%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 01:07:35 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Refutation 0.12s
% 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 : 24 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
modus_ponens,
file('LCL459+1.p',unknown),
[] ).
cnf(10,axiom,
implies_2,
file('LCL459+1.p',unknown),
[] ).
cnf(14,axiom,
and_3,
file('LCL459+1.p',unknown),
[] ).
cnf(22,axiom,
~ kn1,
file('LCL459+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
| kn1 ),
file('LCL459+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ and_3
| is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
file('LCL459+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL459+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ implies_2
| is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
file('LCL459+1.p',unknown),
[] ).
cnf(83,plain,
~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87))),
inference(mrr,[status(thm)],[39,22]),
[iquote('0:MRR:39.1,22.0')] ).
cnf(93,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
inference(mrr,[status(thm)],[51,14]),
[iquote('0:MRR:51.0,14.0')] ).
cnf(103,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(mrr,[status(thm)],[64,10]),
[iquote('0:MRR:64.0,10.0')] ).
cnf(106,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(mrr,[status(thm)],[61,7]),
[iquote('0:MRR:61.1,7.0')] ).
cnf(209,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(res,[status(thm),theory(equality)],[103,106]),
[iquote('0:Res:103.0,106.1')] ).
cnf(442,plain,
is_a_theorem(implies__dfg(u,and__dfg(u,u))),
inference(sor,[status(thm)],[209,93]),
[iquote('0:SoR:209.0,93.0')] ).
cnf(444,plain,
$false,
inference(unc,[status(thm)],[442,83]),
[iquote('0:UnC:442.0,83.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.07/0.33 % Computer : n027.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Fri Sep 4 14:32:27 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.12/0.46
% 0.12/0.46 SPASS V 3.9
% 0.12/0.46 SPASS beiseite: Proof found.
% 0.12/0.46 % SZS status Theorem
% 0.12/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.46 SPASS derived 265 clauses, backtracked 0 clauses, performed 0 splits and kept 226 clauses.
% 0.12/0.46 SPASS allocated 98252 KBytes.
% 0.12/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.12/0.46 0:00:00.03 for the input.
% 0.12/0.46 0:00:00.03 for the FLOTTER CNF translation.
% 0.12/0.46 0:00:00.00 for inferences.
% 0.12/0.46 0:00:00.00 for the backtracking.
% 0.12/0.46 0:00:00.02 for the reduction.
% 0.12/0.46
% 0.12/0.46
% 0.12/0.46 Here is a proof with depth 2, length 15 :
% 0.12/0.46 % SZS output start Refutation
% See solution above
% 0.12/0.46 Formulae used in the proof : hilbert_modus_ponens hilbert_implies_2 hilbert_and_3 rosser_kn1 kn1 and_3 modus_ponens hilbert_implies_1 implies_1 implies_2
% 0.12/0.46
%------------------------------------------------------------------------------