%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL529+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 01:07:41 PM UTC 2026
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 9 unt; 0 nHn; 15 RR)
% Number of literals : 22 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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_strict_implies,
file('LCL529+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL529+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL529+1.p',unknown),
[] ).
cnf(30,axiom,
~ axiom_m2,
file('LCL529+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL529+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL529+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173))
| axiom_m2 ),
file('LCL529+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL529+1.p',unknown),
[] ).
cnf(148,plain,
~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173)),
inference(mrr,[status(thm)],[72,30]),
[iquote('0:MRR:72.1,30.0')] ).
cnf(149,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[68,26]),
[iquote('0:MRR:68.1,26.0')] ).
cnf(154,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[52,15]),
[iquote('0:MRR:52.0,15.0')] ).
cnf(159,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[106,4]),
[iquote('0:MRR:106.0,4.0')] ).
cnf(219,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[159,149]),
[iquote('0:SpR:159.0,149.1')] ).
cnf(301,plain,
is_a_theorem(strict_implies(and__dfg(u,v),u)),
inference(sor,[status(thm)],[219,154]),
[iquote('0:SoR:219.0,154.0')] ).
cnf(305,plain,
$false,
inference(unc,[status(thm)],[301,148]),
[iquote('0:UnC:301.0,148.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL529+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 15:32:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 110 clauses, backtracked 0 clauses, performed 1 splits and kept 194 clauses.
% 0.21/0.48 SPASS allocated 98124 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.48 0:00:00.03 for the input.
% 0.21/0.48 0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.01 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 2, length 15 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : s1_0_op_strict_implies hilbert_and_1 km5_necessitation s1_0_axiom_m2 and_1 necessitation km5_axiom_M axiom_M axiom_m2 op_strict_implies
% 0.21/0.48
%------------------------------------------------------------------------------