%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 : Sun Sep 27 08:13:03 AM UTC 2026
% Result : Theorem 30.91s 4.98s
% Output : CNFRefutation 30.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 6
% Syntax : Number of formulae : 68 ( 10 unt; 1 def)
% Number of atoms : 235 ( 63 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 263 ( 96 ~; 139 |; 13 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ) ).
fof(mDefSub,definition,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ) ).
fof(mSubASymm,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X0)
& aSubsetOf0(X0,X1) )
=> X0 = X1 ) ) ).
fof(m__617,hypothesis,
aSet0(xS) ).
fof(m__617_02,hypothesis,
aElementOf0(xx,xS) ).
fof(m__,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtmndt0(xS,xx))
<=> ( X0 != xx
& aElementOf0(X0,xS)
& aElement0(X0) ) )
& aSet0(sdtmndt0(xS,xx)) )
=> ( ( ! [X0] :
( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
<=> ( ( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx)) )
& aElement0(X0) ) )
& aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
=> sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mEOfElem]) ).
cnf(c9,plain,
( ~ aSet0(X1)
| aElementOf0(sK10(X0,X1),X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c10,plain,
( ~ aSet0(X1)
| ~ aElementOf0(sK10(X0,X1),X0)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mDefSub]) ).
cnf(c13,plain,
( ~ aSubsetOf0(X1,X0)
| X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(clausification,[status(esa)],[mSubASymm]) ).
cnf(c39,plain,
aSet0(xS),
inference(clausification,[status(esa)],[m__617]) ).
cnf(c40,plain,
aElementOf0(xx,xS),
inference(clausification,[status(esa)],[m__617_02]) ).
cnf(c43,plain,
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c44,plain,
( ~ aElement0(X0)
| X0 = xx
| ~ aElementOf0(X0,xS)
| aElementOf0(X0,sdtmndt0(xS,xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c46,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) != xS,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c47,plain,
aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
( X0 = xx
| aElementOf0(X0,sdtmndt0(xS,xx))
| ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c50,plain,
( ~ aElement0(X0)
| ~ aElementOf0(X0,sdtmndt0(xS,xx))
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c51,plain,
( ~ aElement0(X0)
| X0 != xx
| aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( aElementOf0(sK10(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| sK10(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[c9,c49]) ).
cnf(d1,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| aElementOf0(sK10(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),sdtmndt0(xS,xx))
| ~ aSet0(X0)
| sK10(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c47,d0]) ).
cnf(d2,plain,
( aElementOf0(sK10(X0,sdtpldt0(sdtmndt0(xS,xx),xx)),xS)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),X0)
| ~ aSet0(X0)
| sK10(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[d1,c43]) ).
cnf(d3,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c47,d3]) ).
cnf(d5,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c39,d4]) ).
cnf(d6,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c47,d6]) ).
cnf(d8,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c39,d7]) ).
cnf(d9,plain,
( ~ aElement0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElementOf0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0),sdtmndt0(xS,xx))
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c10,c50]) ).
cnf(d10,plain,
( aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElementOf0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0),sdtmndt0(xS,xx))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c47,d9]) ).
cnf(d11,plain,
( ~ aElement0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aElementOf0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0),xS)
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0) = xx
| aSubsetOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),X0))
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[d10,c44]) ).
cnf(d12,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| ~ aSet0(xS)
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[d11,c9]) ).
cnf(d13,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| ~ aSet0(xS)
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c47,d12]) ).
cnf(d14,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElement0(sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS))
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c39,d13]) ).
cnf(d15,plain,
( aElement0(sK10(X1,X0))
| ~ aSet0(X0)
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d16,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c47,d16]) ).
cnf(d18,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c39,d17]) ).
cnf(d19,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| sdtpldt0(sdtmndt0(xS,xx),xx) = xS
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[d18,c13]) ).
cnf(d20,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| sdtpldt0(sdtmndt0(xS,xx),xx) = xS
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c47,d19]) ).
cnf(d21,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c46,d20]) ).
cnf(d22,plain,
( ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[c39,d21]) ).
cnf(d23,plain,
( sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx ),
inference(resolution,[status(thm)],[d22,d5]) ).
cnf(d24,plain,
( sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(superposition,[status(thm)],[d23,c10]) ).
cnf(d25,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c47,d24]) ).
cnf(d26,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[c39,d25]) ).
cnf(d27,plain,
( ~ aElement0(xx)
| aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(equality_resolution,[status(thm)],[c51]) ).
cnf(d28,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c40,c0]) ).
cnf(d29,plain,
aElement0(xx),
inference(resolution,[status(thm)],[c39,d28]) ).
cnf(d30,plain,
aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(resolution,[status(thm)],[d29,d27]) ).
cnf(d31,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
( xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx
| sK10(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) = xx ),
inference(resolution,[status(thm)],[d31,d8]) ).
cnf(d33,plain,
( xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aSet0(xS)
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(xx,xS) ),
inference(superposition,[status(thm)],[d32,c10]) ).
cnf(d34,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aElementOf0(xx,xS)
| ~ aSet0(xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c47,d33]) ).
cnf(d35,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| ~ aElementOf0(xx,xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c39,d34]) ).
cnf(d36,plain,
( aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c40,d35]) ).
cnf(d37,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[d36,c13]) ).
cnf(d38,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c47,d37]) ).
cnf(d39,plain,
( ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c39,d38]) ).
cnf(d40,plain,
( sK10(sdtpldt0(sdtmndt0(xS,xx),xx),xS) = xx
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[d36,d22]) ).
cnf(d41,plain,
( xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
inference(superposition,[status(thm)],[d40,c10]) ).
cnf(d42,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aSet0(xS)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c47,d41]) ).
cnf(d43,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| ~ aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[c39,d42]) ).
cnf(d44,plain,
( aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[d30,d43]) ).
cnf(d45,plain,
( xS = sdtpldt0(sdtmndt0(xS,xx),xx)
| xS = sdtpldt0(sdtmndt0(xS,xx),xx) ),
inference(resolution,[status(thm)],[d44,d39]) ).
cnf(d46,plain,
xS != xS,
inference(demodulation,[status(thm)],[c46,d45]) ).
cnf(d47,plain,
$false,
inference(equality_resolution,[status(thm)],[d46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM534+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 03:08:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.91/4.98 % SZS status Theorem for theBenchmark.p
% 30.91/4.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------