%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 12:24:04 EDT 2022

% Result   : Unsatisfiable 159.31s 159.47s
% Output   : CNFRefutation 159.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   6 unt;   3 nHn;  13 RR)
%            Number of literals    :   22 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :    4 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(a2,axiom,
    ( ~ member(X,Y)
    | little_set(X) ) ).

cnf(infinity2,axiom,
    member(empty_set,infinity) ).

cnf(natural_numbers4,axiom,
    ( member(Z,natural_numbers)
    | ~ little_set(Z)
    | member(empty_set,f44(Z)) ) ).

cnf(natural_numbers6,axiom,
    ( member(Z,natural_numbers)
    | ~ member(Z,f44(Z)) ) ).

cnf(prove_zero_is_a_natural,negated_conjecture,
    ~ member(empty_set,natural_numbers) ).

cnf(refute_0_0,plain,
    ( ~ member(empty_set,f44(empty_set))
    | member(empty_set,natural_numbers) ),
    inference(subst,[],[natural_numbers6:[bind(Z,$fot(empty_set))]]) ).

cnf(refute_0_1,plain,
    ( ~ member(empty_set,infinity)
    | little_set(empty_set) ),
    inference(subst,[],[a2:[bind(X,$fot(empty_set)),bind(Y,$fot(infinity))]]) ).

cnf(refute_0_2,plain,
    little_set(empty_set),
    inference(resolve,[$cnf( member(empty_set,infinity) )],[infinity2,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ little_set(empty_set)
    | member(empty_set,f44(empty_set))
    | member(empty_set,natural_numbers) ),
    inference(subst,[],[natural_numbers4:[bind(Z,$fot(empty_set))]]) ).

cnf(refute_0_4,plain,
    ( member(empty_set,f44(empty_set))
    | member(empty_set,natural_numbers) ),
    inference(resolve,[$cnf( little_set(empty_set) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    member(empty_set,f44(empty_set)),
    inference(resolve,[$cnf( member(empty_set,natural_numbers) )],[refute_0_4,prove_zero_is_a_natural]) ).

cnf(refute_0_6,plain,
    member(empty_set,natural_numbers),
    inference(resolve,[$cnf( member(empty_set,f44(empty_set)) )],[refute_0_5,refute_0_0]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( member(empty_set,natural_numbers) )],[refute_0_6,prove_zero_is_a_natural]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.33  % Computer : n009.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Thu Jul  7 12:04:37 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 159.31/159.47  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 159.31/159.47  
% 159.31/159.47  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 159.31/159.47  
%------------------------------------------------------------------------------