TSTP Solution File: NUM584+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM584+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 12:27:58 EDT 2022

% Result   : Theorem 0.39s 0.56s
% Output   : CNFRefutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   24 (   6 unt;   0 def)
%            Number of atoms       :  151 (  23 equ)
%            Maximal formula atoms :   14 (   6 avg)
%            Number of connectives :  173 (  46   ~;  29   |;  70   &)
%                                         (  13 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn  35   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__3989_02,hypothesis,
    ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( aElement0(W0)
          & aElementOf0(W0,sdtlpdtrp0(xN,xi))
          & W0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
    & aSet0(xQ)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    & sbrdtbr0(xQ) = xk
    & aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ) ).

fof(m__4007,hypothesis,
    ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( aElement0(W0)
          & ( aElementOf0(W0,xQ)
            | W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
    & sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ).

fof(m__4024,hypothesis,
    ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( aElement0(W0)
          & ( aElementOf0(W0,xQ)
            | W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
       => aElementOf0(W0,xS) )
    & aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ).

fof(m__,conjecture,
    ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
      & ! [W0] :
          ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) )
   => ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ! [W0] :
            ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
          <=> ( aElement0(W0)
              & ( aElementOf0(W0,xQ)
                | W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
     => ( ( ( ! [W0] :
                ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
               => aElementOf0(W0,xS) )
            | aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )
          & sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
        | aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ) ) ) ).

fof(subgoal_0,plain,
    ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
      & ! [W0] :
          ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
      & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      & ! [W0] :
          ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
        <=> ( aElement0(W0)
            & ( aElementOf0(W0,xQ)
              | W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
      & ~ ( ( ! [W0] :
                ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
               => aElementOf0(W0,xS) )
            | aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )
          & sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) )
   => aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
        & ! [W0] :
            ( aElementOf0(W0,sdtlpdtrp0(xN,xi))
           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
        & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ! [W0] :
            ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
          <=> ( aElement0(W0)
              & ( aElementOf0(W0,xQ)
                | W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
        & ~ ( ( ! [W0] :
                  ( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
                 => aElementOf0(W0,xS) )
              | aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )
            & sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) )
     => aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK
      | ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
        & ? [W0] :
            ( ~ aElementOf0(W0,xS)
            & aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ~ aElement0(W0)
          | ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
            & ~ aElementOf0(W0,xQ) ) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( sbrdtbr0(xQ) = xk
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
    & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    & aSet0(xQ)
    & aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & ! [W0] :
        ( ~ aElementOf0(W0,xQ)
        | aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ~ aElement0(W0)
          | ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
          | W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ),
    inference(canonicalize,[],[m__3989_02]) ).

fof(normalize_0_2,plain,
    aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ~ aElement0(W0)
          | ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
            & ~ aElementOf0(W0,xQ) ) ) ) ),
    inference(canonicalize,[],[m__4007]) ).

fof(normalize_0_4,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_5,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ~ aElement0(W0)
          | ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
            & ~ aElementOf0(W0,xQ) ) ) ) ),
    inference(simplify,[],[normalize_0_3,normalize_0_2,normalize_0_5]) ).

fof(normalize_0_7,plain,
    aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_9,plain,
    ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
    & aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    & aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtlpdtrp0(xN,xi))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) )
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
        | aElementOf0(W0,xS) )
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( ~ aElement0(W0)
          | ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
            & ~ aElementOf0(W0,xQ) ) ) ) ),
    inference(canonicalize,[],[m__4024]) ).

fof(normalize_0_10,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    <=> ( ~ aElement0(W0)
        | ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
          & ~ aElementOf0(W0,xQ) ) ) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_11,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
    <=> ( ~ aElement0(W0)
        | ( W0 != szmzizndt0(sdtlpdtrp0(xN,xi))
          & ~ aElementOf0(W0,xQ) ) ) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
    & ! [W0] :
        ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
        | aElementOf0(W0,xS) ) ),
    inference(simplify,[],[normalize_0_9,normalize_0_2,normalize_0_7,normalize_0_5,normalize_0_11]) ).

fof(normalize_0_13,plain,
    aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
    inference(conjunct,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      | aElementOf0(W0,xS) ),
    inference(conjunct,[],[normalize_0_12]) ).

fof(normalize_0_15,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
      | aElementOf0(W0,xS) ),
    inference(specialize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_2,normalize_0_7,normalize_0_8,normalize_0_13,normalize_0_15,normalize_0_5,normalize_0_11]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM584+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jul  5 03:30:59 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.56  
% 0.39/0.56  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.39/0.57  
%------------------------------------------------------------------------------