl69_16
<=> memberP(sK19,sK23(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_16])]) ).
fof(f1808,plain,
( memberP(sK19,sK23(sK19))
| ~ ssList(sK22(sK19))
| spl69_4
| ~ spl69_7 ),
inference(subsumption_resolution,[],[f1473,f1497]) ).
fof(f1473,plain,
( memberP(sK19,sK23(sK19))
| ~ ssList(sK22(sK19))
| ~ ssItem(sK23(sK19))
| spl69_4 ),
inference(superposition,[],[f629,f1449]) ).
fof(f1721,plain,
( spl69_2
| spl69_13 ),
inference(avatar_contradiction_clause,[],[f1720]) ).
fof(f1720,plain,
( $false
| spl69_2
| spl69_13 ),
inference(subsumption_resolution,[],[f1719,f374]) ).
fof(f1719,plain,
( ~ ssList(sK18)
| spl69_2
| spl69_13 ),
inference(subsumption_resolution,[],[f1718,f809]) ).
fof(f1718,plain,
( nil = sK18
| ~ ssList(sK18)
| spl69_13 ),
inference(resolution,[],[f1712,f454]) ).
fof(f1712,plain,
( ~ ssList(sK22(sK18))
| spl69_13 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f1717,plain,
( ~ spl69_13
| spl69_14
| spl69_2
| ~ spl69_5 ),
inference(avatar_split_clause,[],[f1708,f1477,f808,f1714,f1710]) ).
fof(f1714,plain,
( spl69_14
<=> memberP(sK18,sK23(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_14])]) ).
fof(f1708,plain,
( memberP(sK18,sK23(sK18))
| ~ ssList(sK22(sK18))
| spl69_2
| ~ spl69_5 ),
inference(subsumption_resolution,[],[f1463,f1478]) ).
fof(f1463,plain,
( memberP(sK18,sK23(sK18))
| ~ ssList(sK22(sK18))
| ~ ssItem(sK23(sK18))
| spl69_2 ),
inference(superposition,[],[f629,f1448]) ).
fof(f1610,plain,
( spl69_4
| spl69_11 ),
inference(avatar_contradiction_clause,[],[f1609]) ).
fof(f1609,plain,
( $false
| spl69_4
| spl69_11 ),
inference(subsumption_resolution,[],[f1608,f375]) ).
fof(f1608,plain,
( ~ ssList(sK19)
| spl69_4
| spl69_11 ),
inference(subsumption_resolution,[],[f1607,f827]) ).
fof(f1607,plain,
( nil = sK19
| ~ ssList(sK19)
| spl69_11 ),
inference(resolution,[],[f1601,f457]) ).
fof(f1601,plain,
( ~ ssItem(hd(sK19))
| spl69_11 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f1606,plain,
( ~ spl69_11
| ~ spl69_12
| spl69_4 ),
inference(avatar_split_clause,[],[f1578,f826,f1603,f1599]) ).
fof(f1603,plain,
( spl69_12
<=> sK19 = tl(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_12])]) ).
fof(f1578,plain,
( sK19 != tl(sK19)
| ~ ssItem(hd(sK19))
| spl69_4 ),
inference(subsumption_resolution,[],[f1577,f375]) ).
fof(f1577,plain,
( sK19 != tl(sK19)
| ~ ssItem(hd(sK19))
| ~ ssList(sK19)
| spl69_4 ),
inference(inner_rewriting,[],[f1575]) ).
fof(f1575,plain,
( sK19 != tl(sK19)
| ~ ssItem(hd(sK19))
| ~ ssList(tl(sK19))
| spl69_4 ),
inference(superposition,[],[f554,f1552]) ).
fof(f1591,plain,
( spl69_2
| spl69_9 ),
inference(avatar_contradiction_clause,[],[f1590]) ).
fof(f1590,plain,
( $false
| spl69_2
| spl69_9 ),
inference(subsumption_resolution,[],[f1589,f374]) ).
fof(f1589,plain,
( ~ ssList(sK18)
| spl69_2
| spl69_9 ),
inference(subsumption_resolution,[],[f1588,f809]) ).
fof(f1588,plain,
( nil = sK18
| ~ ssList(sK18)
| spl69_9 ),
inference(resolution,[],[f1582,f457]) ).
fof(f1582,plain,
( ~ ssItem(hd(sK18))
| spl69_9 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1587,plain,
( ~ spl69_9
| ~ spl69_10
| spl69_2 ),
inference(avatar_split_clause,[],[f1568,f808,f1584,f1580]) ).
fof(f1584,plain,
( spl69_10
<=> sK18 = tl(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_10])]) ).
fof(f1568,plain,
( sK18 != tl(sK18)
| ~ ssItem(hd(sK18))
| spl69_2 ),
inference(subsumption_resolution,[],[f1567,f374]) ).
fof(f1567,plain,
( sK18 != tl(sK18)
| ~ ssItem(hd(sK18))
| ~ ssList(sK18)
| spl69_2 ),
inference(inner_rewriting,[],[f1565]) ).
fof(f1565,plain,
( sK18 != tl(sK18)
| ~ ssItem(hd(sK18))
| ~ ssList(tl(sK18))
| spl69_2 ),
inference(superposition,[],[f554,f1551]) ).
fof(f1507,plain,
( spl69_4
| spl69_7 ),
inference(avatar_contradiction_clause,[],[f1506]) ).
fof(f1506,plain,
( $false
| spl69_4
| spl69_7 ),
inference(subsumption_resolution,[],[f1505,f375]) ).
fof(f1505,plain,
( ~ ssList(sK19)
| spl69_4
| spl69_7 ),
inference(subsumption_resolution,[],[f1504,f827]) ).
fof(f1504,plain,
( nil = sK19
| ~ ssList(sK19)
| spl69_7 ),
inference(resolution,[],[f1498,f455]) ).
fof(f1498,plain,
( ~ ssItem(sK23(sK19))
| spl69_7 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1503,plain,
( ~ spl69_7
| ~ spl69_8
| spl69_4 ),
inference(avatar_split_clause,[],[f1475,f826,f1500,f1496]) ).
fof(f1500,plain,
( spl69_8
<=> sK19 = sK22(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_8])]) ).
fof(f1475,plain,
( sK19 != sK22(sK19)
| ~ ssItem(sK23(sK19))
| spl69_4 ),
inference(subsumption_resolution,[],[f1474,f375]) ).
fof(f1474,plain,
( sK19 != sK22(sK19)
| ~ ssItem(sK23(sK19))
| ~ ssList(sK19)
| spl69_4 ),
inference(inner_rewriting,[],[f1472]) ).
fof(f1472,plain,
( sK19 != sK22(sK19)
| ~ ssItem(sK23(sK19))
| ~ ssList(sK22(sK19))
| spl69_4 ),
inference(superposition,[],[f554,f1449]) ).
fof(f1488,plain,
( spl69_2
| spl69_5 ),
inference(avatar_contradiction_clause,[],[f1487]) ).
fof(f1487,plain,
( $false
| spl69_2
| spl69_5 ),
inference(subsumption_resolution,[],[f1486,f374]) ).
fof(f1486,plain,
( ~ ssList(sK18)
| spl69_2
| spl69_5 ),
inference(subsumption_resolution,[],[f1485,f809]) ).
fof(f1485,plain,
( nil = sK18
| ~ ssList(sK18)
| spl69_5 ),
inference(resolution,[],[f1479,f455]) ).
fof(f1479,plain,
( ~ ssItem(sK23(sK18))
| spl69_5 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f1484,plain,
( ~ spl69_5
| ~ spl69_6
| spl69_2 ),
inference(avatar_split_clause,[],[f1465,f808,f1481,f1477]) ).
fof(f1481,plain,
( spl69_6
<=> sK18 = sK22(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).
fof(f1465,plain,
( sK18 != sK22(sK18)
| ~ ssItem(sK23(sK18))
| spl69_2 ),
inference(subsumption_resolution,[],[f1464,f374]) ).
fof(f1464,plain,
( sK18 != sK22(sK18)
| ~ ssItem(sK23(sK18))
| ~ ssList(sK18)
| spl69_2 ),
inference(inner_rewriting,[],[f1462]) ).
fof(f1462,plain,
( sK18 != sK22(sK18)
| ~ ssItem(sK23(sK18))
| ~ ssList(sK22(sK18))
| spl69_2 ),
inference(superposition,[],[f554,f1448]) ).
fof(f874,plain,
( spl69_2
| ~ spl69_4 ),
inference(avatar_contradiction_clause,[],[f873]) ).
fof(f873,plain,
( $false
| spl69_2
| ~ spl69_4 ),
inference(subsumption_resolution,[],[f872,f374]) ).
fof(f872,plain,
( ~ ssList(sK18)
| spl69_2
| ~ spl69_4 ),
inference(subsumption_resolution,[],[f871,f809]) ).
fof(f871,plain,
( nil = sK18
| ~ ssList(sK18)
| ~ spl69_4 ),
inference(resolution,[],[f832,f550]) ).
fof(f550,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f832,plain,
( rearsegP(nil,sK18)
| ~ spl69_4 ),
inference(superposition,[],[f638,f828]) ).
fof(f828,plain,
( nil = sK19
| ~ spl69_4 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f829,plain,
( spl69_3
| spl69_4 ),
inference(avatar_split_clause,[],[f773,f826,f822]) ).
fof(f822,plain,
( spl69_3
<=> hd(sK19) = sK24(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_3])]) ).
fof(f773,plain,
( nil = sK19
| hd(sK19) = sK24(sK19) ),
inference(resolution,[],[f461,f375]) ).
fof(f819,plain,
~ spl69_2,
inference(avatar_contradiction_clause,[],[f818]) ).
fof(f818,plain,
( $false
| ~ spl69_2 ),
inference(subsumption_resolution,[],[f817,f375]) ).
fof(f817,plain,
( ~ ssList(sK19)
| ~ spl69_2 ),
inference(resolution,[],[f815,f449]) ).
fof(f815,plain,
( ~ segmentP(sK19,nil)
| ~ spl69_2 ),
inference(superposition,[],[f381,f810]) ).
fof(f810,plain,
( nil = sK18
| ~ spl69_2 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f811,plain,
( spl69_1
| spl69_2 ),
inference(avatar_split_clause,[],[f772,f808,f804]) ).
fof(f804,plain,
( spl69_1
<=> hd(sK18) = sK24(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_1])]) ).
fof(f772,plain,
( nil = sK18
| hd(sK18) = sK24(sK18) ),
inference(resolution,[],[f461,f374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC373+1 : TPTP v8.2.0. Released v2.4.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 03:43:07 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (14485)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (14488)WARNING: value z3 for option sas not known
% 0.13/0.37 % (14486)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (14487)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (14489)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (14488)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)
% 0.13/0.37 % (14490)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)
% 0.13/0.37 % (14491)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)
% 0.13/0.37 % (14492)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)
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [3]
% 0.20/0.44 TRYING [4]
% 0.20/0.44 TRYING [4]
% 0.20/0.55 TRYING [5]
% 0.20/0.57 TRYING [5]
% 2.03/0.68 % (14488)First to succeed.
% 2.03/0.69 % (14488)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14485"
% 2.03/0.69 % (14488)Refutation found. Thanks to Tanya!
% 2.03/0.69 % SZS status Theorem for theBenchmark
% 2.03/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.03/0.70 % (14488)------------------------------
% 2.03/0.70 % (14488)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.03/0.70 % (14488)Termination reason: Refutation
% 2.03/0.70
% 2.03/0.70 % (14488)Memory used [KB]: 5828
% 2.03/0.70 % (14488)Time elapsed: 0.323 s
% 2.03/0.70 % (14488)Instructions burned: 661 (million)
% 2.03/0.70 % (14485)Success in time 0.334 s
%------------------------------------------------------------------------------