%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC152+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:02:41 PM UTC 2026
% Result : Theorem 4.35s 1.54s
% Output : Refutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 32
% Syntax : Number of formulae : 254 ( 45 unt; 22 def)
% Number of atoms : 1084 ( 127 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 1525 ( 695 ~; 697 |; 79 &)
% ( 23 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 19 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn 141 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| ~ leq(X5,X4)
| ( ! [X9] :
( ~ ssItem(X9)
| ~ memberP(X7,X9)
| ( leq(X4,X9)
& leq(X9,X5) ) )
& leq(X4,X5) ) ) ) ) ) )
| ( ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X2
| ~ memberP(X3,X10)
| ? [X11] :
( ssItem(X11)
& X10 != X11
& memberP(X3,X11)
& leq(X10,X11) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ~ ssList(X8)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| ~ leq(X5,X4)
| ( ! [X9] :
( ~ ssItem(X9)
| ~ memberP(X7,X9)
| ( leq(X4,X9)
& leq(X9,X5) ) )
& leq(X4,X5) ) ) ) ) ) )
| ( ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X2
| ~ memberP(X3,X10)
| ? [X11] :
( ssItem(X11)
& X10 != X11
& memberP(X3,X11)
& leq(X10,X11) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ssList(X8)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X0
& leq(X5,X4)
& ( ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& ( ~ leq(X4,X9)
| ~ leq(X9,X5) ) )
| ~ leq(X4,X5) ) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ( ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X2
& memberP(X3,X10)
& ! [X11] :
( ~ ssItem(X11)
| X10 = X11
| ~ memberP(X3,X11)
| ~ leq(X10,X11) ) )
| ( nil = X3
& nil = X2 ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f234,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,cons(X1,X5)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f233]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK8(X0,X1))
& ssList(sK9(X0,X1))
& app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f234]) ).
fof(f276,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f146]) ).
fof(f277,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f276]) ).
fof(f278,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f147]) ).
fof(f279,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f278]) ).
fof(f291,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f291]) ).
fof(f295,plain,
( ssList(sK56)
& sK54 = sK56
& sK53 = sK55
& ssList(sK61)
& sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61)
& leq(sK58,sK57)
& ( ( ssItem(sK62)
& memberP(sK60,sK62)
& ( ~ leq(sK57,sK62)
| ~ leq(sK62,sK58) ) )
| ~ leq(sK57,sK58) )
& ssList(sK60)
& ssList(sK59)
& ssItem(sK58)
& ssItem(sK57)
& ( ( ssItem(sK63)
& sK55 = cons(sK63,nil)
& memberP(sK56,sK63)
& ! [X11] :
( ~ ssItem(X11)
| sK63 = X11
| ~ memberP(sK56,X11)
| ~ leq(sK63,X11) ) )
| ( nil = sK56
& nil = sK55 ) )
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61,sK62,sK63]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60),skolemize(X8,sK61),skolemize(X9,sK62),skolemize(X10,sK63)],[f221]) ).
fof(f304,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f387,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f395,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f400,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f413,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f414,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f418,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f478,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f479,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f502,plain,
( sK55 = cons(sK63,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( ssItem(sK63)
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
ssList(sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f509,plain,
ssList(sK60),
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
( ~ leq(sK57,sK62)
| ~ leq(sK62,sK58)
| ~ leq(sK57,sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f511,plain,
( memberP(sK60,sK62)
| ~ leq(sK57,sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f512,plain,
( ssItem(sK62)
| ~ leq(sK57,sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f513,plain,
leq(sK58,sK57),
inference(cnf_transformation,[],[f295]) ).
fof(f514,plain,
sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(cnf_transformation,[],[f295]) ).
fof(f515,plain,
ssList(sK61),
inference(cnf_transformation,[],[f295]) ).
fof(f516,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f519,plain,
sK55 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(definition_unfolding,[],[f514,f516]) ).
fof(f523,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f304]) ).
fof(f549,definition,
sF64 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[sF64])],[function_definition]) ).
fof(f550,plain,
cons(sK57,nil) = sF64,
inference(reorient_equations,[],[f549]) ).
fof(f551,definition,
sF65 = app(sK59,sF64),
introduced(definition,[new_symbols(definition,[sF65])],[function_definition]) ).
fof(f552,plain,
app(sK59,sF64) = sF65,
inference(reorient_equations,[],[f551]) ).
fof(f553,definition,
sF66 = app(sF65,sK60),
introduced(definition,[new_symbols(definition,[sF66])],[function_definition]) ).
fof(f554,plain,
app(sF65,sK60) = sF66,
inference(reorient_equations,[],[f553]) ).
fof(f555,definition,
sF67 = cons(sK58,nil),
introduced(definition,[new_symbols(definition,[sF67])],[function_definition]) ).
fof(f556,plain,
cons(sK58,nil) = sF67,
inference(reorient_equations,[],[f555]) ).
fof(f557,definition,
sF68 = app(sF66,sF67),
introduced(definition,[new_symbols(definition,[sF68])],[function_definition]) ).
fof(f558,plain,
app(sF66,sF67) = sF68,
inference(reorient_equations,[],[f557]) ).
fof(f559,definition,
sF69 = app(sF68,sK61),
introduced(definition,[new_symbols(definition,[sF69])],[function_definition]) ).
fof(f560,plain,
app(sF68,sK61) = sF69,
inference(reorient_equations,[],[f559]) ).
fof(f561,plain,
sK55 = sF69,
inference(definition_folding,[],[f519,f560,f558,f556,f554,f552,f550]) ).
fof(f562,definition,
sF70 = cons(sK63,nil),
introduced(definition,[new_symbols(definition,[sF70])],[function_definition]) ).
fof(f563,plain,
cons(sK63,nil) = sF70,
inference(reorient_equations,[],[f562]) ).
fof(f565,plain,
( sK55 = sF70
| nil = sK55 ),
inference(definition_folding,[],[f502,f563]) ).
fof(f574,definition,
( spl71_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl71_1])],[avatar_definition]) ).
fof(f576,plain,
( nil = sK55
| ~ spl71_1 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f593,definition,
( spl71_5
<=> sK55 = sF70 ),
introduced(definition,[new_symbols(definition,[spl71_5])],[avatar_definition]) ).
fof(f595,plain,
( sK55 = sF70
| ~ spl71_5 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f596,plain,
( spl71_1
| spl71_5 ),
inference(avatar_split_clause,[],[f565,f593,f574]) ).
fof(f599,definition,
( spl71_6
<=> ssItem(sK63) ),
introduced(definition,[new_symbols(definition,[spl71_6])],[avatar_definition]) ).
fof(f601,plain,
( ssItem(sK63)
| ~ spl71_6 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f602,plain,
( spl71_1
| spl71_6 ),
inference(avatar_split_clause,[],[f504,f599,f574]) ).
fof(f605,definition,
( spl71_7
<=> leq(sK57,sK58) ),
introduced(definition,[new_symbols(definition,[spl71_7])],[avatar_definition]) ).
fof(f607,plain,
( ~ leq(sK57,sK58)
| spl71_7 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f609,definition,
( spl71_8
<=> leq(sK62,sK58) ),
introduced(definition,[new_symbols(definition,[spl71_8])],[avatar_definition]) ).
fof(f611,plain,
( ~ leq(sK62,sK58)
| spl71_8 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f613,definition,
( spl71_9
<=> leq(sK57,sK62) ),
introduced(definition,[new_symbols(definition,[spl71_9])],[avatar_definition]) ).
fof(f615,plain,
( ~ leq(sK57,sK62)
| spl71_9 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f616,plain,
( ~ spl71_7
| ~ spl71_8
| ~ spl71_9 ),
inference(avatar_split_clause,[],[f510,f613,f609,f605]) ).
fof(f618,definition,
( spl71_10
<=> memberP(sK60,sK62) ),
introduced(definition,[new_symbols(definition,[spl71_10])],[avatar_definition]) ).
fof(f620,plain,
( memberP(sK60,sK62)
| ~ spl71_10 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f621,plain,
( ~ spl71_7
| spl71_10 ),
inference(avatar_split_clause,[],[f511,f618,f605]) ).
fof(f623,definition,
( spl71_11
<=> ssItem(sK62) ),
introduced(definition,[new_symbols(definition,[spl71_11])],[avatar_definition]) ).
fof(f625,plain,
( ssItem(sK62)
| ~ spl71_11 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f626,plain,
( ~ spl71_7
| spl71_11 ),
inference(avatar_split_clause,[],[f512,f623,f605]) ).
fof(f628,definition,
( spl71_12
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl71_12])],[avatar_definition]) ).
fof(f629,plain,
( ssList(nil)
| ~ spl71_12 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f656,plain,
spl71_12,
inference(avatar_split_clause,[],[f388,f628]) ).
fof(f659,plain,
sK55 = app(sF68,sK61),
inference(forward_demodulation,[],[f560,f561]) ).
fof(f660,plain,
! [X0] :
( memberP(app(X0,sF64),sK57)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(app(X0,sF64)) ),
inference(superposition,[],[f523,f550]) ).
fof(f661,plain,
! [X0] :
( memberP(app(X0,sF67),sK58)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK58)
| ~ ssList(app(X0,sF67)) ),
inference(superposition,[],[f523,f556]) ).
fof(f664,plain,
( ! [X0] :
( memberP(app(X0,sF67),sK58)
| ~ ssList(X0)
| ~ ssItem(sK58)
| ~ ssList(app(X0,sF67)) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f661,f629]) ).
fof(f665,plain,
( ! [X0] :
( memberP(app(X0,sF64),sK57)
| ~ ssList(X0)
| ~ ssItem(sK57)
| ~ ssList(app(X0,sF64)) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f660,f629]) ).
fof(f667,plain,
( ! [X0] :
( memberP(app(X0,sF67),sK58)
| ~ ssList(X0)
| ~ ssList(app(X0,sF67)) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f664,f507]) ).
fof(f668,plain,
( ! [X0] :
( memberP(app(X0,sF64),sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,sF64)) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f665,f506]) ).
fof(f671,plain,
! [X0] :
( ~ memberP(sF64,X0)
| memberP(nil,X0)
| sK57 = X0
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssItem(X0) ),
inference(superposition,[],[f415,f550]) ).
fof(f673,plain,
! [X0] :
( ~ memberP(sF70,X0)
| memberP(nil,X0)
| sK63 = X0
| ~ ssList(nil)
| ~ ssItem(sK63)
| ~ ssItem(X0) ),
inference(superposition,[],[f415,f563]) ).
fof(f674,plain,
( ! [X0] :
( ~ memberP(sF70,X0)
| memberP(nil,X0)
| sK63 = X0
| ~ ssItem(sK63)
| ~ ssItem(X0) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f673,f629]) ).
fof(f676,plain,
( ! [X0] :
( ~ memberP(sF64,X0)
| memberP(nil,X0)
| sK57 = X0
| ~ ssItem(sK57)
| ~ ssItem(X0) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f671,f629]) ).
fof(f677,plain,
( ! [X0] :
( ~ memberP(sF70,X0)
| memberP(nil,X0)
| sK63 = X0
| ~ ssItem(X0) )
| ~ spl71_6
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f674,f601]) ).
fof(f679,plain,
( ! [X0] :
( ~ memberP(sF64,X0)
| memberP(nil,X0)
| sK57 = X0
| ~ ssItem(X0) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f676,f506]) ).
fof(f680,plain,
( ! [X0] :
( ~ memberP(sF70,X0)
| sK63 = X0
| ~ ssItem(X0) )
| ~ spl71_6
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f677,f418]) ).
fof(f682,plain,
( ! [X0] :
( ~ memberP(sF64,X0)
| sK57 = X0
| ~ ssItem(X0) )
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f679,f418]) ).
fof(f683,plain,
( ! [X0] :
( ~ memberP(sK55,X0)
| sK63 = X0
| ~ ssItem(X0) )
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12 ),
inference(forward_demodulation,[],[f680,f595]) ).
fof(f685,plain,
! [X0] :
( memberP(sF66,X0)
| ~ memberP(sK60,X0)
| ~ ssList(sK60)
| ~ ssList(sF65)
| ~ ssItem(X0) ),
inference(superposition,[],[f413,f554]) ).
fof(f690,definition,
( spl71_18
<=> ssList(sF66) ),
introduced(definition,[new_symbols(definition,[spl71_18])],[avatar_definition]) ).
fof(f691,plain,
( ssList(sF66)
| ~ spl71_18 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f692,plain,
( ~ ssList(sF66)
| spl71_18 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f694,definition,
( spl71_19
<=> ssList(sF67) ),
introduced(definition,[new_symbols(definition,[spl71_19])],[avatar_definition]) ).
fof(f695,plain,
( ssList(sF67)
| ~ spl71_19 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f701,plain,
! [X0] :
( memberP(sF66,X0)
| ~ memberP(sK60,X0)
| ~ ssList(sF65)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f685,f509]) ).
fof(f704,definition,
( spl71_21
<=> ssList(sF68) ),
introduced(definition,[new_symbols(definition,[spl71_21])],[avatar_definition]) ).
fof(f705,plain,
( ssList(sF68)
| ~ spl71_21 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f706,plain,
( ~ ssList(sF68)
| spl71_21 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f712,definition,
( spl71_23
<=> ssList(sF65) ),
introduced(definition,[new_symbols(definition,[spl71_23])],[avatar_definition]) ).
fof(f713,plain,
( ssList(sF65)
| ~ spl71_23 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f714,plain,
( ~ ssList(sF65)
| spl71_23 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f716,definition,
( spl71_24
<=> ! [X0] :
( memberP(sF66,X0)
| ~ ssItem(X0)
| ~ memberP(sK60,X0) ) ),
introduced(definition,[new_symbols(definition,[spl71_24])],[avatar_definition]) ).
fof(f717,plain,
( ! [X0] :
( ~ memberP(sK60,X0)
| ~ ssItem(X0)
| memberP(sF66,X0) )
| ~ spl71_24 ),
inference(avatar_component_clause,[],[f716]) ).
fof(f718,plain,
( ~ spl71_23
| spl71_24 ),
inference(avatar_split_clause,[],[f701,f716,f712]) ).
fof(f720,definition,
( spl71_25
<=> ssList(sF64) ),
introduced(definition,[new_symbols(definition,[spl71_25])],[avatar_definition]) ).
fof(f721,plain,
( ssList(sF64)
| ~ spl71_25 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f722,plain,
( ~ ssList(sF64)
| spl71_25 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f728,plain,
! [X0] :
( memberP(sF66,X0)
| ~ memberP(sF65,X0)
| ~ ssList(sK60)
| ~ ssList(sF65)
| ~ ssItem(X0) ),
inference(superposition,[],[f414,f554]) ).
fof(f729,plain,
! [X0] :
( memberP(sF68,X0)
| ~ memberP(sF66,X0)
| ~ ssList(sF67)
| ~ ssList(sF66)
| ~ ssItem(X0) ),
inference(superposition,[],[f414,f558]) ).
fof(f730,plain,
! [X0] :
( memberP(sK55,X0)
| ~ memberP(sF68,X0)
| ~ ssList(sK61)
| ~ ssList(sF68)
| ~ ssItem(X0) ),
inference(superposition,[],[f414,f659]) ).
fof(f731,plain,
( ssList(sF64)
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f387,f550]) ).
fof(f732,plain,
( ssList(sF67)
| ~ ssItem(sK58)
| ~ ssList(nil) ),
inference(superposition,[],[f387,f556]) ).
fof(f735,plain,
( ssList(sF67)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f732,f507]) ).
fof(f736,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| spl71_25 ),
inference(forward_subsumption_resolution,[],[f731,f722]) ).
fof(f738,plain,
( ssList(sF67)
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f735,f629]) ).
fof(f739,plain,
( ~ ssList(nil)
| spl71_25 ),
inference(forward_subsumption_resolution,[],[f736,f506]) ).
fof(f741,plain,
( spl71_19
| ~ spl71_12 ),
inference(avatar_split_clause,[],[f738,f628,f694]) ).
fof(f742,plain,
( $false
| ~ spl71_12
| spl71_25 ),
inference(forward_subsumption_resolution,[],[f739,f629]) ).
fof(f743,plain,
( ~ spl71_12
| spl71_25 ),
inference(avatar_contradiction_clause,[],[f742]) ).
fof(f746,plain,
( ssList(sF65)
| ~ ssList(sF64)
| ~ ssList(sK59) ),
inference(superposition,[],[f400,f552]) ).
fof(f747,plain,
( ssList(sF66)
| ~ ssList(sK60)
| ~ ssList(sF65) ),
inference(superposition,[],[f400,f554]) ).
fof(f748,plain,
( ssList(sF68)
| ~ ssList(sF67)
| ~ ssList(sF66) ),
inference(superposition,[],[f400,f558]) ).
fof(f750,plain,
( ~ ssList(sF64)
| ~ ssList(sK59)
| spl71_23 ),
inference(forward_subsumption_resolution,[],[f746,f714]) ).
fof(f751,plain,
( ~ ssList(sK59)
| spl71_23
| ~ spl71_25 ),
inference(forward_subsumption_resolution,[],[f750,f721]) ).
fof(f752,plain,
( $false
| spl71_23
| ~ spl71_25 ),
inference(forward_subsumption_resolution,[],[f751,f508]) ).
fof(f753,plain,
( spl71_23
| ~ spl71_25 ),
inference(avatar_contradiction_clause,[],[f752]) ).
fof(f754,plain,
! [X0] :
( memberP(sF66,X0)
| ~ memberP(sF65,X0)
| ~ ssList(sF65)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f728,f509]) ).
fof(f755,plain,
( ~ ssList(sK60)
| ~ ssList(sF65)
| spl71_18 ),
inference(forward_subsumption_resolution,[],[f747,f692]) ).
fof(f756,plain,
( ! [X0] :
( ~ memberP(sF65,X0)
| memberP(sF66,X0)
| ~ ssItem(X0) )
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f754,f713]) ).
fof(f757,plain,
( ~ ssList(sF65)
| spl71_18 ),
inference(forward_subsumption_resolution,[],[f755,f509]) ).
fof(f758,plain,
( $false
| spl71_18
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f757,f713]) ).
fof(f759,plain,
( spl71_18
| ~ spl71_23 ),
inference(avatar_contradiction_clause,[],[f758]) ).
fof(f760,plain,
( ! [X0] :
( memberP(sF68,X0)
| ~ memberP(sF66,X0)
| ~ ssList(sF66)
| ~ ssItem(X0) )
| ~ spl71_19 ),
inference(forward_subsumption_resolution,[],[f729,f695]) ).
fof(f761,plain,
( ~ ssList(sF67)
| ~ ssList(sF66)
| spl71_21 ),
inference(forward_subsumption_resolution,[],[f748,f706]) ).
fof(f762,plain,
( ! [X0] :
( ~ memberP(sF66,X0)
| memberP(sF68,X0)
| ~ ssItem(X0) )
| ~ spl71_18
| ~ spl71_19 ),
inference(forward_subsumption_resolution,[],[f760,f691]) ).
fof(f763,plain,
( ~ ssList(sF66)
| ~ spl71_19
| spl71_21 ),
inference(forward_subsumption_resolution,[],[f761,f695]) ).
fof(f764,plain,
( $false
| ~ spl71_18
| ~ spl71_19
| spl71_21 ),
inference(forward_subsumption_resolution,[],[f763,f691]) ).
fof(f765,plain,
( ~ spl71_18
| ~ spl71_19
| spl71_21 ),
inference(avatar_contradiction_clause,[],[f764]) ).
fof(f766,plain,
! [X0] :
( memberP(sK55,X0)
| ~ memberP(sF68,X0)
| ~ ssList(sF68)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f730,f515]) ).
fof(f767,plain,
( ! [X0] :
( ~ memberP(sF68,X0)
| memberP(sK55,X0)
| ~ ssItem(X0) )
| ~ spl71_21 ),
inference(forward_subsumption_resolution,[],[f766,f705]) ).
fof(f768,plain,
( memberP(sF65,sK57)
| ~ ssList(sK59)
| ~ ssList(sF65)
| ~ spl71_12 ),
inference(superposition,[],[f668,f552]) ).
fof(f769,plain,
( memberP(sF65,sK57)
| ~ ssList(sF65)
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f768,f508]) ).
fof(f770,plain,
( memberP(sF65,sK57)
| ~ spl71_12
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f769,f713]) ).
fof(f771,plain,
( memberP(sF68,sK58)
| ~ ssList(sF66)
| ~ ssList(sF68)
| ~ spl71_12 ),
inference(superposition,[],[f667,f558]) ).
fof(f772,plain,
( memberP(sF68,sK58)
| ~ ssList(sF68)
| ~ spl71_12
| ~ spl71_18 ),
inference(forward_subsumption_resolution,[],[f771,f691]) ).
fof(f773,plain,
( memberP(sF68,sK58)
| ~ spl71_12
| ~ spl71_18
| ~ spl71_21 ),
inference(forward_subsumption_resolution,[],[f772,f705]) ).
fof(f775,plain,
( nil != sF67
| ~ ssItem(sK58)
| ~ ssList(nil) ),
inference(superposition,[],[f395,f556]) ).
fof(f778,plain,
( nil != sF67
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f775,f507]) ).
fof(f781,plain,
( nil != sF67
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f778,f629]) ).
fof(f798,plain,
( nil != sF68
| nil = sF67
| ~ ssList(sF67)
| ~ ssList(sF66) ),
inference(superposition,[],[f479,f558]) ).
fof(f800,plain,
( nil != sF68
| ~ ssList(sF67)
| ~ ssList(sF66)
| ~ spl71_12 ),
inference(forward_subsumption_resolution,[],[f798,f781]) ).
fof(f803,plain,
( nil != sF68
| ~ ssList(sF66)
| ~ spl71_12
| ~ spl71_19 ),
inference(forward_subsumption_resolution,[],[f800,f695]) ).
fof(f806,plain,
( nil != sF68
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19 ),
inference(forward_subsumption_resolution,[],[f803,f691]) ).
fof(f817,plain,
( memberP(sF66,sK57)
| ~ ssItem(sK57)
| ~ spl71_12
| ~ spl71_23 ),
inference(resolution,[],[f770,f756]) ).
fof(f818,plain,
( memberP(sF66,sK57)
| ~ spl71_12
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f817,f506]) ).
fof(f835,plain,
( nil != sK55
| nil = sF68
| ~ ssList(sK61)
| ~ ssList(sF68) ),
inference(superposition,[],[f478,f659]) ).
fof(f836,plain,
( memberP(sK55,sK58)
| ~ ssItem(sK58)
| ~ spl71_12
| ~ spl71_18
| ~ spl71_21 ),
inference(resolution,[],[f767,f773]) ).
fof(f837,plain,
( memberP(sK55,sK58)
| ~ spl71_12
| ~ spl71_18
| ~ spl71_21 ),
inference(forward_subsumption_resolution,[],[f836,f507]) ).
fof(f864,plain,
( memberP(sF68,sK57)
| ~ ssItem(sK57)
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_23 ),
inference(resolution,[],[f762,f818]) ).
fof(f865,plain,
( memberP(sF68,sK57)
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f864,f506]) ).
fof(f866,plain,
( memberP(sK55,sK57)
| ~ ssItem(sK57)
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(resolution,[],[f865,f767]) ).
fof(f867,plain,
( memberP(sK55,sK57)
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f866,f506]) ).
fof(f868,plain,
( sK57 = sK63
| ~ ssItem(sK57)
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(resolution,[],[f867,f683]) ).
fof(f869,plain,
( sK57 = sK63
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f868,f506]) ).
fof(f871,plain,
( leq(sK58,sK63)
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(superposition,[],[f513,f869]) ).
fof(f872,plain,
( cons(sK63,nil) = sF64
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(superposition,[],[f550,f869]) ).
fof(f879,plain,
( sF64 = sF70
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(forward_demodulation,[],[f872,f563]) ).
fof(f880,plain,
( sK55 = sF64
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(forward_demodulation,[],[f879,f595]) ).
fof(f916,plain,
( sK58 = sK63
| ~ ssItem(sK58)
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_21 ),
inference(resolution,[],[f837,f683]) ).
fof(f918,plain,
( sK58 = sK63
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_21 ),
inference(forward_subsumption_resolution,[],[f916,f507]) ).
fof(f922,plain,
( ~ leq(sK57,sK63)
| ~ spl71_5
| ~ spl71_6
| spl71_7
| ~ spl71_12
| ~ spl71_18
| ~ spl71_21 ),
inference(superposition,[],[f607,f918]) ).
fof(f926,plain,
( leq(sK63,sK63)
| ~ spl71_5
| ~ spl71_6
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(superposition,[],[f871,f918]) ).
fof(f927,plain,
( ~ leq(sK63,sK63)
| ~ spl71_5
| ~ spl71_6
| spl71_7
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(forward_demodulation,[],[f922,f869]) ).
fof(f930,plain,
( $false
| ~ spl71_5
| ~ spl71_6
| spl71_7
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(forward_subsumption_resolution,[],[f927,f926]) ).
fof(f931,plain,
( ~ spl71_5
| ~ spl71_6
| spl71_7
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(avatar_contradiction_clause,[],[f930]) ).
fof(f935,plain,
( ~ leq(sK63,sK62)
| ~ spl71_5
| ~ spl71_6
| spl71_9
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(forward_demodulation,[],[f615,f869]) ).
fof(f937,plain,
( ~ ssItem(sK62)
| memberP(sF66,sK62)
| ~ spl71_10
| ~ spl71_24 ),
inference(resolution,[],[f620,f717]) ).
fof(f938,plain,
( memberP(sF66,sK62)
| ~ spl71_10
| ~ spl71_11
| ~ spl71_24 ),
inference(forward_subsumption_resolution,[],[f937,f625]) ).
fof(f939,plain,
( memberP(sF68,sK62)
| ~ ssItem(sK62)
| ~ spl71_10
| ~ spl71_11
| ~ spl71_18
| ~ spl71_19
| ~ spl71_24 ),
inference(resolution,[],[f938,f762]) ).
fof(f940,plain,
( memberP(sF68,sK62)
| ~ spl71_10
| ~ spl71_11
| ~ spl71_18
| ~ spl71_19
| ~ spl71_24 ),
inference(forward_subsumption_resolution,[],[f939,f625]) ).
fof(f943,plain,
( memberP(sK55,sK62)
| ~ ssItem(sK62)
| ~ spl71_10
| ~ spl71_11
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_24 ),
inference(resolution,[],[f940,f767]) ).
fof(f944,plain,
( memberP(sK55,sK62)
| ~ spl71_10
| ~ spl71_11
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_24 ),
inference(forward_subsumption_resolution,[],[f943,f625]) ).
fof(f945,plain,
( memberP(sF64,sK62)
| ~ spl71_5
| ~ spl71_6
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(forward_demodulation,[],[f944,f880]) ).
fof(f947,plain,
( sK57 = sK62
| ~ ssItem(sK62)
| ~ spl71_5
| ~ spl71_6
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(resolution,[],[f945,f682]) ).
fof(f948,plain,
( sK57 = sK62
| ~ spl71_5
| ~ spl71_6
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(forward_subsumption_resolution,[],[f947,f625]) ).
fof(f950,plain,
( sK62 = sK63
| ~ spl71_5
| ~ spl71_6
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(forward_demodulation,[],[f948,f869]) ).
fof(f954,plain,
( ~ leq(sK63,sK63)
| ~ spl71_5
| ~ spl71_6
| spl71_9
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(superposition,[],[f935,f950]) ).
fof(f959,plain,
( $false
| ~ spl71_5
| ~ spl71_6
| spl71_9
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(forward_subsumption_resolution,[],[f954,f926]) ).
fof(f960,plain,
( ~ spl71_5
| ~ spl71_6
| spl71_9
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(avatar_contradiction_clause,[],[f959]) ).
fof(f963,plain,
( nil = sF68
| ~ ssList(sK61)
| ~ ssList(sF68)
| ~ spl71_1 ),
inference(forward_subsumption_resolution,[],[f835,f576]) ).
fof(f965,plain,
( ~ ssList(sK61)
| ~ ssList(sF68)
| ~ spl71_1
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19 ),
inference(forward_subsumption_resolution,[],[f963,f806]) ).
fof(f967,plain,
( ~ ssList(sF68)
| ~ spl71_1
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19 ),
inference(forward_subsumption_resolution,[],[f965,f515]) ).
fof(f968,plain,
( $false
| ~ spl71_1
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21 ),
inference(forward_subsumption_resolution,[],[f967,f705]) ).
fof(f969,plain,
( ~ spl71_1
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21 ),
inference(avatar_contradiction_clause,[],[f968]) ).
fof(f973,plain,
( ~ leq(sK62,sK63)
| ~ spl71_5
| ~ spl71_6
| spl71_8
| ~ spl71_12
| ~ spl71_18
| ~ spl71_21 ),
inference(forward_demodulation,[],[f611,f918]) ).
fof(f982,plain,
( ~ leq(sK63,sK63)
| ~ spl71_5
| ~ spl71_6
| spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(forward_demodulation,[],[f973,f950]) ).
fof(f989,plain,
( $false
| ~ spl71_5
| ~ spl71_6
| spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(forward_subsumption_resolution,[],[f982,f926]) ).
fof(f990,plain,
( ~ spl71_5
| ~ spl71_6
| spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(avatar_contradiction_clause,[],[f989]) ).
cnf(s5,plain,
( spl71_1
| spl71_5 ),
inference(sat_conversion,[],[f596]) ).
cnf(s7,plain,
( spl71_1
| spl71_6 ),
inference(sat_conversion,[],[f602]) ).
cnf(s9,plain,
( ~ spl71_7
| ~ spl71_8
| ~ spl71_9 ),
inference(sat_conversion,[],[f616]) ).
cnf(s10,plain,
( ~ spl71_7
| spl71_10 ),
inference(sat_conversion,[],[f621]) ).
cnf(s11,plain,
( ~ spl71_7
| spl71_11 ),
inference(sat_conversion,[],[f626]) ).
cnf(s19,plain,
spl71_12,
inference(sat_conversion,[],[f656]) ).
cnf(s22,plain,
( ~ spl71_23
| spl71_24 ),
inference(sat_conversion,[],[f718]) ).
cnf(s24,plain,
( ~ spl71_12
| spl71_19 ),
inference(sat_conversion,[],[f741]) ).
cnf(s25,plain,
( ~ spl71_12
| spl71_25 ),
inference(sat_conversion,[],[f743]) ).
cnf(s26,plain,
( spl71_23
| ~ spl71_25 ),
inference(sat_conversion,[],[f753]) ).
cnf(s27,plain,
( spl71_18
| ~ spl71_23 ),
inference(sat_conversion,[],[f759]) ).
cnf(s28,plain,
( ~ spl71_18
| ~ spl71_19
| spl71_21 ),
inference(sat_conversion,[],[f765]) ).
cnf(s31,plain,
( ~ spl71_5
| ~ spl71_6
| spl71_7
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23 ),
inference(sat_conversion,[],[f931]) ).
cnf(s32,plain,
( ~ spl71_5
| ~ spl71_6
| spl71_9
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(sat_conversion,[],[f960]) ).
cnf(s33,plain,
( ~ spl71_1
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21 ),
inference(sat_conversion,[],[f969]) ).
cnf(s34,plain,
( ~ spl71_5
| ~ spl71_6
| spl71_8
| ~ spl71_10
| ~ spl71_11
| ~ spl71_12
| ~ spl71_18
| ~ spl71_19
| ~ spl71_21
| ~ spl71_23
| ~ spl71_24 ),
inference(sat_conversion,[],[f990]) ).
cnf(s35,plain,
spl71_25,
inference(rat,[],[s25,s19]) ).
cnf(s36,plain,
spl71_19,
inference(rat,[],[s24,s19]) ).
cnf(s37,plain,
spl71_23,
inference(rat,[],[s26,s35]) ).
cnf(s39,plain,
spl71_18,
inference(rat,[],[s27,s37]) ).
cnf(s40,plain,
spl71_24,
inference(rat,[],[s22,s37]) ).
cnf(s41,plain,
spl71_21,
inference(rat,[],[s28,s36,s39]) ).
cnf(s43,plain,
~ spl71_1,
inference(rat,[],[s33,s41,s36,s19,s39]) ).
cnf(s48,plain,
spl71_6,
inference(rat,[],[s7,s43]) ).
cnf(s49,plain,
spl71_5,
inference(rat,[],[s5,s43]) ).
cnf(s50,plain,
spl71_7,
inference(rat,[],[s31,s37,s41,s36,s39,s19,s48,s49]) ).
cnf(s51,plain,
spl71_11,
inference(rat,[],[s11,s50]) ).
cnf(s52,plain,
spl71_10,
inference(rat,[],[s10,s50]) ).
cnf(s53,plain,
spl71_8,
inference(rat,[],[s34,s40,s37,s41,s36,s39,s19,s51,s49,s48,s52]) ).
cnf(s54,plain,
spl71_9,
inference(rat,[],[s32,s40,s37,s41,s36,s39,s19,s51,s49,s48,s52]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s9,s50,s54,s53]) ).
fof(f1005,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC152+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n026.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 08:12:57 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.35/1.54 % (3688261)Detected formulas, will run a generic FOF schedule.
% 4.35/1.54 % (3688266)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3375181438:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.35/1.54 % (3688269)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1349766579:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.35/1.54 % (3688268)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4046829125:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.35/1.54 % (3688267)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=257539555:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.35/1.54 % (3688272)dis-21_1_sil=8000:lcm=predicate:random_seed=2518112354:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.35/1.54 % (3688271)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2498559496:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.35/1.54 % (3688270)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=174120610:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.35/1.54 % (3688269)Instruction limit reached!
% 4.35/1.54 % (3688269)------------------------------
% 4.35/1.54 % (3688269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688269)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688269)Termination reason: Instruction limit
% 4.35/1.54 % (3688269)Termination phase: Saturation
% 4.35/1.54 % (3688269)Time elapsed: 0.066 s
% 4.35/1.54 % (3688269)Peak memory usage: 89 MB
% 4.35/1.54 % (3688269)Instructions burned: 110 (million)
% 4.35/1.54 % (3688270)Instruction limit reached!
% 4.35/1.54 % (3688270)------------------------------
% 4.35/1.54 % (3688270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688270)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688270)Termination reason: Instruction limit
% 4.35/1.54 % (3688270)Termination phase: Saturation
% 4.35/1.54 % (3688270)Time elapsed: 0.067 s
% 4.35/1.54 % (3688270)Peak memory usage: 88 MB
% 4.35/1.54 % (3688270)Instructions burned: 119 (million)
% 4.35/1.54 % (3688272)Instruction limit reached!
% 4.35/1.54 % (3688272)------------------------------
% 4.35/1.54 % (3688272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688272)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688272)Termination reason: Instruction limit
% 4.35/1.54 % (3688272)Termination phase: Saturation
% 4.35/1.54 % (3688272)Time elapsed: 0.069 s
% 4.35/1.54 % (3688272)Peak memory usage: 91 MB
% 4.35/1.54 % (3688272)Instructions burned: 130 (million)
% 4.35/1.54 % (3688271)Instruction limit reached!
% 4.35/1.54 % (3688271)------------------------------
% 4.35/1.54 % (3688271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688271)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688271)Termination reason: Instruction limit
% 4.35/1.54 % (3688271)Termination phase: Saturation
% 4.35/1.54 % (3688271)Time elapsed: 0.092 s
% 4.35/1.54 % (3688271)Peak memory usage: 90 MB
% 4.35/1.54 % (3688271)Instructions burned: 139 (million)
% 4.35/1.54 % (3688280)lrs+10_1_sil=8000:sp=occurrence:random_seed=4232969674:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.35/1.54 % (3688282)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3412580105:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.35/1.54 % (3688281)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1394946356:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.35/1.54 % (3688283)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=927062580:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.35/1.54 % (3688281)Instruction limit reached!
% 4.35/1.54 % (3688281)------------------------------
% 4.35/1.54 % (3688281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688281)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688281)Termination reason: Instruction limit
% 4.35/1.54 % (3688281)Termination phase: Saturation
% 4.35/1.54 % (3688281)Time elapsed: 0.079 s
% 4.35/1.54 % (3688281)Peak memory usage: 94 MB
% 4.35/1.54 % (3688281)Instructions burned: 158 (million)
% 4.35/1.54 % (3688266)First to succeed.
% 4.35/1.54 % (3688266)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3688261"
% 4.35/1.54 % (3688280)Instruction limit reached!
% 4.35/1.54 % (3688280)------------------------------
% 4.35/1.54 % (3688280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688280)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688280)Termination reason: Instruction limit
% 4.35/1.54 % (3688280)Termination phase: Saturation
% 4.35/1.54 % (3688280)Time elapsed: 0.167 s
% 4.35/1.54 % (3688280)Peak memory usage: 92 MB
% 4.35/1.54 % (3688280)Instructions burned: 286 (million)
% 4.35/1.54 % (3688283)Instruction limit reached!
% 4.35/1.54 % (3688283)------------------------------
% 4.35/1.54 % (3688283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688283)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688283)Termination reason: Instruction limit
% 4.35/1.54 % (3688283)Termination phase: Saturation
% 4.35/1.54 % (3688283)Time elapsed: 0.118 s
% 4.35/1.54 % (3688283)Peak memory usage: 94 MB
% 4.35/1.54 % (3688283)Instructions burned: 249 (million)
% 4.35/1.54 % (3688282)Instruction limit reached!
% 4.35/1.54 % (3688282)------------------------------
% 4.35/1.54 % (3688282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.54 % (3688282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.54 % (3688282)CaDiCaL version: 2.1.3
% 4.35/1.54 % (3688282)Termination reason: Instruction limit
% 4.35/1.54 % (3688282)Termination phase: Saturation
% 4.35/1.54 % (3688282)Time elapsed: 0.206 s
% 4.35/1.54 % (3688282)Peak memory usage: 92 MB
% 4.35/1.54 % (3688282)Instructions burned: 326 (million)
% 4.35/1.54 % (3688288)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1405391951:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.35/1.54 % (3688289)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=94661856:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.35/1.54 % (3688290)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3141699764:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.35/1.54 % (3688266)Refutation found. Thanks to Tanya!
% 4.35/1.54 % SZS status Theorem for theBenchmark
% 4.35/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.30/1.74 % (3688266)------------------------------
% 5.30/1.74 % (3688266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.30/1.74 % (3688266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.74 % (3688266)CaDiCaL version: 2.1.3
% 5.30/1.74 % (3688266)Termination reason: Refutation
% 5.30/1.74 % (3688266)Time elapsed: 0.396 s
% 5.30/1.74 % (3688266)Peak memory usage: 132 MB
% 5.30/1.74 % (3688266)Instructions burned: 1041 (million)
% 5.30/1.74 % (3688266)------------------------------
% 5.30/1.74 % (3688266)------------------------------
% 5.30/1.74 % (3688261)Success in time 0.665 s
% 5.30/1.74 % Vampire exiting
%------------------------------------------------------------------------------