%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL132-1 : TPTP v9.3.1. Released v1.0.0.
% 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 01:06:51 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 8 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(implies__dfg(x__dfg,x__dfg),truth),
file('LCL132-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL132-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL132-1.p',unknown),
[] ).
cnf(80,plain,
equal(implies__dfg(implies__dfg(truth,u),implies__dfg(implies__dfg(u,v),v)),truth),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(117,plain,
equal(implies__dfg(u,implies__dfg(implies__dfg(u,v),v)),truth),
inference(rew,[status(thm),theory(equality)],[2,80]),
[iquote('0:Rew:2.0,80.0')] ).
cnf(192,plain,
equal(implies__dfg(implies__dfg(truth,u),u),truth),
inference(spr,[status(thm),theory(equality)],[117,2]),
[iquote('0:SpR:117.0,2.0')] ).
cnf(220,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[2,192]),
[iquote('0:Rew:2.0,192.0')] ).
cnf(221,plain,
$false,
inference(unc,[status(thm)],[220,1]),
[iquote('0:UnC:220.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL132-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.07/0.34 % Computer : n027.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 20:20:27 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.22/0.49
% 0.22/0.49 SPASS V 3.9
% 0.22/0.49 SPASS beiseite: Proof found.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.49 SPASS derived 158 clauses, backtracked 0 clauses, performed 0 splits and kept 90 clauses.
% 0.22/0.49 SPASS allocated 63465 KBytes.
% 0.22/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.49 0:00:00.06 for the input.
% 0.22/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.49 0:00:00.00 for inferences.
% 0.22/0.49 0:00:00.00 for the backtracking.
% 0.22/0.49 0:00:00.02 for the reduction.
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 Here is a proof with depth 2, length 8 :
% 0.22/0.49 % SZS output start Refutation
% See solution above
% 0.22/0.49 Formulae used in the proof : prove_wajsberg_lemma wajsberg_1 wajsberg_2
% 0.22/0.49
%------------------------------------------------------------------------------