%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL398-1 : TPTP v8.1.0. Released v2.3.0.
% 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 14:36:40 EDT 2022

% Result   : Unsatisfiable 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   8 unt;   0 nHn;  12 RR)
%            Number of literals    :   17 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    file('LCL398-1.p',unknown),
    [] ).

cnf(2,axiom,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
    file('LCL398-1.p',unknown),
    [] ).

cnf(3,axiom,
    is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),u),u)),
    file('LCL398-1.p',unknown),
    [] ).

cnf(4,axiom,
    is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
    file('LCL398-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ is_a_theorem(implies__dfg(not__dfg(implies__dfg(x__dfg,x__dfg)),y__dfg)),
    file('LCL398-1.p',unknown),
    [] ).

cnf(12,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(not__dfg(u),v)) ),
    inference(res,[status(thm),theory(equality)],[4,1]),
    [iquote('0:Res:4.0,1.1')] ).

cnf(13,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.0,1.1')] ).

cnf(16,plain,
    ~ is_a_theorem(implies__dfg(x__dfg,x__dfg)),
    inference(res,[status(thm),theory(equality)],[12,5]),
    [iquote('0:Res:12.1,5.0')] ).

cnf(18,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(not__dfg(u),v),w),implies__dfg(u,w))),
    inference(sor,[status(thm)],[13,4]),
    [iquote('0:SoR:13.0,4.0')] ).

cnf(22,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(not__dfg(u),v),w))
    | is_a_theorem(implies__dfg(u,w)) ),
    inference(res,[status(thm),theory(equality)],[18,1]),
    [iquote('0:Res:18.0,1.1')] ).

cnf(31,plain,
    is_a_theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[22,3]),
    [iquote('0:SoR:22.0,3.0')] ).

cnf(32,plain,
    $false,
    inference(unc,[status(thm)],[31,16]),
    [iquote('0:UnC:31.0,16.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : LCL398-1 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.14  % Command  : run_spass %d %s
% 0.15/0.36  % Computer : n008.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Sat Jul  2 23:13:23 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.22/0.43  
% 0.22/0.43  SPASS V 3.9 
% 0.22/0.43  SPASS beiseite: Proof found.
% 0.22/0.43  % SZS status Theorem
% 0.22/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.22/0.43  SPASS derived 21 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.22/0.43  SPASS allocated 75632 KBytes.
% 0.22/0.43  SPASS spent	0:00:00.06 on the problem.
% 0.22/0.43  		0:00:00.04 for the input.
% 0.22/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.43  		0:00:00.00 for inferences.
% 0.22/0.43  		0:00:00.00 for the backtracking.
% 0.22/0.43  		0:00:00.00 for the reduction.
% 0.22/0.43  
% 0.22/0.43  
% 0.22/0.43  Here is a proof with depth 4, length 12 :
% 0.22/0.43  % SZS output start Refutation
% See solution above
% 0.22/0.43  Formulae used in the proof : condensed_detachment cn_1 cn_2 cn_3 prove_cn_64
% 0.22/0.43  
%------------------------------------------------------------------------------