%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 01:07:42 PM UTC 2026
% Result : Theorem 0.40s 0.68s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 16 unt; 0 nHn; 26 RR)
% Number of literals : 40 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
op_strict_implies,
file('LCL538+1.p',unknown),
[] ).
cnf(10,axiom,
modus_ponens,
file('LCL538+1.p',unknown),
[] ).
cnf(26,axiom,
necessitation,
file('LCL538+1.p',unknown),
[] ).
cnf(28,axiom,
axiom_M,
file('LCL538+1.p',unknown),
[] ).
cnf(31,axiom,
~ modus_ponens_strict_implies,
file('LCL538+1.p',unknown),
[] ).
cnf(34,axiom,
is_a_theorem(skc151),
file('LCL538+1.p',unknown),
[] ).
cnf(39,axiom,
is_a_theorem(strict_implies(skc151,skc150)),
file('LCL538+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ is_a_theorem(skc150)
| modus_ponens_strict_implies ),
file('LCL538+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ axiom_M
| is_a_theorem(implies__dfg(necessarily(u),u)) ),
file('LCL538+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ is_a_theorem(u)
| ~ necessitation
| is_a_theorem(necessarily(u)) ),
file('LCL538+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ op_strict_implies
| equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
file('LCL538+1.p',unknown),
[] ).
cnf(109,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL538+1.p',unknown),
[] ).
cnf(148,plain,
~ is_a_theorem(skc150),
inference(mrr,[status(thm)],[40,31]),
[iquote('0:MRR:40.1,31.0')] ).
cnf(149,plain,
is_a_theorem(implies__dfg(necessarily(u),u)),
inference(mrr,[status(thm)],[47,28]),
[iquote('0:MRR:47.0,28.0')] ).
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(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(190,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,skc150)) ),
inference(res,[status(thm),theory(equality)],[177,148]),
[iquote('0:Res:177.2,148.0')] ).
cnf(198,plain,
~ is_a_theorem(necessarily(skc150)),
inference(res,[status(thm),theory(equality)],[149,190]),
[iquote('0:Res:149.0,190.1')] ).
cnf(202,plain,
~ is_a_theorem(skc150),
inference(sor,[status(thm)],[198,151]),
[iquote('0:SoR:198.0,151.1')] ).
cnf(219,plain,
is_a_theorem(implies__dfg(strict_implies(u,v),implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[161,149]),
[iquote('0:SpR:161.0,149.0')] ).
cnf(415,plain,
( ~ is_a_theorem(strict_implies(u,v))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[219,177]),
[iquote('0:Res:219.0,177.1')] ).
cnf(728,plain,
is_a_theorem(implies__dfg(skc151,skc150)),
inference(sor,[status(thm)],[415,39]),
[iquote('0:SoR:415.0,39.0')] ).
cnf(733,plain,
( ~ is_a_theorem(skc151)
| is_a_theorem(skc150) ),
inference(res,[status(thm),theory(equality)],[728,177]),
[iquote('0:Res:728.0,177.1')] ).
cnf(735,plain,
is_a_theorem(skc150),
inference(ssi,[status(thm)],[733,34]),
[iquote('0:SSi:733.0,34.0')] ).
cnf(736,plain,
$false,
inference(mrr,[status(thm)],[735,202]),
[iquote('0:MRR:735.0,202.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n017.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 : Sat Sep 5 05:35:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.40/0.68
% 0.40/0.68 SPASS V 3.9
% 0.40/0.68 SPASS beiseite: Proof found.
% 0.40/0.68 % SZS status Theorem
% 0.40/0.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.68 SPASS derived 467 clauses, backtracked 0 clauses, performed 1 splits and kept 400 clauses.
% 0.40/0.68 SPASS allocated 98662 KBytes.
% 0.40/0.68 SPASS spent 0:00:00.29 on the problem.
% 0.40/0.68 0:00:00.06 for the input.
% 0.40/0.68 0:00:00.07 for the FLOTTER CNF translation.
% 0.40/0.68 0:00:00.02 for inferences.
% 0.40/0.68 0:00:00.00 for the backtracking.
% 0.40/0.68 0:00:00.08 for the reduction.
% 0.40/0.68
% 0.40/0.68
% 0.40/0.68 Here is a proof with depth 4, length 26 :
% 0.40/0.68 % SZS output start Refutation
% See solution above
% 0.40/0.68 Formulae used in the proof : s1_0_op_strict_implies hilbert_modus_ponens km4b_necessitation km4b_axiom_M s1_0_modus_ponens_strict_implies modus_ponens_strict_implies axiom_M necessitation op_strict_implies modus_ponens hilbert_and_3 and_3
% 0.40/0.68
%------------------------------------------------------------------------------