%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL459+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 14:37:10 EDT 2022

% Result   : Theorem 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   15 (   9 unt;   0 nHn;  15 RR)
%            Number of literals    :   24 (   0 equ;  11 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   5 prp; 0-1 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    modus_ponens,
    file('LCL459+1.p',unknown),
    [] ).

cnf(10,axiom,
    implies_2,
    file('LCL459+1.p',unknown),
    [] ).

cnf(14,axiom,
    and_3,
    file('LCL459+1.p',unknown),
    [] ).

cnf(22,axiom,
    ~ kn1,
    file('LCL459+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87)))
    | kn1 ),
    file('LCL459+1.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ and_3
    | is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))) ),
    file('LCL459+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ is_a_theorem(u)
    | ~ modus_ponens
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    file('LCL459+1.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ implies_2
    | is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))) ),
    file('LCL459+1.p',unknown),
    [] ).

cnf(83,plain,
    ~ is_a_theorem(implies__dfg(skc87,and__dfg(skc87,skc87))),
    inference(mrr,[status(thm)],[39,22]),
    [iquote('0:MRR:39.1,22.0')] ).

cnf(93,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,and__dfg(u,v)))),
    inference(mrr,[status(thm)],[51,14]),
    [iquote('0:MRR:51.0,14.0')] ).

cnf(103,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
    inference(mrr,[status(thm)],[64,10]),
    [iquote('0:MRR:64.0,10.0')] ).

cnf(106,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    inference(mrr,[status(thm)],[61,7]),
    [iquote('0:MRR:61.1,7.0')] ).

cnf(209,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
    | is_a_theorem(implies__dfg(u,v)) ),
    inference(res,[status(thm),theory(equality)],[103,106]),
    [iquote('0:Res:103.0,106.1')] ).

cnf(442,plain,
    is_a_theorem(implies__dfg(u,and__dfg(u,u))),
    inference(sor,[status(thm)],[209,93]),
    [iquote('0:SoR:209.0,93.0')] ).

cnf(444,plain,
    $false,
    inference(unc,[status(thm)],[442,83]),
    [iquote('0:UnC:442.0,83.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL459+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  2 16:40:52 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.49  
% 0.18/0.49  SPASS V 3.9 
% 0.18/0.49  SPASS beiseite: Proof found.
% 0.18/0.49  % SZS status Theorem
% 0.18/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.49  SPASS derived 265 clauses, backtracked 0 clauses, performed 0 splits and kept 226 clauses.
% 0.18/0.49  SPASS allocated 98252 KBytes.
% 0.18/0.49  SPASS spent	0:00:00.14 on the problem.
% 0.18/0.49  		0:00:00.04 for the input.
% 0.18/0.49  		0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.49  		0:00:00.01 for inferences.
% 0.18/0.49  		0:00:00.00 for the backtracking.
% 0.18/0.49  		0:00:00.03 for the reduction.
% 0.18/0.49  
% 0.18/0.49  
% 0.18/0.49  Here is a proof with depth 2, length 15 :
% 0.18/0.49  % SZS output start Refutation
% See solution above
% 0.18/0.49  Formulae used in the proof : hilbert_modus_ponens hilbert_implies_2 hilbert_and_3 rosser_kn1 kn1 and_3 modus_ponens hilbert_implies_1 implies_1 implies_2
% 0.18/0.49  
%------------------------------------------------------------------------------