%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 03:31:59 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (  14 unt;   0 def)
%            Number of atoms       :   36 (   0 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   31 (  16   ~;   7   |;   4   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   27 (   3 sgn  18   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
    ! [B] : ~ member(B,empty_set) ).

fof(subset_defn,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ) ).

fof(prove_empty_set_subset,conjecture,
    ! [B] : subset(empty_set,B) ).

fof(subgoal_0,plain,
    ! [B] : subset(empty_set,B),
    inference(strip,[],[prove_empty_set_subset]) ).

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

fof(normalize_0_0,plain,
    ? [B] : ~ subset(empty_set,B),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ~ subset(empty_set,skolemFOFtoCNF_B),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [B] : ~ member(B,empty_set),
    inference(canonicalize,[],[empty_set_defn]) ).

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

fof(normalize_0_4,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] :
          ( ~ member(D,C)
          & member(D,B) ) ),
    inference(canonicalize,[],[subset_defn]) ).

fof(normalize_0_5,plain,
    ! [B,C] :
      ( ~ subset(B,C)
    <=> ? [D] :
          ( ~ member(D,C)
          & member(D,B) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [B,C,D] :
      ( ( ~ member(skolemFOFtoCNF_D(B,C),C)
        | subset(B,C) )
      & ( member(skolemFOFtoCNF_D(B,C),B)
        | subset(B,C) )
      & ( ~ member(D,B)
        | ~ subset(B,C)
        | member(D,C) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [B,C] :
      ( member(skolemFOFtoCNF_D(B,C),B)
      | subset(B,C) ),
    inference(conjunct,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    ~ subset(empty_set,skolemFOFtoCNF_B),
    inference(canonicalize,[],[normalize_0_1]) ).

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

cnf(refute_0_2,plain,
    ~ member(skolemFOFtoCNF_D(empty_set,X_8),empty_set),
    inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_D(empty_set,X_8)))]]) ).

cnf(refute_0_3,plain,
    ( member(skolemFOFtoCNF_D(B,C),B)
    | subset(B,C) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    ( member(skolemFOFtoCNF_D(empty_set,X_8),empty_set)
    | subset(empty_set,X_8) ),
    inference(subst,[],[refute_0_3:[bind(B,$fot(empty_set)),bind(C,$fot(X_8))]]) ).

cnf(refute_0_5,plain,
    subset(empty_set,X_8),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_D(empty_set,X_8),empty_set) )],[refute_0_4,refute_0_2]) ).

cnf(refute_0_6,plain,
    subset(empty_set,skolemFOFtoCNF_B),
    inference(subst,[],[refute_0_5:[bind(X_8,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( subset(empty_set,skolemFOFtoCNF_B) )],[refute_0_6,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n004.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 12:13:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36  
%------------------------------------------------------------------------------