%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL414-1 : TPTP v8.1.0. Released v2.5.0.
% 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   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 14:36:46 EDT 2022

% Result   : Unsatisfiable 0.18s 0.40s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ a_truth(u)
    | ~ a_truth(implies__dfg(u,v))
    | a_truth(v) ),
    file('LCL414-1.p',unknown),
    [] ).

cnf(2,axiom,
    a_truth(implies__dfg(u,implies__dfg(v,u))),
    file('LCL414-1.p',unknown),
    [] ).

cnf(3,axiom,
    a_truth(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(u,v),implies__dfg(u,w)))),
    file('LCL414-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ a_truth(implies__dfg(sk1,sk1)),
    file('LCL414-1.p',unknown),
    [] ).

cnf(12,plain,
    ( ~ a_truth(implies__dfg(u,implies__dfg(v,w)))
    | a_truth(implies__dfg(implies__dfg(u,v),implies__dfg(u,w))) ),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.0,1.1')] ).

cnf(19,plain,
    a_truth(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
    inference(sor,[status(thm)],[12,2]),
    [iquote('0:SoR:12.0,2.0')] ).

cnf(21,plain,
    ( ~ a_truth(implies__dfg(u,v))
    | a_truth(implies__dfg(u,u)) ),
    inference(res,[status(thm),theory(equality)],[19,1]),
    [iquote('0:Res:19.0,1.1')] ).

cnf(26,plain,
    a_truth(implies__dfg(u,u)),
    inference(sor,[status(thm)],[21,2]),
    [iquote('0:SoR:21.0,2.0')] ).

cnf(27,plain,
    $false,
    inference(unc,[status(thm)],[26,5]),
    [iquote('0:UnC:26.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : LCL414-1 : TPTP v8.1.0. Released v2.5.0.
% 0.00/0.12  % Command  : run_spass %d %s
% 0.11/0.33  % Computer : n018.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sat Jul  2 20:53:19 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.18/0.40  
% 0.18/0.40  SPASS V 3.9 
% 0.18/0.40  SPASS beiseite: Proof found.
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.40  SPASS derived 17 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.18/0.40  SPASS allocated 75619 KBytes.
% 0.18/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.40  		0:00:00.04 for the input.
% 0.18/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40  		0:00:00.00 for inferences.
% 0.18/0.40  		0:00:00.00 for the backtracking.
% 0.18/0.40  		0:00:00.00 for the reduction.
% 0.18/0.40  
% 0.18/0.40  
% 0.18/0.40  Here is a proof with depth 4, length 9 :
% 0.18/0.40  % SZS output start Refutation
% See solution above
% 0.18/0.40  Formulae used in the proof : thm147_1 thm147_2 thm147_3 thm147_5
% 0.18/0.40  
%------------------------------------------------------------------------------