%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL544+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 0.79s 1.11s
% Output : Refutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of clauses : 27 ( 14 unt; 0 nHn; 27 RR)
% Number of literals : 44 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 9 usr; 8 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('LCL544+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL544+1.p',unknown),
[] ).
cnf(13,axiom,
implies_2,
file('LCL544+1.p',unknown),
[] ).
cnf(17,axiom,
and_3,
file('LCL544+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL544+1.p',unknown),
[] ).
cnf(31,axiom,
~ axiom_m4,
file('LCL544+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ kn1
| is_a_theorem(implies__dfg(u,and__dfg(u,u))) ),
file('LCL544+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ is_a_theorem(implies__dfg(skc126,and__dfg(skc126,skc126)))
| kn1 ),
file('LCL544+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL544+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ is_a_theorem(strict_implies(skc177,and__dfg(skc177,skc177)))
| axiom_m4 ),
file('LCL544+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL544+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL544+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL544+1.p',unknown),
[] ).
cnf(112,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL544+1.p',unknown),
[] ).
cnf(149,plain,
~ is_a_theorem(strict_implies(skc177,and__dfg(skc177,skc177))),
inference(mrr,[status(thm)],[75,31]),
[iquote('0:MRR:75.1,31.0')] ).
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(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(164,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[95,17]),
[iquote('0:MRR:95.0,17.0')] ).
cnf(174,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[112,13]),
[iquote('0:MRR:112.0,13.0')] ).
cnf(177,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[109,10]),
[iquote('0:MRR:109.1,10.0')] ).
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(296,plain,
( ~ kn1
| is_a_theorem(strict_implies(u,and__dfg(u,u))) ),
inference(sor,[status(thm)],[219,61]),
[iquote('0:SoR:219.0,61.1')] ).
cnf(315,plain,
~ kn1,
inference(res,[status(thm),theory(equality)],[296,149]),
[iquote('0:Res:296.1,149.0')] ).
cnf(316,plain,
~ is_a_theorem(implies__dfg(skc126,and__dfg(skc126,skc126))),
inference(mrr,[status(thm)],[62,315]),
[iquote('0:MRR:62.1,315.0')] ).
cnf(453,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[174,177]),
[iquote('0:Res:174.0,177.1')] ).
cnf(2051,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(sor,[status(thm)],[453,164]),
[iquote('0:SoR:453.0,164.0')] ).
cnf(2053,plain,
$false,
inference(unc,[status(thm)],[2051,316]),
[iquote('0:UnC:2051.0,316.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL544+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 20:14:38 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.79/1.11
% 0.79/1.11 SPASS V 3.9
% 0.79/1.11 SPASS beiseite: Proof found.
% 0.79/1.11 % SZS status Theorem
% 0.79/1.11 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/1.11 SPASS derived 1463 clauses, backtracked 0 clauses, performed 2 splits and kept 1006 clauses.
% 0.79/1.11 SPASS allocated 100630 KBytes.
% 0.79/1.11 SPASS spent 0:00:00.68 on the problem.
% 0.79/1.11 0:00:00.06 for the input.
% 0.79/1.11 0:00:00.08 for the FLOTTER CNF translation.
% 0.79/1.11 0:00:00.05 for inferences.
% 0.79/1.11 0:00:00.00 for the backtracking.
% 0.79/1.11 0:00:00.42 for the reduction.
% 0.79/1.11
% 0.79/1.11
% 0.79/1.11 Here is a proof with depth 3, length 27 :
% 0.79/1.11 % SZS output start Refutation
% See solution above
% 0.79/1.11 Formulae used in the proof : s1_0_op_strict_implies hilbert_modus_ponens hilbert_implies_2 hilbert_and_3 km4b_necessitation s1_0_axiom_m4 kn1 necessitation km4b_axiom_M axiom_M axiom_m4 and_3 op_strict_implies modus_ponens implies_2
% 0.79/1.11
%------------------------------------------------------------------------------