TSTP Solution File: NUM547+3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM547+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 12:27:37 EDT 2022

% Result   : Theorem 0.19s 0.44s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   14 (   8 unt;   0 def)
%            Number of atoms       :  106 (  16 equ)
%            Maximal formula atoms :   43 (   7 avg)
%            Number of connectives :  118 (  26   ~;  23   |;  52   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   34 (   1 sgn  24   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__2227,hypothesis,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
         => ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xS) )
            & aSubsetOf0(W0,xS)
            & sbrdtbr0(W0) = xk ) )
        & ( ( ( ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xS) ) )
              | aSubsetOf0(W0,xS) )
            & sbrdtbr0(W0) = xk )
         => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
         => ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xT) )
            & aSubsetOf0(W0,xT)
            & sbrdtbr0(W0) = xk ) )
        & ( ( ( ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xT) ) )
              | aSubsetOf0(W0,xT) )
            & sbrdtbr0(W0) = xk )
         => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
    & ! [W0] :
        ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
       => aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ~ ( ! [W0] :
            ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
             => ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xS) )
                & aSubsetOf0(W0,xS)
                & sbrdtbr0(W0) = xk ) )
            & ( ( ( ( aSet0(W0)
                    & ! [W1] :
                        ( aElementOf0(W1,W0)
                       => aElementOf0(W1,xS) ) )
                  | aSubsetOf0(W0,xS) )
                & sbrdtbr0(W0) = xk )
             => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
       => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
          | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ).

fof(m__,conjecture,
    ? [W0] :
      ( ( ( ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xS) ) )
          | aSubsetOf0(W0,xS) )
        & sbrdtbr0(W0) = xk )
      | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) ).

fof(subgoal_0,plain,
    ? [W0] :
      ( ( ( ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xS) ) )
          | aSubsetOf0(W0,xS) )
        & sbrdtbr0(W0) = xk )
      | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ? [W0] :
        ( ( ( ( aSet0(W0)
              & ! [W1] :
                  ( aElementOf0(W1,W0)
                 => aElementOf0(W1,xS) ) )
            | aSubsetOf0(W0,xS) )
          & sbrdtbr0(W0) = xk )
        | aElementOf0(W0,slbdtsldtrb0(xS,xk)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( slbdtsldtrb0(xS,xk) != slcrc0
    & aSet0(slbdtsldtrb0(xS,xk))
    & aSet0(slbdtsldtrb0(xT,xk))
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | ( sbrdtbr0(W0) = xk
          & aSet0(W0)
          & aSubsetOf0(W0,xS)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xS) ) ) )
    & ! [W0] :
        ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
        | ( sbrdtbr0(W0) = xk
          & aSet0(W0)
          & aSubsetOf0(W0,xT)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,xT) ) ) )
    & ! [W0] :
        ( sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xS,xk))
        | ( ~ aSubsetOf0(W0,xS)
          & ( ~ aSet0(W0)
            | ? [W1] :
                ( ~ aElementOf0(W1,xS)
                & aElementOf0(W1,W0) ) ) ) )
    & ! [W0] :
        ( sbrdtbr0(W0) != xk
        | aElementOf0(W0,slbdtsldtrb0(xT,xk))
        | ( ~ aSubsetOf0(W0,xT)
          & ( ~ aSet0(W0)
            | ? [W1] :
                ( ~ aElementOf0(W1,xT)
                & aElementOf0(W1,W0) ) ) ) ) ),
    inference(canonicalize,[],[m__2227]) ).

fof(normalize_0_1,plain,
    ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk)),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    aElementOf0(skolemFOFtoCNF_W0,slbdtsldtrb0(xS,xk)),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( sbrdtbr0(W0) != xk
        | ( ~ aSubsetOf0(W0,xS)
          & ( ~ aSet0(W0)
            | ? [W1] :
                ( ~ aElementOf0(W1,xS)
                & aElementOf0(W1,W0) ) ) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_4,plain,
    ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [W0] : ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)),
    inference(specialize,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    aElementOf0(skolemFOFtoCNF_W0,slbdtsldtrb0(xS,xk)),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ~ aElementOf0(W0,slbdtsldtrb0(xS,xk)),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    ~ aElementOf0(skolemFOFtoCNF_W0,slbdtsldtrb0(xS,xk)),
    inference(subst,[],[refute_0_1:[bind(W0,$fot(skolemFOFtoCNF_W0))]]) ).

cnf(refute_0_3,plain,
    $false,
    inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,slbdtsldtrb0(xS,xk)) )],[refute_0_0,refute_0_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM547+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n011.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jul  7 05:59:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44  
% 0.19/0.44  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.44  
%------------------------------------------------------------------------------