%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL134-1 : TPTP v8.1.0. 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   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 14:34:50 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   12 (  12 unt;   0 nHn;  12 RR)
%            Number of literals    :   12 (   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,truth),truth),
    file('LCL134-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(implies__dfg(truth,u),u),
    file('LCL134-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
    file('LCL134-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
    file('LCL134-1.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(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(218,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)],[220,218]),
    [iquote('0:Rew:220.0,218.0')] ).

cnf(245,plain,
    $false,
    inference(unc,[status(thm)],[244,1]),
    [iquote('0:UnC:244.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL134-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul  3 04:33:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 186 clauses, backtracked 0 clauses, performed 0 splits and kept 98 clauses.
% 0.20/0.44  SPASS allocated 63494 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.20/0.44  		0:00:00.03 for the input.
% 0.20/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.03 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 2, length 12 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : prove_wajsberg_lemma wajsberg_1 wajsberg_2 wajsberg_3
% 0.20/0.44  
%------------------------------------------------------------------------------