%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL469+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 14:37:14 EDT 2022

% Result   : Theorem 0.21s 0.47s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   15 (  10 unt;   0 nHn;  15 RR)
%            Number of literals    :   20 (   0 equ;   7 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   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(2,axiom,
    op_implies_and,
    file('LCL469+1.p',unknown),
    [] ).

cnf(4,axiom,
    op_or,
    file('LCL469+1.p',unknown),
    [] ).

cnf(9,axiom,
    cn2,
    file('LCL469+1.p',unknown),
    [] ).

cnf(12,axiom,
    ~ or_1,
    file('LCL469+1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ is_a_theorem(implies__dfg(skc75,or__dfg(skc75,skc74)))
    | or_1 ),
    file('LCL469+1.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ cn2
    | is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))) ),
    file('LCL469+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ op_implies_and
    | equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)) ),
    file('LCL469+1.p',unknown),
    [] ).

cnf(56,axiom,
    ( ~ op_or
    | equal(not__dfg(and__dfg(not__dfg(u),not__dfg(v))),or__dfg(u,v)) ),
    file('LCL469+1.p',unknown),
    [] ).

cnf(73,plain,
    ~ is_a_theorem(implies__dfg(skc75,or__dfg(skc75,skc74))),
    inference(mrr,[status(thm)],[25,12]),
    [iquote('0:MRR:25.1,12.0')] ).

cnf(75,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(not__dfg(u),v))),
    inference(mrr,[status(thm)],[36,9]),
    [iquote('0:MRR:36.0,9.0')] ).

cnf(77,plain,
    equal(not__dfg(and__dfg(u,not__dfg(v))),implies__dfg(u,v)),
    inference(mrr,[status(thm)],[50,2]),
    [iquote('0:MRR:50.0,2.0')] ).

cnf(78,plain,
    ( ~ op_or
    | equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)) ),
    inference(rew,[status(thm),theory(equality)],[77,56]),
    [iquote('0:Rew:77.0,56.1')] ).

cnf(79,plain,
    equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
    inference(mrr,[status(thm)],[78,4]),
    [iquote('0:MRR:78.0,4.0')] ).

cnf(80,plain,
    is_a_theorem(implies__dfg(u,or__dfg(u,v))),
    inference(rew,[status(thm),theory(equality)],[79,75]),
    [iquote('0:Rew:79.0,75.0')] ).

cnf(82,plain,
    $false,
    inference(unc,[status(thm)],[80,73]),
    [iquote('0:UnC:80.0,73.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL469+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul  4 01:51:41 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.47  
% 0.21/0.47  SPASS V 3.9 
% 0.21/0.47  SPASS beiseite: Proof found.
% 0.21/0.47  % SZS status Theorem
% 0.21/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.47  SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 45 clauses.
% 0.21/0.47  SPASS allocated 97844 KBytes.
% 0.21/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.21/0.47  		0:00:00.03 for the input.
% 0.21/0.47  		0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.47  		0:00:00.00 for inferences.
% 0.21/0.47  		0:00:00.00 for the backtracking.
% 0.21/0.47  		0:00:00.00 for the reduction.
% 0.21/0.47  
% 0.21/0.47  
% 0.21/0.47  Here is a proof with depth 0, length 15 :
% 0.21/0.47  % SZS output start Refutation
% See solution above
% 0.21/0.47  Formulae used in the proof : hilbert_op_implies_and luka_op_or luka_cn2 hilbert_or_1 or_1 cn2 op_implies_and op_or
% 0.21/0.47  
%------------------------------------------------------------------------------