TSTP Solution File: NUM588+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM588+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n006.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  : 300s
% DateTime : Fri May  3 02:50:04 EDT 2024

% Result   : Theorem 4.28s 1.17s
% Output   : CNFRefutation 4.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   25 (   5 unt;   0 def)
%            Number of atoms       :  545 (  61 equ)
%            Maximal formula atoms :   80 (  21 avg)
%            Number of connectives :  695 ( 175   ~; 129   |; 347   &)
%                                         (  10 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  10 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :  138 (   0 sgn  98   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f88,conjecture,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ! [X1] :
          ( ( isCountable0(X1)
            & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
            & aSet0(X1)
            & ! [X2] :
                ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X2
                  & aElementOf0(X2,sdtlpdtrp0(xN,X0))
                  & aElement0(X2) ) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X2] :
                ( aElementOf0(X2,sdtlpdtrp0(xN,X0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
         => ! [X2] :
              ( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
                & sbrdtbr0(X2) = xk
                & aSubsetOf0(X2,X1)
                & ! [X3] :
                    ( aElementOf0(X3,X2)
                   => aElementOf0(X3,X1) )
                & aSet0(X2) )
             => ( ( ! [X3] :
                      ( aElementOf0(X3,sdtlpdtrp0(xN,X0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
               => ( ( ! [X3] :
                        ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                      <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                          & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                          & aElement0(X3) ) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
                 => ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
                    | aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                    | ! [X3] :
                        ( aElementOf0(X3,X2)
                       => aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f89,negated_conjecture,
    ~ ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
       => ! [X1] :
            ( ( isCountable0(X1)
              & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X2] :
                  ( aElementOf0(X2,X1)
                 => aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
              & aSet0(X1)
              & ! [X2] :
                  ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X2
                    & aElementOf0(X2,sdtlpdtrp0(xN,X0))
                    & aElement0(X2) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X2] :
                  ( aElementOf0(X2,sdtlpdtrp0(xN,X0))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
           => ! [X2] :
                ( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
                  & sbrdtbr0(X2) = xk
                  & aSubsetOf0(X2,X1)
                  & ! [X3] :
                      ( aElementOf0(X3,X2)
                     => aElementOf0(X3,X1) )
                  & aSet0(X2) )
               => ( ( ! [X3] :
                        ( aElementOf0(X3,sdtlpdtrp0(xN,X0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) )
                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
                 => ( ( ! [X3] :
                          ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                        <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                            & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                            & aElement0(X3) ) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
                   => ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
                      | aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                      | ! [X3] :
                          ( aElementOf0(X3,X2)
                         => aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f88]) ).

fof(f104,plain,
    ~ ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
       => ! [X1] :
            ( ( isCountable0(X1)
              & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X2] :
                  ( aElementOf0(X2,X1)
                 => aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
              & aSet0(X1)
              & ! [X3] :
                  ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                    & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                    & aElement0(X3) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X4] :
                  ( aElementOf0(X4,sdtlpdtrp0(xN,X0))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
           => ! [X5] :
                ( ( aElementOf0(X5,slbdtsldtrb0(X1,xk))
                  & sbrdtbr0(X5) = xk
                  & aSubsetOf0(X5,X1)
                  & ! [X6] :
                      ( aElementOf0(X6,X5)
                     => aElementOf0(X6,X1) )
                  & aSet0(X5) )
               => ( ( ! [X7] :
                        ( aElementOf0(X7,sdtlpdtrp0(xN,X0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) )
                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
                 => ( ( ! [X8] :
                          ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                        <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
                            & aElementOf0(X8,sdtlpdtrp0(xN,X0))
                            & aElement0(X8) ) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
                   => ( aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
                      | aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                      | ! [X9] :
                          ( aElementOf0(X9,X5)
                         => aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ) ) ),
    inference(rectify,[],[f89]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X5] :
              ( ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
              & ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ? [X9] :
                  ( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                  & aElementOf0(X9,X5) )
              & ! [X8] :
                  ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
                    & aElementOf0(X8,sdtlpdtrp0(xN,X0))
                    & aElement0(X8) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X7] :
                  ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
                  | ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
              & aElementOf0(X5,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X5) = xk
              & aSubsetOf0(X5,X1)
              & ! [X6] :
                  ( aElementOf0(X6,X1)
                  | ~ aElementOf0(X6,X5) )
              & aSet0(X5) )
          & isCountable0(X1)
          & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X2] :
              ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              | ~ aElementOf0(X2,X1) )
          & aSet0(X1)
          & ! [X3] :
              ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                & aElement0(X3) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X4] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
              | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      & aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f104]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X5] :
              ( ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
              & ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ? [X9] :
                  ( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                  & aElementOf0(X9,X5) )
              & ! [X8] :
                  ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
                    & aElementOf0(X8,sdtlpdtrp0(xN,X0))
                    & aElement0(X8) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X7] :
                  ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
                  | ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
              & aElementOf0(X5,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X5) = xk
              & aSubsetOf0(X5,X1)
              & ! [X6] :
                  ( aElementOf0(X6,X1)
                  | ~ aElementOf0(X6,X5) )
              & aSet0(X5) )
          & isCountable0(X1)
          & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X2] :
              ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              | ~ aElementOf0(X2,X1) )
          & aSet0(X1)
          & ! [X3] :
              ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                & aElement0(X3) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X4] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
              | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      & aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f221]) ).

fof(f391,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X5] :
              ( ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
              & ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ? [X9] :
                  ( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                  & aElementOf0(X9,X5) )
              & ! [X8] :
                  ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                    | szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
                    | ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
                    | ~ aElement0(X8) )
                  & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
                      & aElementOf0(X8,sdtlpdtrp0(xN,X0))
                      & aElement0(X8) )
                    | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X7] :
                  ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
                  | ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
              & aElementOf0(X5,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X5) = xk
              & aSubsetOf0(X5,X1)
              & ! [X6] :
                  ( aElementOf0(X6,X1)
                  | ~ aElementOf0(X6,X5) )
              & aSet0(X5) )
          & isCountable0(X1)
          & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X2] :
              ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              | ~ aElementOf0(X2,X1) )
          & aSet0(X1)
          & ! [X3] :
              ( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                | szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
                | ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
                | ~ aElement0(X3) )
              & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                  & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                  & aElement0(X3) )
                | ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X4] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
              | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      & aElementOf0(X0,szNzAzT0) ),
    inference(nnf_transformation,[],[f222]) ).

fof(f392,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X5] :
              ( ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
              & ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ? [X9] :
                  ( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                  & aElementOf0(X9,X5) )
              & ! [X8] :
                  ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                    | szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
                    | ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
                    | ~ aElement0(X8) )
                  & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
                      & aElementOf0(X8,sdtlpdtrp0(xN,X0))
                      & aElement0(X8) )
                    | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X7] :
                  ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
                  | ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
              & aElementOf0(X5,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X5) = xk
              & aSubsetOf0(X5,X1)
              & ! [X6] :
                  ( aElementOf0(X6,X1)
                  | ~ aElementOf0(X6,X5) )
              & aSet0(X5) )
          & isCountable0(X1)
          & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X2] :
              ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              | ~ aElementOf0(X2,X1) )
          & aSet0(X1)
          & ! [X3] :
              ( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                | szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
                | ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
                | ~ aElement0(X3) )
              & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                  & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                  & aElement0(X3) )
                | ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X4] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
              | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      & aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f391]) ).

fof(f393,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
              & ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ? [X3] :
                  ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                  & aElementOf0(X3,X2) )
              & ! [X4] :
                  ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                    | szmzizndt0(sdtlpdtrp0(xN,X0)) = X4
                    | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0))
                    | ~ aElement0(X4) )
                  & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X4
                      & aElementOf0(X4,sdtlpdtrp0(xN,X0))
                      & aElement0(X4) )
                    | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              & ! [X5] :
                  ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
                  | ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
              & aElementOf0(X2,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X2) = xk
              & aSubsetOf0(X2,X1)
              & ! [X6] :
                  ( aElementOf0(X6,X1)
                  | ~ aElementOf0(X6,X2) )
              & aSet0(X2) )
          & isCountable0(X1)
          & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X7] :
              ( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              | ~ aElementOf0(X7,X1) )
          & aSet0(X1)
          & ! [X8] :
              ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                | szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
                | ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
                | ~ aElement0(X8) )
              & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
                  & aElementOf0(X8,sdtlpdtrp0(xN,X0))
                  & aElement0(X8) )
                | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X9] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9)
              | ~ aElementOf0(X9,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      & aElementOf0(X0,szNzAzT0) ),
    inference(rectify,[],[f392]) ).

fof(f394,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
                & ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                & ? [X3] :
                    ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                    & aElementOf0(X3,X2) )
                & ! [X4] :
                    ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                      | szmzizndt0(sdtlpdtrp0(xN,X0)) = X4
                      | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0))
                      | ~ aElement0(X4) )
                    & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X4
                        & aElementOf0(X4,sdtlpdtrp0(xN,X0))
                        & aElement0(X4) )
                      | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                & ! [X5] :
                    ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
                    | ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
                & aElementOf0(X2,slbdtsldtrb0(X1,xk))
                & sbrdtbr0(X2) = xk
                & aSubsetOf0(X2,X1)
                & ! [X6] :
                    ( aElementOf0(X6,X1)
                    | ~ aElementOf0(X6,X2) )
                & aSet0(X2) )
            & isCountable0(X1)
            & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X7] :
                ( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                | ~ aElementOf0(X7,X1) )
            & aSet0(X1)
            & ! [X8] :
                ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
                  | szmzizndt0(sdtlpdtrp0(xN,X0)) = X8
                  | ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
                  | ~ aElement0(X8) )
                & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X8
                    & aElementOf0(X8,sdtlpdtrp0(xN,X0))
                    & aElement0(X8) )
                  | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X9] :
                ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X9)
                | ~ aElementOf0(X9,sdtlpdtrp0(xN,X0)) )
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
        & aElementOf0(X0,szNzAzT0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
              & ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
              & ? [X3] :
                  ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
                  & aElementOf0(X3,X2) )
              & ! [X4] :
                  ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
                    | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4
                    | ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
                    | ~ aElement0(X4) )
                  & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4
                      & aElementOf0(X4,sdtlpdtrp0(xN,sK53))
                      & aElement0(X4) )
                    | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
              & ! [X5] :
                  ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5)
                  | ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53)) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
              & aElementOf0(X2,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X2) = xk
              & aSubsetOf0(X2,X1)
              & ! [X6] :
                  ( aElementOf0(X6,X1)
                  | ~ aElementOf0(X6,X2) )
              & aSet0(X2) )
          & isCountable0(X1)
          & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          & ! [X7] :
              ( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
              | ~ aElementOf0(X7,X1) )
          & aSet0(X1)
          & ! [X8] :
              ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
                | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X8
                | ~ aElementOf0(X8,sdtlpdtrp0(xN,sK53))
                | ~ aElement0(X8) )
              & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X8
                  & aElementOf0(X8,sdtlpdtrp0(xN,sK53))
                  & aElement0(X8) )
                | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          & ! [X9] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X9)
              | ~ aElementOf0(X9,sdtlpdtrp0(xN,sK53)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53)) )
      & aElementOf0(sK53,szNzAzT0) ) ),
    introduced(choice_axiom,[]) ).

fof(f395,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
            & ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
            & ? [X3] :
                ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
                & aElementOf0(X3,X2) )
            & ! [X4] :
                ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
                  | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4
                  | ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
                  | ~ aElement0(X4) )
                & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4
                    & aElementOf0(X4,sdtlpdtrp0(xN,sK53))
                    & aElement0(X4) )
                  | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
            & ! [X5] :
                ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5)
                | ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53)) )
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
            & aElementOf0(X2,slbdtsldtrb0(X1,xk))
            & sbrdtbr0(X2) = xk
            & aSubsetOf0(X2,X1)
            & ! [X6] :
                ( aElementOf0(X6,X1)
                | ~ aElementOf0(X6,X2) )
            & aSet0(X2) )
        & isCountable0(X1)
        & aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
        & ! [X7] :
            ( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
            | ~ aElementOf0(X7,X1) )
        & aSet0(X1)
        & ! [X8] :
            ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
              | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X8
              | ~ aElementOf0(X8,sdtlpdtrp0(xN,sK53))
              | ~ aElement0(X8) )
            & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X8
                & aElementOf0(X8,sdtlpdtrp0(xN,sK53))
                & aElement0(X8) )
              | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
        & ! [X9] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X9)
            | ~ aElementOf0(X9,sdtlpdtrp0(xN,sK53)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53)) )
   => ( ? [X2] :
          ( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
          & ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          & ? [X3] :
              ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
              & aElementOf0(X3,X2) )
          & ! [X4] :
              ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
                | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4
                | ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
                | ~ aElement0(X4) )
              & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4
                  & aElementOf0(X4,sdtlpdtrp0(xN,sK53))
                  & aElement0(X4) )
                | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          & ! [X5] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5)
              | ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
          & aElementOf0(X2,slbdtsldtrb0(sK54,xk))
          & sbrdtbr0(X2) = xk
          & aSubsetOf0(X2,sK54)
          & ! [X6] :
              ( aElementOf0(X6,sK54)
              | ~ aElementOf0(X6,X2) )
          & aSet0(X2) )
      & isCountable0(sK54)
      & aSubsetOf0(sK54,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
      & ! [X7] :
          ( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          | ~ aElementOf0(X7,sK54) )
      & aSet0(sK54)
      & ! [X8] :
          ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
            | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X8
            | ~ aElementOf0(X8,sdtlpdtrp0(xN,sK53))
            | ~ aElement0(X8) )
          & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X8
              & aElementOf0(X8,sdtlpdtrp0(xN,sK53))
              & aElement0(X8) )
            | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
      & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
      & ! [X9] :
          ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X9)
          | ~ aElementOf0(X9,sdtlpdtrp0(xN,sK53)) )
      & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53)) ) ),
    introduced(choice_axiom,[]) ).

fof(f396,plain,
    ( ? [X2] :
        ( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
        & ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
        & ? [X3] :
            ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
            & aElementOf0(X3,X2) )
        & ! [X4] :
            ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
              | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4
              | ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
              | ~ aElement0(X4) )
            & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4
                & aElementOf0(X4,sdtlpdtrp0(xN,sK53))
                & aElement0(X4) )
              | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
        & ! [X5] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5)
            | ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
        & aElementOf0(X2,slbdtsldtrb0(sK54,xk))
        & sbrdtbr0(X2) = xk
        & aSubsetOf0(X2,sK54)
        & ! [X6] :
            ( aElementOf0(X6,sK54)
            | ~ aElementOf0(X6,X2) )
        & aSet0(X2) )
   => ( ~ aElementOf0(sK55,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
      & ~ aSubsetOf0(sK55,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
      & ? [X3] :
          ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          & aElementOf0(X3,sK55) )
      & ! [X4] :
          ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
            | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4
            | ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
            | ~ aElement0(X4) )
          & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4
              & aElementOf0(X4,sdtlpdtrp0(xN,sK53))
              & aElement0(X4) )
            | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
      & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
      & ! [X5] :
          ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5)
          | ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53)) )
      & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
      & aElementOf0(sK55,slbdtsldtrb0(sK54,xk))
      & xk = sbrdtbr0(sK55)
      & aSubsetOf0(sK55,sK54)
      & ! [X6] :
          ( aElementOf0(X6,sK54)
          | ~ aElementOf0(X6,sK55) )
      & aSet0(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f397,plain,
    ( ? [X3] :
        ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
        & aElementOf0(X3,sK55) )
   => ( ~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
      & aElementOf0(sK56,sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f398,plain,
    ( ~ aElementOf0(sK55,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
    & ~ aSubsetOf0(sK55,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
    & ~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
    & aElementOf0(sK56,sK55)
    & ! [X4] :
        ( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4
          | ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
          | ~ aElement0(X4) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4
            & aElementOf0(X4,sdtlpdtrp0(xN,sK53))
            & aElement0(X4) )
          | ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
    & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
    & ! [X5] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5)
        | ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
    & aElementOf0(sK55,slbdtsldtrb0(sK54,xk))
    & xk = sbrdtbr0(sK55)
    & aSubsetOf0(sK55,sK54)
    & ! [X6] :
        ( aElementOf0(X6,sK54)
        | ~ aElementOf0(X6,sK55) )
    & aSet0(sK55)
    & isCountable0(sK54)
    & aSubsetOf0(sK54,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
    & ! [X7] :
        ( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
        | ~ aElementOf0(X7,sK54) )
    & aSet0(sK54)
    & ! [X8] :
        ( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
          | szmzizndt0(sdtlpdtrp0(xN,sK53)) = X8
          | ~ aElementOf0(X8,sdtlpdtrp0(xN,sK53))
          | ~ aElement0(X8) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,sK53)) != X8
            & aElementOf0(X8,sdtlpdtrp0(xN,sK53))
            & aElement0(X8) )
          | ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
    & aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
    & ! [X9] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X9)
        | ~ aElementOf0(X9,sdtlpdtrp0(xN,sK53)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
    & aElementOf0(sK53,szNzAzT0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f393,f397,f396,f395,f394]) ).

fof(f707,plain,
    ! [X7] :
      ( aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
      | ~ aElementOf0(X7,sK54) ),
    inference(cnf_transformation,[],[f398]) ).

fof(f711,plain,
    ! [X6] :
      ( aElementOf0(X6,sK54)
      | ~ aElementOf0(X6,sK55) ),
    inference(cnf_transformation,[],[f398]) ).

fof(f722,plain,
    aElementOf0(sK56,sK55),
    inference(cnf_transformation,[],[f398]) ).

fof(f723,plain,
    ~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))),
    inference(cnf_transformation,[],[f398]) ).

cnf(c_350,negated_conjecture,
    ~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))),
    inference(cnf_transformation,[],[f723]) ).

cnf(c_351,negated_conjecture,
    aElementOf0(sK56,sK55),
    inference(cnf_transformation,[],[f722]) ).

cnf(c_362,negated_conjecture,
    ( ~ aElementOf0(X0,sK55)
    | aElementOf0(X0,sK54) ),
    inference(cnf_transformation,[],[f711]) ).

cnf(c_366,negated_conjecture,
    ( ~ aElementOf0(X0,sK54)
    | aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ),
    inference(cnf_transformation,[],[f707]) ).

cnf(c_992,plain,
    ( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
    | ~ aElementOf0(X0,sK55) ),
    inference(prop_impl_just,[status(thm)],[c_362,c_366]) ).

cnf(c_993,plain,
    ( ~ aElementOf0(X0,sK55)
    | aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ),
    inference(renaming,[status(thm)],[c_992]) ).

cnf(c_12618,plain,
    ( ~ aElementOf0(sK56,sK55)
    | aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ),
    inference(instantiation,[status(thm)],[c_993]) ).

cnf(c_12619,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_12618,c_350,c_351]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM588+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n006.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  : 300
% 0.13/0.34  % DateTime : Thu May  2 19:32:04 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.28/1.17  % SZS status Started for theBenchmark.p
% 4.28/1.17  % SZS status Theorem for theBenchmark.p
% 4.28/1.17  
% 4.28/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.28/1.17  
% 4.28/1.17  ------  iProver source info
% 4.28/1.17  
% 4.28/1.17  git: date: 2024-05-02 19:28:25 +0000
% 4.28/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.28/1.17  git: non_committed_changes: false
% 4.28/1.17  
% 4.28/1.17  ------ Parsing...
% 4.28/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.28/1.17  
% 4.28/1.17  ------ Preprocessing... sup_sim: 0  pe_s  pe:1:0s pe:2:0s pe_e 
% 4.28/1.17  
% 4.28/1.17  ------ Preprocessing... gs_s  sp: 4 0s  gs_e  scvd_s sp: 7 0s scvd_e  snvd_s sp: 0 0s snvd_e 
% 4.28/1.17  
% 4.28/1.17  ------ Preprocessing...
% 4.28/1.17  ------ Proving...
% 4.28/1.17  ------ Problem Properties 
% 4.28/1.17  
% 4.28/1.17  
% 4.28/1.17  clauses                                 362
% 4.28/1.17  conjectures                             21
% 4.28/1.17  EPR                                     76
% 4.28/1.17  Horn                                    285
% 4.28/1.17  unary                                   42
% 4.28/1.17  binary                                  123
% 4.28/1.17  lits                                    1110
% 4.28/1.17  lits eq                                 128
% 4.28/1.17  fd_pure                                 0
% 4.28/1.17  fd_pseudo                               0
% 4.28/1.17  fd_cond                                 11
% 4.28/1.17  fd_pseudo_cond                          39
% 4.28/1.17  AC symbols                              0
% 4.28/1.17  
% 4.28/1.17  ------ Input Options Time Limit: Unbounded
% 4.28/1.17  
% 4.28/1.17  
% 4.28/1.17  ------ 
% 4.28/1.17  Current options:
% 4.28/1.17  ------ 
% 4.28/1.17  
% 4.28/1.17  
% 4.28/1.17  
% 4.28/1.17  
% 4.28/1.17  ------ Proving...
% 4.28/1.17  
% 4.28/1.17  
% 4.28/1.17  % SZS status Theorem for theBenchmark.p
% 4.28/1.17  
% 4.28/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/1.17  
% 4.28/1.18  
%------------------------------------------------------------------------------