%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL169-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n002.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 01:06:54 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 6 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ theorem(or__dfg(not__dfg(or__dfg(not__dfg(p),not__dfg(p))),not__dfg(p))),
file('LCL169-1.p',unknown),
[] ).
cnf(2,axiom,
axiom(or__dfg(not__dfg(or__dfg(u,u)),u)),
file('LCL169-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ axiom(u)
| theorem(u) ),
file('LCL169-1.p',unknown),
[] ).
cnf(10,plain,
~ axiom(or__dfg(not__dfg(or__dfg(not__dfg(p),not__dfg(p))),not__dfg(p))),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.1,1.0')] ).
cnf(13,plain,
$false,
inference(mrr,[status(thm)],[10,2]),
[iquote('0:MRR:10.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL169-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n002.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 : Sun Sep 6 02:03:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.22/0.49
% 0.22/0.49 SPASS V 3.9
% 0.22/0.49 SPASS beiseite: Proof found.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.49 SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.22/0.49 SPASS allocated 75608 KBytes.
% 0.22/0.49 SPASS spent 0:00:00.10 on the problem.
% 0.22/0.49 0:00:00.06 for the input.
% 0.22/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.49 0:00:00.00 for inferences.
% 0.22/0.49 0:00:00.00 for the backtracking.
% 0.22/0.49 0:00:00.00 for the reduction.
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 Here is a proof with depth 1, length 5 :
% 0.22/0.49 % SZS output start Refutation
% See solution above
% 0.22/0.49 Formulae used in the proof : prove_this axiom_1_2 rule_1
% 0.22/0.49
%------------------------------------------------------------------------------