%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 01:07:34 PM UTC 2026
% Result : Theorem 0.22s 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 29 RR)
% Number of literals : 43 ( 0 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 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_or,
file('LCL453+1.p',unknown),
[] ).
cnf(5,axiom,
op_implies_and,
file('LCL453+1.p',unknown),
[] ).
cnf(7,axiom,
modus_ponens,
file('LCL453+1.p',unknown),
[] ).
cnf(9,axiom,
implies_1,
file('LCL453+1.p',unknown),
[] ).
cnf(10,axiom,
implies_2,
file('LCL453+1.p',unknown),
[] ).
cnf(17,axiom,
or_3,
file('LCL453+1.p',unknown),
[] ).
cnf(22,axiom,
~ cn3,
file('LCL453+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ implies_1
| is_a_theorem(implies__dfg(u,implies__dfg(v,u))) ),
file('LCL453+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(skc98),skc98),skc98))
| cn3 ),
file('LCL453+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ op_implies_and
| equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
file('LCL453+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ is_a_theorem(u)
| ~ modus_ponens
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL453+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('LCL453+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ op_or
| equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
file('LCL453+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ or_3
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,v),implies__dfg(or__dfg(u,w),v)))) ),
file('LCL453+1.p',unknown),
[] ).
cnf(89,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(mrr,[status(thm)],[28,9]),
[iquote('0:MRR:28.0,9.0')] ).
cnf(90,plain,
~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(skc98),skc98),skc98)),
inference(mrr,[status(thm)],[49,22]),
[iquote('0:MRR:49.1,22.0')] ).
cnf(95,plain,
equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
inference(mrr,[status(thm)],[60,5]),
[iquote('0:MRR:60.0,5.0')] ).
cnf(96,plain,
( ~ op_or
| equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
inference(rew,[status(thm),theory(equality)],[95,66]),
[iquote('0:Rew:95.0,66.1')] ).
cnf(97,plain,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
inference(mrr,[status(thm)],[96,4]),
[iquote('0:MRR:96.0,4.0')] ).
cnf(100,plain,
~ is_a_theorem(implies__dfg(or__dfg(skc98,skc98),skc98)),
inference(rew,[status(thm),theory(equality)],[97,90]),
[iquote('0:Rew:97.0,90.0')] ).
cnf(102,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(105,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(112,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,v),implies__dfg(or__dfg(u,w),v)))),
inference(mrr,[status(thm)],[79,17]),
[iquote('0:MRR:79.0,17.0')] ).
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)],[102,105]),
[iquote('0:Res:102.0,105.1')] ).
cnf(419,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(u,u),v))),
inference(sor,[status(thm)],[209,112]),
[iquote('0:SoR:209.0,112.0')] ).
cnf(424,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[209,89]),
[iquote('0:SoR:209.0,89.0')] ).
cnf(526,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(or__dfg(u,u),v)) ),
inference(res,[status(thm),theory(equality)],[419,105]),
[iquote('0:Res:419.0,105.1')] ).
cnf(668,plain,
is_a_theorem(implies__dfg(or__dfg(u,u),u)),
inference(sor,[status(thm)],[526,424]),
[iquote('0:SoR:526.0,424.0')] ).
cnf(679,plain,
$false,
inference(unc,[status(thm)],[668,100]),
[iquote('0:UnC:668.0,100.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 12:36:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.22/0.51
% 0.22/0.51 SPASS V 3.9
% 0.22/0.51 SPASS beiseite: Proof found.
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.51 SPASS derived 430 clauses, backtracked 0 clauses, performed 0 splits and kept 300 clauses.
% 0.22/0.51 SPASS allocated 98575 KBytes.
% 0.22/0.51 SPASS spent 0:00:00.12 on the problem.
% 0.22/0.51 0:00:00.03 for the input.
% 0.22/0.51 0:00:00.03 for the FLOTTER CNF translation.
% 0.22/0.51 0:00:00.01 for inferences.
% 0.22/0.51 0:00:00.00 for the backtracking.
% 0.22/0.51 0:00:00.03 for the reduction.
% 0.22/0.51
% 0.22/0.51
% 0.22/0.51 Here is a proof with depth 4, length 29 :
% 0.22/0.51 % SZS output start Refutation
% See solution above
% 0.22/0.51 Formulae used in the proof : hilbert_op_or hilbert_op_implies_and hilbert_modus_ponens hilbert_implies_1 hilbert_implies_2 hilbert_or_3 luka_cn3 implies_1 cn3 op_implies_and modus_ponens implies_2 hilbert_and_3 and_3 op_or or_3
% 0.22/0.51
%------------------------------------------------------------------------------