%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM395+1 : TPTP v8.1.0. Released v3.2.0.
% 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 12:26:23 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (  11 unt;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   41 (  20   ~;  13   |;   5   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :    6 (   0 sgn   5   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t27_ordinal1,conjecture,
    ordinal(empty_set) ).

fof(d4_ordinal1,axiom,
    ! [A] :
      ( ordinal(A)
    <=> ( epsilon_transitive(A)
        & epsilon_connected(A) ) ) ).

fof(l18_ordinal1,axiom,
    ( epsilon_transitive(empty_set)
    & epsilon_connected(empty_set) ) ).

fof(subgoal_0,plain,
    ordinal(empty_set),
    inference(strip,[],[t27_ordinal1]) ).

fof(negate_0_0,plain,
    ~ ordinal(empty_set),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( epsilon_connected(empty_set)
    & epsilon_transitive(empty_set) ),
    inference(canonicalize,[],[l18_ordinal1]) ).

fof(normalize_0_1,plain,
    epsilon_transitive(empty_set),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A] :
      ( ~ ordinal(A)
    <=> ( ~ epsilon_connected(A)
        | ~ epsilon_transitive(A) ) ),
    inference(canonicalize,[],[d4_ordinal1]) ).

fof(normalize_0_3,plain,
    ! [A] :
      ( ~ ordinal(A)
    <=> ( ~ epsilon_connected(A)
        | ~ epsilon_transitive(A) ) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A] :
      ( ( ~ ordinal(A)
        | epsilon_connected(A) )
      & ( ~ ordinal(A)
        | epsilon_transitive(A) )
      & ( ~ epsilon_connected(A)
        | ~ epsilon_transitive(A)
        | ordinal(A) ) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A] :
      ( ~ epsilon_connected(A)
      | ~ epsilon_transitive(A)
      | ordinal(A) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    epsilon_connected(empty_set),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_7,plain,
    ~ ordinal(empty_set),
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    epsilon_transitive(empty_set),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ epsilon_connected(A)
    | ~ epsilon_transitive(A)
    | ordinal(A) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    ( ~ epsilon_connected(empty_set)
    | ~ epsilon_transitive(empty_set)
    | ordinal(empty_set) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(empty_set))]]) ).

cnf(refute_0_3,plain,
    ( ~ epsilon_connected(empty_set)
    | ordinal(empty_set) ),
    inference(resolve,[$cnf( epsilon_transitive(empty_set) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    epsilon_connected(empty_set),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_5,plain,
    ordinal(empty_set),
    inference(resolve,[$cnf( epsilon_connected(empty_set) )],[refute_0_4,refute_0_3]) ).

cnf(refute_0_6,plain,
    ~ ordinal(empty_set),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( ordinal(empty_set) )],[refute_0_5,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM395+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n024.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 : Thu Jul  7 02:09:14 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------