%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET901+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n003.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 03:38:13 EDT 2022

% Result   : Theorem 0.18s 0.34s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   16 (   4 unt;   0 def)
%            Number of atoms       :   64 (  48 equ)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  101 (  53   ~;   3   |;  35   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn  30   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t42_zfmisc_1,conjecture,
    ! [A,B,C] :
      ( subset(A,unordered_pair(B,C))
    <=> ~ ( A != empty_set
          & A != singleton(B)
          & A != singleton(C)
          & A != unordered_pair(B,C) ) ) ).

fof(l46_zfmisc_1,axiom,
    ! [A,B,C] :
      ( subset(A,unordered_pair(B,C))
    <=> ~ ( A != empty_set
          & A != singleton(B)
          & A != singleton(C)
          & A != unordered_pair(B,C) ) ) ).

fof(subgoal_0,plain,
    ! [A,B,C] :
      ( ( subset(A,unordered_pair(B,C))
        & A != empty_set
        & A != singleton(B)
        & A != singleton(C) )
     => A = unordered_pair(B,C) ),
    inference(strip,[],[t42_zfmisc_1]) ).

fof(subgoal_1,plain,
    ! [A,B,C] :
      ( ~ ( A != empty_set
          & A != singleton(B)
          & A != singleton(C)
          & A != unordered_pair(B,C) )
     => subset(A,unordered_pair(B,C)) ),
    inference(strip,[],[t42_zfmisc_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B,C] :
        ( ( subset(A,unordered_pair(B,C))
          & A != empty_set
          & A != singleton(B)
          & A != singleton(C) )
       => A = unordered_pair(B,C) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B,C] :
      ( A != empty_set
      & A != singleton(B)
      & A != singleton(C)
      & A != unordered_pair(B,C)
      & subset(A,unordered_pair(B,C)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [A,B,C] :
      ( ~ subset(A,unordered_pair(B,C))
    <=> ( A != empty_set
        & A != singleton(B)
        & A != singleton(C)
        & A != unordered_pair(B,C) ) ),
    inference(canonicalize,[],[l46_zfmisc_1]) ).

fof(normalize_0_2,plain,
    ! [A,B,C] :
      ( ~ subset(A,unordered_pair(B,C))
    <=> ( A != empty_set
        & A != singleton(B)
        & A != singleton(C)
        & A != unordered_pair(B,C) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_3]) ).

fof(negate_1_0,plain,
    ~ ! [A,B,C] :
        ( ~ ( A != empty_set
            & A != singleton(B)
            & A != singleton(C)
            & A != unordered_pair(B,C) )
       => subset(A,unordered_pair(B,C)) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ? [A,B,C] :
      ( ~ subset(A,unordered_pair(B,C))
      & ( A = empty_set
        | A = singleton(B)
        | A = singleton(C)
        | A = unordered_pair(B,C) ) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ! [A,B,C] :
      ( ~ subset(A,unordered_pair(B,C))
    <=> ( A != empty_set
        & A != singleton(B)
        & A != singleton(C)
        & A != unordered_pair(B,C) ) ),
    inference(canonicalize,[],[l46_zfmisc_1]) ).

fof(normalize_1_2,plain,
    ! [A,B,C] :
      ( ~ subset(A,unordered_pair(B,C))
    <=> ( A != empty_set
        & A != singleton(B)
        & A != singleton(C)
        & A != unordered_pair(B,C) ) ),
    inference(specialize,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    $false,
    inference(simplify,[],[normalize_1_0,normalize_1_2]) ).

cnf(refute_1_0,plain,
    $false,
    inference(canonicalize,[],[normalize_1_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET901+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.11/0.33  % Computer : n003.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jul 10 13:51:14 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.18/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.34  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.34  
% 0.18/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.34  
%------------------------------------------------------------------------------