%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL529+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 14:37:31 EDT 2022

% Result   : Theorem 0.17s 0.49s
% Output   : Refutation 0.17s
% 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    :   22 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    7 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    op_strict_implies,
    file('LCL529+1.p',unknown),
    [] ).

cnf(15,axiom,
    and_1,
    file('LCL529+1.p',unknown),
    [] ).

cnf(26,axiom,
    necessitation,
    file('LCL529+1.p',unknown),
    [] ).

cnf(30,axiom,
    ~ axiom_m2,
    file('LCL529+1.p',unknown),
    [] ).

cnf(52,axiom,
    ( ~ and_1
    | is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
    file('LCL529+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ is_a_theorem(u)
    | ~ necessitation
    | is_a_theorem(necessarily(u)) ),
    file('LCL529+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173))
    | axiom_m2 ),
    file('LCL529+1.p',unknown),
    [] ).

cnf(106,axiom,
    ( ~ op_strict_implies
    | equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
    file('LCL529+1.p',unknown),
    [] ).

cnf(148,plain,
    ~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173)),
    inference(mrr,[status(thm)],[72,30]),
    [iquote('0:MRR:72.1,30.0')] ).

cnf(149,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(necessarily(u)) ),
    inference(mrr,[status(thm)],[68,26]),
    [iquote('0:MRR:68.1,26.0')] ).

cnf(154,plain,
    is_a_theorem(implies__dfg(and__dfg(u,v),u)),
    inference(mrr,[status(thm)],[52,15]),
    [iquote('0:MRR:52.0,15.0')] ).

cnf(159,plain,
    equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
    inference(mrr,[status(thm)],[106,4]),
    [iquote('0:MRR:106.0,4.0')] ).

cnf(219,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(strict_implies(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[159,149]),
    [iquote('0:SpR:159.0,149.1')] ).

cnf(301,plain,
    is_a_theorem(strict_implies(and__dfg(u,v),u)),
    inference(sor,[status(thm)],[219,154]),
    [iquote('0:SoR:219.0,154.0')] ).

cnf(305,plain,
    $false,
    inference(unc,[status(thm)],[301,148]),
    [iquote('0:UnC:301.0,148.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LCL529+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n027.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sat Jul  2 11:22:08 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.17/0.49  
% 0.17/0.49  SPASS V 3.9 
% 0.17/0.49  SPASS beiseite: Proof found.
% 0.17/0.49  % SZS status Theorem
% 0.17/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.17/0.49  SPASS derived 110 clauses, backtracked 0 clauses, performed 1 splits and kept 194 clauses.
% 0.17/0.49  SPASS allocated 98124 KBytes.
% 0.17/0.49  SPASS spent	0:00:00.15 on the problem.
% 0.17/0.49  		0:00:00.04 for the input.
% 0.17/0.49  		0:00:00.06 for the FLOTTER CNF translation.
% 0.17/0.49  		0:00:00.00 for inferences.
% 0.17/0.49  		0:00:00.00 for the backtracking.
% 0.17/0.49  		0:00:00.02 for the reduction.
% 0.17/0.49  
% 0.17/0.49  
% 0.17/0.49  Here is a proof with depth 2, length 15 :
% 0.17/0.49  % SZS output start Refutation
% See solution above
% 0.17/0.49  Formulae used in the proof : s1_0_op_strict_implies hilbert_and_1 km5_necessitation s1_0_axiom_m2 and_1 necessitation km5_axiom_M axiom_M axiom_m2 op_strict_implies
% 0.17/0.49  
%------------------------------------------------------------------------------