%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n001.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 01:07:27 PM UTC 2026
% Result : Theorem 0.24s 0.52s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ a_truth(implies__dfg(skc1,skc1)),
file('LCL414+1.p',unknown),
[] ).
cnf(2,axiom,
a_truth(implies__dfg(u,implies__dfg(v,u))),
file('LCL414+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ a_truth(u)
| ~ a_truth(implies__dfg(u,v))
| a_truth(v) ),
file('LCL414+1.p',unknown),
[] ).
cnf(5,axiom,
a_truth(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(u,v),implies__dfg(u,w)))),
file('LCL414+1.p',unknown),
[] ).
cnf(12,plain,
( ~ a_truth(implies__dfg(u,implies__dfg(v,w)))
| a_truth(implies__dfg(implies__dfg(u,v),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[5,3]),
[iquote('0:Res:5.0,3.1')] ).
cnf(19,plain,
a_truth(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.0,2.0')] ).
cnf(21,plain,
( ~ a_truth(implies__dfg(u,v))
| a_truth(implies__dfg(u,u)) ),
inference(res,[status(thm),theory(equality)],[19,3]),
[iquote('0:Res:19.0,3.1')] ).
cnf(26,plain,
a_truth(implies__dfg(u,u)),
inference(sor,[status(thm)],[21,2]),
[iquote('0:SoR:21.0,2.0')] ).
cnf(27,plain,
$false,
inference(unc,[status(thm)],[26,1]),
[iquote('0:UnC:26.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 13:05:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.24/0.52
% 0.24/0.52 SPASS V 3.9
% 0.24/0.52 SPASS beiseite: Proof found.
% 0.24/0.52 % SZS status Theorem
% 0.24/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.52 SPASS derived 17 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.24/0.52 SPASS allocated 97591 KBytes.
% 0.24/0.52 SPASS spent 0:00:00.15 on the problem.
% 0.24/0.52 0:00:00.06 for the input.
% 0.24/0.52 0:00:00.04 for the FLOTTER CNF translation.
% 0.24/0.52 0:00:00.00 for inferences.
% 0.24/0.52 0:00:00.00 for the backtracking.
% 0.24/0.52 0:00:00.00 for the reduction.
% 0.24/0.52
% 0.24/0.52
% 0.24/0.52 Here is a proof with depth 4, length 9 :
% 0.24/0.52 % SZS output start Refutation
% See solution above
% 0.24/0.52 Formulae used in the proof : thm147
% 0.24/0.52
%------------------------------------------------------------------------------