%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE027+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 01:52:13 PM UTC 2026
% Result : Theorem 3.11s 0.98s
% Output : CNFRefutation 3.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 43 unt; 0 def)
% Number of atoms : 133 ( 66 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 105 ( 45 ~; 33 |; 19 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 99 !; 10 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,conjecture,
! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> ( leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
& leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> ( leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
& leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f20,plain,
? [X0,X1,X2,X3,X4] :
( test(X4)
& test(X3)
& ( ~ leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
| ~ leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f21,plain,
? [X0,X1,X2,X3,X4] :
( test(X4)
& test(X3)
& ( ~ leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
| ~ leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f24,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f25,plain,
( test(sK4)
& test(sK3)
& ( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)))
| ~ leq(addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f30,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(flattening,[],[f30]) ).
fof(f33,plain,
test(sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)))
| ~ leq(addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f39,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f49,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f50,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f31]) ).
fof(f51,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f56,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f42]) ).
tcf(c_49,negated_conjecture,
( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)))
| ~ leq(addition(multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1))),multiplication(c(sK3),sK2)),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,negated_conjecture,
test(sK3),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f47]) ).
tcf(c_66,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f49]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X0,X1) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_72,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f55]) ).
tcf(c_91,negated_conjecture,
( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(c(sK3),sK2),multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1)))))
| ~ leq(addition(multiplication(c(sK3),sK2),multiplication(sK3,addition(multiplication(sK3,sK0),multiplication(c(sK3),sK1)))),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ),
inference(theory_normalisation,[status(thm)],[c_49,c_55,c_56]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_747,plain,
( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(sK3,multiplication(sK3,sK0)),addition(multiplication(c(sK3),sK2),multiplication(sK3,multiplication(c(sK3),sK1)))))
| ~ leq(addition(multiplication(sK3,multiplication(sK3,sK0)),addition(multiplication(c(sK3),sK2),multiplication(sK3,multiplication(c(sK3),sK1)))),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ),
inference(demodulation,[status(thm)],[c_91,c_53,c_744]) ).
tcf(c_773,plain,
complement(sK3,c(sK3)),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_816,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_56,c_66]) ).
tcf(c_823,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_54,c_57]) ).
tcf(c_878,plain,
multiplication(sK3,c(sK3)) = zero,
inference(superposition,[status(thm)],[c_773,c_69]) ).
tcf(c_907,plain,
addition(c(sK3),sK3) = one,
inference(superposition,[status(thm)],[c_773,c_70]) ).
tcf(c_916,plain,
addition(sK3,c(sK3)) = one,
inference(theory_normalisation,[status(thm)],[c_907,c_55,c_56]) ).
tcf(c_1000,plain,
! [X0: $i] : addition(multiplication(X0,sK3),multiplication(X0,c(sK3))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_916,c_53]) ).
tcf(c_1003,plain,
! [X0: $i] : addition(multiplication(X0,sK3),multiplication(X0,c(sK3))) = X0,
inference(light_normalisation,[status(thm)],[c_1000,c_72]) ).
tcf(c_1132,plain,
! [X0: $i] : multiplication(sK3,multiplication(c(sK3),X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_878,c_63]) ).
tcf(c_1148,plain,
! [X0: $i] : multiplication(sK3,multiplication(c(sK3),X0)) = zero,
inference(light_normalisation,[status(thm)],[c_1132,c_64]) ).
tcf(c_1155,plain,
( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(sK3,multiplication(sK3,sK0)),addition(multiplication(c(sK3),sK2),zero)))
| ~ leq(addition(multiplication(sK3,multiplication(sK3,sK0)),addition(multiplication(c(sK3),sK2),zero)),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ),
inference(demodulation,[status(thm)],[c_747,c_1148]) ).
tcf(c_1156,plain,
( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(zero,addition(multiplication(sK3,multiplication(sK3,sK0)),multiplication(c(sK3),sK2))))
| ~ leq(addition(zero,addition(multiplication(sK3,multiplication(sK3,sK0)),multiplication(c(sK3),sK2))),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ),
inference(theory_normalisation,[status(thm)],[c_1155,c_55,c_56]) ).
tcf(c_1326,plain,
( ~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(sK3,multiplication(sK3,sK0)),multiplication(c(sK3),sK2)))
| ~ leq(addition(multiplication(sK3,multiplication(sK3,sK0)),multiplication(c(sK3),sK2)),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))) ),
inference(demodulation,[status(thm)],[c_1156,c_816]) ).
tcf(c_1954,plain,
addition(multiplication(sK3,sK3),zero) = sK3,
inference(superposition,[status(thm)],[c_878,c_1003]) ).
tcf(c_1962,plain,
addition(zero,multiplication(sK3,sK3)) = sK3,
inference(theory_normalisation,[status(thm)],[c_1954,c_55,c_56]) ).
tcf(c_2016,plain,
multiplication(sK3,sK3) = sK3,
inference(demodulation,[status(thm)],[c_1962,c_816]) ).
tcf(c_2017,plain,
! [X0: $i] : multiplication(sK3,multiplication(sK3,X0)) = multiplication(sK3,X0),
inference(superposition,[status(thm)],[c_2016,c_63]) ).
tcf(c_2021,plain,
~ leq(addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2)),addition(multiplication(sK3,sK0),multiplication(c(sK3),sK2))),
inference(demodulation,[status(thm)],[c_1326,c_2017]) ).
tcf(c_2022,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2021,c_823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE027+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Wed Sep 23 18:40:36 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.32
% 0.06/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.06/0.32
% 0.06/0.32 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 3.11/0.98 % SZS status Started for theBenchmark.p
% 3.11/0.98 % SZS status Theorem for theBenchmark.p
% 3.11/0.98
% 3.11/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.11/0.98
% 3.11/0.98 % ------ iProver source info
% 3.11/0.98
% 3.11/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 3.11/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.11/0.98 % git: non_committed_changes: false
% 3.11/0.98
% 3.11/0.98 % ------ Parsing...
% 3.11/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.11/0.98
% 3.11/0.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.11/0.98
% 3.11/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.11/0.98
% 3.11/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.11/0.98 % ------ Proving...
% 3.11/0.98 % ------ Problem Properties
% 3.11/0.98
% 3.11/0.98 %
% 3.11/0.98 % clauses 24
% 3.11/0.98 % conjectures 3
% 3.11/0.98 % EPR 3
% 3.11/0.98 % Horn 23
% 3.11/0.98 % unary 13
% 3.11/0.98 % binary 9
% 3.11/0.98 % lits 38
% 3.11/0.98 % lits eq 20
% 3.11/0.98 % fd_pure 0
% 3.11/0.98 % fd_pseudo 0
% 3.11/0.98 % fd_cond 0
% 3.11/0.98 % fd_pseudo_cond 1
% 3.11/0.98 % AC symbols 1
% 3.11/0.98
% 3.11/0.98 % ------ Schedule dynamic 5 is on
% 3.11/0.98
% 3.11/0.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.11/0.98
% 3.11/0.98
% 3.11/0.98 % ------
% 3.11/0.98 % Current options:
% 3.11/0.98 % ------
% 3.11/0.98
% 3.11/0.98
% 3.11/0.98 %
% 3.11/0.98
% 3.11/0.98 % ------ Proving...
% 3.11/0.98 %
% 3.11/0.98
% 3.11/0.98 % SZS status Theorem for theBenchmark.p
% 3.11/0.98
% 3.11/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.11/0.98
% 3.11/0.98
%------------------------------------------------------------------------------