%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL465+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : Mon Sep 7 01:07:36 PM UTC 2026
% Result : Theorem 0.23s 0.54s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 6 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
cn1,
file('LCL465+1.p',unknown),
[] ).
cnf(12,axiom,
~ implies_3,
file('LCL465+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc67,skc66),implies__dfg(implies__dfg(skc66,skc65),implies__dfg(skc67,skc65))))
| implies_3 ),
file('LCL465+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ cn1
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL465+1.p',unknown),
[] ).
cnf(87,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[63,8]),
[iquote('0:MRR:63.0,8.0')] ).
cnf(88,plain,
$false,
inference(mrr,[status(thm)],[60,87,12]),
[iquote('0:MRR:60.0,60.1,87.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL465+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 21:21:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.23/0.54
% 0.23/0.54 SPASS V 3.9
% 0.23/0.54 SPASS beiseite: Proof found.
% 0.23/0.54 % SZS status Theorem
% 0.23/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.54 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 63 clauses.
% 0.23/0.54 SPASS allocated 97815 KBytes.
% 0.23/0.54 SPASS spent 0:00:00.16 on the problem.
% 0.23/0.54 0:00:00.06 for the input.
% 0.23/0.54 0:00:00.05 for the FLOTTER CNF translation.
% 0.23/0.54 0:00:00.00 for inferences.
% 0.23/0.54 0:00:00.00 for the backtracking.
% 0.23/0.54 0:00:00.00 for the reduction.
% 0.23/0.54
% 0.23/0.54
% 0.23/0.54 Here is a proof with depth 0, length 6 :
% 0.23/0.54 % SZS output start Refutation
% See solution above
% 0.23/0.54 Formulae used in the proof : luka_cn1 hilbert_implies_3 implies_3 cn1
% 0.23/0.54
%------------------------------------------------------------------------------