%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN623-1 : TPTP v9.3.1. Released v2.5.0.
% 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 03:41:14 PM UTC 2026
% Result : Unsatisfiable 3.89s 1.33s
% Output : CNFRefutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 67 ( 30 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 169 ( 83 ~; 86 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X0] : p8(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_2) ).
fof(f5,negated_conjecture,
! [X0] : p3(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_5) ).
fof(f6,negated_conjecture,
! [X0] : p2(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_6) ).
fof(f10,negated_conjecture,
p18(c26,c25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18_10) ).
fof(f11,negated_conjecture,
p3(c22,c23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_11) ).
fof(f12,negated_conjecture,
p2(c24,c25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_12) ).
fof(f13,negated_conjecture,
~ p16(c22,c21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p16_13) ).
fof(f14,negated_conjecture,
p3(c23,f4(c24,c20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_14) ).
fof(f15,negated_conjecture,
p16(f4(c19,c20),c21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_15) ).
fof(f20,negated_conjecture,
! [X2,X0,X1] :
( ~ p3(X2,X1)
| ~ p3(X2,X0)
| p3(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_20) ).
fof(f25,negated_conjecture,
! [X0,X1] :
( ~ p16(f4(f6(c27,c25),X0),X1)
| p16(f4(c25,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_25) ).
fof(f26,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ p16(X2,X3)
| ~ p8(X3,X1)
| ~ p3(X2,X0)
| p16(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_26) ).
fof(f32,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ p3(X1,X3)
| ~ p2(X0,X2)
| p3(f4(X0,X1),f4(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_32) ).
fof(f34,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ p16(f4(X3,f13(f15(c28,X0),X3)),f9(f11(c29,X0),X3))
| ~ p16(f4(c19,X1),X2)
| ~ p18(c26,X3)
| ~ p2(X0,X3)
| p16(f4(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_34) ).
fof(f35,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ p16(f4(c19,X1),X2)
| ~ p18(c26,X3)
| ~ p2(X0,X3)
| p16(f4(f6(c27,X3),f13(f15(c28,X0),X3)),f9(f11(c29,X0),X3))
| p16(f4(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_35) ).
tcf(c_85,negated_conjecture,
! [X0: $i] : p8(X0,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_88,negated_conjecture,
! [X0: $i] : p3(X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_89,negated_conjecture,
! [X0: $i] : p2(X0,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,negated_conjecture,
p18(c26,c25),
inference(cnf_transformation,[],[f10]) ).
tcf(c_94,negated_conjecture,
p3(c22,c23),
inference(cnf_transformation,[],[f11]) ).
tcf(c_95,negated_conjecture,
p2(c24,c25),
inference(cnf_transformation,[],[f12]) ).
tcf(c_96,negated_conjecture,
~ p16(c22,c21),
inference(cnf_transformation,[],[f13]) ).
tcf(c_97,negated_conjecture,
p3(c23,f4(c24,c20)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_98,negated_conjecture,
p16(f4(c19,c20),c21),
inference(cnf_transformation,[],[f15]) ).
tcf(c_103,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( p3(X1,X2)
| ~ p3(X0,X2)
| ~ p3(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_108,negated_conjecture,
! [X0: $i,X1: $i] :
( p16(f4(c25,X0),X1)
| ~ p16(f4(f6(c27,c25),X0),X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_109,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p16(X3,X1)
| ~ p16(X2,X0)
| ~ p3(X2,X3)
| ~ p8(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_115,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p3(f4(X2,X0),f4(X3,X1))
| ~ p2(X2,X3)
| ~ p3(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_117,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p16(f4(X1,X2),X3)
| ~ p18(c26,X0)
| ~ p2(X1,X0)
| ~ p16(f4(c19,X2),X3)
| ~ p16(f4(X0,f13(f15(c28,X1),X0)),f9(f11(c29,X1),X0)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_118,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( p16(f4(X2,X0),X1)
| p16(f4(f6(c27,X3),f13(f15(c28,X2),X3)),f9(f11(c29,X2),X3))
| ~ p18(c26,X3)
| ~ p2(X2,X3)
| ~ p16(f4(c19,X0),X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_122,plain,
p2(c25,c25),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_297,negated_conjecture,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_p16_2: iProver_p16_2,X0_iProver_f4_1: iProver_f4_1,X1_iProver_f4_1: iProver_f4_1] :
( p16(f4(X0_iProver_f4_1,X0_iProver_f4_2),X0_iProver_p16_2)
| p16(f4(f6(c27,X1_iProver_f4_1),f13(f15(c28,X0_iProver_f4_1),X1_iProver_f4_1)),f9(f11(c29,X0_iProver_f4_1),X1_iProver_f4_1))
| ~ p18(c26,X1_iProver_f4_1)
| ~ p2(X0_iProver_f4_1,X1_iProver_f4_1)
| ~ p16(f4(c19,X0_iProver_f4_2),X0_iProver_p16_2) ),
inference(subtyping,[status(esa)],[c_118]) ).
tcf(c_298,negated_conjecture,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_p16_2: iProver_p16_2,X0_iProver_f4_1: iProver_f4_1,X1_iProver_f4_1: iProver_f4_1] :
( p16(f4(X1_iProver_f4_1,X0_iProver_f4_2),X0_iProver_p16_2)
| ~ p18(c26,X0_iProver_f4_1)
| ~ p2(X1_iProver_f4_1,X0_iProver_f4_1)
| ~ p16(f4(c19,X0_iProver_f4_2),X0_iProver_p16_2)
| ~ p16(f4(X0_iProver_f4_1,f13(f15(c28,X1_iProver_f4_1),X0_iProver_f4_1)),f9(f11(c29,X1_iProver_f4_1),X0_iProver_f4_1)) ),
inference(subtyping,[status(esa)],[c_117]) ).
tcf(c_300,negated_conjecture,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_f4_1: iProver_f4_1,X1_iProver_f4_2: iProver_f4_2,X1_iProver_f4_1: iProver_f4_1] :
( p3(f4(X0_iProver_f4_1,X0_iProver_f4_2),f4(X1_iProver_f4_1,X1_iProver_f4_2))
| ~ p2(X0_iProver_f4_1,X1_iProver_f4_1)
| ~ p3(X0_iProver_f4_2,X1_iProver_f4_2) ),
inference(subtyping,[status(esa)],[c_115]) ).
tcf(c_306,negated_conjecture,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_p16_2: iProver_p16_2,X1_iProver_f4_2: iProver_f4_2,X1_iProver_p16_2: iProver_p16_2] :
( p16(X1_iProver_f4_2,X1_iProver_p16_2)
| ~ p16(X0_iProver_f4_2,X0_iProver_p16_2)
| ~ p3(X0_iProver_f4_2,X1_iProver_f4_2)
| ~ p8(X0_iProver_p16_2,X1_iProver_p16_2) ),
inference(subtyping,[status(esa)],[c_109]) ).
tcf(c_307,negated_conjecture,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_p16_2: iProver_p16_2] :
( p16(f4(c25,X0_iProver_f4_2),X0_iProver_p16_2)
| ~ p16(f4(f6(c27,c25),X0_iProver_f4_2),X0_iProver_p16_2) ),
inference(subtyping,[status(esa)],[c_108]) ).
tcf(c_312,negated_conjecture,
! [X0_iProver_f4_2: iProver_f4_2,X1_iProver_f4_2: iProver_f4_2,X2_iProver_f4_2: iProver_f4_2] :
( p3(X1_iProver_f4_2,X2_iProver_f4_2)
| ~ p3(X0_iProver_f4_2,X2_iProver_f4_2)
| ~ p3(X0_iProver_f4_2,X1_iProver_f4_2) ),
inference(subtyping,[status(esa)],[c_103]) ).
tcf(c_317,negated_conjecture,
p16(f4(c19,c20),c21),
inference(subtyping,[status(esa)],[c_98]) ).
tcf(c_318,negated_conjecture,
p3(c23,f4(c24,c20)),
inference(subtyping,[status(esa)],[c_97]) ).
tcf(c_321,negated_conjecture,
p3(c22,c23),
inference(subtyping,[status(esa)],[c_94]) ).
tcf(c_327,negated_conjecture,
! [X0_iProver_f4_2: iProver_f4_2] : p3(X0_iProver_f4_2,X0_iProver_f4_2),
inference(subtyping,[status(esa)],[c_88]) ).
tcf(c_330,negated_conjecture,
! [X0_iProver_p16_2: iProver_p16_2] : p8(X0_iProver_p16_2,X0_iProver_p16_2),
inference(subtyping,[status(esa)],[c_85]) ).
tcf(c_335,plain,
p3(c20,c20),
inference(instantiation,[status(thm)],[c_327]) ).
tcf(c_338,plain,
p8(c21,c21),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_347,plain,
( p16(f4(c25,c20),c21)
| ~ p18(c26,c25)
| ~ p2(c25,c25)
| ~ p16(f4(c19,c20),c21)
| ~ p16(f4(c25,f13(f15(c28,c25),c25)),f9(f11(c29,c25),c25)) ),
inference(instantiation,[status(thm)],[c_298]) ).
tcf(c_477,plain,
! [X0_iProver_f4_1: iProver_f4_1] :
( p16(f4(c25,f13(f15(c28,X0_iProver_f4_1),c25)),f9(f11(c29,X0_iProver_f4_1),c25))
| ~ p16(f4(f6(c27,c25),f13(f15(c28,X0_iProver_f4_1),c25)),f9(f11(c29,X0_iProver_f4_1),c25)) ),
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_478,plain,
( p16(f4(c25,f13(f15(c28,c25),c25)),f9(f11(c29,c25),c25))
| ~ p16(f4(f6(c27,c25),f13(f15(c28,c25),c25)),f9(f11(c29,c25),c25)) ),
inference(instantiation,[status(thm)],[c_477]) ).
tcf(c_576,plain,
! [X0_iProver_f4_2: iProver_f4_2] :
( p3(c23,X0_iProver_f4_2)
| ~ p3(c22,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_321,c_312]) ).
tcf(c_577,plain,
! [X0_iProver_f4_2: iProver_f4_2] :
( p3(f4(c24,c20),X0_iProver_f4_2)
| ~ p3(c23,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_318,c_312]) ).
tcf(c_681,plain,
p3(c23,c22),
inference(superposition,[status(thm)],[c_327,c_576]) ).
tcf(c_934,plain,
! [X0_iProver_f4_1: iProver_f4_1,X1_iProver_f4_1: iProver_f4_1] :
( p16(f4(X0_iProver_f4_1,c20),c21)
| p16(f4(f6(c27,X1_iProver_f4_1),f13(f15(c28,X0_iProver_f4_1),X1_iProver_f4_1)),f9(f11(c29,X0_iProver_f4_1),X1_iProver_f4_1))
| ~ p18(c26,X1_iProver_f4_1)
| ~ p2(X0_iProver_f4_1,X1_iProver_f4_1) ),
inference(superposition,[status(thm)],[c_317,c_297]) ).
tcf(c_935,plain,
( p16(f4(c25,c20),c21)
| p16(f4(f6(c27,c25),f13(f15(c28,c25),c25)),f9(f11(c29,c25),c25))
| ~ p18(c26,c25)
| ~ p2(c25,c25) ),
inference(instantiation,[status(thm)],[c_934]) ).
tcf(c_964,plain,
! [X0_iProver_p16_2: iProver_p16_2,X1_iProver_p16_2: iProver_p16_2] :
( p16(c22,X1_iProver_p16_2)
| ~ p16(c23,X0_iProver_p16_2)
| ~ p8(X0_iProver_p16_2,X1_iProver_p16_2) ),
inference(superposition,[status(thm)],[c_681,c_306]) ).
tcf(c_967,plain,
( p16(c22,c21)
| ~ p16(c23,c21)
| ~ p8(c21,c21) ),
inference(instantiation,[status(thm)],[c_964]) ).
tcf(c_1093,plain,
! [X0_iProver_f4_2: iProver_f4_2,X1_iProver_f4_2: iProver_f4_2] :
( p3(X1_iProver_f4_2,X0_iProver_f4_2)
| ~ p3(c23,X1_iProver_f4_2)
| ~ p3(f4(c24,c20),X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_577,c_312]) ).
tcf(c_2318,plain,
! [X0_iProver_f4_2: iProver_f4_2] :
( p3(c23,X0_iProver_f4_2)
| ~ p3(c22,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_321,c_312]) ).
tcf(c_2319,plain,
! [X0_iProver_f4_2: iProver_f4_2] :
( p3(f4(c24,c20),X0_iProver_f4_2)
| ~ p3(c23,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_318,c_312]) ).
tcf(c_2351,plain,
p3(c23,c23),
inference(superposition,[status(thm)],[c_321,c_2318]) ).
tcf(c_2405,plain,
! [X0_iProver_f4_2: iProver_f4_2,X1_iProver_f4_2: iProver_f4_2] :
( p3(X1_iProver_f4_2,X0_iProver_f4_2)
| ~ p3(c23,X1_iProver_f4_2)
| ~ p3(c23,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_2319,c_1093]) ).
tcf(c_2428,plain,
! [X0_iProver_f4_2: iProver_f4_2] :
( p3(X0_iProver_f4_2,c23)
| ~ p3(c23,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_2351,c_2405]) ).
tcf(c_2430,plain,
p3(f4(c24,c20),c23),
inference(superposition,[status(thm)],[c_318,c_2428]) ).
tcf(c_2448,plain,
! [X0_iProver_f4_2: iProver_f4_2] :
( p3(c23,X0_iProver_f4_2)
| ~ p3(f4(c24,c20),X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_2430,c_312]) ).
tcf(c_2451,plain,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_f4_1: iProver_f4_1] :
( p3(c23,f4(X0_iProver_f4_1,X0_iProver_f4_2))
| ~ p2(c24,X0_iProver_f4_1)
| ~ p3(c20,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_300,c_2448]) ).
tcf(c_2462,plain,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_f4_1: iProver_f4_1] :
( p3(f4(X0_iProver_f4_1,X0_iProver_f4_2),c23)
| ~ p2(c24,X0_iProver_f4_1)
| ~ p3(c20,X0_iProver_f4_2) ),
inference(superposition,[status(thm)],[c_2451,c_2428]) ).
tcf(c_2873,plain,
! [X0_iProver_f4_2: iProver_f4_2,X0_iProver_p16_2: iProver_p16_2,X0_iProver_f4_1: iProver_f4_1,X1_iProver_p16_2: iProver_p16_2] :
( p16(c23,X1_iProver_p16_2)
| ~ p2(c24,X0_iProver_f4_1)
| ~ p3(c20,X0_iProver_f4_2)
| ~ p8(X0_iProver_p16_2,X1_iProver_p16_2)
| ~ p16(f4(X0_iProver_f4_1,X0_iProver_f4_2),X0_iProver_p16_2) ),
inference(superposition,[status(thm)],[c_2462,c_306]) ).
tcf(c_2881,plain,
( p16(c23,c21)
| ~ p2(c24,c25)
| ~ p3(c20,c20)
| ~ p8(c21,c21)
| ~ p16(f4(c25,c20),c21) ),
inference(instantiation,[status(thm)],[c_2873]) ).
tcf(c_2882,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2881,c_967,c_935,c_478,c_347,c_338,c_335,c_98,c_96,c_122,c_93,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN623-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 01:54:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 3.89/1.33 % SZS status Started for theBenchmark.p
% 3.89/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 3.89/1.33
% 3.89/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.89/1.33
% 3.89/1.33 % ------ iProver source info
% 3.89/1.33
% 3.89/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 3.89/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.89/1.33 % git: non_committed_changes: false
% 3.89/1.33
% 3.89/1.33 % ------ Parsing...% successful
% 3.89/1.33
% 3.89/1.33
% 3.89/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.89/1.33
% 3.89/1.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.89/1.33
% 3.89/1.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.89/1.33 % ------ Proving...
% 3.89/1.33 % ------ Problem Properties
% 3.89/1.33
% 3.89/1.33 %
% 3.89/1.33 % clauses 35
% 3.89/1.33 % conjectures 35
% 3.89/1.33 % EPR 24
% 3.89/1.33 % Horn 34
% 3.89/1.33 % unary 15
% 3.89/1.33 % binary 1
% 3.89/1.33 % lits 80
% 3.89/1.33 % lits eq 0
% 3.89/1.33 % fd_pure 0
% 3.89/1.33 % fd_pseudo 0
% 3.89/1.33 % fd_cond 0
% 3.89/1.33 % fd_pseudo_cond 0
% 3.89/1.33 % AC symbols 0
% 3.89/1.33
% 3.89/1.33 % ------ Input Options Time Limit: Unbounded
% 3.89/1.33
% 3.89/1.33
% 3.89/1.33 % ------
% 3.89/1.33 % Current options:
% 3.89/1.33 % ------
% 3.89/1.33
% 3.89/1.33
% 3.89/1.33 %
% 3.89/1.33
% 3.89/1.33 % ------ Proving...
% 3.89/1.33 %
% 3.89/1.33
% 3.89/1.33 % SZS status Unsatisfiable for theBenchmark.p
% 3.89/1.33
% 3.89/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.89/1.33
% 3.89/1.33
%------------------------------------------------------------------------------