%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 : 600s
% DateTime : Sat Jul 16 05:26:02 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 85 ( 24 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 163 ( 80 ~; 59 |; 10 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 126 ( 8 sgn 78 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ) ).
fof(a4_defns,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ) ).
fof(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ) ).
fof(ax9_basics,axiom,
! [L,M] :
( ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) )
=> ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ).
fof(con,conjecture,
! [L,M] :
( unequally_directed_lines(L,M)
<=> unequally_directed_opposite_lines(L,reverse_line(M)) ) ).
fof(subgoal_0,plain,
! [L,M] :
( unequally_directed_lines(L,M)
=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [L,M] :
( unequally_directed_opposite_lines(L,reverse_line(M))
=> unequally_directed_lines(L,M) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M] :
( unequally_directed_lines(L,M)
=> unequally_directed_opposite_lines(L,reverse_line(M)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[a4_defns]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) )
& ( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [L,M] :
( ~ unequally_directed_opposite_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
& unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a1_defns]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax8_basics]) ).
fof(normalize_0_12,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_15,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax9_basics]) ).
fof(normalize_0_16,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_0_18,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_18]) ).
cnf(refute_0_0,plain,
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ equally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
| ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(reverse_line(skolemFOFtoCNF_M)))]]) ).
cnf(refute_0_2,plain,
~ unequally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( ~ unequally_directed_lines(X_36,reverse_line(X_37))
| unequally_directed_opposite_lines(X_36,X_37) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_5,plain,
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( unequally_directed_lines(X_36,X_37)
| unequally_directed_lines(X_36,reverse_line(X_37)) ),
inference(subst,[],[refute_0_5:[bind(L,$fot(X_36)),bind(M,$fot(X_37))]]) ).
cnf(refute_0_7,plain,
( unequally_directed_lines(X_36,X_37)
| unequally_directed_opposite_lines(X_36,X_37) ),
inference(resolve,[$cnf( unequally_directed_lines(X_36,reverse_line(X_37)) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
| unequally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(skolemFOFtoCNF_L)),bind(X_37,$fot(reverse_line(skolemFOFtoCNF_M)))]]) ).
cnf(refute_0_9,plain,
unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
~ equally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( equally_directed_lines(X_38,reverse_line(X_39))
| unequally_directed_lines(X_38,reverse_line(X_39)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_38)),bind(Y,$fot(reverse_line(X_39)))]]) ).
cnf(refute_0_14,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_15,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_16,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_15:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_18,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ unequally_directed_lines(X_38,X_39)
| ~ unequally_directed_lines(X_38,reverse_line(X_39)) ),
inference(subst,[],[refute_0_18:[bind(L,$fot(X_38)),bind(M,$fot(X_39))]]) ).
cnf(refute_0_20,plain,
( ~ unequally_directed_lines(X_38,X_39)
| equally_directed_lines(X_38,reverse_line(X_39)) ),
inference(resolve,[$cnf( unequally_directed_lines(X_38,reverse_line(X_39)) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| equally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) ),
inference(subst,[],[refute_0_20:[bind(X_38,$fot(skolemFOFtoCNF_L)),bind(X_39,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_22,plain,
equally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_11,refute_0_21]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( equally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_22,refute_0_10]) ).
fof(negate_1_0,plain,
~ ! [L,M] :
( unequally_directed_opposite_lines(L,reverse_line(M))
=> unequally_directed_lines(L,M) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax9_basics]) ).
fof(normalize_1_1,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_1_3,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [L,M] :
( ~ unequally_directed_lines(L,M)
& unequally_directed_opposite_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_6,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1)
& unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1)) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1)),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a1_defns]) ).
fof(normalize_1_9,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax8_basics]) ).
fof(normalize_1_13,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1),
inference(conjunct,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_1_0,refute_1_1]) ).
cnf(refute_1_3,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_1_1:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_1_4,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( ~ unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(reverse_line(skolemFOFtoCNF_M_1)))
| ~ unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1)) ),
inference(subst,[],[refute_1_4:[bind(L,$fot(skolemFOFtoCNF_L_1)),bind(M,$fot(reverse_line(skolemFOFtoCNF_M_1)))]]) ).
cnf(refute_1_6,plain,
unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1)),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_7,plain,
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_8,plain,
( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1))
| unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(reverse_line(skolemFOFtoCNF_M_1))) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(skolemFOFtoCNF_L_1)),bind(Y,$fot(reverse_line(skolemFOFtoCNF_M_1)))]]) ).
cnf(refute_1_9,plain,
unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(reverse_line(skolemFOFtoCNF_M_1))),
inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1)) )],[refute_1_6,refute_1_8]) ).
cnf(refute_1_10,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1)),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(reverse_line(skolemFOFtoCNF_M_1))) )],[refute_1_9,refute_1_5]) ).
cnf(refute_1_11,plain,
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_12,plain,
( unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1))
| unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1) ),
inference(subst,[],[refute_1_11:[bind(L,$fot(skolemFOFtoCNF_L_1)),bind(M,$fot(skolemFOFtoCNF_M_1))]]) ).
cnf(refute_1_13,plain,
unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1),
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L_1,reverse_line(skolemFOFtoCNF_M_1)) )],[refute_1_12,refute_1_10]) ).
cnf(refute_1_14,plain,
~ unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_15,plain,
$false,
inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L_1,skolemFOFtoCNF_M_1) )],[refute_1_13,refute_1_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 12:19:08 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.40
%------------------------------------------------------------------------------