%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n031.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 0.46s 0.71s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 10 unt; 0 nHn; 15 RR)
% Number of literals : 20 ( 0 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_or,
file('LCL452+1.p',unknown),
[] ).
cnf(5,axiom,
op_implies_and,
file('LCL452+1.p',unknown),
[] ).
cnf(15,axiom,
or_1,
file('LCL452+1.p',unknown),
[] ).
cnf(22,axiom,
~ cn2,
file('LCL452+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ or_1
| is_a_theorem(implies__dfg(u,or__dfg(u,v))) ),
file('LCL452+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ is_a_theorem(implies__dfg(skc97,implies__dfg(not__dfg(skc97),skc96)))
| cn2 ),
file('LCL452+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL452+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL452+1.p',unknown),
[] ).
cnf(85,plain,
is_a_theorem(implies__dfg(u,or__dfg(u,v))),
inference(mrr,[status(thm)],[34,15]),
[iquote('0:MRR:34.0,15.0')] ).
cnf(90,plain,
~ is_a_theorem(implies__dfg(skc97,implies__dfg(not__dfg(skc97),skc96))),
inference(mrr,[status(thm)],[47,22]),
[iquote('0:MRR:47.1,22.0')] ).
cnf(95,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[60,5]),
[iquote('0:MRR:60.0,5.0')] ).
cnf(96,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[95,66]),
[iquote('0:Rew:95.0,66.1')] ).
cnf(97,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[96,4]),
[iquote('0:MRR:96.0,4.0')] ).
cnf(98,plain,
~ is_a_theorem(implies__dfg(skc97,or__dfg(skc97,skc96))),
inference(rew,[status(thm),theory(equality)],[97,90]),
[iquote('0:Rew:97.0,90.0')] ).
cnf(101,plain,
$false,
inference(mrr,[status(thm)],[98,85]),
[iquote('0:MRR:98.0,85.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL452+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_spass %d %s
% 0.20/0.44 % Computer : n031.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sat Sep 5 01:07:09 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.46/0.71
% 0.46/0.71 SPASS V 3.9
% 0.46/0.71 SPASS beiseite: Proof found.
% 0.46/0.71 % SZS status Theorem
% 0.46/0.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.71 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.46/0.71 SPASS allocated 97861 KBytes.
% 0.46/0.71 SPASS spent 0:00:00.24 on the problem.
% 0.46/0.71 0:00:00.09 for the input.
% 0.46/0.71 0:00:00.08 for the FLOTTER CNF translation.
% 0.46/0.71 0:00:00.00 for inferences.
% 0.46/0.71 0:00:00.00 for the backtracking.
% 0.46/0.71 0:00:00.00 for the reduction.
% 0.46/0.71
% 0.46/0.71
% 0.46/0.71 Here is a proof with depth 0, length 15 :
% 0.46/0.71 % SZS output start Refutation
% See solution above
% 0.46/0.71 Formulae used in the proof : hilbert_op_or hilbert_op_implies_and hilbert_or_1 luka_cn2 or_1 cn2 op_implies_and op_or
% 0.46/0.71
%------------------------------------------------------------------------------