%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 01:07:34 PM UTC 2026
% Result : Theorem 0.22s 0.56s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 4 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(11,axiom,
implies_3,
file('LCL451+1.p',unknown),
[] ).
cnf(22,axiom,
~ cn1,
file('LCL451+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ implies_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))) ),
file('LCL451+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(skc95,skc94),implies__dfg(implies__dfg(skc94,skc93),implies__dfg(skc95,skc93))))
| cn1 ),
file('LCL451+1.p',unknown),
[] ).
cnf(107,plain,
~ is_a_theorem(implies__dfg(implies__dfg(skc95,skc94),implies__dfg(implies__dfg(skc94,skc93),implies__dfg(skc95,skc93)))),
inference(mrr,[status(thm)],[74,22]),
[iquote('0:MRR:74.1,22.0')] ).
cnf(109,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
inference(mrr,[status(thm)],[69,11]),
[iquote('0:MRR:69.0,11.0')] ).
cnf(110,plain,
$false,
inference(unc,[status(thm)],[109,107]),
[iquote('0:UnC:109.0,107.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL451+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 20:40:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.22/0.56
% 0.22/0.56 SPASS V 3.9
% 0.22/0.56 SPASS beiseite: Proof found.
% 0.22/0.56 % SZS status Theorem
% 0.22/0.56 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.56 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 65 clauses.
% 0.22/0.56 SPASS allocated 97839 KBytes.
% 0.22/0.56 SPASS spent 0:00:00.16 on the problem.
% 0.22/0.56 0:00:00.06 for the input.
% 0.22/0.56 0:00:00.05 for the FLOTTER CNF translation.
% 0.22/0.56 0:00:00.00 for inferences.
% 0.22/0.56 0:00:00.00 for the backtracking.
% 0.22/0.56 0:00:00.00 for the reduction.
% 0.22/0.56
% 0.22/0.56
% 0.22/0.56 Here is a proof with depth 0, length 7 :
% 0.22/0.56 % SZS output start Refutation
% See solution above
% 0.22/0.56 Formulae used in the proof : hilbert_implies_3 luka_cn1 implies_3 cn1
% 0.22/0.56
%------------------------------------------------------------------------------