%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM228-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 : Mon Jul 18 12:25:14 EDT 2022

% Result   : Unsatisfiable 0.69s 0.92s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (   5 unt;   5 nHn;  11 RR)
%            Number of literals    :   25 (  12 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :    6 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(regularity1,axiom,
    ( X = null_class
    | member(regular(X),X) ) ).

cnf(recursion_equation_functions1,axiom,
    ( ~ member(X,recursion_equation_functions(Z))
    | function(Z) ) ).

cnf(prove_corollary_1,negated_conjecture,
    ~ function(z) ).

cnf(prove_corollary_2,negated_conjecture,
    recursion_equation_functions(z) != null_class ).

cnf(refute_0_0,plain,
    ( recursion_equation_functions(X_178) = null_class
    | member(regular(recursion_equation_functions(X_178)),recursion_equation_functions(X_178)) ),
    inference(subst,[],[regularity1:[bind(X,$fot(recursion_equation_functions(X_178)))]]) ).

cnf(refute_0_1,plain,
    ( ~ member(regular(recursion_equation_functions(X_178)),recursion_equation_functions(X_178))
    | function(X_178) ),
    inference(subst,[],[recursion_equation_functions1:[bind(X,$fot(regular(recursion_equation_functions(X_178)))),bind(Z,$fot(X_178))]]) ).

cnf(refute_0_2,plain,
    ( recursion_equation_functions(X_178) = null_class
    | function(X_178) ),
    inference(resolve,[$cnf( member(regular(recursion_equation_functions(X_178)),recursion_equation_functions(X_178)) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( recursion_equation_functions(z) = null_class
    | function(z) ),
    inference(subst,[],[refute_0_2:[bind(X_178,$fot(z))]]) ).

cnf(refute_0_4,plain,
    ( null_class != null_class
    | recursion_equation_functions(z) != null_class
    | recursion_equation_functions(z) = null_class ),
    introduced(tautology,[equality,[$cnf( $equal(recursion_equation_functions(z),null_class) ),[1],$fot(null_class)]]) ).

cnf(refute_0_5,plain,
    ( null_class != null_class
    | recursion_equation_functions(z) = null_class
    | function(z) ),
    inference(resolve,[$cnf( $equal(recursion_equation_functions(z),null_class) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( null_class != null_class
    | function(z) ),
    inference(resolve,[$cnf( $equal(recursion_equation_functions(z),null_class) )],[refute_0_5,prove_corollary_2]) ).

cnf(refute_0_7,plain,
    null_class = null_class,
    introduced(tautology,[refl,[$fot(null_class)]]) ).

cnf(refute_0_8,plain,
    function(z),
    inference(resolve,[$cnf( $equal(null_class,null_class) )],[refute_0_7,refute_0_6]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( function(z) )],[refute_0_8,prove_corollary_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM228-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n024.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 : Thu Jul  7 07:38:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.69/0.92  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.69/0.92  
% 0.69/0.92  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.77/0.93  
%------------------------------------------------------------------------------