%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : Mon Sep 7 01:07:39 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : Refutation 0.09s
% 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,
kn2,
file('LCL506+1.p',unknown),
[] ).
cnf(12,axiom,
~ and_1,
file('LCL506+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ is_a_theorem(implies__dfg(and__dfg(skc69,skc68),skc69))
| and_1 ),
file('LCL506+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ kn2
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL506+1.p',unknown),
[] ).
cnf(73,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[30,9]),
[iquote('0:MRR:30.0,9.0')] ).
cnf(75,plain,
$false,
inference(mrr,[status(thm)],[21,73,12]),
[iquote('0:MRR:21.0,21.1,73.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL506+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : run_spass %d %s
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 4 22:27:27 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.09/0.38
% 0.09/0.38 SPASS V 3.9
% 0.09/0.38 SPASS beiseite: Proof found.
% 0.09/0.38 % SZS status Theorem
% 0.09/0.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.09/0.38 SPASS allocated 97812 KBytes.
% 0.09/0.38 SPASS spent 0:00:00.08 on the problem.
% 0.09/0.38 0:00:00.03 for the input.
% 0.09/0.38 0:00:00.02 for the FLOTTER CNF translation.
% 0.09/0.38 0:00:00.00 for inferences.
% 0.09/0.38 0:00:00.00 for the backtracking.
% 0.09/0.38 0:00:00.00 for the reduction.
% 0.09/0.38
% 0.09/0.38
% 0.09/0.38 Here is a proof with depth 0, length 6 :
% 0.09/0.38 % SZS output start Refutation
% See solution above
% 0.09/0.38 Formulae used in the proof : rosser_kn2 hilbert_and_1 and_1 kn2
% 0.09/0.38
%------------------------------------------------------------------------------