%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 01:07:43 PM UTC 2026
% Result : Theorem 0.33s 0.60s
% Output : Refutation 0.33s
% 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('LCL542+1.p',unknown),
[] ).
cnf(15,axiom,
and_1,
file('LCL542+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL542+1.p',unknown),
[] ).
cnf(31,axiom,
~ axiom_m2,
file('LCL542+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ and_1
| is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
file('LCL542+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL542+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173))
| axiom_m2 ),
file('LCL542+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL542+1.p',unknown),
[] ).
cnf(149,plain,
~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173)),
inference(mrr,[status(thm)],[73,31]),
[iquote('0:MRR:73.1,31.0')] ).
cnf(151,plain,
( ~ is_a_theorem(u)
| is_a_theorem(necessarily(u)) ),
inference(mrr,[status(thm)],[69,26]),
[iquote('0:MRR:69.1,26.0')] ).
cnf(156,plain,
is_a_theorem(implies__dfg(and__dfg(u,v),u)),
inference(mrr,[status(thm)],[53,15]),
[iquote('0:MRR:53.0,15.0')] ).
cnf(161,plain,
equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
inference(mrr,[status(thm)],[107,4]),
[iquote('0:MRR:107.0,4.0')] ).
cnf(219,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(strict_implies(u,v)) ),
inference(spr,[status(thm),theory(equality)],[161,151]),
[iquote('0:SpR:161.0,151.1')] ).
cnf(294,plain,
is_a_theorem(strict_implies(and__dfg(u,v),u)),
inference(sor,[status(thm)],[219,156]),
[iquote('0:SoR:219.0,156.0')] ).
cnf(305,plain,
$false,
inference(unc,[status(thm)],[294,149]),
[iquote('0:UnC:294.0,149.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n029.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 21:51:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.33/0.60
% 0.33/0.60 SPASS V 3.9
% 0.33/0.60 SPASS beiseite: Proof found.
% 0.33/0.60 % SZS status Theorem
% 0.33/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/0.60 SPASS derived 111 clauses, backtracked 0 clauses, performed 1 splits and kept 197 clauses.
% 0.33/0.60 SPASS allocated 98124 KBytes.
% 0.33/0.60 SPASS spent 0:00:00.22 on the problem.
% 0.33/0.60 0:00:00.06 for the input.
% 0.33/0.60 0:00:00.08 for the FLOTTER CNF translation.
% 0.33/0.60 0:00:00.00 for inferences.
% 0.33/0.60 0:00:00.00 for the backtracking.
% 0.33/0.60 0:00:00.03 for the reduction.
% 0.33/0.60
% 0.33/0.60
% 0.33/0.60 Here is a proof with depth 2, length 15 :
% 0.33/0.60 % SZS output start Refutation
% See solution above
% 0.33/0.60 Formulae used in the proof : s1_0_op_strict_implies hilbert_and_1 km4b_necessitation s1_0_axiom_m2 and_1 necessitation km4b_axiom_M axiom_M axiom_m2 op_strict_implies
% 0.33/0.60
%------------------------------------------------------------------------------