%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 07:28:30 AM UTC 2026
% Result : Unsatisfiable 3.68s 1.54s
% Output : CNFRefutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 11
% Syntax : Number of formulae : 103 ( 28 unt; 0 def)
% Number of atoms : 259 ( 258 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 270 ( 114 ~; 156 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 76 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_4,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_15,axiom,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_18,axiom,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_21,axiom,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(sk_c6) != sk_c7
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c7
| inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != VAR_2
| multiply(sk_c7,VAR_2) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c6) != sk_c7
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c7
| inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
cnf(c_1654,plain,
( inverse(sk_c6) != sk_c7
| inverse(A) != sk_c8
| inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_26,plain,
( inverse(sk_c6) != sk_c7
| inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1654]) ).
cnf(c_27,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_1655,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1656,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1655]) ).
cnf(c_28,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1656]) ).
cnf(c_39,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_42,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_70,plain,
( multiply(sk_c7,sk_c6) = identity
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_80,plain,
( multiply(sk_c7,sk_c6) = identity
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_88,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_91,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_28]) ).
cnf(c_92,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_28]) ).
cnf(c_135,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_28,c_28]) ).
cnf(c_136,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_135,c_91]) ).
cnf(c_142,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_136,c_2]) ).
cnf(c_1657,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_42,c_28]) ).
cnf(c_146,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_136,c_1657]) ).
cnf(c_149,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_146,c_2]) ).
cnf(c_1658,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_88,c_28]) ).
cnf(c_269,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_136,c_1658]) ).
cnf(c_272,plain,
( multiply(sk_c7,sk_c6) = identity
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_269,c_2]) ).
cnf(c_1659,plain,
( inverse(sk_c5) = sk_c8
| identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_149,c_5]) ).
cnf(c_305,plain,
( identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_1659]) ).
cnf(c_310,plain,
( multiply(sk_c8,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_305,c_2]) ).
cnf(c_1660,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_310,c_28]) ).
cnf(c_327,plain,
( inverse(sk_c8) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_136,c_1660]) ).
cnf(c_337,plain,
( multiply(sk_c5,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_327,c_2]) ).
cnf(c_1661,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_337,c_4]) ).
cnf(c_385,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1661]) ).
cnf(c_1662,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_337,c_39]) ).
cnf(c_402,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1662]) ).
cnf(c_1663,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_402,c_28]) ).
cnf(c_545,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_136,c_1663]) ).
cnf(c_552,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_545,c_2]) ).
cnf(c_1664,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_552,c_385]) ).
cnf(c_1665,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1664]) ).
cnf(c_786,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_1665]) ).
cnf(c_878,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_786,c_272]) ).
cnf(c_1666,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_786,c_142]) ).
cnf(c_918,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_786,c_1666]) ).
cnf(c_919,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_786,c_136]) ).
cnf(c_1667,plain,
( multiply(sk_c7,sk_c6) = identity
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_919,c_80]) ).
cnf(c_1668,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_786,c_1667]) ).
cnf(c_921,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_1668]) ).
cnf(c_923,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_786,c_70]) ).
cnf(c_927,plain,
multiply(inverse(A),A) = sk_c7,
inference(paramod,[status(thm)],[c_786,c_2]) ).
cnf(c_928,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_786,c_1]) ).
cnf(c_1669,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c7 = sk_c3 ),
inference(paramod,[status(thm)],[c_918,c_878]) ).
cnf(c_1670,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c3 ),
inference(paramod,[status(thm)],[c_928,c_1669]) ).
cnf(c_929,plain,
( sk_c6 = sk_c7
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_1670]) ).
cnf(c_1671,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != C
| C != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_928,c_27]) ).
cnf(c_1672,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != C
| C != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_919,c_1671]) ).
cnf(c_1673,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != C
| sk_c6 != C
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1672]) ).
cnf(c_1018,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != C
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1673]) ).
cnf(c_1674,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_928,c_923]) ).
cnf(c_1022,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_928,c_1674]) ).
cnf(c_1023,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_928,c_921]) ).
cnf(c_1675,plain,
C = multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_1132,plain,
( inverse(sk_c6) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(resolve,[status(thm)],[c_1018,c_1675]) ).
cnf(c_1676,plain,
( inverse(sk_c6) != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_918,c_1132]) ).
cnf(c_1677,plain,
( inverse(sk_c6) != sk_c7
| sk_c7 != sk_c6
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_928,c_1676]) ).
cnf(c_1678,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1677]) ).
cnf(c_1208,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1678]) ).
cnf(c_1679,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_929,c_1023]) ).
cnf(c_1223,plain,
( sk_c4 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_1679]) ).
cnf(c_1680,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1223,c_1022]) ).
cnf(c_1681,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_1680]) ).
cnf(c_1682,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_1681]) ).
cnf(c_1396,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_1682]) ).
cnf(c_1683,plain,
( inverse(sk_c6) != sk_c7
| sk_c7 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1396,c_1208]) ).
cnf(c_1684,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1396,c_1683]) ).
cnf(c_1685,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_918,c_1684]) ).
cnf(c_1686,plain,
( sk_c7 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1685]) ).
cnf(c_1464,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1686]) ).
cnf(c_1687,plain,
multiply(A,sk_c7) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_135,c_919]) ).
cnf(c_1688,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_919,c_1687]) ).
cnf(c_1615,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_1688]) ).
cnf(c_1689,plain,
inverse(inverse(sk_c8)) != sk_c8,
inference(resolve,[status(thm)],[c_927,c_1464]) ).
cnf(c_1690,plain,
sk_c8 != sk_c8,
inference(paramod,[status(thm)],[c_1615,c_1689]) ).
cnf(c_1653,plain,
$false,
inference(copy,[status(thm)],[c_1690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43 % Computer : n005.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8046.5625MB
% 0.11/0.43 % OS : Linux 6.8.0-71-generic
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Fri Sep 25 14:42:03 UTC 2026
% 0.11/0.44 % CPUTime :
% 0.11/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.44 % Process 3719985 was started by sandbox on n005,
% 0.11/0.44 % Fri Sep 25 14:42:03 2026
% 0.11/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.44
% 0.11/0.44 % From the command line: assign(max_seconds, 300).
% 3.68/1.54
% 3.68/1.54 % SZS status Unsatisfiable for theBenchmark
% 3.68/1.54
% 3.68/1.54 % Proof 1 at 0.35 (+ 0.11) seconds.
% 3.68/1.54 % Length of proof is 55.
% 3.68/1.54 % Level of proof is 20.
% 3.68/1.54 % Maximum clause weight is 49.000.
% 3.68/1.54 % Given clauses 178.
% 3.68/1.54
% 3.68/1.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
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