%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL484+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 01:07:37 PM UTC 2026
% Result : Theorem 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 11 RR)
% Number of literals : 14 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_implies_or,
file('LCL484+1.p',unknown),
[] ).
cnf(9,axiom,
r2,
file('LCL484+1.p',unknown),
[] ).
cnf(14,axiom,
~ implies_1,
file('LCL484+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ is_a_theorem(implies__dfg(skc62,implies__dfg(skc61,skc62)))
| implies_1 ),
file('LCL484+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ r2
| is_a_theorem(implies__dfg(u,or__dfg(v,u))) ),
file('LCL484+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ op_implies_or
| equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)) ),
file('LCL484+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(78,plain,
~ is_a_theorem(implies__dfg(skc62,implies__dfg(skc61,skc62))),
inference(mrr,[status(thm)],[21,14]),
[iquote('0:MRR:21.1,14.0')] ).
cnf(79,plain,
equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
inference(mrr,[status(thm)],[51,4]),
[iquote('0:MRR:51.0,4.0')] ).
cnf(114,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(spr,[status(thm),theory(equality)],[79,75]),
[iquote('0:SpR:79.0,75.0')] ).
cnf(118,plain,
$false,
inference(unc,[status(thm)],[114,78]),
[iquote('0:UnC:114.0,78.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL484+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 09:47:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.21/0.54
% 0.21/0.54 SPASS V 3.9
% 0.21/0.54 SPASS beiseite: Proof found.
% 0.21/0.54 % SZS status Theorem
% 0.21/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.54 SPASS derived 21 clauses, backtracked 0 clauses, performed 0 splits and kept 74 clauses.
% 0.21/0.54 SPASS allocated 97853 KBytes.
% 0.21/0.54 SPASS spent 0:00:00.16 on the problem.
% 0.21/0.54 0:00:00.06 for the input.
% 0.21/0.54 0:00:00.05 for the FLOTTER CNF translation.
% 0.21/0.54 0:00:00.00 for inferences.
% 0.21/0.54 0:00:00.00 for the backtracking.
% 0.21/0.54 0:00:00.01 for the reduction.
% 0.21/0.54
% 0.21/0.54
% 0.21/0.54 Here is a proof with depth 1, length 11 :
% 0.21/0.54 % SZS output start Refutation
% See solution above
% 0.21/0.54 Formulae used in the proof : principia_op_implies_or principia_r2 hilbert_implies_1 implies_1 r2 op_implies_or
% 0.21/0.54
%------------------------------------------------------------------------------