TSTP Solution File: FLD027-1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : FLD027-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 : Wed Aug 30 22:33:00 EDT 2023
% Result : Unsatisfiable 151.77s 20.81s
% Output : CNFRefutation 151.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 75 ( 9 unt; 6 nHn; 75 RR)
% Number of literals : 192 ( 0 equ; 118 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_50,plain,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(c_51,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(c_52,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_4) ).
cnf(c_53,negated_conjecture,
equalish(multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_equal) ).
cnf(c_54,negated_conjecture,
~ equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_b_6) ).
cnf(c_59,plain,
( ~ defined(X0)
| ~ defined(X1)
| ~ defined(X2)
| equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(c_60,plain,
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(c_61,plain,
( ~ defined(X0)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(c_62,plain,
( ~ defined(X0)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(c_67,plain,
( ~ defined(X0)
| ~ defined(X1)
| defined(multiply(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(c_69,plain,
( ~ defined(X0)
| defined(multiplicative_inverse(X0))
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(c_76,plain,
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(c_77,plain,
( ~ equalish(X0,X1)
| ~ equalish(X1,X2)
| equalish(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(c_79,plain,
( ~ equalish(X0,X1)
| ~ defined(X2)
| equalish(multiply(X0,X2),multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(c_258,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a))
| equalish(a,additive_identity) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_259,plain,
( ~ defined(b)
| defined(multiplicative_inverse(b))
| equalish(b,additive_identity) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_260,plain,
( ~ defined(a)
| equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)
| equalish(a,additive_identity) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_261,plain,
( ~ defined(b)
| equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity)
| equalish(b,additive_identity) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_272,plain,
( ~ equalish(X0,b)
| ~ equalish(a,X0)
| equalish(a,b) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_299,plain,
( ~ equalish(X0,a)
| equalish(a,X0) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_300,plain,
( ~ equalish(X0,X1)
| ~ equalish(a,X0)
| equalish(a,X1) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_309,plain,
( ~ defined(b)
| equalish(multiply(multiplicative_identity,b),b) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_313,plain,
( ~ equalish(X0,X1)
| ~ equalish(X1,b)
| equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_329,plain,
( ~ equalish(X0,X1)
| ~ equalish(X1,multiplicative_identity)
| equalish(X0,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_345,plain,
( ~ equalish(multiply(multiplicative_identity,a),a)
| equalish(a,multiply(multiplicative_identity,a)) ),
inference(instantiation,[status(thm)],[c_299]) ).
cnf(c_346,plain,
( ~ defined(a)
| equalish(multiply(multiplicative_identity,a),a) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_451,plain,
( ~ equalish(X0,multiply(multiplicative_identity,b))
| ~ equalish(multiply(multiplicative_identity,b),b)
| equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_313]) ).
cnf(c_483,plain,
( ~ equalish(X0,multiply(b,multiplicative_inverse(b)))
| ~ equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity)
| equalish(X0,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_329]) ).
cnf(c_505,plain,
( ~ equalish(multiply(multiplicative_inverse(b),b),multiply(b,multiplicative_inverse(b)))
| ~ equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity)
| equalish(multiply(multiplicative_inverse(b),b),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_483]) ).
cnf(c_506,plain,
( ~ defined(multiplicative_inverse(b))
| ~ defined(b)
| equalish(multiply(multiplicative_inverse(b),b),multiply(b,multiplicative_inverse(b))) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_567,plain,
( ~ equalish(multiply(multiplicative_identity,a),X0)
| ~ equalish(a,multiply(multiplicative_identity,a))
| equalish(a,X0) ),
inference(instantiation,[status(thm)],[c_300]) ).
cnf(c_1005,plain,
( ~ equalish(X0,multiply(multiplicative_identity,b))
| ~ equalish(X1,X0)
| equalish(X1,multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_1007,plain,
( ~ equalish(X0,multiplicative_identity)
| ~ defined(b)
| equalish(multiply(X0,b),multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_1394,plain,
( ~ equalish(X0,multiply(multiplicative_inverse(b),b))
| ~ equalish(multiply(multiplicative_inverse(b),b),multiplicative_identity)
| equalish(X0,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_329]) ).
cnf(c_1596,plain,
( ~ equalish(X0,multiply(multiplicative_identity,a))
| equalish(multiply(multiplicative_identity,a),X0) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_2089,plain,
( ~ equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity)
| ~ defined(b)
| equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_1007]) ).
cnf(c_2121,plain,
( ~ equalish(X0,multiplicative_identity)
| ~ defined(a)
| equalish(multiply(X0,a),multiply(multiplicative_identity,a)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_3164,plain,
( ~ equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b))
| ~ equalish(X0,multiply(multiply(a,multiplicative_inverse(a)),b))
| equalish(X0,multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_1005]) ).
cnf(c_5697,plain,
( ~ equalish(X0,multiplicative_inverse(b))
| ~ defined(b)
| equalish(multiply(X0,b),multiply(multiplicative_inverse(b),b)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_10506,plain,
( ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiply(a,multiplicative_inverse(a)),b))
| ~ equalish(multiply(multiply(a,multiplicative_inverse(a)),b),multiply(multiplicative_identity,b))
| equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiplicative_identity,b)) ),
inference(instantiation,[status(thm)],[c_3164]) ).
cnf(c_10507,plain,
( ~ defined(multiplicative_inverse(a))
| ~ defined(a)
| ~ defined(b)
| equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiply(a,multiplicative_inverse(a)),b)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_24267,plain,
( ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),multiply(multiplicative_identity,b))
| ~ equalish(multiply(multiplicative_identity,b),b)
| equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b) ),
inference(instantiation,[status(thm)],[c_451]) ).
cnf(c_40663,plain,
( ~ equalish(X0,X1)
| ~ equalish(X1,b)
| equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_69282,plain,
( ~ equalish(X0,multiply(a,multiply(multiplicative_inverse(a),b)))
| ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b)
| equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_40663]) ).
cnf(c_72489,plain,
( ~ equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(a,multiply(multiplicative_inverse(a),b)))
| ~ equalish(multiply(a,multiply(multiplicative_inverse(a),b)),b)
| equalish(multiply(multiply(multiplicative_inverse(a),b),a),b) ),
inference(instantiation,[status(thm)],[c_69282]) ).
cnf(c_72490,plain,
( ~ defined(multiply(multiplicative_inverse(a),b))
| ~ defined(a)
| equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(a,multiply(multiplicative_inverse(a),b))) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_262219,plain,
( ~ equalish(X0,b)
| ~ equalish(a,X0)
| equalish(a,b) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_262261,plain,
( ~ equalish(X0,X1)
| ~ equalish(a,X0)
| equalish(a,X1) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_262269,plain,
( ~ equalish(a,X0)
| ~ equalish(X0,b) ),
inference(global_subsumption_just,[status(thm)],[c_262219,c_54,c_272]) ).
cnf(c_262270,plain,
( ~ equalish(X0,b)
| ~ equalish(a,X0) ),
inference(renaming,[status(thm)],[c_262269]) ).
cnf(c_262300,plain,
( ~ equalish(X0,X1)
| ~ equalish(X1,multiplicative_identity)
| equalish(X0,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_263078,plain,
( ~ equalish(X0,multiply(multiplicative_inverse(b),b))
| ~ equalish(multiply(multiplicative_inverse(b),b),multiplicative_identity)
| equalish(X0,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_262300]) ).
cnf(c_263102,plain,
( ~ equalish(multiply(multiplicative_identity,a),X0)
| ~ equalish(a,multiply(multiplicative_identity,a))
| equalish(a,X0) ),
inference(instantiation,[status(thm)],[c_262261]) ).
cnf(c_263559,plain,
( ~ equalish(X0,multiply(multiplicative_identity,a))
| ~ equalish(X1,X0)
| equalish(X1,multiply(multiplicative_identity,a)) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_263561,plain,
( ~ equalish(X0,multiplicative_identity)
| ~ defined(a)
| equalish(multiply(X0,a),multiply(multiplicative_identity,a)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_264649,plain,
( ~ equalish(multiply(multiplicative_identity,a),X0)
| equalish(a,X0) ),
inference(global_subsumption_just,[status(thm)],[c_263102,c_49,c_345,c_346,c_567]) ).
cnf(c_265554,plain,
( ~ equalish(X0,multiply(multiplicative_inverse(b),b))
| equalish(X0,multiplicative_identity) ),
inference(global_subsumption_just,[status(thm)],[c_263078,c_50,c_52,c_259,c_261,c_505,c_506,c_1394]) ).
cnf(c_265567,plain,
( ~ equalish(multiply(X0,b),multiply(multiplicative_inverse(b),b))
| equalish(multiply(X0,b),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_265554]) ).
cnf(c_265568,plain,
( ~ equalish(X0,multiplicative_inverse(b))
| ~ defined(b)
| equalish(multiply(X0,b),multiply(multiplicative_inverse(b),b)) ),
inference(instantiation,[status(thm)],[c_79]) ).
cnf(c_266751,plain,
( ~ equalish(X0,multiplicative_identity)
| equalish(multiply(X0,a),multiply(multiplicative_identity,a)) ),
inference(global_subsumption_just,[status(thm)],[c_263561,c_49,c_2121]) ).
cnf(c_286650,plain,
( ~ defined(multiply(multiplicative_inverse(a),b))
| ~ defined(a)
| equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(a,multiply(multiplicative_inverse(a),b))) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_290933,plain,
( ~ equalish(X0,multiplicative_inverse(b))
| equalish(multiply(X0,b),multiply(multiplicative_inverse(b),b)) ),
inference(global_subsumption_just,[status(thm)],[c_265568,c_50,c_5697]) ).
cnf(c_290936,plain,
( ~ equalish(multiplicative_inverse(a),multiplicative_inverse(b))
| equalish(multiply(multiplicative_inverse(a),b),multiply(multiplicative_inverse(b),b)) ),
inference(instantiation,[status(thm)],[c_290933]) ).
cnf(c_292054,plain,
( ~ equalish(multiply(multiplicative_inverse(a),b),multiply(multiplicative_inverse(b),b))
| equalish(multiply(multiplicative_inverse(a),b),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_265567]) ).
cnf(c_293905,plain,
( ~ equalish(multiply(multiplicative_inverse(a),b),multiplicative_identity)
| equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(multiplicative_identity,a)) ),
inference(instantiation,[status(thm)],[c_266751]) ).
cnf(c_295995,plain,
( ~ equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(multiplicative_identity,a))
| ~ equalish(X0,multiply(multiply(multiplicative_inverse(a),b),a))
| equalish(X0,multiply(multiplicative_identity,a)) ),
inference(instantiation,[status(thm)],[c_263559]) ).
cnf(c_334060,plain,
( ~ defined(multiply(multiplicative_inverse(a),b))
| equalish(multiply(multiply(multiplicative_inverse(a),b),a),multiply(a,multiply(multiplicative_inverse(a),b))) ),
inference(global_subsumption_just,[status(thm)],[c_286650,c_49,c_72490]) ).
cnf(c_334062,plain,
( ~ defined(multiplicative_inverse(a))
| ~ defined(b)
| defined(multiply(multiplicative_inverse(a),b)) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_481949,plain,
( ~ equalish(X0,X1)
| ~ equalish(X1,b)
| equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_552247,plain,
( ~ equalish(X0,multiply(multiply(multiplicative_inverse(a),b),a))
| ~ equalish(multiply(multiply(multiplicative_inverse(a),b),a),b)
| equalish(X0,b) ),
inference(instantiation,[status(thm)],[c_481949]) ).
cnf(c_554889,plain,
~ equalish(X0,multiply(multiply(multiplicative_inverse(a),b),a)),
inference(global_subsumption_just,[status(thm)],[c_552247,c_50,c_49,c_51,c_53,c_258,c_260,c_309,c_1596,c_2089,c_10506,c_10507,c_24267,c_72489,c_262270,c_264649,c_290936,c_292054,c_293905,c_295995,c_334060,c_334062,c_552247]) ).
cnf(c_554893,plain,
~ equalish(multiply(multiplicative_inverse(a),multiply(b,a)),multiply(multiply(multiplicative_inverse(a),b),a)),
inference(instantiation,[status(thm)],[c_554889]) ).
cnf(c_554894,plain,
( ~ defined(multiplicative_inverse(a))
| ~ defined(a)
| ~ defined(b)
| equalish(multiply(multiplicative_inverse(a),multiply(b,a)),multiply(multiply(multiplicative_inverse(a),b),a)) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_554895,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_554894,c_554893,c_258,c_51,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD027-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 00:37:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 151.77/20.81 % SZS status Started for theBenchmark.p
% 151.77/20.81 % SZS status Unsatisfiable for theBenchmark.p
% 151.77/20.81
% 151.77/20.81 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 151.77/20.81
% 151.77/20.81 ------ iProver source info
% 151.77/20.81
% 151.77/20.81 git: date: 2023-05-31 18:12:56 +0000
% 151.77/20.81 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 151.77/20.81 git: non_committed_changes: false
% 151.77/20.81 git: last_make_outside_of_git: false
% 151.77/20.81
% 151.77/20.81 ------ Parsing...successful
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e
% 151.77/20.81
% 151.77/20.81 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 151.77/20.81 ------ Proving...
% 151.77/20.81 ------ Problem Properties
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81 clauses 33
% 151.77/20.81 conjectures 4
% 151.77/20.81 EPR 15
% 151.77/20.81 Horn 30
% 151.77/20.81 unary 9
% 151.77/20.81 binary 6
% 151.77/20.81 lits 79
% 151.77/20.81 lits eq 0
% 151.77/20.81 fd_pure 0
% 151.77/20.81 fd_pseudo 0
% 151.77/20.81 fd_cond 0
% 151.77/20.81 fd_pseudo_cond 0
% 151.77/20.81 AC symbols 0
% 151.77/20.81
% 151.77/20.81 ------ Schedule dynamic 5 is on
% 151.77/20.81
% 151.77/20.81 ------ no equalities: superposition off
% 151.77/20.81
% 151.77/20.81 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81 ------
% 151.77/20.81 Current options:
% 151.77/20.81 ------
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81 ------ Proving...
% 151.77/20.81 Proof_search_loop: time out after: 30316 full_loop iterations
% 151.77/20.81
% 151.77/20.81 ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81 ------
% 151.77/20.81 Current options:
% 151.77/20.81 ------
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81 ------ Proving...
% 151.77/20.81
% 151.77/20.81
% 151.77/20.81 % SZS status Unsatisfiable for theBenchmark.p
% 151.77/20.81
% 151.77/20.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 151.77/20.81
% 151.77/20.82
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