TSTP Solution File: GRP071-1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRP071-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:57:15 EDT 2023
% Result : Unsatisfiable 126.86s 17.80s
% Output : CNFRefutation 126.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 3
% Syntax : Number of clauses : 85 ( 81 unt; 0 nHn; 6 RR)
% Number of literals : 91 ( 90 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 284 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
divide(inverse(divide(X0,divide(X1,divide(X2,X3)))),divide(divide(X3,X2),X0)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c_50,plain,
divide(X0,inverse(X1)) = multiply(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_51,negated_conjecture,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_166,plain,
divide(inverse(divide(X0,divide(X1,multiply(X2,X3)))),divide(divide(inverse(X3),X2),X0)) = X1,
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_167,plain,
divide(inverse(divide(inverse(X0),divide(X1,divide(X2,X3)))),multiply(divide(X3,X2),X0)) = X1,
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_169,plain,
divide(inverse(divide(X0,divide(X1,divide(inverse(X2),X3)))),divide(multiply(X3,X2),X0)) = X1,
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_171,plain,
divide(inverse(divide(X0,X1)),divide(divide(X2,divide(X3,X4)),X0)) = inverse(divide(X2,divide(X1,divide(X4,X3)))),
inference(superposition,[status(thm)],[c_49,c_49]) ).
cnf(c_457,plain,
divide(inverse(X0),multiply(divide(X1,X2),divide(divide(X2,X1),divide(X0,divide(X3,X4))))) = divide(X4,X3),
inference(superposition,[status(thm)],[c_49,c_167]) ).
cnf(c_458,plain,
divide(inverse(X0),multiply(divide(X1,X2),divide(divide(X2,X1),divide(X0,multiply(X3,X4))))) = divide(inverse(X4),X3),
inference(superposition,[status(thm)],[c_166,c_167]) ).
cnf(c_466,plain,
divide(inverse(divide(inverse(X0),divide(X1,divide(inverse(X2),X3)))),multiply(multiply(X3,X2),X0)) = X1,
inference(superposition,[status(thm)],[c_50,c_167]) ).
cnf(c_470,plain,
divide(inverse(divide(X0,divide(X1,X2))),divide(divide(multiply(divide(X3,X4),X5),inverse(divide(inverse(X5),divide(X2,divide(X4,X3))))),X0)) = X1,
inference(superposition,[status(thm)],[c_167,c_49]) ).
cnf(c_819,plain,
divide(inverse(X0),multiply(divide(X1,X2),divide(divide(X2,X1),divide(X0,divide(inverse(X3),X4))))) = multiply(X4,X3),
inference(superposition,[status(thm)],[c_169,c_167]) ).
cnf(c_174990,plain,
divide(inverse(divide(X0,divide(X1,multiply(X2,X3)))),divide(divide(inverse(X3),X2),X0)) = X1,
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_174993,plain,
divide(inverse(divide(X0,divide(X1,divide(inverse(X2),X3)))),divide(multiply(X3,X2),X0)) = X1,
inference(superposition,[status(thm)],[c_50,c_49]) ).
cnf(c_176394,plain,
inverse(divide(X0,divide(divide(X1,divide(divide(X2,X3),X0)),divide(X3,X2)))) = X1,
inference(superposition,[status(thm)],[c_171,c_49]) ).
cnf(c_176405,plain,
inverse(divide(inverse(X0),divide(divide(X1,multiply(divide(X2,X3),X0)),divide(X3,X2)))) = X1,
inference(superposition,[status(thm)],[c_171,c_174990]) ).
cnf(c_176669,plain,
inverse(inverse(divide(X0,divide(X1,divide(inverse(divide(divide(X2,X3),X1)),divide(X3,X2)))))) = X0,
inference(superposition,[status(thm)],[c_171,c_176394]) ).
cnf(c_176674,plain,
inverse(divide(X0,divide(divide(X1,divide(multiply(X2,X3),X0)),divide(inverse(X3),X2)))) = X1,
inference(superposition,[status(thm)],[c_50,c_176394]) ).
cnf(c_176695,plain,
multiply(X0,divide(X1,divide(divide(X2,divide(divide(X3,X4),X1)),divide(X4,X3)))) = divide(X0,X2),
inference(superposition,[status(thm)],[c_176394,c_50]) ).
cnf(c_176711,plain,
divide(X0,divide(divide(X1,inverse(X2)),X3)) = divide(X0,divide(multiply(X1,X2),X3)),
inference(superposition,[status(thm)],[c_176394,c_174993]) ).
cnf(c_177252,plain,
inverse(divide(inverse(X0),divide(divide(X1,multiply(multiply(X2,X3),X0)),divide(inverse(X3),X2)))) = X1,
inference(superposition,[status(thm)],[c_50,c_176405]) ).
cnf(c_177495,plain,
multiply(X0,divide(X1,divide(divide(X2,divide(multiply(X3,X4),X1)),divide(inverse(X4),X3)))) = divide(X0,X2),
inference(superposition,[status(thm)],[c_176674,c_50]) ).
cnf(c_177882,plain,
inverse(divide(divide(inverse(divide(divide(X0,X1),divide(X2,X3))),divide(X1,X0)),divide(X4,divide(X3,X2)))) = inverse(inverse(X4)),
inference(superposition,[status(thm)],[c_49,c_176669]) ).
cnf(c_177890,plain,
inverse(inverse(divide(X0,divide(inverse(X1),divide(inverse(multiply(divide(X2,X3),X1)),divide(X3,X2)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_176669]) ).
cnf(c_182099,plain,
divide(inverse(X0),multiply(divide(X1,X2),divide(divide(X2,X1),divide(X0,divide(inverse(X3),X4))))) = divide(multiply(divide(X5,X6),divide(divide(X6,X5),divide(X7,multiply(X4,X3)))),inverse(X7)),
inference(superposition,[status(thm)],[c_458,c_457]) ).
cnf(c_182128,plain,
divide(multiply(divide(X0,X1),divide(divide(X1,X0),divide(X2,multiply(X3,X4)))),inverse(X2)) = multiply(X3,X4),
inference(light_normalisation,[status(thm)],[c_182099,c_819]) ).
cnf(c_182390,plain,
multiply(multiply(divide(X0,X1),divide(divide(X1,X0),divide(X2,multiply(X3,X4)))),X2) = multiply(X3,X4),
inference(demodulation,[status(thm)],[c_182128,c_50]) ).
cnf(c_182426,plain,
multiply(multiply(divide(X0,X1),divide(divide(X1,X0),divide(X2,divide(X3,X4)))),X2) = divide(X3,X4),
inference(superposition,[status(thm)],[c_176695,c_182390]) ).
cnf(c_182568,plain,
multiply(multiply(divide(X0,X1),divide(divide(X1,X0),divide(X2,X3))),X2) = X3,
inference(superposition,[status(thm)],[c_466,c_182426]) ).
cnf(c_182677,plain,
multiply(divide(divide(X0,X1),X2),divide(X2,divide(multiply(X3,X4),divide(X1,X0)))) = divide(inverse(X4),X3),
inference(superposition,[status(thm)],[c_177495,c_182568]) ).
cnf(c_186004,plain,
multiply(multiply(divide(X0,X1),X2),divide(inverse(X2),divide(multiply(X3,X4),divide(X1,X0)))) = divide(inverse(X4),X3),
inference(superposition,[status(thm)],[c_50,c_182677]) ).
cnf(c_209554,plain,
divide(inverse(inverse(X0)),divide(divide(X1,X2),divide(inverse(divide(divide(X3,X4),divide(X1,X2))),divide(X4,X3)))) = X0,
inference(superposition,[status(thm)],[c_177882,c_49]) ).
cnf(c_210299,plain,
divide(inverse(inverse(X0)),divide(X1,divide(inverse(divide(divide(X2,X3),X1)),divide(X3,X2)))) = X0,
inference(superposition,[status(thm)],[c_209554,c_209554]) ).
cnf(c_210664,plain,
divide(inverse(X0),multiply(multiply(divide(X1,X2),divide(divide(X2,X1),X3)),inverse(X0))) = X3,
inference(superposition,[status(thm)],[c_210299,c_466]) ).
cnf(c_211243,plain,
divide(X0,multiply(multiply(divide(X1,X2),divide(divide(X2,X1),X3)),X0)) = X3,
inference(superposition,[status(thm)],[c_177890,c_210664]) ).
cnf(c_211587,plain,
inverse(divide(inverse(X0),divide(X1,divide(inverse(divide(divide(X2,X3),X1)),divide(X3,X2))))) = X0,
inference(superposition,[status(thm)],[c_211243,c_177252]) ).
cnf(c_217301,plain,
divide(divide(inverse(divide(divide(X0,X1),divide(X2,X3))),divide(X1,X0)),divide(X4,divide(X3,X2))) = inverse(X4),
inference(superposition,[status(thm)],[c_49,c_211587]) ).
cnf(c_226759,plain,
inverse(divide(divide(X0,divide(divide(X1,X2),X3)),divide(X2,X1))) = inverse(divide(X0,inverse(X3))),
inference(superposition,[status(thm)],[c_217301,c_176394]) ).
cnf(c_227466,plain,
inverse(divide(divide(X0,divide(divide(X1,X2),X3)),divide(X2,X1))) = inverse(multiply(X0,X3)),
inference(demodulation,[status(thm)],[c_226759,c_50]) ).
cnf(c_227469,plain,
inverse(divide(inverse(divide(X0,divide(X1,divide(X2,X3)))),divide(divide(X3,X2),X0))) = inverse(multiply(inverse(divide(X4,X1)),X4)),
inference(superposition,[status(thm)],[c_171,c_227466]) ).
cnf(c_227730,plain,
inverse(multiply(inverse(divide(X0,X1)),X0)) = inverse(X1),
inference(light_normalisation,[status(thm)],[c_227469,c_49]) ).
cnf(c_228483,plain,
divide(inverse(inverse(X0)),divide(X1,divide(inverse(divide(divide(X2,X3),X1)),divide(X3,X2)))) = multiply(inverse(divide(X4,X0)),X4),
inference(superposition,[status(thm)],[c_227730,c_210299]) ).
cnf(c_228572,plain,
multiply(inverse(divide(X0,X1)),X0) = X1,
inference(light_normalisation,[status(thm)],[c_228483,c_210299]) ).
cnf(c_229223,plain,
divide(divide(X0,divide(divide(X1,X2),X3)),divide(X2,X1)) = multiply(X0,X3),
inference(superposition,[status(thm)],[c_176394,c_228572]) ).
cnf(c_229237,plain,
multiply(inverse(X0),inverse(divide(X1,divide(X0,divide(X2,X3))))) = divide(divide(X3,X2),X1),
inference(superposition,[status(thm)],[c_49,c_228572]) ).
cnf(c_229238,plain,
multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(superposition,[status(thm)],[c_50,c_228572]) ).
cnf(c_229265,plain,
multiply(multiply(divide(X0,X1),divide(divide(X1,X0),X2)),X3) = multiply(inverse(X2),X3),
inference(superposition,[status(thm)],[c_211243,c_228572]) ).
cnf(c_229384,plain,
inverse(divide(X0,multiply(X1,X0))) = X1,
inference(demodulation,[status(thm)],[c_176394,c_229223]) ).
cnf(c_229385,plain,
multiply(X0,divide(X1,multiply(X2,X1))) = divide(X0,X2),
inference(demodulation,[status(thm)],[c_176695,c_229223]) ).
cnf(c_229410,plain,
divide(X0,multiply(inverse(X1),X0)) = X1,
inference(demodulation,[status(thm)],[c_211243,c_229265]) ).
cnf(c_230804,plain,
multiply(inverse(X0),inverse(divide(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_228572,c_229238]) ).
cnf(c_231367,plain,
divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(superposition,[status(thm)],[c_230804,c_229410]) ).
cnf(c_231681,plain,
divide(divide(X0,multiply(X1,X0)),divide(inverse(X2),X1)) = X2,
inference(superposition,[status(thm)],[c_229385,c_229410]) ).
cnf(c_235899,plain,
multiply(inverse(divide(X0,multiply(X1,X0))),inverse(divide(X2,X3))) = divide(divide(X1,inverse(X3)),X2),
inference(superposition,[status(thm)],[c_231681,c_229237]) ).
cnf(c_235925,plain,
divide(divide(X0,inverse(X1)),X2) = multiply(X0,inverse(divide(X2,X1))),
inference(light_normalisation,[status(thm)],[c_235899,c_229384]) ).
cnf(c_235926,plain,
multiply(X0,inverse(divide(X1,X2))) = divide(multiply(X0,X2),X1),
inference(light_normalisation,[status(thm)],[c_235925,c_50]) ).
cnf(c_235933,plain,
divide(multiply(inverse(X0),X0),X1) = inverse(X1),
inference(demodulation,[status(thm)],[c_230804,c_235926]) ).
cnf(c_236336,plain,
divide(divide(inverse(divide(X0,multiply(X1,X0))),X1),X2) = inverse(X2),
inference(superposition,[status(thm)],[c_229385,c_235933]) ).
cnf(c_236365,plain,
multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(superposition,[status(thm)],[c_235933,c_50]) ).
cnf(c_236462,plain,
divide(divide(X0,X0),X1) = inverse(X1),
inference(light_normalisation,[status(thm)],[c_236336,c_229384]) ).
cnf(c_236465,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| inverse(inverse(a2)) != a2 ),
inference(demodulation,[status(thm)],[c_51,c_236365]) ).
cnf(c_236946,plain,
divide(inverse(divide(X0,divide(X1,divide(X2,X2)))),inverse(X0)) = X1,
inference(superposition,[status(thm)],[c_236462,c_49]) ).
cnf(c_238315,plain,
divide(X0,divide(X1,X1)) = X0,
inference(demodulation,[status(thm)],[c_236946,c_231367]) ).
cnf(c_238332,plain,
divide(X0,multiply(inverse(X1),X1)) = X0,
inference(superposition,[status(thm)],[c_50,c_238315]) ).
cnf(c_238335,plain,
divide(X0,inverse(divide(X1,X1))) = X0,
inference(superposition,[status(thm)],[c_236462,c_238315]) ).
cnf(c_238466,plain,
divide(inverse(divide(divide(X0,X1),divide(X2,X3))),divide(X1,X0)) = inverse(divide(X3,X2)),
inference(superposition,[status(thm)],[c_238315,c_217301]) ).
cnf(c_238534,plain,
divide(inverse(divide(X0,X1)),divide(X2,divide(X0,X1))) = inverse(X2),
inference(demodulation,[status(thm)],[c_217301,c_238466]) ).
cnf(c_239348,plain,
multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_238332,c_228572]) ).
cnf(c_239436,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(backward_subsumption_resolution,[status(thm)],[c_236465,c_239348]) ).
cnf(c_239558,plain,
multiply(X0,divide(X1,X1)) = X0,
inference(demodulation,[status(thm)],[c_238335,c_50]) ).
cnf(c_239574,plain,
multiply(X0,inverse(divide(X1,X1))) = X0,
inference(superposition,[status(thm)],[c_236462,c_239558]) ).
cnf(c_239635,plain,
inverse(divide(divide(X0,X0),X1)) = X1,
inference(superposition,[status(thm)],[c_239558,c_228572]) ).
cnf(c_239642,plain,
inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_239635,c_236462]) ).
cnf(c_250070,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[c_239436,c_239642]) ).
cnf(c_250071,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(equality_resolution_simp,[status(thm)],[c_250070]) ).
cnf(c_254890,plain,
divide(multiply(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_239574,c_235926]) ).
cnf(c_254910,plain,
inverse(divide(X0,X1)) = divide(X1,X0),
inference(superposition,[status(thm)],[c_228572,c_254890]) ).
cnf(c_254911,plain,
divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_229238,c_254890]) ).
cnf(c_254958,plain,
multiply(multiply(divide(X0,X1),X2),divide(inverse(X2),X3)) = divide(inverse(divide(X1,X0)),X3),
inference(superposition,[status(thm)],[c_254890,c_186004]) ).
cnf(c_255407,plain,
divide(X0,divide(X1,X2)) = multiply(X0,divide(X2,X1)),
inference(superposition,[status(thm)],[c_254910,c_50]) ).
cnf(c_256179,plain,
divide(inverse(multiply(X0,divide(X1,X2))),divide(divide(multiply(divide(X3,X4),X5),inverse(divide(inverse(X5),divide(X1,divide(X4,X3))))),X0)) = X2,
inference(light_normalisation,[status(thm)],[c_470,c_255407]) ).
cnf(c_256180,plain,
multiply(divide(divide(X0,X1),X2),multiply(X2,X1)) = X0,
inference(demodulation,[status(thm)],[c_256179,c_50,c_176711,c_238534,c_254910,c_254911,c_254958,c_255407]) ).
cnf(c_256192,plain,
multiply(divide(X0,X1),multiply(X1,X2)) = multiply(X0,X2),
inference(superposition,[status(thm)],[c_254890,c_256180]) ).
cnf(c_259032,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_254890,c_256192]) ).
cnf(c_259079,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_250071,c_259032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP071-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:31:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 126.86/17.80 % SZS status Started for theBenchmark.p
% 126.86/17.80 % SZS status Unsatisfiable for theBenchmark.p
% 126.86/17.80
% 126.86/17.80 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 126.86/17.80
% 126.86/17.80 ------ iProver source info
% 126.86/17.80
% 126.86/17.80 git: date: 2023-05-31 18:12:56 +0000
% 126.86/17.80 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 126.86/17.80 git: non_committed_changes: false
% 126.86/17.80 git: last_make_outside_of_git: false
% 126.86/17.80
% 126.86/17.80 ------ Parsing...successful
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80 ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e
% 126.86/17.80
% 126.86/17.80 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 126.86/17.80
% 126.86/17.80 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 126.86/17.80 ------ Proving...
% 126.86/17.80 ------ Problem Properties
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80 clauses 3
% 126.86/17.80 conjectures 1
% 126.86/17.80 EPR 0
% 126.86/17.80 Horn 3
% 126.86/17.80 unary 2
% 126.86/17.80 binary 0
% 126.86/17.80 lits 5
% 126.86/17.80 lits eq 5
% 126.86/17.80 fd_pure 0
% 126.86/17.80 fd_pseudo 0
% 126.86/17.80 fd_cond 0
% 126.86/17.80 fd_pseudo_cond 0
% 126.86/17.80 AC symbols 0
% 126.86/17.80
% 126.86/17.80 ------ Schedule dynamic 5 is on
% 126.86/17.80
% 126.86/17.80 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80 ------
% 126.86/17.80 Current options:
% 126.86/17.80 ------
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80 ------ Proving...
% 126.86/17.80 Proof_search_loop: time out after: 5244 full_loop iterations
% 126.86/17.80
% 126.86/17.80 ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80 ------
% 126.86/17.80 Current options:
% 126.86/17.80 ------
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80 ------ Proving...
% 126.86/17.80
% 126.86/17.80
% 126.86/17.80 % SZS status Unsatisfiable for theBenchmark.p
% 126.86/17.80
% 126.86/17.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 126.86/17.80
% 126.86/17.80
%------------------------------------------------------------------------------