%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL141-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 0.46s 0.72s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 37 RR)
% Number of literals : 37 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(implies__dfg(not__dfg(x__dfg),not__dfg(y__dfg)),implies__dfg(y__dfg,x__dfg)),
file('LCL141-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL141-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL141-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL141-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL141-1.p',unknown),
[] ).
cnf(9,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u),truth),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
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(350,plain,
equal(implies__dfg(truth,implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),truth),
inference(spr,[status(thm),theory(equality)],[262,3]),
[iquote('0:SpR:262.0,3.0')] ).
cnf(365,plain,
equal(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w)),truth),
inference(rew,[status(thm),theory(equality)],[2,350]),
[iquote('0:Rew:2.0,350.0')] ).
cnf(399,plain,
equal(implies__dfg(truth,implies__dfg(not__dfg(truth),u)),truth),
inference(spr,[status(thm),theory(equality)],[9,365]),
[iquote('0:SpR:9.0,365.0')] ).
cnf(402,plain,
equal(implies__dfg(truth,implies__dfg(not__dfg(u),implies__dfg(u,v))),truth),
inference(spr,[status(thm),theory(equality)],[5,365]),
[iquote('0:SpR:5.0,365.0')] ).
cnf(408,plain,
equal(implies__dfg(not__dfg(truth),u),truth),
inference(rew,[status(thm),theory(equality)],[2,399]),
[iquote('0:Rew:2.0,399.0')] ).
cnf(414,plain,
equal(implies__dfg(not__dfg(u),implies__dfg(u,v)),truth),
inference(rew,[status(thm),theory(equality)],[2,402]),
[iquote('0:Rew:2.0,402.0')] ).
cnf(502,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(truth)),not__dfg(truth)),implies__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[408,4]),
[iquote('0:SpR:408.0,4.0')] ).
cnf(522,plain,
equal(implies__dfg(implies__dfg(u,not__dfg(truth)),not__dfg(truth)),u),
inference(rew,[status(thm),theory(equality)],[2,502]),
[iquote('0:Rew:2.0,502.0')] ).
cnf(577,plain,
equal(implies__dfg(not__dfg(implies__dfg(u,not__dfg(truth))),u),truth),
inference(spr,[status(thm),theory(equality)],[522,414]),
[iquote('0:SpR:522.0,414.0')] ).
cnf(712,plain,
equal(implies__dfg(truth,implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth)))),truth),
inference(spr,[status(thm),theory(equality)],[577,5]),
[iquote('0:SpR:577.0,5.0')] ).
cnf(738,plain,
equal(implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth))),truth),
inference(rew,[status(thm),theory(equality)],[2,712]),
[iquote('0:Rew:2.0,712.0')] ).
cnf(755,plain,
equal(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u),u),implies__dfg(truth,implies__dfg(not__dfg(u),not__dfg(truth)))),
inference(spr,[status(thm),theory(equality)],[738,4]),
[iquote('0:SpR:738.0,4.0')] ).
cnf(786,plain,
equal(implies__dfg(not__dfg(u),not__dfg(truth)),u),
inference(rew,[status(thm),theory(equality)],[2,755,9]),
[iquote('0:Rew:2.0,755.0,9.0,755.0,2.0,755.0')] ).
cnf(824,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(implies__dfg(v,not__dfg(truth)),u)),truth),
inference(spr,[status(thm),theory(equality)],[786,3]),
[iquote('0:SpR:786.0,3.0')] ).
cnf(827,plain,
equal(implies__dfg(u,not__dfg(truth)),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[786,522]),
[iquote('0:SpR:786.0,522.0')] ).
cnf(832,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[827,786]),
[iquote('0:Rew:827.0,786.0')] ).
cnf(859,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(not__dfg(v),u)),truth),
inference(rew,[status(thm),theory(equality)],[827,824]),
[iquote('0:Rew:827.0,824.0')] ).
cnf(1594,plain,
equal(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),v),implies__dfg(not__dfg(v),u)),implies__dfg(not__dfg(v),u)),implies__dfg(truth,implies__dfg(not__dfg(u),v))),
inference(spr,[status(thm),theory(equality)],[859,4]),
[iquote('0:SpR:859.0,4.0')] ).
cnf(1664,plain,
equal(implies__dfg(not__dfg(u),v),implies__dfg(not__dfg(v),u)),
inference(rew,[status(thm),theory(equality)],[2,1594,859]),
[iquote('0:Rew:2.0,1594.0,859.0,1594.0,2.0,1594.0')] ).
cnf(1751,plain,
equal(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),
inference(spr,[status(thm),theory(equality)],[832,1664]),
[iquote('0:SpR:832.0,1664.0')] ).
cnf(1755,plain,
$false,
inference(unc,[status(thm)],[1751,1]),
[iquote('0:UnC:1751.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL141-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.12/0.35 % Computer : n008.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8046.5625MB
% 0.12/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun Sep 6 01:01:38 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.46/0.72
% 0.46/0.72 SPASS V 3.9
% 0.46/0.72 SPASS beiseite: Proof found.
% 0.46/0.72 % SZS status Theorem
% 0.46/0.72 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.72 SPASS derived 1148 clauses, backtracked 0 clauses, performed 0 splits and kept 273 clauses.
% 0.46/0.72 SPASS allocated 65342 KBytes.
% 0.46/0.72 SPASS spent 0:00:00.32 on the problem.
% 0.46/0.72 0:00:00.06 for the input.
% 0.46/0.72 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.72 0:00:00.02 for inferences.
% 0.46/0.72 0:00:00.00 for the backtracking.
% 0.46/0.72 0:00:00.21 for the reduction.
% 0.46/0.72
% 0.46/0.72
% 0.46/0.72 Here is a proof with depth 10, length 37 :
% 0.46/0.72 % SZS output start Refutation
% See solution above
% 0.46/0.72 Formulae used in the proof : prove_wajsberg_lemma wajsberg_1 wajsberg_2 wajsberg_3 wajsberg_4
% 0.46/0.72
%------------------------------------------------------------------------------