%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET604+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 : Tue Jul 19 03:35:51 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   25 (  16 unt;   0 def)
%            Number of atoms       :   37 (  23 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   29 (  17   ~;   8   |;   1   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   23 (   3 sgn  16   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(empty_set_subset,axiom,
    ! [B] : subset(empty_set,B) ).

fof(difference_empty_set,axiom,
    ! [B,C] :
      ( difference(B,C) = empty_set
    <=> subset(B,C) ) ).

fof(prove_no_difference_with_empty_set,conjecture,
    ! [B] : difference(empty_set,B) = empty_set ).

fof(subgoal_0,plain,
    ! [B] : difference(empty_set,B) = empty_set,
    inference(strip,[],[prove_no_difference_with_empty_set]) ).

fof(negate_0_0,plain,
    ~ ! [B] : difference(empty_set,B) = empty_set,
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [B] : difference(empty_set,B) != empty_set,
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    difference(empty_set,skolemFOFtoCNF_B) != empty_set,
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [B] : subset(empty_set,B),
    inference(canonicalize,[],[empty_set_subset]) ).

fof(normalize_0_3,plain,
    ! [B] : subset(empty_set,B),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [B,C] :
      ( difference(B,C) != empty_set
    <=> ~ subset(B,C) ),
    inference(canonicalize,[],[difference_empty_set]) ).

fof(normalize_0_5,plain,
    ! [B,C] :
      ( difference(B,C) != empty_set
    <=> ~ subset(B,C) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [B,C] :
      ( ( difference(B,C) != empty_set
        | subset(B,C) )
      & ( ~ subset(B,C)
        | difference(B,C) = empty_set ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [B,C] :
      ( ~ subset(B,C)
      | difference(B,C) = empty_set ),
    inference(conjunct,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    difference(empty_set,skolemFOFtoCNF_B) != empty_set,
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    subset(empty_set,B),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    subset(empty_set,X_9),
    inference(subst,[],[refute_0_1:[bind(B,$fot(X_9))]]) ).

cnf(refute_0_3,plain,
    ( ~ subset(B,C)
    | difference(B,C) = empty_set ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    ( ~ subset(empty_set,X_9)
    | difference(empty_set,X_9) = empty_set ),
    inference(subst,[],[refute_0_3:[bind(B,$fot(empty_set)),bind(C,$fot(X_9))]]) ).

cnf(refute_0_5,plain,
    difference(empty_set,X_9) = empty_set,
    inference(resolve,[$cnf( subset(empty_set,X_9) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    difference(empty_set,skolemFOFtoCNF_B) = empty_set,
    inference(subst,[],[refute_0_5:[bind(X_9,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_7,plain,
    ( difference(empty_set,skolemFOFtoCNF_B) != empty_set
    | empty_set != empty_set
    | difference(empty_set,skolemFOFtoCNF_B) = empty_set ),
    introduced(tautology,[equality,[$cnf( ~ $equal(difference(empty_set,skolemFOFtoCNF_B),empty_set) ),[0],$fot(empty_set)]]) ).

cnf(refute_0_8,plain,
    ( empty_set != empty_set
    | difference(empty_set,skolemFOFtoCNF_B) = empty_set ),
    inference(resolve,[$cnf( $equal(difference(empty_set,skolemFOFtoCNF_B),empty_set) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    empty_set != empty_set,
    inference(resolve,[$cnf( $equal(difference(empty_set,skolemFOFtoCNF_B),empty_set) )],[refute_0_8,refute_0_0]) ).

cnf(refute_0_10,plain,
    empty_set = empty_set,
    introduced(tautology,[refl,[$fot(empty_set)]]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_10,refute_0_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET604+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n018.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 : Sun Jul 10 14:11:42 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------