%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL398-1 : TPTP v9.3.1. Released v2.3.0.
% 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 01:07:25 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 17 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL398-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL398-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
file('LCL398-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
file('LCL398-1.p',unknown),
[] ).
cnf(5,axiom,
~ is_a_theorem(implies__dfg(not__dfg(implies__dfg(x__dfg,x__dfg)),y__dfg)),
file('LCL398-1.p',unknown),
[] ).
cnf(12,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(not__dfg(u),v)) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(13,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(16,plain,
~ is_a_theorem(implies__dfg(x__dfg,x__dfg)),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.1,5.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),v),w),implies__dfg(u,w))),
inference(sor,[status(thm)],[13,4]),
[iquote('0:SoR:13.0,4.0')] ).
cnf(22,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
| is_a_theorem(implies__dfg(u,w)) ),
inference(res,[status(thm),theory(equality)],[18,1]),
[iquote('0:Res:18.0,1.1')] ).
cnf(31,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[22,3]),
[iquote('0:SoR:22.0,3.0')] ).
cnf(32,plain,
$false,
inference(unc,[status(thm)],[31,16]),
[iquote('0:UnC:31.0,16.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL398-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.36 % Computer : n019.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 17:53:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.44
% 0.10/0.44 SPASS V 3.9
% 0.10/0.44 SPASS beiseite: Proof found.
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44 SPASS derived 21 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.10/0.44 SPASS allocated 75632 KBytes.
% 0.10/0.44 SPASS spent 0:00:00.06 on the problem.
% 0.10/0.44 0:00:00.03 for the input.
% 0.10/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.10/0.44 0:00:00.00 for inferences.
% 0.10/0.44 0:00:00.00 for the backtracking.
% 0.10/0.44 0:00:00.00 for the reduction.
% 0.10/0.44
% 0.10/0.44
% 0.10/0.44 Here is a proof with depth 4, length 12 :
% 0.10/0.44 % SZS output start Refutation
% See solution above
% 0.10/0.44 Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_64
% 0.10/0.44
%------------------------------------------------------------------------------