%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC172+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 : n010.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 01:02:46 PM UTC 2026
% Result : Theorem 4.66s 1.58s
% Output : Refutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of formulae : 221 ( 41 unt; 16 def)
% Number of atoms : 879 ( 197 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 1203 ( 545 ~; 540 |; 64 &)
% ( 18 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 16 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 132 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
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(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
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(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
fof(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)
=> app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) )
| neq(X4,X5) ) )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X9,X8) ) )
& ( 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)
=> app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) )
| neq(X4,X5) ) )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X2
| ~ memberP(X3,X8)
| ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X3,X9)
& leq(X9,X8) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
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(f129,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
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(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f204]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ? [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ~ neq(X4,X5) )
& ssItem(X4) )
& ( ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X2
& memberP(X3,X8)
& ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X3,X9)
| ~ leq(X9,X8) ) )
| ( nil = X3
& nil = X2 ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f98]) ).
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(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
& ssItem(sK58)
& sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60)
& ssList(sK60)
& ssList(sK59)
& ~ neq(sK57,sK58)
& ssItem(sK57)
& ( ( ssItem(sK61)
& sK55 = cons(sK61,nil)
& memberP(sK56,sK61)
& ! [X9] :
( ~ ssItem(X9)
| sK61 = X9
| ~ memberP(sK56,X9)
| ~ leq(X9,sK61) ) )
| ( 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]),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)],[f221]) ).
fof(f297,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f231]) ).
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(f398,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f399,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f400,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
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(f481,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f483,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( sK55 = cons(sK61,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( ssItem(sK61)
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
~ neq(sK57,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,
sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(cnf_transformation,[],[f295]) ).
fof(f511,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f295]) ).
fof(f512,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f515,plain,
sK55 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(definition_unfolding,[],[f510,f512]) ).
fof(f517,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f512]) ).
fof(f519,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(f545,definition,
sF62 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[sF62])],[function_definition]) ).
fof(f546,plain,
cons(sK57,nil) = sF62,
inference(reorient_equations,[],[f545]) ).
fof(f547,definition,
sF63 = app(sK59,sF62),
introduced(definition,[new_symbols(definition,[sF63])],[function_definition]) ).
fof(f548,plain,
app(sK59,sF62) = sF63,
inference(reorient_equations,[],[f547]) ).
fof(f549,definition,
sF64 = cons(sK58,nil),
introduced(definition,[new_symbols(definition,[sF64])],[function_definition]) ).
fof(f550,plain,
cons(sK58,nil) = sF64,
inference(reorient_equations,[],[f549]) ).
fof(f551,definition,
sF65 = app(sF63,sF64),
introduced(definition,[new_symbols(definition,[sF65])],[function_definition]) ).
fof(f552,plain,
app(sF63,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,plain,
sK55 = sF66,
inference(definition_folding,[],[f515,f554,f552,f550,f548,f546]) ).
fof(f556,definition,
sF67 = cons(sK61,nil),
introduced(definition,[new_symbols(definition,[sF67])],[function_definition]) ).
fof(f557,plain,
cons(sK61,nil) = sF67,
inference(reorient_equations,[],[f556]) ).
fof(f559,plain,
( sK55 = sF67
| nil = sK55 ),
inference(definition_folding,[],[f502,f557]) ).
fof(f568,definition,
( spl68_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl68_1])],[avatar_definition]) ).
fof(f570,plain,
( nil = sK55
| ~ spl68_1 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f587,definition,
( spl68_5
<=> sK55 = sF67 ),
introduced(definition,[new_symbols(definition,[spl68_5])],[avatar_definition]) ).
fof(f589,plain,
( sK55 = sF67
| ~ spl68_5 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f590,plain,
( spl68_1
| spl68_5 ),
inference(avatar_split_clause,[],[f559,f587,f568]) ).
fof(f593,definition,
( spl68_6
<=> ssItem(sK61) ),
introduced(definition,[new_symbols(definition,[spl68_6])],[avatar_definition]) ).
fof(f595,plain,
( ssItem(sK61)
| ~ spl68_6 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f596,plain,
( spl68_1
| spl68_6 ),
inference(avatar_split_clause,[],[f504,f593,f568]) ).
fof(f599,definition,
( spl68_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl68_7])],[avatar_definition]) ).
fof(f600,plain,
( ssList(nil)
| ~ spl68_7 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f627,plain,
spl68_7,
inference(avatar_split_clause,[],[f388,f599]) ).
fof(f630,plain,
sK55 = app(sF65,sK60),
inference(forward_demodulation,[],[f554,f555]) ).
fof(f631,plain,
( sK57 = sK58
| ~ ssItem(sK58)
| ~ ssItem(sK57) ),
inference(resolution,[],[f507,f297]) ).
fof(f642,definition,
( spl68_15
<=> sK57 = sK58 ),
introduced(definition,[new_symbols(definition,[spl68_15])],[avatar_definition]) ).
fof(f644,plain,
( sK57 = sK58
| ~ spl68_15 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f646,plain,
( sK57 = sK58
| ~ ssItem(sK57) ),
inference(forward_subsumption_resolution,[],[f631,f511]) ).
fof(f647,plain,
sK57 = sK58,
inference(forward_subsumption_resolution,[],[f646,f506]) ).
fof(f648,plain,
spl68_15,
inference(avatar_split_clause,[],[f647,f642]) ).
fof(f651,plain,
( cons(sK57,nil) = sF64
| ~ spl68_15 ),
inference(superposition,[],[f550,f644]) ).
fof(f652,plain,
( sF62 = sF64
| ~ spl68_15 ),
inference(forward_demodulation,[],[f651,f546]) ).
fof(f653,plain,
( sF65 = app(sF63,sF62)
| ~ spl68_15 ),
inference(superposition,[],[f552,f652]) ).
fof(f656,plain,
! [X0] :
( ~ memberP(sF67,X0)
| memberP(nil,X0)
| sK61 = X0
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssItem(X0) ),
inference(superposition,[],[f415,f557]) ).
fof(f657,plain,
( ! [X0] :
( ~ memberP(sF67,X0)
| memberP(nil,X0)
| sK61 = X0
| ~ ssItem(sK61)
| ~ ssItem(X0) )
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f656,f600]) ).
fof(f669,plain,
! [X0] :
( memberP(app(X0,sF62),sK57)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(app(X0,sF62)) ),
inference(superposition,[],[f519,f546]) ).
fof(f674,plain,
( ! [X0] :
( memberP(app(X0,sF62),sK57)
| ~ ssList(X0)
| ~ ssItem(sK57)
| ~ ssList(app(X0,sF62)) )
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f669,f600]) ).
fof(f677,plain,
( ! [X0] :
( memberP(app(X0,sF62),sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,sF62)) )
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f674,f506]) ).
fof(f683,plain,
( nil != sF62
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f395,f546]) ).
fof(f688,plain,
( nil != sF62
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f683,f506]) ).
fof(f691,plain,
( nil != sF62
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f688,f600]) ).
fof(f695,plain,
( ssList(sF62)
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f387,f546]) ).
fof(f700,plain,
( ssList(sF62)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f695,f506]) ).
fof(f703,plain,
( ssList(sF62)
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f700,f600]) ).
fof(f706,plain,
( ssList(sF63)
| ~ ssList(sF62)
| ~ ssList(sK59) ),
inference(superposition,[],[f400,f548]) ).
fof(f708,plain,
( ssList(sF65)
| ~ ssList(sF64)
| ~ ssList(sF63) ),
inference(superposition,[],[f400,f552]) ).
fof(f709,plain,
( ~ ssList(sF62)
| ssList(sF65)
| ~ ssList(sF63)
| ~ spl68_15 ),
inference(forward_demodulation,[],[f708,f652]) ).
fof(f710,plain,
( ssList(sF63)
| ~ ssList(sK59)
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f706,f703]) ).
fof(f711,plain,
( ssList(sF65)
| ~ ssList(sF63)
| ~ spl68_7
| ~ spl68_15 ),
inference(forward_subsumption_resolution,[],[f709,f703]) ).
fof(f712,plain,
( ssList(sF63)
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f710,f508]) ).
fof(f714,definition,
( spl68_16
<=> ssList(sF63) ),
introduced(definition,[new_symbols(definition,[spl68_16])],[avatar_definition]) ).
fof(f715,plain,
( ssList(sF63)
| ~ spl68_16 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f718,definition,
( spl68_17
<=> ssList(sF65) ),
introduced(definition,[new_symbols(definition,[spl68_17])],[avatar_definition]) ).
fof(f720,plain,
( ssList(sF65)
| ~ spl68_17 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f721,plain,
( ~ spl68_16
| spl68_17
| ~ spl68_7
| ~ spl68_15 ),
inference(avatar_split_clause,[],[f711,f642,f599,f718,f714]) ).
fof(f722,plain,
( spl68_16
| ~ spl68_7 ),
inference(avatar_split_clause,[],[f712,f599,f714]) ).
fof(f729,plain,
( sF65 = app(sF65,nil)
| ~ spl68_17 ),
inference(resolution,[],[f720,f481]) ).
fof(f731,plain,
( nil != sF63
| nil = sF62
| ~ ssList(sF62)
| ~ ssList(sK59) ),
inference(superposition,[],[f479,f548]) ).
fof(f733,plain,
( nil != sF65
| nil = sF64
| ~ ssList(sF64)
| ~ ssList(sF63) ),
inference(superposition,[],[f479,f552]) ).
fof(f734,plain,
( nil != sF65
| nil = sF64
| ~ ssList(sF64)
| ~ spl68_16 ),
inference(forward_subsumption_resolution,[],[f733,f715]) ).
fof(f735,plain,
( nil != sF63
| ~ ssList(sF62)
| ~ ssList(sK59)
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f731,f691]) ).
fof(f736,plain,
( nil = sF62
| nil != sF65
| ~ ssList(sF64)
| ~ spl68_15
| ~ spl68_16 ),
inference(forward_demodulation,[],[f734,f652]) ).
fof(f737,plain,
( nil != sF63
| ~ ssList(sK59)
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f735,f703]) ).
fof(f738,plain,
( nil != sF65
| ~ ssList(sF64)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16 ),
inference(forward_subsumption_resolution,[],[f736,f691]) ).
fof(f739,plain,
( nil != sF63
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f737,f508]) ).
fof(f740,plain,
( ~ ssList(sF62)
| nil != sF65
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16 ),
inference(forward_demodulation,[],[f738,f652]) ).
fof(f741,plain,
( nil != sF65
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16 ),
inference(forward_subsumption_resolution,[],[f740,f703]) ).
fof(f751,plain,
( nil != sK55
| nil = sF65
| ~ ssList(sK60)
| ~ ssList(sF65) ),
inference(superposition,[],[f478,f630]) ).
fof(f758,plain,
( memberP(sF65,sK57)
| ~ ssList(sF63)
| ~ ssList(sF65)
| ~ spl68_7
| ~ spl68_15 ),
inference(superposition,[],[f677,f653]) ).
fof(f762,plain,
( memberP(sF65,sK57)
| ~ ssList(sF65)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16 ),
inference(forward_subsumption_resolution,[],[f758,f715]) ).
fof(f763,plain,
( memberP(sF65,sK57)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f762,f720]) ).
fof(f859,definition,
( spl68_20
<=> nil = sK60 ),
introduced(definition,[new_symbols(definition,[spl68_20])],[avatar_definition]) ).
fof(f860,plain,
( nil != sK60
| spl68_20 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f861,plain,
( nil = sK60
| ~ spl68_20 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f927,plain,
( ! [X0] :
( ~ ssItem(X0)
| nil = tl(cons(X0,nil)) )
| ~ spl68_7 ),
inference(resolution,[],[f399,f600]) ).
fof(f946,plain,
! [X0] :
( ~ ssList(X0)
| tl(app(X0,sK55)) = app(tl(X0),sK55)
| nil = X0 ),
inference(resolution,[],[f483,f517]) ).
fof(f949,plain,
! [X0] :
( ~ ssList(X0)
| tl(app(X0,sK60)) = app(tl(X0),sK60)
| nil = X0 ),
inference(resolution,[],[f483,f509]) ).
fof(f1000,plain,
( sK55 = app(sF65,nil)
| ~ spl68_20 ),
inference(superposition,[],[f630,f861]) ).
fof(f1001,plain,
( sK55 = sF65
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1000,f729]) ).
fof(f1016,plain,
( tl(app(sF65,sK60)) = app(tl(sF65),sK60)
| nil = sF65
| ~ spl68_17 ),
inference(resolution,[],[f949,f720]) ).
fof(f1017,plain,
( tl(app(sF65,sK60)) = app(tl(sF65),sK60)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1016,f741]) ).
fof(f1176,plain,
( nil != sK55
| ~ ssList(sK60)
| ~ ssList(sF65)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16 ),
inference(forward_subsumption_resolution,[],[f751,f741]) ).
fof(f1183,plain,
( nil != sK55
| ~ ssList(sF65)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16 ),
inference(forward_subsumption_resolution,[],[f1176,f509]) ).
fof(f1187,plain,
( nil != sK55
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1183,f720]) ).
fof(f1198,plain,
( ! [X0] :
( ~ memberP(sF67,X0)
| memberP(nil,X0)
| sK61 = X0
| ~ ssItem(X0) )
| ~ spl68_6
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f657,f595]) ).
fof(f1208,plain,
( ! [X0] :
( ~ memberP(sF67,X0)
| sK61 = X0
| ~ ssItem(X0) )
| ~ spl68_6
| ~ spl68_7 ),
inference(forward_subsumption_resolution,[],[f1198,f418]) ).
fof(f1216,plain,
( ! [X0] :
( ~ memberP(sK55,X0)
| sK61 = X0
| ~ ssItem(X0) )
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7 ),
inference(forward_demodulation,[],[f1208,f589]) ).
fof(f1224,plain,
( ! [X0] :
( ~ memberP(sF65,X0)
| sK61 = X0
| ~ ssItem(X0) )
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1216,f1001]) ).
fof(f1234,plain,
( nil = tl(cons(sK61,nil))
| ~ spl68_6
| ~ spl68_7 ),
inference(resolution,[],[f595,f927]) ).
fof(f1239,plain,
( nil = tl(sF67)
| ~ spl68_6
| ~ spl68_7 ),
inference(forward_demodulation,[],[f1234,f557]) ).
fof(f1243,plain,
( nil = tl(sK55)
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7 ),
inference(forward_demodulation,[],[f1239,f589]) ).
fof(f1247,plain,
( nil = tl(sF65)
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1243,f1001]) ).
fof(f1249,plain,
( sK57 = sK61
| ~ ssItem(sK57)
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(resolution,[],[f1224,f763]) ).
fof(f1250,plain,
( sK57 = sK61
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_subsumption_resolution,[],[f1249,f506]) ).
fof(f1253,plain,
( cons(sK61,nil) = sF62
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(superposition,[],[f546,f1250]) ).
fof(f1260,plain,
( sF62 = sF67
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1253,f557]) ).
fof(f1262,plain,
( sK55 = sF62
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1260,f589]) ).
fof(f1264,plain,
( sF62 = sF65
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1262,f1001]) ).
fof(f1293,plain,
( tl(app(sF63,sK55)) = app(tl(sF63),sK55)
| nil = sF63
| ~ spl68_16 ),
inference(resolution,[],[f946,f715]) ).
fof(f1296,plain,
( tl(app(sF63,sK55)) = app(tl(sF63),sK55)
| ~ spl68_7
| ~ spl68_16 ),
inference(forward_subsumption_resolution,[],[f1293,f739]) ).
fof(f1304,plain,
( tl(app(sF63,sF65)) = app(tl(sF63),sF65)
| ~ spl68_7
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1296,f1001]) ).
fof(f1312,plain,
( tl(app(sF63,sF62)) = app(tl(sF63),sF62)
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1304,f1264]) ).
fof(f1353,plain,
( tl(sF65) = app(tl(sF63),sF62)
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1312,f653]) ).
fof(f1361,plain,
( nil = app(tl(sF63),sF62)
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_demodulation,[],[f1353,f1247]) ).
fof(f1374,plain,
( nil != nil
| nil = sF62
| ~ ssList(sF62)
| ~ ssList(tl(sF63))
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(superposition,[],[f479,f1361]) ).
fof(f1376,plain,
( nil = sF62
| ~ ssList(sF62)
| ~ ssList(tl(sF63))
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(trivial_inequality_removal,[],[f1374]) ).
fof(f1378,plain,
( ~ ssList(sF62)
| ~ ssList(tl(sF63))
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_subsumption_resolution,[],[f1376,f691]) ).
fof(f1383,plain,
( ~ ssList(tl(sF63))
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(forward_subsumption_resolution,[],[f1378,f703]) ).
fof(f1385,definition,
( spl68_26
<=> ssList(tl(sF63)) ),
introduced(definition,[new_symbols(definition,[spl68_26])],[avatar_definition]) ).
fof(f1387,plain,
( ~ ssList(tl(sF63))
| spl68_26 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f1396,plain,
( ~ spl68_26
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20 ),
inference(avatar_split_clause,[],[f1383,f859,f718,f714,f642,f599,f593,f587,f1385]) ).
fof(f1561,plain,
( tl(sK55) = app(tl(sF65),sK60)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1017,f630]) ).
fof(f1568,plain,
( $false
| ~ spl68_1
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1187,f570]) ).
fof(f1569,plain,
( ~ spl68_1
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(avatar_contradiction_clause,[],[f1568]) ).
fof(f1634,plain,
( nil = tl(cons(sK61,nil))
| ~ spl68_6
| ~ spl68_7 ),
inference(resolution,[],[f595,f927]) ).
fof(f1639,plain,
( nil = tl(sF67)
| ~ spl68_6
| ~ spl68_7 ),
inference(forward_demodulation,[],[f1634,f557]) ).
fof(f1643,plain,
( nil = tl(sK55)
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7 ),
inference(forward_demodulation,[],[f1639,f589]) ).
fof(f1723,plain,
( nil != tl(sK55)
| nil = sK60
| ~ ssList(sK60)
| ~ ssList(tl(sF65))
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(superposition,[],[f479,f1561]) ).
fof(f1726,plain,
( nil = sK60
| ~ ssList(sK60)
| ~ ssList(tl(sF65))
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1723,f1643]) ).
fof(f1732,plain,
( ~ ssList(sK60)
| ~ ssList(tl(sF65))
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| spl68_20 ),
inference(forward_subsumption_resolution,[],[f1726,f860]) ).
fof(f1737,plain,
( ~ ssList(tl(sF65))
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| spl68_20 ),
inference(forward_subsumption_resolution,[],[f1732,f509]) ).
fof(f1739,definition,
( spl68_44
<=> ssList(tl(sF65)) ),
introduced(definition,[new_symbols(definition,[spl68_44])],[avatar_definition]) ).
fof(f1741,plain,
( ~ ssList(tl(sF65))
| spl68_44 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f1749,plain,
( ~ spl68_44
| ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| spl68_20 ),
inference(avatar_split_clause,[],[f1737,f859,f718,f714,f642,f599,f593,f587,f1739]) ).
fof(f1988,plain,
( nil = sF63
| ~ ssList(sF63)
| spl68_26 ),
inference(resolution,[],[f398,f1387]) ).
fof(f1990,plain,
( nil = sF65
| ~ ssList(sF65)
| spl68_44 ),
inference(resolution,[],[f398,f1741]) ).
fof(f2013,plain,
( ~ ssList(sF65)
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| spl68_44 ),
inference(forward_subsumption_resolution,[],[f1990,f741]) ).
fof(f2015,plain,
( ~ ssList(sF63)
| ~ spl68_7
| spl68_26 ),
inference(forward_subsumption_resolution,[],[f1988,f739]) ).
fof(f2016,plain,
( $false
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| spl68_44 ),
inference(forward_subsumption_resolution,[],[f2013,f720]) ).
fof(f2017,plain,
( ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| spl68_44 ),
inference(avatar_contradiction_clause,[],[f2016]) ).
fof(f2020,plain,
( $false
| ~ spl68_7
| ~ spl68_16
| spl68_26 ),
inference(forward_subsumption_resolution,[],[f2015,f715]) ).
fof(f2021,plain,
( ~ spl68_7
| ~ spl68_16
| spl68_26 ),
inference(avatar_contradiction_clause,[],[f2020]) ).
cnf(s5,plain,
( spl68_1
| spl68_5 ),
inference(sat_conversion,[],[f590]) ).
cnf(s7,plain,
( spl68_1
| spl68_6 ),
inference(sat_conversion,[],[f596]) ).
cnf(s16,plain,
spl68_7,
inference(sat_conversion,[],[f627]) ).
cnf(s18,plain,
spl68_15,
inference(sat_conversion,[],[f648]) ).
cnf(s20,plain,
( ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| spl68_17 ),
inference(sat_conversion,[],[f721]) ).
cnf(s21,plain,
( ~ spl68_7
| spl68_16 ),
inference(sat_conversion,[],[f722]) ).
cnf(s37,plain,
( ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| ~ spl68_20
| ~ spl68_26 ),
inference(sat_conversion,[],[f1396]) ).
cnf(s57,plain,
( ~ spl68_1
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17 ),
inference(sat_conversion,[],[f1569]) ).
cnf(s64,plain,
( ~ spl68_5
| ~ spl68_6
| ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| spl68_20
| ~ spl68_44 ),
inference(sat_conversion,[],[f1749]) ).
cnf(s77,plain,
( ~ spl68_7
| ~ spl68_15
| ~ spl68_16
| ~ spl68_17
| spl68_44 ),
inference(sat_conversion,[],[f2017]) ).
cnf(s79,plain,
( ~ spl68_7
| ~ spl68_16
| spl68_26 ),
inference(sat_conversion,[],[f2021]) ).
cnf(s84,plain,
spl68_16,
inference(rat,[],[s21,s16]) ).
cnf(s86,plain,
spl68_26,
inference(rat,[],[s79,s16,s84]) ).
cnf(s87,plain,
spl68_17,
inference(rat,[],[s20,s16,s18,s84]) ).
cnf(s88,plain,
~ spl68_1,
inference(rat,[],[s57,s87,s16,s18,s84]) ).
cnf(s90,plain,
spl68_44,
inference(rat,[],[s77,s84,s16,s18,s87]) ).
cnf(s94,plain,
spl68_6,
inference(rat,[],[s7,s88]) ).
cnf(s96,plain,
spl68_5,
inference(rat,[],[s5,s88]) ).
cnf(s104,plain,
spl68_20,
inference(rat,[],[s64,s90,s94,s87,s84,s18,s16,s96]) ).
cnf(s106,plain,
$false,
inference(rat,[],[s37,s86,s94,s87,s84,s18,s16,s104,s96]) ).
fof(f2022,plain,
$false,
inference(avatar_sat_refutation,[],[s106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC172+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 08:16:17 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 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
% 4.66/1.58 % (1766247)Detected formulas, will run a generic FOF schedule.
% 4.66/1.58 % (1766252)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=1554166141:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.66/1.58 % (1766253)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=2683492206:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.66/1.58 % (1766258)dis-21_1_sil=8000:lcm=predicate:random_seed=4254749560: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)
% 4.66/1.58 % (1766254)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=3529629924:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.66/1.58 % (1766255)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1816182900:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.66/1.58 % (1766256)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=443861314:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.66/1.58 % (1766257)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2003539134:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.66/1.58 % (1766255)Instruction limit reached!
% 4.66/1.58 % (1766255)------------------------------
% 4.66/1.58 % (1766255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766255)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766255)Termination reason: Instruction limit
% 4.66/1.58 % (1766255)Termination phase: Saturation
% 4.66/1.58 % (1766255)Time elapsed: 0.066 s
% 4.66/1.58 % (1766255)Peak memory usage: 89 MB
% 4.66/1.58 % (1766255)Instructions burned: 110 (million)
% 4.66/1.58 % (1766256)Instruction limit reached!
% 4.66/1.58 % (1766256)------------------------------
% 4.66/1.58 % (1766256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766256)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766256)Termination reason: Instruction limit
% 4.66/1.58 % (1766256)Termination phase: Saturation
% 4.66/1.58 % (1766256)Time elapsed: 0.066 s
% 4.66/1.58 % (1766256)Peak memory usage: 88 MB
% 4.66/1.58 % (1766256)Instructions burned: 120 (million)
% 4.66/1.58 % (1766258)Instruction limit reached!
% 4.66/1.58 % (1766258)------------------------------
% 4.66/1.58 % (1766258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766258)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766258)Termination reason: Instruction limit
% 4.66/1.58 % (1766258)Termination phase: Saturation
% 4.66/1.58 % (1766258)Time elapsed: 0.073 s
% 4.66/1.58 % (1766258)Peak memory usage: 90 MB
% 4.66/1.58 % (1766258)Instructions burned: 130 (million)
% 4.66/1.58 % (1766257)Instruction limit reached!
% 4.66/1.58 % (1766257)------------------------------
% 4.66/1.58 % (1766257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766257)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766257)Termination reason: Instruction limit
% 4.66/1.58 % (1766257)Termination phase: Saturation
% 4.66/1.58 % (1766257)Time elapsed: 0.094 s
% 4.66/1.58 % (1766257)Peak memory usage: 90 MB
% 4.66/1.58 % (1766257)Instructions burned: 140 (million)
% 4.66/1.58 % (1766267)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3672464205:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.66/1.58 % (1766266)lrs+10_1_sil=8000:sp=occurrence:random_seed=826510680:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.66/1.58 % (1766268)lrs+1011_1_sil=32000:sp=occurrence:random_seed=176820041:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.66/1.58 % (1766269)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=337580519:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.66/1.58 % (1766267)Instruction limit reached!
% 4.66/1.58 % (1766267)------------------------------
% 4.66/1.58 % (1766267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766267)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766267)Termination reason: Instruction limit
% 4.66/1.58 % (1766267)Termination phase: Saturation
% 4.66/1.58 % (1766267)Time elapsed: 0.074 s
% 4.66/1.58 % (1766267)Peak memory usage: 91 MB
% 4.66/1.58 % (1766267)Instructions burned: 158 (million)
% 4.66/1.58 % (1766269)Instruction limit reached!
% 4.66/1.58 % (1766269)------------------------------
% 4.66/1.58 % (1766269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766269)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766269)Termination reason: Instruction limit
% 4.66/1.58 % (1766269)Termination phase: Saturation
% 4.66/1.58 % (1766269)Time elapsed: 0.117 s
% 4.66/1.58 % (1766269)Peak memory usage: 94 MB
% 4.66/1.58 % (1766269)Instructions burned: 248 (million)
% 4.66/1.58 % (1766266)Instruction limit reached!
% 4.66/1.58 % (1766266)------------------------------
% 4.66/1.58 % (1766266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766266)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766266)Termination reason: Instruction limit
% 4.66/1.58 % (1766266)Termination phase: Saturation
% 4.66/1.58 % (1766266)Time elapsed: 0.165 s
% 4.66/1.58 % (1766266)Peak memory usage: 92 MB
% 4.66/1.58 % (1766266)Instructions burned: 285 (million)
% 4.66/1.58 % (1766252)First to succeed.
% 4.66/1.58 % (1766252)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1766247"
% 4.66/1.58 % (1766268)Instruction limit reached!
% 4.66/1.58 % (1766268)------------------------------
% 4.66/1.58 % (1766268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.66/1.58 % (1766268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.66/1.58 % (1766268)CaDiCaL version: 2.1.3
% 4.66/1.58 % (1766268)Termination reason: Instruction limit
% 4.66/1.58 % (1766268)Termination phase: Saturation
% 4.66/1.58 % (1766268)Time elapsed: 0.201 s
% 4.66/1.58 % (1766268)Peak memory usage: 92 MB
% 4.66/1.58 % (1766268)Instructions burned: 325 (million)
% 4.66/1.58 % (1766274)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2423147746:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.66/1.58 % (1766274)Also succeeded, but the first one will report.
% 4.66/1.58 % (1766275)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1114128103:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.66/1.58 % (1766276)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1633389841:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.66/1.58 % (1766252)Refutation found. Thanks to Tanya!
% 4.66/1.58 % SZS status Theorem for theBenchmark
% 4.66/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.80/1.78 % (1766252)------------------------------
% 5.80/1.78 % (1766252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.80/1.78 % (1766252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.80/1.78 % (1766252)CaDiCaL version: 2.1.3
% 5.80/1.78 % (1766252)Termination reason: Refutation
% 5.80/1.78 % (1766252)Time elapsed: 0.458 s
% 5.80/1.78 % (1766252)Peak memory usage: 132 MB
% 5.80/1.78 % (1766252)Instructions burned: 1196 (million)
% 5.80/1.78 % (1766252)------------------------------
% 5.80/1.78 % (1766252)------------------------------
% 5.80/1.78 % (1766247)Success in time 0.751 s
% 5.80/1.78 % Vampire exiting
%------------------------------------------------------------------------------