%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL491+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 01:07:38 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 : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
r2,
file('LCL491+1.p',unknown),
[] ).
cnf(14,axiom,
~ or_2,
file('LCL491+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ is_a_theorem(implies__dfg(skc76,or__dfg(skc77,skc76)))
| or_2 ),
file('LCL491+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL491+1.p',unknown),
[] ).
cnf(75,plain,
is_a_theorem(implies__dfg(u,or__dfg(v,u))),
inference(mrr,[status(thm)],[36,9]),
[iquote('0:MRR:36.0,9.0')] ).
cnf(77,plain,
$false,
inference(mrr,[status(thm)],[29,75,14]),
[iquote('0:MRR:29.0,29.1,75.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL491+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.37 % Computer : n008.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 : Fri Sep 4 14:10:38 UTC 2026
% 0.09/0.37 % 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 0 clauses, backtracked 0 clauses, performed 0 splits and kept 22 clauses.
% 0.23/0.54 SPASS allocated 97812 KBytes.
% 0.23/0.54 SPASS spent 0:00:00.15 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 : principia_r2 hilbert_or_2 or_2 r2
% 0.23/0.54
%------------------------------------------------------------------------------