%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO274+1 : TPTP v9.3.1. Released v4.1.0.
% 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 01:20:39 PM UTC 2026
% Result : Theorem 12.42s 4.69s
% Output : CNFRefutation 12.42s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f35ERROR: Could not build tree for root c_63096ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( rline(vd1092)
& ron(vd1080,vd1092)
& ron(vd1089,vd1092) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(s2(plural(the(227))), 0), and(pred(s1(plural(the(227))), 0), pred(the(227), 0)))') ).
fof(f4,axiom,
vf(vd1089,vd1080) = vf(vd1085,vd1080),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(226, 1090, 1)') ).
fof(f5,axiom,
vf(vd1089,vd1085) = vf(vd1089,vd1080),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(226, 1090, 0)') ).
fof(f6,axiom,
rpoint(vd1089),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(226, 0)') ).
fof(f7,axiom,
vd1085 = vd1086,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(225, 4)') ).
fof(f8,axiom,
vd1085 != vd1080,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(225), 1087, 0)') ).
fof(f9,axiom,
rpoint(vd1086),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(225, 1)') ).
fof(f10,axiom,
? [X0] :
( rpoint(X0)
& vd1080 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s1(plural(224)))') ).
fof(f11,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 ) )
=> vf(X0,X1) = vf(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))') ).
fof(f12,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 ) )
=> ( vf(X0,X1) = v0
<=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))') ).
fof(f13,axiom,
! [X0,X1] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X2] :
( rpoint(X2)
& X1 = X2 )
& X0 != X1 )
=> ? [X4] :
( rline(X4)
& ron(X0,X4)
& ron(X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))') ).
fof(f14,axiom,
vd1085 != vd1081,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(225), 1088, 0)') ).
fof(f15,axiom,
vd1080 != vd1081,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(224, 5)') ).
fof(f16,axiom,
? [X0] :
( rpoint(X0)
& vd1081 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s2(plural(224)))') ).
fof(f124,plain,
? [X0] :
( rline(X0)
& ron(vd1080,X0)
& ron(vd1089,X0)
& vd1092 != X0 ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X2] :
( ~ rpoint(X2)
| X1 != X2 )
| vf(X0,X1) = vf(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f126,plain,
! [X0,X1] :
( ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X2] :
( ~ rpoint(X2)
| X1 != X2 )
| vf(X0,X1) = vf(X1,X0) ),
inference(flattening,[],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X2] :
( ~ rpoint(X2)
| X1 != X2 )
| ( vf(X0,X1) = v0
<=> X0 = X1 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f128,plain,
! [X0,X1] :
( ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X2] :
( ~ rpoint(X2)
| X1 != X2 )
| ( vf(X0,X1) = v0
<=> X0 = X1 ) ),
inference(flattening,[],[f127]) ).
fof(f224,plain,
! [X0,X1,X2,X3] :
( ! [X7] :
( ~ rpoint(X7)
| X0 != X7 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| X0 = X1
| ! [X5] :
( ~ rline(X5)
| X2 != X5 )
| ! [X4] :
( ~ rline(X4)
| X3 != X4 )
| ~ ron(X0,X2)
| ~ ron(X0,X3)
| ~ ron(X1,X2)
| ~ ron(X1,X3)
| X2 = X3 ),
inference(ennf_transformation,[],[f67]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( ! [X7] :
( ~ rpoint(X7)
| X0 != X7 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| X0 = X1
| ! [X5] :
( ~ rline(X5)
| X2 != X5 )
| ! [X4] :
( ~ rline(X4)
| X3 != X4 )
| ~ ron(X0,X2)
| ~ ron(X0,X3)
| ~ ron(X1,X2)
| ~ ron(X1,X3)
| X2 = X3 ),
inference(flattening,[],[f224]) ).
fof(f321,plain,
( rline(sK1)
& ron(vd1080,sK1)
& ron(vd1089,sK1)
& vd1092 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f124]) ).
fof(f322,plain,
( rpoint(sK2)
& vd1080 = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f10]) ).
fof(f323,plain,
! [X0,X1] :
( ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X2] :
( ~ rpoint(X2)
| X1 != X2 )
| ( ( vf(X0,X1) != v0
| X0 = X1 )
& ( X0 != X1
| vf(X0,X1) = v0 ) ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f394,plain,
rline(sK1),
inference(cnf_transformation,[],[f321]) ).
fof(f395,plain,
ron(vd1080,sK1),
inference(cnf_transformation,[],[f321]) ).
fof(f396,plain,
ron(vd1089,sK1),
inference(cnf_transformation,[],[f321]) ).
fof(f397,plain,
vd1092 != sK1,
inference(cnf_transformation,[],[f321]) ).
fof(f398,plain,
rline(vd1092),
inference(cnf_transformation,[],[f3]) ).
fof(f399,plain,
ron(vd1080,vd1092),
inference(cnf_transformation,[],[f3]) ).
fof(f400,plain,
ron(vd1089,vd1092),
inference(cnf_transformation,[],[f3]) ).
fof(f401,plain,
vf(vd1089,vd1080) = vf(vd1085,vd1080),
inference(cnf_transformation,[],[f4]) ).
fof(f403,plain,
rpoint(vd1089),
inference(cnf_transformation,[],[f6]) ).
fof(f404,plain,
vd1085 = vd1086,
inference(cnf_transformation,[],[f7]) ).
fof(f405,plain,
vd1080 != vd1085,
inference(cnf_transformation,[],[f8]) ).
fof(f406,plain,
rpoint(vd1086),
inference(cnf_transformation,[],[f9]) ).
fof(f407,plain,
rpoint(sK2),
inference(cnf_transformation,[],[f322]) ).
fof(f408,plain,
vd1080 = sK2,
inference(cnf_transformation,[],[f322]) ).
fof(f409,plain,
! [X2,X3,X0,X1] :
( ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X2)
| X1 != X2
| vf(X0,X1) = vf(X1,X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X2)
| X1 != X2
| vf(X0,X1) != v0
| X0 = X1 ),
inference(cnf_transformation,[],[f323]) ).
fof(f461,plain,
v0 = vd684,
inference(cnf_transformation,[],[f35]) ).
fof(f503,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ rpoint(X7)
| X0 != X7
| ~ rpoint(X6)
| X1 != X6
| X0 = X1
| ~ rline(X5)
| X2 != X5
| ~ rline(X4)
| X3 != X4
| ~ ron(X0,X2)
| ~ ron(X0,X3)
| ~ ron(X1,X2)
| ~ ron(X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[],[f225]) ).
fof(f641,plain,
ron(sK2,sK1),
inference(definition_unfolding,[],[f395,f408]) ).
fof(f642,plain,
ron(sK2,vd1092),
inference(definition_unfolding,[],[f399,f408]) ).
fof(f643,plain,
vf(vd1089,sK2) = vf(vd1086,sK2),
inference(definition_unfolding,[],[f401,f408,f404,f408]) ).
fof(f645,plain,
vd1086 != sK2,
inference(definition_unfolding,[],[f405,f408,f404]) ).
fof(f647,plain,
! [X2,X3,X0,X1] :
( ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X2)
| X1 != X2
| vf(X0,X1) != vd684
| X0 = X1 ),
inference(definition_unfolding,[],[f410,f461]) ).
fof(f657,plain,
! [X2,X3,X0] :
( ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X2)
| vf(X0,X2) = vf(X2,X0) ),
inference(equality_resolution,[],[f409]) ).
fof(f658,plain,
! [X2,X3] :
( ~ rpoint(X3)
| ~ rpoint(X2)
| vf(X3,X2) = vf(X2,X3) ),
inference(equality_resolution,[],[f657]) ).
fof(f662,plain,
! [X2,X3,X0] :
( ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X2)
| vf(X0,X2) != vd684
| X0 = X2 ),
inference(equality_resolution,[],[f647]) ).
fof(f663,plain,
! [X2,X3] :
( ~ rpoint(X3)
| ~ rpoint(X2)
| vd684 != vf(X3,X2)
| X2 = X3 ),
inference(equality_resolution,[],[f662]) ).
fof(f928,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ rpoint(X7)
| X0 != X7
| ~ rpoint(X6)
| X1 != X6
| X0 = X1
| ~ rline(X5)
| X2 != X5
| ~ rline(X4)
| ~ ron(X0,X2)
| ~ ron(X0,X4)
| ~ ron(X1,X2)
| ~ ron(X1,X4)
| X2 = X4 ),
inference(equality_resolution,[],[f503]) ).
fof(f929,plain,
! [X0,X1,X6,X7,X4,X5] :
( ~ rpoint(X7)
| X0 != X7
| ~ rpoint(X6)
| X1 != X6
| X0 = X1
| ~ rline(X5)
| ~ rline(X4)
| ~ ron(X0,X5)
| ~ ron(X0,X4)
| ~ ron(X1,X5)
| ~ ron(X1,X4)
| X4 = X5 ),
inference(equality_resolution,[],[f928]) ).
fof(f930,plain,
! [X0,X6,X7,X4,X5] :
( ~ rpoint(X7)
| X0 != X7
| ~ rpoint(X6)
| X0 = X6
| ~ rline(X5)
| ~ rline(X4)
| ~ ron(X0,X5)
| ~ ron(X0,X4)
| ~ ron(X6,X5)
| ~ ron(X6,X4)
| X4 = X5 ),
inference(equality_resolution,[],[f929]) ).
fof(f931,plain,
! [X6,X7,X4,X5] :
( ~ rpoint(X7)
| ~ rpoint(X6)
| X6 = X7
| ~ rline(X5)
| ~ rline(X4)
| ~ ron(X7,X5)
| ~ ron(X7,X4)
| ~ ron(X6,X5)
| ~ ron(X6,X4)
| X4 = X5 ),
inference(equality_resolution,[],[f930]) ).
tcf(c_49,negated_conjecture,
vd1092 != sK1,
inference(cnf_transformation,[],[f397]) ).
tcf(c_50,negated_conjecture,
ron(vd1089,sK1),
inference(cnf_transformation,[],[f396]) ).
tcf(c_51,negated_conjecture,
ron(sK2,sK1),
inference(cnf_transformation,[],[f641]) ).
tcf(c_52,negated_conjecture,
rline(sK1),
inference(cnf_transformation,[],[f394]) ).
tcf(c_53,plain,
ron(vd1089,vd1092),
inference(cnf_transformation,[],[f400]) ).
tcf(c_54,plain,
ron(sK2,vd1092),
inference(cnf_transformation,[],[f642]) ).
tcf(c_55,plain,
rline(vd1092),
inference(cnf_transformation,[],[f398]) ).
tcf(c_56,plain,
vf(vd1089,sK2) = vf(vd1086,sK2),
inference(cnf_transformation,[],[f643]) ).
tcf(c_58,plain,
rpoint(vd1089),
inference(cnf_transformation,[],[f403]) ).
tcf(c_59,plain,
sK2 != vd1086,
inference(cnf_transformation,[],[f645]) ).
tcf(c_60,plain,
rpoint(vd1086),
inference(cnf_transformation,[],[f406]) ).
tcf(c_61,plain,
rpoint(sK2),
inference(cnf_transformation,[],[f407]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( vf(X0,X1) = vf(X1,X0) )
| ~ rpoint(X1)
| ~ rpoint(X0) ),
inference(cnf_transformation,[],[f658]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( vf(X0,X0) = vd684 )
| ~ rpoint(X0) ),
inference(cnf_transformation,[],[f1337]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ rpoint(X1)
| ~ rpoint(X0)
| ( vf(X0,X1) != vd684 ) ),
inference(cnf_transformation,[],[f663]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ( X0 = X3 )
| ~ rpoint(X3)
| ~ rpoint(X0)
| ~ rline(X2)
| ~ rline(X1)
| ~ ron(X3,X2)
| ~ ron(X3,X1)
| ~ ron(X0,X2)
| ~ ron(X0,X1) ),
inference(cnf_transformation,[],[f931]) ).
tcf(c_14649,negated_conjecture,
rline(sK1),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_14650,negated_conjecture,
ron(sK2,sK1),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_14651,negated_conjecture,
ron(vd1089,sK1),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_14652,negated_conjecture,
vd1092 != sK1,
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_20852,plain,
vf(sK2,sK2) = vd684,
inference(superposition,[status(thm)],[c_61,c_63]) ).
tcf(c_21251,plain,
! [X0: $i] :
( ( vf(X0,vd1089) = vf(vd1089,X0) )
| ~ rpoint(X0) ),
inference(superposition,[status(thm)],[c_58,c_62]) ).
tcf(c_21252,plain,
! [X0: $i] :
( ( vf(X0,vd1086) = vf(vd1086,X0) )
| ~ rpoint(X0) ),
inference(superposition,[status(thm)],[c_60,c_62]) ).
tcf(c_21801,plain,
vf(vd1089,sK2) = vf(sK2,vd1089),
inference(superposition,[status(thm)],[c_61,c_21251]) ).
tcf(c_21848,plain,
vf(sK2,vd1089) = vf(vd1086,sK2),
inference(demodulation,[status(thm)],[c_56,c_21801]) ).
tcf(c_22215,plain,
vf(sK2,vd1086) = vf(vd1086,sK2),
inference(superposition,[status(thm)],[c_61,c_21252]) ).
tcf(c_22233,plain,
vf(sK2,vd1089) = vf(sK2,vd1086),
inference(light_normalisation,[status(thm)],[c_22215,c_21848]) ).
tcf(c_25280,plain,
( ( sK2 = vd1086 )
| ~ rpoint(vd1086)
| ~ rpoint(sK2)
| ( vf(sK2,vd1089) != vd684 ) ),
inference(superposition,[status(thm)],[c_22233,c_64]) ).
tcf(c_25299,plain,
vf(sK2,vd1089) != vd684,
inference(forward_subsumption_resolution,[status(thm)],[c_25280,c_59,c_60,c_61]) ).
tcf(c_62134,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK1 )
| ( X0 = sK2 )
| ~ rpoint(sK2)
| ~ rline(sK1)
| ~ rpoint(X0)
| ~ rline(X1)
| ~ ron(sK2,X1)
| ~ ron(X0,sK1)
| ~ ron(X0,X1) ),
inference(superposition,[status(thm)],[c_14650,c_154]) ).
tcf(c_62179,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK1 )
| ( X0 = sK2 )
| ~ rpoint(X0)
| ~ rline(X1)
| ~ ron(sK2,X1)
| ~ ron(X0,sK1)
| ~ ron(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62134,c_61,c_14649]) ).
tcf(c_62698,plain,
( ( vd1089 = sK2 )
| ( vd1092 = sK1 )
| ~ rpoint(vd1089)
| ~ rline(vd1092)
| ~ ron(sK2,vd1092)
| ~ ron(vd1089,sK1) ),
inference(superposition,[status(thm)],[c_53,c_62179]) ).
tcf(c_62726,plain,
vd1089 = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_62698,c_14652,c_58,c_55,c_54,c_14651]) ).
tcf(c_63024,plain,
vf(sK2,sK2) != vd684,
inference(demodulation,[status(thm)],[c_25299,c_62726]) ).
tcf(c_63096,plain,
$false,
inference(ground_joinability,[status(thm)],[c_63024,c_20852]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO274+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 11:47:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 12.42/4.69 % SZS status Started for theBenchmark.p
% 12.42/4.69 % SZS status Theorem for theBenchmark.p
% 12.42/4.69
% 12.42/4.69 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.42/4.69
% 12.42/4.69 % ------ iProver source info
% 12.42/4.69
% 12.42/4.69 % git: date: 2026-07-19 20:42:38 +0200
% 12.42/4.69 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.42/4.69 % git: non_committed_changes: false
% 12.42/4.69
% 12.42/4.69 % ------ Parsing...
% 12.42/4.69 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.42/4.69
% 12.42/4.69 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 12.42/4.69
% 12.42/4.69 % ------ Preprocessing... gs_s sp: 14 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.42/4.69
% 12.42/4.69 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 12.42/4.69 % ------ Proving...
% 12.42/4.69 % ------ Problem Properties
% 12.42/4.69
% 12.42/4.69 %
% 12.42/4.69 % clauses 249
% 12.42/4.69 % conjectures 4
% 12.42/4.69 % EPR 67
% 12.42/4.69 % Horn 173
% 12.42/4.69 % unary 18
% 12.42/4.69 % binary 42
% 12.42/4.69 % lits 1459
% 12.42/4.70 % lits eq 169
% 12.42/4.70 % fd_pure 0
% 12.42/4.70 % fd_pseudo 0
% 12.42/4.70 % fd_cond 0
% 12.42/4.70 % fd_pseudo_cond 45
% 12.42/4.70 % AC symbols 0
% 12.42/4.70
% 12.42/4.70 % ------ Schedule dynamic 5 is on
% 12.42/4.70
% 12.42/4.70 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 12.42/4.70
% 12.42/4.70
% 12.42/4.70 % ------
% 12.42/4.70 % Current options:
% 12.42/4.70 % ------
% 12.42/4.70
% 12.42/4.70
% 12.42/4.70 %
% 12.42/4.70
% 12.42/4.70 % ------ Proving...
% 12.42/4.70 %
% 12.42/4.70
% 12.42/4.70 % SZS status Theorem for theBenchmark.p
% 12.42/4.70
% 12.42/4.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.42/4.70
% 12.42/4.70
%------------------------------------------------------------------------------