%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL133-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 0.23s 0.49s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(implies__dfg(u,v),implies__dfg(v,u)),
file('LCL133-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(y__dfg,x__dfg),
file('LCL133-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(truth,u),u),
file('LCL133-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL133-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL133-1.p',unknown),
[] ).
cnf(7,plain,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(not__dfg(v),not__dfg(u))),truth),
inference(rew,[status(thm),theory(equality)],[1,6]),
[iquote('0:Rew:1.0,6.0')] ).
cnf(8,plain,
equal(implies__dfg(u,implies__dfg(v,u)),implies__dfg(v,implies__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[1,5]),
[iquote('0:Rew:1.0,5.0,1.0,5.0')] ).
cnf(10,plain,
equal(implies__dfg(u,truth),u),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(24,plain,
equal(implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth))),truth),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(29,plain,
equal(implies__dfg(not__dfg(truth),not__dfg(truth)),truth),
inference(spr,[status(thm),theory(equality)],[24,3]),
[iquote('0:SpR:24.0,3.0')] ).
cnf(58,plain,
equal(implies__dfg(u,implies__dfg(truth,u)),implies__dfg(u,truth)),
inference(spr,[status(thm),theory(equality)],[8,3]),
[iquote('0:SpR:8.0,3.0')] ).
cnf(74,plain,
equal(implies__dfg(u,implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u)),implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),truth)),
inference(spr,[status(thm),theory(equality)],[24,8]),
[iquote('0:SpR:24.0,8.0')] ).
cnf(88,plain,
equal(implies__dfg(u,u),u),
inference(rew,[status(thm),theory(equality)],[3,58,10]),
[iquote('0:Rew:3.0,58.0,10.0,58.0')] ).
cnf(90,plain,
equal(not__dfg(truth),truth),
inference(rew,[status(thm),theory(equality)],[88,29]),
[iquote('0:Rew:88.0,29.0')] ).
cnf(92,plain,
equal(implies__dfg(u,implies__dfg(not__dfg(u),truth)),truth),
inference(rew,[status(thm),theory(equality)],[90,24]),
[iquote('0:Rew:90.0,24.0')] ).
cnf(98,plain,
equal(implies__dfg(u,not__dfg(u)),truth),
inference(rew,[status(thm),theory(equality)],[10,92]),
[iquote('0:Rew:10.0,92.0')] ).
cnf(117,plain,
equal(implies__dfg(u,implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth)))),implies__dfg(not__dfg(u),not__dfg(truth))),
inference(rew,[status(thm),theory(equality)],[1,74,10]),
[iquote('0:Rew:1.0,74.0,10.0,74.0')] ).
cnf(118,plain,
equal(implies__dfg(u,implies__dfg(u,implies__dfg(not__dfg(u),truth))),implies__dfg(not__dfg(u),truth)),
inference(rew,[status(thm),theory(equality)],[90,117]),
[iquote('0:Rew:90.0,117.0')] ).
cnf(119,plain,
equal(implies__dfg(u,implies__dfg(u,not__dfg(u))),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[10,118]),
[iquote('0:Rew:10.0,118.0')] ).
cnf(120,plain,
equal(implies__dfg(u,truth),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[98,119]),
[iquote('0:Rew:98.0,119.0')] ).
cnf(121,plain,
equal(not__dfg(u),u),
inference(rew,[status(thm),theory(equality)],[10,120]),
[iquote('0:Rew:10.0,120.0')] ).
cnf(126,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[121,98]),
[iquote('0:Rew:121.0,98.0')] ).
cnf(127,plain,
equal(u,truth),
inference(rew,[status(thm),theory(equality)],[88,126]),
[iquote('0:Rew:88.0,126.0')] ).
cnf(144,plain,
equal(u,v),
inference(spr,[status(thm),theory(equality)],[127]),
[iquote('0:SpR:127.0,127.0')] ).
cnf(145,plain,
$false,
inference(unc,[status(thm)],[144,2]),
[iquote('0:UnC:144.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL133-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 08:03:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.23/0.49
% 0.23/0.49 SPASS V 3.9
% 0.23/0.49 SPASS beiseite: Proof found.
% 0.23/0.49 % SZS status Theorem
% 0.23/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.49 SPASS derived 94 clauses, backtracked 0 clauses, performed 0 splits and kept 25 clauses.
% 0.23/0.49 SPASS allocated 63201 KBytes.
% 0.23/0.49 SPASS spent 0:00:00.11 on the problem.
% 0.23/0.49 0:00:00.06 for the input.
% 0.23/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.49 0:00:00.00 for inferences.
% 0.23/0.49 0:00:00.00 for the backtracking.
% 0.23/0.49 0:00:00.01 for the reduction.
% 0.23/0.49
% 0.23/0.49
% 0.23/0.49 Here is a proof with depth 2, length 25 :
% 0.23/0.49 % SZS output start Refutation
% See solution above
% 0.23/0.49 Formulae used in the proof : lemma_antecedent prove_wajsberg_lemma wajsberg_1 wajsberg_3 wajsberg_4
% 0.23/0.49
%------------------------------------------------------------------------------