%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL135-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 15 RR)
% Number of literals : 15 ( 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(implies__dfg(x__dfg,implies__dfg(y__dfg,x__dfg)),truth),
file('LCL135-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL135-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL135-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL135-1.p',unknown),
[] ).
cnf(18,plain,
equal(implies__dfg(u,u),implies__dfg(implies__dfg(u,truth),truth)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
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(90,plain,
equal(implies__dfg(implies__dfg(u,truth),implies__dfg(v,implies__dfg(u,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(219,plain,
equal(implies__dfg(u,implies__dfg(u,u)),truth),
inference(spr,[status(thm),theory(equality)],[18,117]),
[iquote('0:SpR:18.0,117.0')] ).
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(244,plain,
equal(implies__dfg(u,truth),truth),
inference(rew,[status(thm),theory(equality)],[220,219]),
[iquote('0:Rew:220.0,219.0')] ).
cnf(251,plain,
equal(implies__dfg(truth,implies__dfg(u,implies__dfg(v,u))),truth),
inference(rew,[status(thm),theory(equality)],[244,90]),
[iquote('0:Rew:244.0,90.0')] ).
cnf(262,plain,
equal(implies__dfg(u,implies__dfg(v,u)),truth),
inference(rew,[status(thm),theory(equality)],[2,251]),
[iquote('0:Rew:2.0,251.0')] ).
cnf(263,plain,
$false,
inference(unc,[status(thm)],[262,1]),
[iquote('0:UnC:262.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL135-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 18:15:19 UTC 2026
% 0.10/0.36 % 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/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 SPASS derived 195 clauses, backtracked 0 clauses, performed 0 splits and kept 86 clauses.
% 0.22/0.51 SPASS allocated 63500 KBytes.
% 0.22/0.51 SPASS spent 0:00:00.13 on the problem.
% 0.22/0.51 0:00:00.06 for the input.
% 0.22/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.51 0:00:00.00 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 2, length 15 :
% 0.22/0.51 % SZS output start Refutation
% See solution above
% 0.22/0.51 Formulae used in the proof : prove_wajsberg_lemma wajsberg_1 wajsberg_2 wajsberg_3
% 0.22/0.51
%------------------------------------------------------------------------------