%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 01:07:40 PM UTC 2026
% Result : Theorem 0.21s 0.56s
% 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(6,axiom,
op_equiv,
file('LCL512+1.p',unknown),
[] ).
cnf(9,axiom,
kn2,
file('LCL512+1.p',unknown),
[] ).
cnf(12,axiom,
~ equivalence_1,
file('LCL512+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ kn2
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL512+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ is_a_theorem(implies__dfg(equiv__dfg(skc82,skc81),implies__dfg(skc82,skc81)))
| equivalence_1 ),
file('LCL512+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ op_equiv
| equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)) ),
file('LCL512+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(76,plain,
~ is_a_theorem(implies__dfg(equiv__dfg(skc82,skc81),implies__dfg(skc82,skc81))),
inference(mrr,[status(thm)],[44,12]),
[iquote('0:MRR:44.1,12.0')] ).
cnf(88,plain,
equal(and__dfg(implies__dfg(u,v),implies__dfg(v,u)),equiv__dfg(u,v)),
inference(mrr,[status(thm)],[58,6]),
[iquote('0:MRR:58.0,6.0')] ).
cnf(225,plain,
is_a_theorem(implies__dfg(equiv__dfg(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[88,73]),
[iquote('0:SpR:88.0,73.0')] ).
cnf(231,plain,
$false,
inference(unc,[status(thm)],[225,76]),
[iquote('0:UnC:225.0,76.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL512+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 17:15:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.21/0.56
% 0.21/0.56 SPASS V 3.9
% 0.21/0.56 SPASS beiseite: Proof found.
% 0.21/0.56 % SZS status Theorem
% 0.21/0.56 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.56 SPASS derived 125 clauses, backtracked 0 clauses, performed 0 splits and kept 133 clauses.
% 0.21/0.56 SPASS allocated 97872 KBytes.
% 0.21/0.56 SPASS spent 0:00:00.19 on the problem.
% 0.21/0.56 0:00:00.06 for the input.
% 0.21/0.56 0:00:00.06 for the FLOTTER CNF translation.
% 0.21/0.56 0:00:00.00 for inferences.
% 0.21/0.56 0:00:00.00 for the backtracking.
% 0.21/0.56 0:00:00.02 for the reduction.
% 0.21/0.56
% 0.21/0.56
% 0.21/0.56 Here is a proof with depth 1, length 11 :
% 0.21/0.56 % SZS output start Refutation
% See solution above
% 0.21/0.56 Formulae used in the proof : rosser_op_equiv rosser_kn2 hilbert_equivalence_1 kn2 equivalence_1 op_equiv
% 0.21/0.56
%------------------------------------------------------------------------------