%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 01:33:51 PM UTC 2026
% Result : Unsatisfiable 37.94s 6.03s
% Output : CNFRefutation 37.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 161 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[],[f3]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0))))) = inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),inverse(multiply(inverse(X3),X3)))))),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1)))),inverse(multiply(inverse(multiply(X2,multiply(X1,X3))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1)))))))))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(X3)))),inverse(multiply(inverse(X4),X4))))),
inference(superposition,[status(thm)],[c_51,c_95]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1)))),inverse(multiply(inverse(multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),inverse(multiply(inverse(X3),X3))))))),multiply(X1,inverse(X5)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1)))))))))) = X5,
inference(superposition,[status(thm)],[c_95,c_51]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0))))))) = X2,
inference(superposition,[status(thm)],[c_95,c_51]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))),inverse(multiply(inverse(X0),X0))))) = X2,
inference(superposition,[status(thm)],[c_95,c_51]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))) = inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),inverse(multiply(inverse(X3),X3)))))),
inference(superposition,[status(thm)],[c_133,c_51]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),inverse(multiply(inverse(X1),X1)))))))) = X2,
inference(superposition,[status(thm)],[c_289,c_133]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,inverse(X2))))))),inverse(multiply(inverse(X1),X1))) = X2,
inference(superposition,[status(thm)],[c_289,c_51]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),X3)),inverse(multiply(inverse(X0),X0))))))) = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))))),
inference(superposition,[status(thm)],[c_454,c_454]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),X0)),X3)),inverse(multiply(inverse(X0),X0)))))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_470,c_51]) ).
tcf(c_2078,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))))))) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c_470,c_727]) ).
tcf(c_3805,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(inverse(X1),X1))))))))) = X2,
inference(superposition,[status(thm)],[c_610,c_454]) ).
tcf(c_4237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(superposition,[status(thm)],[c_123,c_3805]) ).
tcf(c_4248,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X1)))),multiply(X0,inverse(multiply(inverse(X1),X1)))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_2078,c_3805]) ).
tcf(c_5143,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_4248,c_4248]) ).
tcf(c_5430,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(X0)),inverse(X0))))))) = X0,
inference(superposition,[status(thm)],[c_5143,c_51]) ).
tcf(c_5440,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X3),X3))))))) = X2,
inference(superposition,[status(thm)],[c_5143,c_123]) ).
tcf(c_5443,plain,
! [X0: $i] : multiply(multiply(inverse(X0),X0),a2) != a2,
inference(superposition,[status(thm)],[c_5143,c_52]) ).
tcf(c_5492,plain,
! [X0: $i,X1: $i] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X0),X0))))))) = X0,
inference(superposition,[status(thm)],[c_5143,c_123]) ).
tcf(c_5497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(X0),X1)),multiply(inverse(X2),X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X0)),
inference(superposition,[status(thm)],[c_5143,c_4237]) ).
tcf(c_5510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(superposition,[status(thm)],[c_5143,c_4237]) ).
tcf(c_6407,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))))))) = X0,
inference(superposition,[status(thm)],[c_5143,c_5492]) ).
tcf(c_6676,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),X1)),a2) != a2,
inference(superposition,[status(thm)],[c_5497,c_5443]) ).
tcf(c_6767,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),X1))),multiply(inverse(X2),X2)),a2) != a2,
inference(superposition,[status(thm)],[c_5497,c_6676]) ).
tcf(c_7132,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2)))))) = X0,
inference(superposition,[status(thm)],[c_5143,c_5430]) ).
tcf(c_7439,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,multiply(inverse(X1),X1))),multiply(X0,multiply(inverse(X2),X2))),a2) != a2,
inference(superposition,[status(thm)],[c_4237,c_6767]) ).
tcf(c_7530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(inverse(multiply(inverse(X0),X1)),multiply(inverse(X2),X2))),multiply(inverse(multiply(X3,X1)),multiply(X3,X0))),a2) != a2,
inference(superposition,[status(thm)],[c_4237,c_7439]) ).
tcf(c_8310,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X1),X1)))) = inverse(multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_5143,c_7132]) ).
tcf(c_8441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(multiply(inverse(multiply(inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X3),X3))),multiply(X4,multiply(inverse(X4),X0))),a2) != a2,
inference(superposition,[status(thm)],[c_7132,c_7530]) ).
tcf(c_8444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X3),X3)) = multiply(X4,multiply(inverse(X4),X0)),
inference(superposition,[status(thm)],[c_7132,c_5497]) ).
tcf(c_8455,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X1,multiply(inverse(X2),X2)),
inference(light_normalisation,[status(thm)],[c_8444,c_7132]) ).
tcf(c_8457,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,multiply(inverse(X1),X1))),multiply(X2,multiply(inverse(X2),X0))),a2) != a2,
inference(light_normalisation,[status(thm)],[c_8441,c_7132]) ).
tcf(c_8844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(inverse(multiply(X1,X2)),multiply(X1,X2))) = multiply(X3,multiply(inverse(X3),X0)),
inference(superposition,[status(thm)],[c_5510,c_8455]) ).
tcf(c_8975,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X2,multiply(inverse(X2),X1)),
inference(superposition,[status(thm)],[c_8455,c_8455]) ).
tcf(c_10510,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,multiply(inverse(X0),X1))),multiply(X2,multiply(inverse(X2),X1))),a2) != a2,
inference(superposition,[status(thm)],[c_8975,c_8457]) ).
tcf(c_12109,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),inverse(multiply(inverse(X1),X1)))) = X0,
inference(superposition,[status(thm)],[c_8310,c_7132]) ).
tcf(c_12303,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X0)) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[c_8310,c_12109]) ).
tcf(c_12310,plain,
! [X0: $i,X1: $i] : inverse(inverse(multiply(X0,multiply(inverse(X1),X1)))) = X0,
inference(demodulation,[status(thm)],[c_6407,c_12109]) ).
tcf(c_13021,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(X0),X0)),a2) != a2,
inference(superposition,[status(thm)],[c_12303,c_10510]) ).
tcf(c_13023,plain,
multiply(inverse(multiply(inverse(a2),a2)),a2) != a2,
inference(instantiation,[status(thm)],[c_13021]) ).
tcf(c_13625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2))),multiply(X2,multiply(X1,X3)))) = multiply(X4,multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(X3)))),
inference(demodulation,[status(thm)],[c_112,c_12109]) ).
tcf(c_14489,plain,
! [X0: $i,X1: $i] : inverse(inverse(multiply(X0,multiply(inverse(X0),X1)))) = X1,
inference(superposition,[status(thm)],[c_8975,c_12310]) ).
tcf(c_19025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2))),multiply(X2,multiply(X1,inverse(X3))))) = X3,
inference(demodulation,[status(thm)],[c_119,c_5440,c_12109]) ).
tcf(c_19268,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(inverse(X2))))) = X2,
inference(superposition,[status(thm)],[c_19025,c_13625]) ).
tcf(c_44303,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),inverse(inverse(X1)))) = X1,
inference(superposition,[status(thm)],[c_19268,c_8844]) ).
tcf(c_44901,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),inverse(inverse(X1))) = inverse(inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[c_44303,c_14489]) ).
tcf(c_46305,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(inverse(multiply(X0,X1)))) = X1,
inference(superposition,[status(thm)],[c_44901,c_44303]) ).
tcf(c_46598,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(inverse(X1),X0)),X2)) = multiply(X1,X2),
inference(superposition,[status(thm)],[c_46305,c_19268]) ).
tcf(c_49245,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),inverse(inverse(multiply(X1,X2)))) = multiply(inverse(multiply(inverse(X1),X0)),X2),
inference(superposition,[status(thm)],[c_46598,c_46305]) ).
tcf(c_49407,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(demodulation,[status(thm)],[c_46305,c_49245]) ).
tcf(c_49408,plain,
multiply(inverse(multiply(inverse(a2),a2)),a2) = a2,
inference(instantiation,[status(thm)],[c_49407]) ).
tcf(c_49409,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_49408,c_13023]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP416-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.59 % Computer : n005.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Wed Sep 23 14:42:18 UTC 2026
% 0.10/0.60 % CPUTime :
% 0.10/0.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.63 Running UEQ theorem proving
% 0.16/0.63 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.64
% 0.16/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.64
% 0.16/0.64 % Detected problem language: tptp
% 0.16/0.66 % Proving...
% 37.94/6.03 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 37.94/6.03 % SZS status Started for theBenchmark.p
% 37.94/6.03 % SZS status Unsatisfiable for theBenchmark.p
% 37.94/6.03
% 37.94/6.03 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 37.94/6.03
% 37.94/6.03 % ------ iProver source info
% 37.94/6.03
% 37.94/6.03 % git: date: 2026-07-19 20:42:38 +0200
% 37.94/6.03 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 37.94/6.03 % git: non_committed_changes: false
% 37.94/6.03
% 37.94/6.03 % ------ Parsing...% successful
% 37.94/6.03
% 37.94/6.03
% 37.94/6.03 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 37.94/6.03
% 37.94/6.03 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 37.94/6.03
% 37.94/6.03 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 37.94/6.03
% 37.94/6.03 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 37.94/6.03 % ------ Proving...
% 37.94/6.03 % ------ Problem Properties
% 37.94/6.03
% 37.94/6.03 %
% 37.94/6.03 % clauses 2
% 37.94/6.03 % conjectures 1
% 37.94/6.03 % EPR 0
% 37.94/6.03 % Horn 2
% 37.94/6.03 % unary 2
% 37.94/6.03 % binary 0
% 37.94/6.03 % lits 2
% 37.94/6.03 % lits eq 2
% 37.94/6.03 % fd_pure 0
% 37.94/6.03 % fd_pseudo 0
% 37.94/6.03 % fd_cond 0
% 37.94/6.03 % fd_pseudo_cond 0
% 37.94/6.03 % AC symbols 0
% 37.94/6.03
% 37.94/6.03 % ------ Input Options Time Limit: Unbounded
% 37.94/6.03
% 37.94/6.03
% 37.94/6.03 % ------
% 37.94/6.03 % Current options:
% 37.94/6.03 % ------
% 37.94/6.03
% 37.94/6.03
% 37.94/6.03 %
% 37.94/6.03
% 37.94/6.03 % ------ Proving...
% 37.94/6.03 %
% 37.94/6.03
% 37.94/6.03 % SZS status Unsatisfiable for theBenchmark.p
% 37.94/6.03
% 37.94/6.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 37.94/6.03
% 37.94/6.03
%------------------------------------------------------------------------------