TSTP Solution File: SWC183+1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWC183+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n029.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 : Mon Jun 24 16:36:15 EDT 2024
% Result : Theorem 1.42s 0.59s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 58
% Syntax : Number of formulae : 368 ( 32 unt; 0 def)
% Number of atoms : 1524 ( 397 equ)
% Maximal formula atoms : 42 ( 4 avg)
% Number of connectives : 1921 ( 765 ~; 832 |; 230 &)
% ( 32 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 21 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 13 con; 0-2 aty)
% Number of variables : 301 ( 207 !; 94 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7012,plain,
$false,
inference(avatar_sat_refutation,[],[f631,f636,f653,f1194,f1299,f1309,f1617,f1641,f1735,f1745,f2018,f2029,f2358,f3199,f3208,f3519,f3539,f3876,f3905,f3907,f7003]) ).
fof(f7003,plain,
( ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(avatar_contradiction_clause,[],[f7002]) ).
fof(f7002,plain,
( $false
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(subsumption_resolution,[],[f6987,f801]) ).
fof(f801,plain,
nil != sF62,
inference(subsumption_resolution,[],[f800,f379]) ).
fof(f379,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f800,plain,
( nil != sF62
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f799,f358]) ).
fof(f358,plain,
ssItem(sK11),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
( ( ( nil = sK8
& nil = sK9 )
| ( ! [X5] :
( ~ leq(sK10,X5)
| ~ memberP(sK9,X5)
| sK10 = X5
| ~ ssItem(X5) )
& memberP(sK9,sK10)
& sK8 = cons(sK10,nil)
& ssItem(sK10) ) )
& ( memberP(sK13,sK11)
| memberP(sK12,sK11) )
& sK6 = app(app(sK12,cons(sK11,nil)),sK13)
& ssList(sK13)
& ssList(sK12)
& ssItem(sK11)
& sK6 = sK8
& sK7 = sK9
& ssList(sK9)
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f99,f239,f238,f237,f236,f235,f234,f233,f232]) ).
fof(f232,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = X0
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& sK6 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f233,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& sK6 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& sK6 = X2
& sK7 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f234,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& sK6 = X2
& sK7 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil = sK8
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = sK8
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& sK6 = sK8
& sK7 = X3
& ssList(X3) )
& ssList(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f235,plain,
( ? [X3] :
( ( ( nil = sK8
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = sK8
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& sK6 = sK8
& sK7 = X3
& ssList(X3) )
=> ( ( ( nil = sK8
& nil = sK9 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(sK9,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(sK9,X4)
& cons(X4,nil) = sK8
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& sK6 = sK8
& sK7 = sK9
& ssList(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f236,plain,
( ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(sK9,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(sK9,X4)
& cons(X4,nil) = sK8
& ssItem(X4) )
=> ( ! [X5] :
( ~ leq(sK10,X5)
| ~ memberP(sK9,X5)
| sK10 = X5
| ~ ssItem(X5) )
& memberP(sK9,sK10)
& sK8 = cons(sK10,nil)
& ssItem(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f237,plain,
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = sK6
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
=> ( ? [X7] :
( ? [X8] :
( ( memberP(X8,sK11)
| memberP(X7,sK11) )
& sK6 = app(app(X7,cons(sK11,nil)),X8)
& ssList(X8) )
& ssList(X7) )
& ssItem(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f238,plain,
( ? [X7] :
( ? [X8] :
( ( memberP(X8,sK11)
| memberP(X7,sK11) )
& sK6 = app(app(X7,cons(sK11,nil)),X8)
& ssList(X8) )
& ssList(X7) )
=> ( ? [X8] :
( ( memberP(X8,sK11)
| memberP(sK12,sK11) )
& sK6 = app(app(sK12,cons(sK11,nil)),X8)
& ssList(X8) )
& ssList(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f239,plain,
( ? [X8] :
( ( memberP(X8,sK11)
| memberP(sK12,sK11) )
& sK6 = app(app(sK12,cons(sK11,nil)),X8)
& ssList(X8) )
=> ( ( memberP(sK13,sK11)
| memberP(sK12,sK11) )
& sK6 = app(app(sK12,cons(sK11,nil)),sK13)
& ssList(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ? [X6] :
( ? [X7] :
( ? [X8] :
( ( memberP(X8,X6)
| memberP(X7,X6) )
& app(app(X7,cons(X6,nil)),X8) = X0
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2
| ~ ssItem(X4) ) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ( ~ memberP(X8,X6)
& ~ memberP(X7,X6) )
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil != X2
| nil != X3 )
& ! [X7] :
( ? [X8] :
( leq(X7,X8)
& memberP(X3,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X3,X7)
| cons(X7,nil) != X2
| ~ ssItem(X7) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( nil != X2
| nil != X3 )
& ! [X7] :
( ? [X8] :
( leq(X7,X8)
& memberP(X3,X8)
& X7 != X8
& ssItem(X8) )
| ~ memberP(X3,X7)
| cons(X7,nil) != X2
| ~ ssItem(X7) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ( ~ memberP(X6,X4)
& ~ memberP(X5,X4) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f799,plain,
( nil != sF62
| ~ ssItem(sK11)
| ~ ssList(nil) ),
inference(superposition,[],[f524,f603]) ).
fof(f603,plain,
cons(sK11,nil) = sF62,
introduced(function_definition,[new_symbols(definition,[sF62])]) ).
fof(f524,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6987,plain,
( nil = sF62
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(superposition,[],[f3810,f6792]) ).
fof(f6792,plain,
( sF62 = tl(sF63)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(subsumption_resolution,[],[f6791,f741]) ).
fof(f741,plain,
ssList(sF62),
inference(subsumption_resolution,[],[f740,f379]) ).
fof(f740,plain,
( ssList(sF62)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f739,f358]) ).
fof(f739,plain,
( ssList(sF62)
| ~ ssItem(sK11)
| ~ ssList(nil) ),
inference(superposition,[],[f523,f603]) ).
fof(f523,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f6791,plain,
( sF62 = tl(sF63)
| ~ ssList(sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(subsumption_resolution,[],[f6774,f635]) ).
fof(f635,plain,
( ssItem(sK10)
| ~ spl65_5 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f633,plain,
( spl65_5
<=> ssItem(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_5])]) ).
fof(f6774,plain,
( sF62 = tl(sF63)
| ~ ssItem(sK10)
| ~ ssList(sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(superposition,[],[f526,f6376]) ).
fof(f6376,plain,
( sF63 = cons(sK10,sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(subsumption_resolution,[],[f6335,f741]) ).
fof(f6335,plain,
( sF63 = cons(sK10,sF62)
| ~ ssList(sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| ~ spl65_49 ),
inference(superposition,[],[f3821,f3937]) ).
fof(f3937,plain,
( sF63 = app(sF63,sF62)
| ~ spl65_49 ),
inference(superposition,[],[f604,f2028]) ).
fof(f2028,plain,
( sK12 = sF63
| ~ spl65_49 ),
inference(avatar_component_clause,[],[f2026]) ).
fof(f2026,plain,
( spl65_49
<=> sK12 = sF63 ),
introduced(avatar_definition,[new_symbols(naming,[spl65_49])]) ).
fof(f604,plain,
app(sK12,sF62) = sF63,
introduced(function_definition,[new_symbols(definition,[sF63])]) ).
fof(f3821,plain,
( ! [X0] :
( app(sF63,X0) = cons(sK10,X0)
| ~ ssList(X0) )
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47 ),
inference(superposition,[],[f1817,f2017]) ).
fof(f2017,plain,
( sK8 = sF63
| ~ spl65_47 ),
inference(avatar_component_clause,[],[f2015]) ).
fof(f2015,plain,
( spl65_47
<=> sK8 = sF63 ),
introduced(avatar_definition,[new_symbols(naming,[spl65_47])]) ).
fof(f1817,plain,
( ! [X0] :
( cons(sK10,X0) = app(sK8,X0)
| ~ ssList(X0) )
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23 ),
inference(subsumption_resolution,[],[f1794,f635]) ).
fof(f1794,plain,
( ! [X0] :
( cons(sK10,X0) = app(sK8,X0)
| ~ ssItem(sK10)
| ~ ssList(X0) )
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23 ),
inference(superposition,[],[f528,f1311]) ).
fof(f1311,plain,
( sK8 = cons(sK10,nil)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23 ),
inference(superposition,[],[f1269,f1298]) ).
fof(f1298,plain,
( sK10 = sK18(sK8)
| ~ spl65_23 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f1296,plain,
( spl65_23
<=> sK10 = sK18(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_23])]) ).
fof(f1269,plain,
( sK8 = cons(sK18(sK8),nil)
| ~ spl65_4
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1268,f354]) ).
fof(f354,plain,
ssList(sK8),
inference(cnf_transformation,[],[f240]) ).
fof(f1268,plain,
( sK8 = cons(sK18(sK8),nil)
| ~ ssList(sK8)
| ~ spl65_4
| ~ spl65_5 ),
inference(resolution,[],[f1264,f448]) ).
fof(f448,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK18(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK18(X0),nil) = X0
& ssItem(sK18(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f264,f265]) ).
fof(f265,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK18(X0),nil) = X0
& ssItem(sK18(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f264,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f263]) ).
fof(f263,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f1264,plain,
( singletonP(sK8)
| ~ spl65_4
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1263,f354]) ).
fof(f1263,plain,
( ~ ssList(sK8)
| singletonP(sK8)
| ~ spl65_4
| ~ spl65_5 ),
inference(forward_demodulation,[],[f1262,f630]) ).
fof(f630,plain,
( sK8 = sF61
| ~ spl65_4 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f628,plain,
( spl65_4
<=> sK8 = sF61 ),
introduced(avatar_definition,[new_symbols(naming,[spl65_4])]) ).
fof(f1262,plain,
( ~ ssList(sF61)
| singletonP(sK8)
| ~ spl65_4
| ~ spl65_5 ),
inference(forward_demodulation,[],[f1261,f600]) ).
fof(f600,plain,
cons(sK10,nil) = sF61,
introduced(function_definition,[new_symbols(definition,[sF61])]) ).
fof(f1261,plain,
( singletonP(sK8)
| ~ ssList(cons(sK10,nil))
| ~ spl65_4
| ~ spl65_5 ),
inference(forward_demodulation,[],[f1260,f630]) ).
fof(f1260,plain,
( singletonP(sF61)
| ~ ssList(cons(sK10,nil))
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1257,f635]) ).
fof(f1257,plain,
( singletonP(sF61)
| ~ ssItem(sK10)
| ~ ssList(cons(sK10,nil)) ),
inference(superposition,[],[f581,f600]) ).
fof(f581,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f449]) ).
fof(f449,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f528,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f526,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f3810,plain,
( nil = tl(sF63)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_47 ),
inference(superposition,[],[f1231,f2017]) ).
fof(f1231,plain,
( nil = tl(sK8)
| ~ spl65_4
| ~ spl65_5 ),
inference(forward_demodulation,[],[f1230,f630]) ).
fof(f1230,plain,
( nil = tl(sF61)
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1229,f379]) ).
fof(f1229,plain,
( nil = tl(sF61)
| ~ ssList(nil)
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1223,f635]) ).
fof(f1223,plain,
( nil = tl(sF61)
| ~ ssItem(sK10)
| ~ ssList(nil) ),
inference(superposition,[],[f526,f600]) ).
fof(f3907,plain,
( ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| spl65_46
| ~ spl65_62 ),
inference(avatar_contradiction_clause,[],[f3906]) ).
fof(f3906,plain,
( $false
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| spl65_46
| ~ spl65_62 ),
inference(subsumption_resolution,[],[f3055,f3062]) ).
fof(f3062,plain,
( ~ ssList(tl(sF63))
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| spl65_46 ),
inference(subsumption_resolution,[],[f3034,f2013]) ).
fof(f2013,plain,
( ~ frontsegP(sF63,sK8)
| spl65_46 ),
inference(avatar_component_clause,[],[f2011]) ).
fof(f2011,plain,
( spl65_46
<=> frontsegP(sF63,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_46])]) ).
fof(f3034,plain,
( frontsegP(sF63,sK8)
| ~ ssList(tl(sF63))
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23 ),
inference(superposition,[],[f1930,f2879]) ).
fof(f2879,plain,
( sF63 = cons(sK10,tl(sF63))
| ~ spl65_4
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f2878,f755]) ).
fof(f755,plain,
ssList(sF63),
inference(subsumption_resolution,[],[f754,f359]) ).
fof(f359,plain,
ssList(sK12),
inference(cnf_transformation,[],[f240]) ).
fof(f754,plain,
( ssList(sF63)
| ~ ssList(sK12) ),
inference(subsumption_resolution,[],[f750,f741]) ).
fof(f750,plain,
( ssList(sF63)
| ~ ssList(sF62)
| ~ ssList(sK12) ),
inference(superposition,[],[f533,f604]) ).
fof(f533,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f2878,plain,
( sF63 = cons(sK10,tl(sF63))
| ~ ssList(sF63)
| ~ spl65_4
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f2871,f1487]) ).
fof(f1487,plain,
nil != sF63,
inference(subsumption_resolution,[],[f1486,f359]) ).
fof(f1486,plain,
( nil != sF63
| ~ ssList(sK12) ),
inference(subsumption_resolution,[],[f1485,f741]) ).
fof(f1485,plain,
( nil != sF63
| ~ ssList(sF62)
| ~ ssList(sK12) ),
inference(subsumption_resolution,[],[f1482,f801]) ).
fof(f1482,plain,
( nil != sF63
| nil = sF62
| ~ ssList(sF62)
| ~ ssList(sK12) ),
inference(superposition,[],[f552,f604]) ).
fof(f552,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f2871,plain,
( sF63 = cons(sK10,tl(sF63))
| nil = sF63
| ~ ssList(sF63)
| ~ spl65_4
| ~ spl65_5 ),
inference(superposition,[],[f442,f2828]) ).
fof(f2828,plain,
( sK10 = hd(sF63)
| ~ spl65_4
| ~ spl65_5 ),
inference(forward_demodulation,[],[f2369,f1243]) ).
fof(f1243,plain,
( sK10 = hd(sK8)
| ~ spl65_4
| ~ spl65_5 ),
inference(forward_demodulation,[],[f1242,f630]) ).
fof(f1242,plain,
( sK10 = hd(sF61)
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1241,f379]) ).
fof(f1241,plain,
( sK10 = hd(sF61)
| ~ ssList(nil)
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1238,f635]) ).
fof(f1238,plain,
( sK10 = hd(sF61)
| ~ ssItem(sK10)
| ~ ssList(nil) ),
inference(superposition,[],[f527,f600]) ).
fof(f527,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f2369,plain,
hd(sK8) = hd(sF63),
inference(forward_demodulation,[],[f2368,f606]) ).
fof(f606,plain,
sK8 = sF64,
inference(definition_folding,[],[f570,f605,f604,f603]) ).
fof(f605,plain,
app(sF63,sK13) = sF64,
introduced(function_definition,[new_symbols(definition,[sF64])]) ).
fof(f570,plain,
sK8 = app(app(sK12,cons(sK11,nil)),sK13),
inference(definition_unfolding,[],[f361,f357]) ).
fof(f357,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f240]) ).
fof(f361,plain,
sK6 = app(app(sK12,cons(sK11,nil)),sK13),
inference(cnf_transformation,[],[f240]) ).
fof(f2368,plain,
hd(sF63) = hd(sF64),
inference(subsumption_resolution,[],[f2367,f755]) ).
fof(f2367,plain,
( hd(sF63) = hd(sF64)
| ~ ssList(sF63) ),
inference(subsumption_resolution,[],[f2366,f360]) ).
fof(f360,plain,
ssList(sK13),
inference(cnf_transformation,[],[f240]) ).
fof(f2366,plain,
( hd(sF63) = hd(sF64)
| ~ ssList(sK13)
| ~ ssList(sF63) ),
inference(subsumption_resolution,[],[f2337,f1487]) ).
fof(f2337,plain,
( hd(sF63) = hd(sF64)
| nil = sF63
| ~ ssList(sK13)
| ~ ssList(sF63) ),
inference(superposition,[],[f534,f605]) ).
fof(f534,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f442,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f154]) ).
fof(f154,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f1930,plain,
( ! [X0] :
( frontsegP(cons(sK10,X0),sK8)
| ~ ssList(X0) )
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23 ),
inference(subsumption_resolution,[],[f1920,f354]) ).
fof(f1920,plain,
( ! [X0] :
( frontsegP(cons(sK10,X0),sK8)
| ~ ssList(X0)
| ~ ssList(sK8) )
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23 ),
inference(duplicate_literal_removal,[],[f1912]) ).
fof(f1912,plain,
( ! [X0] :
( frontsegP(cons(sK10,X0),sK8)
| ~ ssList(X0)
| ~ ssList(sK8)
| ~ ssList(X0) )
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23 ),
inference(superposition,[],[f655,f1817]) ).
fof(f655,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f597,f533]) ).
fof(f597,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f551]) ).
fof(f551,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK58(X0,X1)) = X0
& ssList(sK58(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f344,f345]) ).
fof(f345,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK58(X0,X1)) = X0
& ssList(sK58(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,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,[],[f343]) ).
fof(f343,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f3055,plain,
( ssList(tl(sF63))
| ~ spl65_62 ),
inference(avatar_component_clause,[],[f3054]) ).
fof(f3054,plain,
( spl65_62
<=> ssList(tl(sF63)) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_62])]) ).
fof(f3905,plain,
spl65_62,
inference(avatar_contradiction_clause,[],[f3904]) ).
fof(f3904,plain,
( $false
| spl65_62 ),
inference(subsumption_resolution,[],[f3903,f755]) ).
fof(f3903,plain,
( ~ ssList(sF63)
| spl65_62 ),
inference(subsumption_resolution,[],[f3902,f1487]) ).
fof(f3902,plain,
( nil = sF63
| ~ ssList(sF63)
| spl65_62 ),
inference(resolution,[],[f3056,f441]) ).
fof(f441,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f3056,plain,
( ~ ssList(tl(sF63))
| spl65_62 ),
inference(avatar_component_clause,[],[f3054]) ).
fof(f3876,plain,
( ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| spl65_48
| spl65_50
| ~ spl65_51
| ~ spl65_66
| ~ spl65_71 ),
inference(avatar_contradiction_clause,[],[f3875]) ).
fof(f3875,plain,
( $false
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| spl65_48
| spl65_50
| ~ spl65_51
| ~ spl65_66
| ~ spl65_71 ),
inference(subsumption_resolution,[],[f3874,f2024]) ).
fof(f2024,plain,
( ~ frontsegP(sK12,sF63)
| spl65_48 ),
inference(avatar_component_clause,[],[f2022]) ).
fof(f2022,plain,
( spl65_48
<=> frontsegP(sK12,sF63) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_48])]) ).
fof(f3874,plain,
( frontsegP(sK12,sF63)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_47
| spl65_50
| ~ spl65_51
| ~ spl65_66
| ~ spl65_71 ),
inference(superposition,[],[f3593,f2017]) ).
fof(f3593,plain,
( frontsegP(sK12,sK8)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| spl65_50
| ~ spl65_51
| ~ spl65_66
| ~ spl65_71 ),
inference(subsumption_resolution,[],[f3067,f3568]) ).
fof(f3568,plain,
( ssList(tl(sK12))
| ~ spl65_66
| ~ spl65_71 ),
inference(forward_demodulation,[],[f3171,f3198]) ).
fof(f3198,plain,
( sK14(sK12) = tl(sK12)
| ~ spl65_71 ),
inference(avatar_component_clause,[],[f3196]) ).
fof(f3196,plain,
( spl65_71
<=> sK14(sK12) = tl(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_71])]) ).
fof(f3171,plain,
( ssList(sK14(sK12))
| ~ spl65_66 ),
inference(avatar_component_clause,[],[f3170]) ).
fof(f3170,plain,
( spl65_66
<=> ssList(sK14(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_66])]) ).
fof(f3067,plain,
( frontsegP(sK12,sK8)
| ~ ssList(tl(sK12))
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| spl65_50
| ~ spl65_51 ),
inference(superposition,[],[f1930,f2895]) ).
fof(f2895,plain,
( sK12 = cons(sK10,tl(sK12))
| ~ spl65_4
| ~ spl65_5
| spl65_50
| ~ spl65_51 ),
inference(subsumption_resolution,[],[f2894,f359]) ).
fof(f2894,plain,
( sK12 = cons(sK10,tl(sK12))
| ~ ssList(sK12)
| ~ spl65_4
| ~ spl65_5
| spl65_50
| ~ spl65_51 ),
inference(subsumption_resolution,[],[f2889,f2352]) ).
fof(f2352,plain,
( nil != sK12
| spl65_50 ),
inference(avatar_component_clause,[],[f2351]) ).
fof(f2351,plain,
( spl65_50
<=> nil = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl65_50])]) ).
fof(f2889,plain,
( sK12 = cons(sK10,tl(sK12))
| nil = sK12
| ~ ssList(sK12)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_51 ),
inference(superposition,[],[f442,f2829]) ).
fof(f2829,plain,
( sK10 = hd(sK12)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_51 ),
inference(forward_demodulation,[],[f2357,f2828]) ).
fof(f2357,plain,
( hd(sK12) = hd(sF63)
| ~ spl65_51 ),
inference(avatar_component_clause,[],[f2355]) ).
fof(f2355,plain,
( spl65_51
<=> hd(sK12) = hd(sF63) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_51])]) ).
fof(f3539,plain,
( ~ spl65_4
| ~ spl65_5
| ~ spl65_7
| spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(avatar_contradiction_clause,[],[f3538]) ).
fof(f3538,plain,
( $false
| ~ spl65_4
| ~ spl65_5
| ~ spl65_7
| spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f3537,f3523]) ).
fof(f3523,plain,
( ~ memberP(nil,sK10)
| ~ spl65_4
| ~ spl65_5
| spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(forward_demodulation,[],[f3522,f3495]) ).
fof(f3495,plain,
( nil = sK13
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(forward_demodulation,[],[f3494,f1233]) ).
fof(f1233,plain,
nil = tl(sF62),
inference(subsumption_resolution,[],[f1232,f379]) ).
fof(f1232,plain,
( nil = tl(sF62)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f1224,f358]) ).
fof(f1224,plain,
( nil = tl(sF62)
| ~ ssItem(sK11)
| ~ ssList(nil) ),
inference(superposition,[],[f526,f603]) ).
fof(f3494,plain,
( sK13 = tl(sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f3493,f360]) ).
fof(f3493,plain,
( sK13 = tl(sF62)
| ~ ssList(sK13)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f3473,f635]) ).
fof(f3473,plain,
( sK13 = tl(sF62)
| ~ ssItem(sK10)
| ~ ssList(sK13)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(superposition,[],[f526,f3440]) ).
fof(f3440,plain,
( sF62 = cons(sK10,sK13)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(forward_demodulation,[],[f3439,f2783]) ).
fof(f2783,plain,
( sK8 = sF62
| ~ spl65_4
| ~ spl65_5
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(superposition,[],[f2749,f1311]) ).
fof(f2749,plain,
( cons(sK10,nil) = sF62
| ~ spl65_4
| ~ spl65_5
| ~ spl65_41
| ~ spl65_50 ),
inference(forward_demodulation,[],[f2748,f1734]) ).
fof(f1734,plain,
( nil = sK14(sF62)
| ~ spl65_41 ),
inference(avatar_component_clause,[],[f1732]) ).
fof(f1732,plain,
( spl65_41
<=> nil = sK14(sF62) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_41])]) ).
fof(f2748,plain,
( sF62 = cons(sK10,sK14(sF62))
| ~ spl65_4
| ~ spl65_5
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f2747,f741]) ).
fof(f2747,plain,
( sF62 = cons(sK10,sK14(sF62))
| ~ ssList(sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f2743,f801]) ).
fof(f2743,plain,
( sF62 = cons(sK10,sK14(sF62))
| nil = sF62
| ~ ssList(sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_50 ),
inference(superposition,[],[f1446,f2737]) ).
fof(f2737,plain,
( sK10 = hd(sF62)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_50 ),
inference(forward_demodulation,[],[f2736,f1243]) ).
fof(f2736,plain,
( hd(sF62) = hd(sK8)
| ~ spl65_50 ),
inference(forward_demodulation,[],[f2369,f2409]) ).
fof(f2409,plain,
( sF62 = sF63
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f2398,f741]) ).
fof(f2398,plain,
( sF62 = sF63
| ~ ssList(sF62)
| ~ spl65_50 ),
inference(superposition,[],[f2378,f436]) ).
fof(f436,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f2378,plain,
( sF63 = app(nil,sF62)
| ~ spl65_50 ),
inference(superposition,[],[f604,f2353]) ).
fof(f2353,plain,
( nil = sK12
| ~ spl65_50 ),
inference(avatar_component_clause,[],[f2351]) ).
fof(f1446,plain,
! [X0] :
( cons(hd(X0),sK14(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f1443]) ).
fof(f1443,plain,
! [X0] :
( cons(hd(X0),sK14(X0)) = X0
| nil = X0
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f439,f1423]) ).
fof(f1423,plain,
! [X0] :
( hd(X0) = sK15(X0)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f1422,f437]) ).
fof(f437,plain,
! [X0] :
( ssList(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0] :
( ( cons(sK15(X0),sK14(X0)) = X0
& ssItem(sK15(X0))
& ssList(sK14(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f149,f257,f256]) ).
fof(f256,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK14(X0)) = X0
& ssItem(X2) )
& ssList(sK14(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK14(X0)) = X0
& ssItem(X2) )
=> ( cons(sK15(X0),sK14(X0)) = X0
& ssItem(sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f1422,plain,
! [X0] :
( hd(X0) = sK15(X0)
| ~ ssList(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f1413,f438]) ).
fof(f438,plain,
! [X0] :
( ssItem(sK15(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f1413,plain,
! [X0] :
( hd(X0) = sK15(X0)
| ~ ssItem(sK15(X0))
| ~ ssList(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f527,f439]) ).
fof(f439,plain,
! [X0] :
( cons(sK15(X0),sK14(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f3439,plain,
( sK8 = cons(sK10,sK13)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_50 ),
inference(forward_demodulation,[],[f3438,f2741]) ).
fof(f2741,plain,
( sK10 = sK11
| ~ spl65_4
| ~ spl65_5
| ~ spl65_50 ),
inference(superposition,[],[f2737,f1245]) ).
fof(f1245,plain,
sK11 = hd(sF62),
inference(subsumption_resolution,[],[f1244,f379]) ).
fof(f1244,plain,
( sK11 = hd(sF62)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f1239,f358]) ).
fof(f1239,plain,
( sK11 = hd(sF62)
| ~ ssItem(sK11)
| ~ ssList(nil) ),
inference(superposition,[],[f527,f603]) ).
fof(f3438,plain,
( sK8 = cons(sK11,sK13)
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f3423,f360]) ).
fof(f3423,plain,
( sK8 = cons(sK11,sK13)
| ~ ssList(sK13)
| ~ spl65_50 ),
inference(superposition,[],[f2732,f1820]) ).
fof(f1820,plain,
! [X0] :
( cons(sK11,X0) = app(sF62,X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f1796,f358]) ).
fof(f1796,plain,
! [X0] :
( cons(sK11,X0) = app(sF62,X0)
| ~ ssItem(sK11)
| ~ ssList(X0) ),
inference(superposition,[],[f528,f603]) ).
fof(f2732,plain,
( sK8 = app(sF62,sK13)
| ~ spl65_50 ),
inference(forward_demodulation,[],[f2410,f606]) ).
fof(f2410,plain,
( sF64 = app(sF62,sK13)
| ~ spl65_50 ),
inference(superposition,[],[f605,f2409]) ).
fof(f3522,plain,
( ~ memberP(sK13,sK10)
| ~ spl65_4
| ~ spl65_5
| spl65_8
| ~ spl65_50 ),
inference(forward_demodulation,[],[f651,f2741]) ).
fof(f651,plain,
( ~ memberP(sK13,sK11)
| spl65_8 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f650,plain,
( spl65_8
<=> memberP(sK13,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_8])]) ).
fof(f3537,plain,
( memberP(nil,sK10)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_7
| ~ spl65_50 ),
inference(forward_demodulation,[],[f3536,f2353]) ).
fof(f3536,plain,
( memberP(sK12,sK10)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_7
| ~ spl65_50 ),
inference(forward_demodulation,[],[f648,f2741]) ).
fof(f648,plain,
( memberP(sK12,sK11)
| ~ spl65_7 ),
inference(avatar_component_clause,[],[f646]) ).
fof(f646,plain,
( spl65_7
<=> memberP(sK12,sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_7])]) ).
fof(f3519,plain,
( ~ spl65_4
| ~ spl65_5
| ~ spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(avatar_contradiction_clause,[],[f3518]) ).
fof(f3518,plain,
( $false
| ~ spl65_4
| ~ spl65_5
| ~ spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(subsumption_resolution,[],[f3516,f635]) ).
fof(f3516,plain,
( ~ ssItem(sK10)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(resolution,[],[f3514,f380]) ).
fof(f380,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f3514,plain,
( memberP(nil,sK10)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(forward_demodulation,[],[f3498,f2741]) ).
fof(f3498,plain,
( memberP(nil,sK11)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_8
| ~ spl65_23
| ~ spl65_41
| ~ spl65_50 ),
inference(superposition,[],[f652,f3495]) ).
fof(f652,plain,
( memberP(sK13,sK11)
| ~ spl65_8 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f3208,plain,
( spl65_50
| spl65_66 ),
inference(avatar_contradiction_clause,[],[f3207]) ).
fof(f3207,plain,
( $false
| spl65_50
| spl65_66 ),
inference(subsumption_resolution,[],[f3206,f359]) ).
fof(f3206,plain,
( ~ ssList(sK12)
| spl65_50
| spl65_66 ),
inference(subsumption_resolution,[],[f3204,f2352]) ).
fof(f3204,plain,
( nil = sK12
| ~ ssList(sK12)
| spl65_66 ),
inference(resolution,[],[f3172,f437]) ).
fof(f3172,plain,
( ~ ssList(sK14(sK12))
| spl65_66 ),
inference(avatar_component_clause,[],[f3170]) ).
fof(f3199,plain,
( ~ spl65_66
| spl65_71
| ~ spl65_4
| ~ spl65_5
| spl65_50
| ~ spl65_51 ),
inference(avatar_split_clause,[],[f3194,f2355,f2351,f633,f628,f3196,f3170]) ).
fof(f3194,plain,
( sK14(sK12) = tl(sK12)
| ~ ssList(sK14(sK12))
| ~ spl65_4
| ~ spl65_5
| spl65_50
| ~ spl65_51 ),
inference(subsumption_resolution,[],[f3161,f635]) ).
fof(f3161,plain,
( sK14(sK12) = tl(sK12)
| ~ ssItem(sK10)
| ~ ssList(sK14(sK12))
| ~ spl65_4
| ~ spl65_5
| spl65_50
| ~ spl65_51 ),
inference(superposition,[],[f526,f2893]) ).
fof(f2893,plain,
( sK12 = cons(sK10,sK14(sK12))
| ~ spl65_4
| ~ spl65_5
| spl65_50
| ~ spl65_51 ),
inference(subsumption_resolution,[],[f2892,f359]) ).
fof(f2892,plain,
( sK12 = cons(sK10,sK14(sK12))
| ~ ssList(sK12)
| ~ spl65_4
| ~ spl65_5
| spl65_50
| ~ spl65_51 ),
inference(subsumption_resolution,[],[f2888,f2352]) ).
fof(f2888,plain,
( sK12 = cons(sK10,sK14(sK12))
| nil = sK12
| ~ ssList(sK12)
| ~ spl65_4
| ~ spl65_5
| ~ spl65_51 ),
inference(superposition,[],[f1446,f2829]) ).
fof(f2358,plain,
( spl65_50
| spl65_51 ),
inference(avatar_split_clause,[],[f2349,f2355,f2351]) ).
fof(f2349,plain,
( hd(sK12) = hd(sF63)
| nil = sK12 ),
inference(subsumption_resolution,[],[f2348,f359]) ).
fof(f2348,plain,
( hd(sK12) = hd(sF63)
| nil = sK12
| ~ ssList(sK12) ),
inference(subsumption_resolution,[],[f2334,f741]) ).
fof(f2334,plain,
( hd(sK12) = hd(sF63)
| nil = sK12
| ~ ssList(sF62)
| ~ ssList(sK12) ),
inference(superposition,[],[f534,f604]) ).
fof(f2029,plain,
( ~ spl65_48
| spl65_49 ),
inference(avatar_split_clause,[],[f2020,f2026,f2022]) ).
fof(f2020,plain,
( sK12 = sF63
| ~ frontsegP(sK12,sF63) ),
inference(subsumption_resolution,[],[f2019,f359]) ).
fof(f2019,plain,
( sK12 = sF63
| ~ frontsegP(sK12,sF63)
| ~ ssList(sK12) ),
inference(subsumption_resolution,[],[f1997,f755]) ).
fof(f1997,plain,
( sK12 = sF63
| ~ frontsegP(sK12,sF63)
| ~ ssList(sF63)
| ~ ssList(sK12) ),
inference(resolution,[],[f539,f917]) ).
fof(f917,plain,
frontsegP(sF63,sK12),
inference(subsumption_resolution,[],[f916,f359]) ).
fof(f916,plain,
( frontsegP(sF63,sK12)
| ~ ssList(sK12) ),
inference(subsumption_resolution,[],[f912,f741]) ).
fof(f912,plain,
( frontsegP(sF63,sK12)
| ~ ssList(sF62)
| ~ ssList(sK12) ),
inference(superposition,[],[f655,f604]) ).
fof(f539,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f2018,plain,
( ~ spl65_46
| spl65_47 ),
inference(avatar_split_clause,[],[f2009,f2015,f2011]) ).
fof(f2009,plain,
( sK8 = sF63
| ~ frontsegP(sF63,sK8) ),
inference(subsumption_resolution,[],[f2008,f755]) ).
fof(f2008,plain,
( sK8 = sF63
| ~ frontsegP(sF63,sK8)
| ~ ssList(sF63) ),
inference(subsumption_resolution,[],[f1994,f354]) ).
fof(f1994,plain,
( sK8 = sF63
| ~ frontsegP(sF63,sK8)
| ~ ssList(sK8)
| ~ ssList(sF63) ),
inference(resolution,[],[f539,f920]) ).
fof(f920,plain,
frontsegP(sK8,sF63),
inference(forward_demodulation,[],[f919,f606]) ).
fof(f919,plain,
frontsegP(sF64,sF63),
inference(subsumption_resolution,[],[f918,f755]) ).
fof(f918,plain,
( frontsegP(sF64,sF63)
| ~ ssList(sF63) ),
inference(subsumption_resolution,[],[f913,f360]) ).
fof(f913,plain,
( frontsegP(sF64,sF63)
| ~ ssList(sK13)
| ~ ssList(sF63) ),
inference(superposition,[],[f655,f605]) ).
fof(f1745,plain,
spl65_39,
inference(avatar_contradiction_clause,[],[f1744]) ).
fof(f1744,plain,
( $false
| spl65_39 ),
inference(subsumption_resolution,[],[f1743,f379]) ).
fof(f1743,plain,
( ~ ssList(nil)
| spl65_39 ),
inference(forward_demodulation,[],[f1742,f1233]) ).
fof(f1742,plain,
( ~ ssList(tl(sF62))
| spl65_39 ),
inference(subsumption_resolution,[],[f1741,f741]) ).
fof(f1741,plain,
( ~ ssList(tl(sF62))
| ~ ssList(sF62)
| spl65_39 ),
inference(subsumption_resolution,[],[f1737,f801]) ).
fof(f1737,plain,
( ~ ssList(tl(sF62))
| nil = sF62
| ~ ssList(sF62)
| spl65_39 ),
inference(superposition,[],[f1723,f1421]) ).
fof(f1421,plain,
! [X0] :
( tl(X0) = sK14(X0)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f1420,f437]) ).
fof(f1420,plain,
! [X0] :
( tl(X0) = sK14(X0)
| ~ ssList(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f1412,f438]) ).
fof(f1412,plain,
! [X0] :
( tl(X0) = sK14(X0)
| ~ ssItem(sK15(X0))
| ~ ssList(sK14(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f526,f439]) ).
fof(f1723,plain,
( ~ ssList(sK14(sF62))
| spl65_39 ),
inference(avatar_component_clause,[],[f1721]) ).
fof(f1721,plain,
( spl65_39
<=> ssList(sK14(sF62)) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_39])]) ).
fof(f1735,plain,
( ~ spl65_39
| spl65_41
| ~ spl65_34 ),
inference(avatar_split_clause,[],[f1730,f1614,f1732,f1721]) ).
fof(f1614,plain,
( spl65_34
<=> sK11 = sK15(sF62) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_34])]) ).
fof(f1730,plain,
( nil = sK14(sF62)
| ~ ssList(sK14(sF62))
| ~ spl65_34 ),
inference(forward_demodulation,[],[f1729,f1233]) ).
fof(f1729,plain,
( tl(sF62) = sK14(sF62)
| ~ ssList(sK14(sF62))
| ~ spl65_34 ),
inference(subsumption_resolution,[],[f1710,f358]) ).
fof(f1710,plain,
( tl(sF62) = sK14(sF62)
| ~ ssItem(sK11)
| ~ ssList(sK14(sF62))
| ~ spl65_34 ),
inference(superposition,[],[f526,f1654]) ).
fof(f1654,plain,
( sF62 = cons(sK11,sK14(sF62))
| ~ spl65_34 ),
inference(subsumption_resolution,[],[f1653,f741]) ).
fof(f1653,plain,
( sF62 = cons(sK11,sK14(sF62))
| ~ ssList(sF62)
| ~ spl65_34 ),
inference(subsumption_resolution,[],[f1648,f801]) ).
fof(f1648,plain,
( sF62 = cons(sK11,sK14(sF62))
| nil = sF62
| ~ ssList(sF62)
| ~ spl65_34 ),
inference(superposition,[],[f439,f1616]) ).
fof(f1616,plain,
( sK11 = sK15(sF62)
| ~ spl65_34 ),
inference(avatar_component_clause,[],[f1614]) ).
fof(f1641,plain,
spl65_33,
inference(avatar_contradiction_clause,[],[f1640]) ).
fof(f1640,plain,
( $false
| spl65_33 ),
inference(subsumption_resolution,[],[f1639,f358]) ).
fof(f1639,plain,
( ~ ssItem(sK11)
| spl65_33 ),
inference(forward_demodulation,[],[f1638,f1245]) ).
fof(f1638,plain,
( ~ ssItem(hd(sF62))
| spl65_33 ),
inference(subsumption_resolution,[],[f1637,f741]) ).
fof(f1637,plain,
( ~ ssItem(hd(sF62))
| ~ ssList(sF62)
| spl65_33 ),
inference(subsumption_resolution,[],[f1633,f801]) ).
fof(f1633,plain,
( ~ ssItem(hd(sF62))
| nil = sF62
| ~ ssList(sF62)
| spl65_33 ),
inference(superposition,[],[f1612,f1423]) ).
fof(f1612,plain,
( ~ ssItem(sK15(sF62))
| spl65_33 ),
inference(avatar_component_clause,[],[f1610]) ).
fof(f1610,plain,
( spl65_33
<=> ssItem(sK15(sF62)) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_33])]) ).
fof(f1617,plain,
( ~ spl65_33
| spl65_34 ),
inference(avatar_split_clause,[],[f1608,f1614,f1610]) ).
fof(f1608,plain,
( sK11 = sK15(sF62)
| ~ ssItem(sK15(sF62)) ),
inference(forward_demodulation,[],[f1607,f1245]) ).
fof(f1607,plain,
( hd(sF62) = sK15(sF62)
| ~ ssItem(sK15(sF62)) ),
inference(subsumption_resolution,[],[f1599,f379]) ).
fof(f1599,plain,
( hd(sF62) = sK15(sF62)
| ~ ssItem(sK15(sF62))
| ~ ssList(nil) ),
inference(superposition,[],[f527,f1522]) ).
fof(f1522,plain,
sF62 = cons(sK15(sF62),nil),
inference(subsumption_resolution,[],[f1521,f741]) ).
fof(f1521,plain,
( sF62 = cons(sK15(sF62),nil)
| ~ ssList(sF62) ),
inference(subsumption_resolution,[],[f1507,f801]) ).
fof(f1507,plain,
( sF62 = cons(sK15(sF62),nil)
| nil = sF62
| ~ ssList(sF62) ),
inference(superposition,[],[f1437,f1233]) ).
fof(f1437,plain,
! [X0] :
( cons(sK15(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f1428]) ).
fof(f1428,plain,
! [X0] :
( cons(sK15(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f439,f1421]) ).
fof(f1309,plain,
( ~ spl65_4
| ~ spl65_5
| spl65_22 ),
inference(avatar_contradiction_clause,[],[f1308]) ).
fof(f1308,plain,
( $false
| ~ spl65_4
| ~ spl65_5
| spl65_22 ),
inference(subsumption_resolution,[],[f1307,f354]) ).
fof(f1307,plain,
( ~ ssList(sK8)
| ~ spl65_4
| ~ spl65_5
| spl65_22 ),
inference(subsumption_resolution,[],[f1306,f1264]) ).
fof(f1306,plain,
( ~ singletonP(sK8)
| ~ ssList(sK8)
| spl65_22 ),
inference(resolution,[],[f1294,f447]) ).
fof(f447,plain,
! [X0] :
( ssItem(sK18(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1294,plain,
( ~ ssItem(sK18(sK8))
| spl65_22 ),
inference(avatar_component_clause,[],[f1292]) ).
fof(f1292,plain,
( spl65_22
<=> ssItem(sK18(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl65_22])]) ).
fof(f1299,plain,
( ~ spl65_22
| spl65_23
| ~ spl65_4
| ~ spl65_5 ),
inference(avatar_split_clause,[],[f1290,f633,f628,f1296,f1292]) ).
fof(f1290,plain,
( sK10 = sK18(sK8)
| ~ ssItem(sK18(sK8))
| ~ spl65_4
| ~ spl65_5 ),
inference(forward_demodulation,[],[f1289,f1243]) ).
fof(f1289,plain,
( hd(sK8) = sK18(sK8)
| ~ ssItem(sK18(sK8))
| ~ spl65_4
| ~ spl65_5 ),
inference(subsumption_resolution,[],[f1284,f379]) ).
fof(f1284,plain,
( hd(sK8) = sK18(sK8)
| ~ ssItem(sK18(sK8))
| ~ ssList(nil)
| ~ spl65_4
| ~ spl65_5 ),
inference(superposition,[],[f527,f1269]) ).
fof(f1194,plain,
~ spl65_2,
inference(avatar_contradiction_clause,[],[f1193]) ).
fof(f1193,plain,
( $false
| ~ spl65_2 ),
inference(subsumption_resolution,[],[f1192,f741]) ).
fof(f1192,plain,
( ~ ssList(sF62)
| ~ spl65_2 ),
inference(subsumption_resolution,[],[f1185,f969]) ).
fof(f969,plain,
( sF62 != sF63
| ~ spl65_2 ),
inference(superposition,[],[f801,f925]) ).
fof(f925,plain,
( nil = sF63
| ~ spl65_2 ),
inference(subsumption_resolution,[],[f924,f755]) ).
fof(f924,plain,
( nil = sF63
| ~ ssList(sF63)
| ~ spl65_2 ),
inference(resolution,[],[f921,f521]) ).
fof(f521,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f921,plain,
( frontsegP(nil,sF63)
| ~ spl65_2 ),
inference(forward_demodulation,[],[f920,f620]) ).
fof(f620,plain,
( nil = sK8
| ~ spl65_2 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f618,plain,
( spl65_2
<=> nil = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl65_2])]) ).
fof(f1185,plain,
( sF62 = sF63
| ~ ssList(sF62)
| ~ spl65_2 ),
inference(resolution,[],[f973,f815]) ).
fof(f815,plain,
rearsegP(sF63,sF62),
inference(subsumption_resolution,[],[f814,f741]) ).
fof(f814,plain,
( rearsegP(sF63,sF62)
| ~ ssList(sF62) ),
inference(subsumption_resolution,[],[f810,f359]) ).
fof(f810,plain,
( rearsegP(sF63,sF62)
| ~ ssList(sK12)
| ~ ssList(sF62) ),
inference(superposition,[],[f654,f604]) ).
fof(f654,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f595,f533]) ).
fof(f595,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f544]) ).
fof(f544,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK55(X0,X1),X1) = X0
& ssList(sK55(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f335,f336]) ).
fof(f336,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK55(X0,X1),X1) = X0
& ssList(sK55(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,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,[],[f334]) ).
fof(f334,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f973,plain,
( ! [X0] :
( ~ rearsegP(sF63,X0)
| sF63 = X0
| ~ ssList(X0) )
| ~ spl65_2 ),
inference(forward_demodulation,[],[f962,f925]) ).
fof(f962,plain,
( ! [X0] :
( ~ rearsegP(sF63,X0)
| nil = X0
| ~ ssList(X0) )
| ~ spl65_2 ),
inference(superposition,[],[f519,f925]) ).
fof(f519,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f326,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f653,plain,
( spl65_7
| spl65_8 ),
inference(avatar_split_clause,[],[f362,f650,f646]) ).
fof(f362,plain,
( memberP(sK13,sK11)
| memberP(sK12,sK11) ),
inference(cnf_transformation,[],[f240]) ).
fof(f636,plain,
( spl65_5
| spl65_2 ),
inference(avatar_split_clause,[],[f367,f618,f633]) ).
fof(f367,plain,
( nil = sK8
| ssItem(sK10) ),
inference(cnf_transformation,[],[f240]) ).
fof(f631,plain,
( spl65_4
| spl65_2 ),
inference(avatar_split_clause,[],[f601,f618,f628]) ).
fof(f601,plain,
( nil = sK8
| sK8 = sF61 ),
inference(definition_folding,[],[f368,f600]) ).
fof(f368,plain,
( nil = sK8
| sK8 = cons(sK10,nil) ),
inference(cnf_transformation,[],[f240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SWC183+1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.14 % Command : run_vampire %s %d THM
% 0.12/0.35 % Computer : n029.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Jun 20 05:01:09 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.37 Running first-order theorem proving
% 0.12/0.37 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.44 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (17764)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.22/0.44 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (17762)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.22/0.44 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (17763)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.22/0.44 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (17760)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.22/0.44 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (17765)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.22/0.44 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (17761)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.22/0.45 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.45 % (17759)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.22/0.50 % (17763)Instruction limit reached!
% 0.22/0.50 % (17763)------------------------------
% 0.22/0.50 % (17763)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.50 % (17763)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.50 % (17763)Termination reason: Time limit
% 0.22/0.50 % (17763)Termination phase: Saturation
% 0.22/0.50
% 0.22/0.50 % (17763)Memory used [KB]: 2228
% 0.22/0.50 % (17763)Time elapsed: 0.060 s
% 0.22/0.50 % (17763)Instructions burned: 109 (million)
% 0.22/0.51 % (17765)Instruction limit reached!
% 0.22/0.51 % (17765)------------------------------
% 0.22/0.51 % (17765)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.51 % (17765)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.51 % (17765)Termination reason: Time limit
% 0.22/0.51 % (17765)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (17765)Memory used [KB]: 2058
% 0.22/0.51 % (17765)Time elapsed: 0.068 s
% 0.22/0.51 % (17765)Instructions burned: 124 (million)
% 0.22/0.51 % (17764)Instruction limit reached!
% 0.22/0.51 % (17764)------------------------------
% 0.22/0.51 % (17764)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.51 % (17764)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.51 % (17764)Termination reason: Time limit
% 0.22/0.51 % (17764)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (17764)Memory used [KB]: 3636
% 0.22/0.51 % (17764)Time elapsed: 0.076 s
% 0.22/0.51 % (17764)Instructions burned: 132 (million)
% 0.22/0.56 % (17758)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.56 % (17766)lrs+1011_1:1_sil=16000:sos=on:erd=off:i=126:nm=2:ep=RST_0 on theBenchmark for (2998ds/126Mi)
% 1.42/0.58 % (17758)Running in auto input_syntax mode. Trying TPTP
% 1.42/0.58 % (17767)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:st=1.5:i=145:ss=axioms:sgt=4_0 on theBenchmark for (2998ds/145Mi)
% 1.42/0.58 % (17759)First to succeed.
% 1.42/0.58 % (17759)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17758"
% 1.42/0.59 % (17758)Running in auto input_syntax mode. Trying TPTP
% 1.42/0.59 % (17759)Refutation found. Thanks to Tanya!
% 1.42/0.59 % SZS status Theorem for theBenchmark
% 1.42/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.59 % (17759)------------------------------
% 1.42/0.59 % (17759)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.42/0.59 % (17759)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.42/0.59 % (17759)Termination reason: Refutation
% 1.42/0.59
% 1.42/0.59 % (17759)Memory used [KB]: 3411
% 1.42/0.59 % (17759)Time elapsed: 0.134 s
% 1.42/0.59 % (17759)Instructions burned: 217 (million)
% 1.42/0.59 % (17759)------------------------------
% 1.42/0.59 % (17759)------------------------------
% 1.42/0.59 % (17758)Success in time 0.203 s
%------------------------------------------------------------------------------