%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% 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 01:06:43 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL076-2.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u))),
file('LCL076-2.p',unknown),
[] ).
cnf(5,axiom,
is_a_theorem(implies__dfg(not__dfg(not__dfg(u)),u)),
file('LCL076-2.p',unknown),
[] ).
cnf(6,axiom,
~ is_a_theorem(implies__dfg(a,not__dfg(not__dfg(a)))),
file('LCL076-2.p',unknown),
[] ).
cnf(15,plain,
( ~ is_a_theorem(implies__dfg(not__dfg(u),not__dfg(v)))
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(19,plain,
is_a_theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
inference(sor,[status(thm)],[15,5]),
[iquote('0:SoR:15.0,5.0')] ).
cnf(20,plain,
$false,
inference(unc,[status(thm)],[19,6]),
[iquote('0:UnC:19.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n018.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 : Fri Sep 4 19:43:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.21/0.49
% 0.21/0.49 SPASS V 3.9
% 0.21/0.49 SPASS beiseite: Proof found.
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.49 SPASS derived 7 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.21/0.49 SPASS allocated 75600 KBytes.
% 0.21/0.49 SPASS spent 0:00:00.10 on the problem.
% 0.21/0.49 0:00:00.06 for the input.
% 0.21/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.49 0:00:00.00 for inferences.
% 0.21/0.49 0:00:00.00 for the backtracking.
% 0.21/0.49 0:00:00.00 for the reduction.
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 Here is a proof with depth 2, length 7 :
% 0.21/0.49 % SZS output start Refutation
% See solution above
% 0.21/0.49 Formulae used in the proof : condensed_detachment cn_49 extra_lemma prove_cn_40
% 0.21/0.49
%------------------------------------------------------------------------------