%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO555+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 01:18:09 PM UTC 2026
% Result : Theorem 24.97s 3.60s
% Output : Proof 24.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 106 ( 66 unt; 0 def)
% Number of atoms : 214 ( 58 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 153 ( 45 ~; 39 |; 58 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 232 ( 0 sgn 140 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,K,I] :
( ( coll(I,A,B)
& perp(I,D,A,B)
& coll(K,A,B)
& perp(K,E,A,B)
& coll(H,A,C)
& perp(H,F,A,C)
& coll(G,B,C)
& perp(G,F,B,C)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(H,K,I,G) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012015) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,K,I] :
( ( coll(I,A,B)
& perp(I,D,A,B)
& coll(K,A,B)
& perp(K,E,A,B)
& coll(H,A,C)
& perp(H,F,A,C)
& coll(G,B,C)
& perp(G,F,B,C)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(H,K,I,G) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,K,I] :
( ~ cyclic(H,K,I,G)
& coll(I,A,B)
& perp(I,D,A,B)
& coll(K,A,B)
& perp(K,E,A,B)
& coll(H,A,C)
& perp(H,F,A,C)
& coll(G,B,C)
& perp(G,F,B,C)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk27,sk28,sk29,sk26)
& coll(sk29,sk20,sk21)
& perp(sk29,sk23,sk20,sk21)
& coll(sk28,sk20,sk21)
& perp(sk28,sk24,sk20,sk21)
& coll(sk27,sk20,sk22)
& perp(sk27,sk25,sk20,sk22)
& coll(sk26,sk21,sk22)
& perp(sk26,sk25,sk21,sk22)
& coll(sk25,sk20,sk21)
& perp(sk25,sk22,sk20,sk21)
& coll(sk24,sk20,sk22)
& perp(sk24,sk21,sk20,sk22)
& coll(sk23,sk21,sk22)
& perp(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29])],[f94_nnf]) ).
cnf(c114,plain,
coll(sk23,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
coll(sk23,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h0,plain,
coll(sk22,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi114,hi114]) ).
cnf(c120,plain,
coll(sk26,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk26,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h9,plain,
coll(sk22,sk22,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi120,hi120]) ).
cnf(h45,plain,
coll(sk26,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h9,h0]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h129,plain,
coll(sk26,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h45]) ).
cnf(h289,plain,
coll(sk23,sk23,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h129,h129]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c113,plain,
perp(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h993,plain,
perp(sk21,sk22,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h1008,plain,
para(sk23,sk20,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi113,h993]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h1543,plain,
eqangle(sk23,sk20,V0,V1,sk23,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h1008]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h18069,plain,
cyclic(sk20,sk26,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h1543,h289]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h18092,plain,
cyclic(sk20,sk23,sk26,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h18069]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h18135,plain,
cyclic(sk20,sk23,sk23,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi13,h18092]) ).
cnf(c122,plain,
coll(sk27,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
coll(sk27,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h12,plain,
coll(sk22,sk22,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi122,hi122]) ).
cnf(h56,plain,
coll(sk27,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h12,h0]) ).
cnf(h150,plain,
coll(sk27,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h56]) ).
cnf(h353,plain,
coll(sk23,sk23,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,h150,h150]) ).
cnf(h18068,plain,
cyclic(sk20,sk27,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h1543,h353]) ).
cnf(h18089,plain,
cyclic(sk20,sk23,sk27,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h18068]) ).
cnf(h18129,plain,
cyclic(sk20,sk23,sk23,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi13,h18089]) ).
fof(f16,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD17) ).
fof(f16_nnf,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,cyclic(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h18233,plain,
cyclic(sk23,sk23,sk27,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi16,h18129,h18135]) ).
cnf(h2,plain,
coll(sk23,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi114]) ).
cnf(h25,plain,
coll(sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h2]) ).
cnf(c124,plain,
coll(sk28,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi124,negated_conjecture,
coll(sk28,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(h15,plain,
coll(sk21,sk21,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi124,hi124]) ).
cnf(h89,plain,
coll(sk28,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h15,h25]) ).
cnf(h207,plain,
coll(sk28,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h89]) ).
cnf(h484,plain,
coll(sk23,sk23,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi2,h207,h207]) ).
cnf(h18066,plain,
cyclic(sk20,sk28,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h1543,h484]) ).
cnf(h18083,plain,
cyclic(sk20,sk23,sk28,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h18066]) ).
cnf(h18118,plain,
cyclic(sk20,sk23,sk23,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi13,h18083]) ).
cnf(h18221,plain,
cyclic(sk23,sk23,sk27,sk28) = true,
inference(hyper_resolution,[status(thm)],[hi16,h18129,h18118]) ).
cnf(h25961,plain,
cyclic(sk23,sk27,sk28,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi16,h18221,h18233]) ).
cnf(c126,plain,
coll(sk29,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi126,negated_conjecture,
coll(sk29,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(h18,plain,
coll(sk21,sk21,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi126,hi126]) ).
cnf(h88,plain,
coll(sk29,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h18,h25]) ).
cnf(h206,plain,
coll(sk29,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h88]) ).
cnf(h473,plain,
coll(sk23,sk23,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi2,h206,h206]) ).
cnf(h18067,plain,
cyclic(sk20,sk29,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi42,h1543,h473]) ).
cnf(h18086,plain,
cyclic(sk20,sk23,sk29,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi14,h18067]) ).
cnf(h18123,plain,
cyclic(sk20,sk23,sk23,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi13,h18086]) ).
cnf(h18220,plain,
cyclic(sk23,sk23,sk27,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi16,h18129,h18123]) ).
cnf(h25914,plain,
cyclic(sk23,sk27,sk28,sk29) = true,
inference(hyper_resolution,[status(thm)],[hi16,h18221,h18220]) ).
cnf(t52,plain,
cyclic(sk27,sk28,sk29,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi16,h25914,h25961]) ).
cnf(t3076,plain,
cyclic(sk27,sk28,sk29,sk26) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(c127,plain,
~ cyclic(sk27,sk28,sk29,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk27,sk28,sk29,sk26) != true,
inference(equality_encoding,[status(esa)],[c127]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3076]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO555+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 12:22:51 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.97/3.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.97/3.60 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------