%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL542+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 14:37:35 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% 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('LCL542+1.p',unknown),
    [] ).

cnf(15,axiom,
    and_1,
    file('LCL542+1.p',unknown),
    [] ).

cnf(26,axiom,
    necessitation,
    file('LCL542+1.p',unknown),
    [] ).

cnf(31,axiom,
    ~ axiom_m2,
    file('LCL542+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ and_1
    | is_a_theorem(implies__dfg(and__dfg(u,v),u)) ),
    file('LCL542+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ is_a_theorem(u)
    | ~ necessitation
    | is_a_theorem(necessarily(u)) ),
    file('LCL542+1.p',unknown),
    [] ).

cnf(73,axiom,
    ( ~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173))
    | axiom_m2 ),
    file('LCL542+1.p',unknown),
    [] ).

cnf(107,axiom,
    ( ~ op_strict_implies
    | equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)) ),
    file('LCL542+1.p',unknown),
    [] ).

cnf(149,plain,
    ~ is_a_theorem(strict_implies(and__dfg(skc173,skc172),skc173)),
    inference(mrr,[status(thm)],[73,31]),
    [iquote('0:MRR:73.1,31.0')] ).

cnf(151,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(necessarily(u)) ),
    inference(mrr,[status(thm)],[69,26]),
    [iquote('0:MRR:69.1,26.0')] ).

cnf(156,plain,
    is_a_theorem(implies__dfg(and__dfg(u,v),u)),
    inference(mrr,[status(thm)],[53,15]),
    [iquote('0:MRR:53.0,15.0')] ).

cnf(161,plain,
    equal(necessarily(implies__dfg(u,v)),strict_implies(u,v)),
    inference(mrr,[status(thm)],[107,4]),
    [iquote('0:MRR:107.0,4.0')] ).

cnf(219,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(strict_implies(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[161,151]),
    [iquote('0:SpR:161.0,151.1')] ).

cnf(294,plain,
    is_a_theorem(strict_implies(and__dfg(u,v),u)),
    inference(sor,[status(thm)],[219,156]),
    [iquote('0:SoR:219.0,156.0')] ).

cnf(305,plain,
    $false,
    inference(unc,[status(thm)],[294,149]),
    [iquote('0:UnC:294.0,149.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL542+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jul  2 16:39:37 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.51  
% 0.19/0.51  SPASS V 3.9 
% 0.19/0.51  SPASS beiseite: Proof found.
% 0.19/0.51  % SZS status Theorem
% 0.19/0.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.51  SPASS derived 111 clauses, backtracked 0 clauses, performed 1 splits and kept 197 clauses.
% 0.19/0.51  SPASS allocated 98124 KBytes.
% 0.19/0.51  SPASS spent	0:00:00.15 on the problem.
% 0.19/0.51  		0:00:00.04 for the input.
% 0.19/0.51  		0:00:00.06 for the FLOTTER CNF translation.
% 0.19/0.51  		0:00:00.00 for inferences.
% 0.19/0.51  		0:00:00.00 for the backtracking.
% 0.19/0.51  		0:00:00.02 for the reduction.
% 0.19/0.51  
% 0.19/0.51  
% 0.19/0.51  Here is a proof with depth 2, length 15 :
% 0.19/0.51  % SZS output start Refutation
% See solution above
% 0.19/0.51  Formulae used in the proof : s1_0_op_strict_implies hilbert_and_1 km4b_necessitation s1_0_axiom_m2 and_1 necessitation km4b_axiom_M axiom_M axiom_m2 op_strict_implies
% 0.19/0.51  
%------------------------------------------------------------------------------