TSTP Solution File: NUM592+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM592+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n032.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 : Thu Aug 31 11:31:42 EDT 2023

% Result   : Theorem 16.67s 3.04s
% Output   : CNFRefutation 16.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   56 (  11 unt;   0 def)
%            Number of atoms       :  395 (  63 equ)
%            Maximal formula atoms :   21 (   7 avg)
%            Number of connectives :  477 ( 138   ~; 114   |; 187   &)
%                                         (   9 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   2 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   9 con; 0-2 aty)
%            Number of variables   :  109 (   0 sgn;  76   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f91,axiom,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( aElementOf0(X0,xY)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xi))
          & aElement0(X0) ) )
    & aSet0(xY)
    & ! [X0] :
        ( aElementOf0(X0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4448_02) ).

fof(f93,axiom,
    ( ! [X0] :
        ( ( ( aElementOf0(X0,slbdtsldtrb0(xX,xk))
            | ( sbrdtbr0(X0) = xk
              & ( aSubsetOf0(X0,xX)
                | ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xX) ) ) ) )
          & aSet0(X0) )
       => xu = sdtlpdtrp0(xd,X0) )
    & isCountable0(xX)
    & aSubsetOf0(xX,xY)
    & ! [X0] :
        ( aElementOf0(X0,xX)
       => aElementOf0(X0,xY) )
    & aSet0(xX)
    & aElementOf0(xu,xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4545) ).

fof(f94,conjecture,
    ? [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
                & sbrdtbr0(X2) = xk
                & aSubsetOf0(X2,X1)
                & ! [X3] :
                    ( aElementOf0(X3,X2)
                   => aElementOf0(X3,X1) )
                & aSet0(X2) )
             => sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 )
          & isCountable0(X1)
          & ( ( ! [X2] :
                  ( aElementOf0(X2,sdtlpdtrp0(xN,xi))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) )
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
           => ( ( ! [X2] :
                    ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                  <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X2
                      & aElementOf0(X2,sdtlpdtrp0(xN,xi))
                      & aElement0(X2) ) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
             => ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                | ( ! [X2] :
                      ( aElementOf0(X2,X1)
                     => aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
                  & aSet0(X1) ) ) ) ) )
      & aElementOf0(X0,xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f95,negated_conjecture,
    ~ ? [X0] :
        ( ? [X1] :
            ( ! [X2] :
                ( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
                  & sbrdtbr0(X2) = xk
                  & aSubsetOf0(X2,X1)
                  & ! [X3] :
                      ( aElementOf0(X3,X2)
                     => aElementOf0(X3,X1) )
                  & aSet0(X2) )
               => sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 )
            & isCountable0(X1)
            & ( ( ! [X2] :
                    ( aElementOf0(X2,sdtlpdtrp0(xN,xi))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) )
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
             => ( ( ! [X2] :
                      ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                    <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X2
                        & aElementOf0(X2,sdtlpdtrp0(xN,xi))
                        & aElement0(X2) ) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
               => ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                  | ( ! [X2] :
                        ( aElementOf0(X2,X1)
                       => aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
                    & aSet0(X1) ) ) ) ) )
        & aElementOf0(X0,xT) ),
    inference(negated_conjecture,[],[f94]) ).

fof(f111,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( aElementOf0(X0,xY)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xi))
          & aElement0(X0) ) )
    & aSet0(xY)
    & ! [X1] :
        ( aElementOf0(X1,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(rectify,[],[f91]) ).

fof(f113,plain,
    ( ! [X0] :
        ( ( ( aElementOf0(X0,slbdtsldtrb0(xX,xk))
            | ( sbrdtbr0(X0) = xk
              & ( aSubsetOf0(X0,xX)
                | ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xX) ) ) ) )
          & aSet0(X0) )
       => xu = sdtlpdtrp0(xd,X0) )
    & isCountable0(xX)
    & aSubsetOf0(xX,xY)
    & ! [X2] :
        ( aElementOf0(X2,xX)
       => aElementOf0(X2,xY) )
    & aSet0(xX)
    & aElementOf0(xu,xT) ),
    inference(rectify,[],[f93]) ).

fof(f114,plain,
    ~ ? [X0] :
        ( ? [X1] :
            ( ! [X2] :
                ( ( aElementOf0(X2,slbdtsldtrb0(X1,xk))
                  & sbrdtbr0(X2) = xk
                  & aSubsetOf0(X2,X1)
                  & ! [X3] :
                      ( aElementOf0(X3,X2)
                     => aElementOf0(X3,X1) )
                  & aSet0(X2) )
               => sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 )
            & isCountable0(X1)
            & ( ( ! [X4] :
                    ( aElementOf0(X4,sdtlpdtrp0(xN,xi))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X4) )
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
             => ( ( ! [X5] :
                      ( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                    <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X5
                        & aElementOf0(X5,sdtlpdtrp0(xN,xi))
                        & aElement0(X5) ) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
               => ( aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                  | ( ! [X6] :
                        ( aElementOf0(X6,X1)
                       => aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
                    & aSet0(X1) ) ) ) ) )
        & aElementOf0(X0,xT) ),
    inference(rectify,[],[f95]) ).

fof(f233,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( aElementOf0(X0,xY)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xi))
          & aElement0(X0) ) )
    & aSet0(xY)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(ennf_transformation,[],[f111]) ).

fof(f236,plain,
    ( ! [X0] :
        ( xu = sdtlpdtrp0(xd,X0)
        | ( ~ aElementOf0(X0,slbdtsldtrb0(xX,xk))
          & ( sbrdtbr0(X0) != xk
            | ( ~ aSubsetOf0(X0,xX)
              & ? [X1] :
                  ( ~ aElementOf0(X1,xX)
                  & aElementOf0(X1,X0) ) ) ) )
        | ~ aSet0(X0) )
    & isCountable0(xX)
    & aSubsetOf0(xX,xY)
    & ! [X2] :
        ( aElementOf0(X2,xY)
        | ~ aElementOf0(X2,xX) )
    & aSet0(xX)
    & aElementOf0(xu,xT) ),
    inference(ennf_transformation,[],[f113]) ).

fof(f237,plain,
    ( ! [X0] :
        ( xu = sdtlpdtrp0(xd,X0)
        | ( ~ aElementOf0(X0,slbdtsldtrb0(xX,xk))
          & ( sbrdtbr0(X0) != xk
            | ( ~ aSubsetOf0(X0,xX)
              & ? [X1] :
                  ( ~ aElementOf0(X1,xX)
                  & aElementOf0(X1,X0) ) ) ) )
        | ~ aSet0(X0) )
    & isCountable0(xX)
    & aSubsetOf0(xX,xY)
    & ! [X2] :
        ( aElementOf0(X2,xY)
        | ~ aElementOf0(X2,xX) )
    & aSet0(xX)
    & aElementOf0(xu,xT) ),
    inference(flattening,[],[f236]) ).

fof(f238,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
              & aElementOf0(X2,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X2) = xk
              & aSubsetOf0(X2,X1)
              & ! [X3] :
                  ( aElementOf0(X3,X1)
                  | ~ aElementOf0(X3,X2) )
              & aSet0(X2) )
          | ~ isCountable0(X1)
          | ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                  & aElementOf0(X6,X1) )
              | ~ aSet0(X1) )
            & ! [X5] :
                ( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
              <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X5
                  & aElementOf0(X5,sdtlpdtrp0(xN,xi))
                  & aElement0(X5) ) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
            & ! [X4] :
                ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X4)
                | ~ aElementOf0(X4,sdtlpdtrp0(xN,xi)) )
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) )
      | ~ aElementOf0(X0,xT) ),
    inference(ennf_transformation,[],[f114]) ).

fof(f239,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
              & aElementOf0(X2,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X2) = xk
              & aSubsetOf0(X2,X1)
              & ! [X3] :
                  ( aElementOf0(X3,X1)
                  | ~ aElementOf0(X3,X2) )
              & aSet0(X2) )
          | ~ isCountable0(X1)
          | ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                  & aElementOf0(X6,X1) )
              | ~ aSet0(X1) )
            & ! [X5] :
                ( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
              <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X5
                  & aElementOf0(X5,sdtlpdtrp0(xN,xi))
                  & aElement0(X5) ) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
            & ! [X4] :
                ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X4)
                | ~ aElementOf0(X4,sdtlpdtrp0(xN,xi)) )
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ) )
      | ~ aElementOf0(X0,xT) ),
    inference(flattening,[],[f238]) ).

fof(f269,plain,
    ( ! [X5] :
        ( aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X5
          & aElementOf0(X5,sdtlpdtrp0(xN,xi))
          & aElement0(X5) ) )
    | ~ sP22 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).

fof(f270,plain,
    ! [X1] :
      ( ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ( ? [X6] :
              ( ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
              & aElementOf0(X6,X1) )
          | ~ aSet0(X1) )
        & sP22
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ! [X4] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X4)
            | ~ aElementOf0(X4,sdtlpdtrp0(xN,xi)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
      | ~ sP23(X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).

fof(f271,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
              & aElementOf0(X2,slbdtsldtrb0(X1,xk))
              & sbrdtbr0(X2) = xk
              & aSubsetOf0(X2,X1)
              & ! [X3] :
                  ( aElementOf0(X3,X1)
                  | ~ aElementOf0(X3,X2) )
              & aSet0(X2) )
          | ~ isCountable0(X1)
          | sP23(X1) )
      | ~ aElementOf0(X0,xT) ),
    inference(definition_folding,[],[f239,f270,f269]) ).

fof(f431,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( ( aElementOf0(X0,xY)
          | szmzizndt0(sdtlpdtrp0(xN,xi)) = X0
          | ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
          | ~ aElement0(X0) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
            & aElementOf0(X0,sdtlpdtrp0(xN,xi))
            & aElement0(X0) )
          | ~ aElementOf0(X0,xY) ) )
    & aSet0(xY)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(nnf_transformation,[],[f233]) ).

fof(f432,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( ( aElementOf0(X0,xY)
          | szmzizndt0(sdtlpdtrp0(xN,xi)) = X0
          | ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
          | ~ aElement0(X0) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
            & aElementOf0(X0,sdtlpdtrp0(xN,xi))
            & aElement0(X0) )
          | ~ aElementOf0(X0,xY) ) )
    & aSet0(xY)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(flattening,[],[f431]) ).

fof(f438,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ aElementOf0(X1,xX)
          & aElementOf0(X1,X0) )
     => ( ~ aElementOf0(sK63(X0),xX)
        & aElementOf0(sK63(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f439,plain,
    ( ! [X0] :
        ( xu = sdtlpdtrp0(xd,X0)
        | ( ~ aElementOf0(X0,slbdtsldtrb0(xX,xk))
          & ( sbrdtbr0(X0) != xk
            | ( ~ aSubsetOf0(X0,xX)
              & ~ aElementOf0(sK63(X0),xX)
              & aElementOf0(sK63(X0),X0) ) ) )
        | ~ aSet0(X0) )
    & isCountable0(xX)
    & aSubsetOf0(xX,xY)
    & ! [X2] :
        ( aElementOf0(X2,xY)
        | ~ aElementOf0(X2,xX) )
    & aSet0(xX)
    & aElementOf0(xu,xT) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f237,f438]) ).

fof(f440,plain,
    ! [X1] :
      ( ( ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ( ? [X6] :
              ( ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
              & aElementOf0(X6,X1) )
          | ~ aSet0(X1) )
        & sP22
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ! [X4] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X4)
            | ~ aElementOf0(X4,sdtlpdtrp0(xN,xi)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
      | ~ sP23(X1) ),
    inference(nnf_transformation,[],[f270]) ).

fof(f441,plain,
    ! [X0] :
      ( ( ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ( ? [X1] :
              ( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
              & aElementOf0(X1,X0) )
          | ~ aSet0(X0) )
        & sP22
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ! [X2] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
      | ~ sP23(X0) ),
    inference(rectify,[],[f440]) ).

fof(f442,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
          & aElementOf0(X1,X0) )
     => ( ~ aElementOf0(sK64(X0),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & aElementOf0(sK64(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f443,plain,
    ! [X0] :
      ( ( ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ( ( ~ aElementOf0(sK64(X0),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
            & aElementOf0(sK64(X0),X0) )
          | ~ aSet0(X0) )
        & sP22
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
        & ! [X2] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
      | ~ sP23(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK64])],[f441,f442]) ).

fof(f447,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
          & aElementOf0(X2,slbdtsldtrb0(X1,xk))
          & sbrdtbr0(X2) = xk
          & aSubsetOf0(X2,X1)
          & ! [X3] :
              ( aElementOf0(X3,X1)
              | ~ aElementOf0(X3,X2) )
          & aSet0(X2) )
     => ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK65(X0,X1)) != X0
        & aElementOf0(sK65(X0,X1),slbdtsldtrb0(X1,xk))
        & xk = sbrdtbr0(sK65(X0,X1))
        & aSubsetOf0(sK65(X0,X1),X1)
        & ! [X3] :
            ( aElementOf0(X3,X1)
            | ~ aElementOf0(X3,sK65(X0,X1)) )
        & aSet0(sK65(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f448,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK65(X0,X1)) != X0
            & aElementOf0(sK65(X0,X1),slbdtsldtrb0(X1,xk))
            & xk = sbrdtbr0(sK65(X0,X1))
            & aSubsetOf0(sK65(X0,X1),X1)
            & ! [X3] :
                ( aElementOf0(X3,X1)
                | ~ aElementOf0(X3,sK65(X0,X1)) )
            & aSet0(sK65(X0,X1)) )
          | ~ isCountable0(X1)
          | sP23(X1) )
      | ~ aElementOf0(X0,xT) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f271,f447]) ).

fof(f783,plain,
    xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
    inference(cnf_transformation,[],[f432]) ).

fof(f784,plain,
    xd = sdtlpdtrp0(xC,xi),
    inference(cnf_transformation,[],[f432]) ).

fof(f800,plain,
    aElementOf0(xu,xT),
    inference(cnf_transformation,[],[f439]) ).

fof(f803,plain,
    aSubsetOf0(xX,xY),
    inference(cnf_transformation,[],[f439]) ).

fof(f804,plain,
    isCountable0(xX),
    inference(cnf_transformation,[],[f439]) ).

fof(f808,plain,
    ! [X0] :
      ( xu = sdtlpdtrp0(xd,X0)
      | ~ aElementOf0(X0,slbdtsldtrb0(xX,xk))
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f439]) ).

fof(f815,plain,
    ! [X0] :
      ( ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
      | ~ sP23(X0) ),
    inference(cnf_transformation,[],[f443]) ).

fof(f820,plain,
    ! [X0,X1] :
      ( aSet0(sK65(X0,X1))
      | ~ isCountable0(X1)
      | sP23(X1)
      | ~ aElementOf0(X0,xT) ),
    inference(cnf_transformation,[],[f448]) ).

fof(f824,plain,
    ! [X0,X1] :
      ( aElementOf0(sK65(X0,X1),slbdtsldtrb0(X1,xk))
      | ~ isCountable0(X1)
      | sP23(X1)
      | ~ aElementOf0(X0,xT) ),
    inference(cnf_transformation,[],[f448]) ).

fof(f825,plain,
    ! [X0,X1] :
      ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK65(X0,X1)) != X0
      | ~ isCountable0(X1)
      | sP23(X1)
      | ~ aElementOf0(X0,xT) ),
    inference(cnf_transformation,[],[f448]) ).

cnf(c_376,plain,
    sdtlpdtrp0(xC,xi) = xd,
    inference(cnf_transformation,[],[f784]) ).

cnf(c_377,plain,
    sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) = xY,
    inference(cnf_transformation,[],[f783]) ).

cnf(c_400,plain,
    ( ~ aElementOf0(X0,slbdtsldtrb0(xX,xk))
    | ~ aSet0(X0)
    | sdtlpdtrp0(xd,X0) = xu ),
    inference(cnf_transformation,[],[f808]) ).

cnf(c_404,plain,
    isCountable0(xX),
    inference(cnf_transformation,[],[f804]) ).

cnf(c_405,plain,
    aSubsetOf0(xX,xY),
    inference(cnf_transformation,[],[f803]) ).

cnf(c_408,plain,
    aElementOf0(xu,xT),
    inference(cnf_transformation,[],[f800]) ).

cnf(c_409,plain,
    ( ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
    | ~ sP23(X0) ),
    inference(cnf_transformation,[],[f815]) ).

cnf(c_420,negated_conjecture,
    ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK65(X0,X1)) != X0
    | ~ aElementOf0(X0,xT)
    | ~ isCountable0(X1)
    | sP23(X1) ),
    inference(cnf_transformation,[],[f825]) ).

cnf(c_421,negated_conjecture,
    ( ~ aElementOf0(X0,xT)
    | ~ isCountable0(X1)
    | aElementOf0(sK65(X0,X1),slbdtsldtrb0(X1,xk))
    | sP23(X1) ),
    inference(cnf_transformation,[],[f824]) ).

cnf(c_425,negated_conjecture,
    ( ~ aElementOf0(X0,xT)
    | ~ isCountable0(X1)
    | aSet0(sK65(X0,X1))
    | sP23(X1) ),
    inference(cnf_transformation,[],[f820]) ).

cnf(c_3143,plain,
    ( ~ aSubsetOf0(X0,xY)
    | ~ sP23(X0) ),
    inference(light_normalisation,[status(thm)],[c_409,c_377]) ).

cnf(c_3148,plain,
    ( sdtlpdtrp0(xd,sK65(X0,X1)) != X0
    | ~ aElementOf0(X0,xT)
    | ~ isCountable0(X1)
    | sP23(X1) ),
    inference(light_normalisation,[status(thm)],[c_420,c_376]) ).

cnf(c_16991,plain,
    ( sdtlpdtrp0(xd,sK65(X0,xX)) != X0
    | ~ aElementOf0(X0,xT)
    | ~ isCountable0(xX)
    | sP23(xX) ),
    inference(instantiation,[status(thm)],[c_3148]) ).

cnf(c_17016,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ isCountable0(xX)
    | aElementOf0(sK65(X0,xX),slbdtsldtrb0(xX,xk))
    | sP23(xX) ),
    inference(instantiation,[status(thm)],[c_421]) ).

cnf(c_17091,plain,
    ( ~ aElementOf0(X0,xT)
    | ~ isCountable0(xX)
    | aSet0(sK65(X0,xX))
    | sP23(xX) ),
    inference(instantiation,[status(thm)],[c_425]) ).

cnf(c_17302,plain,
    ( sdtlpdtrp0(xd,sK65(xu,xX)) != xu
    | ~ aElementOf0(xu,xT)
    | ~ isCountable0(xX)
    | sP23(xX) ),
    inference(instantiation,[status(thm)],[c_16991]) ).

cnf(c_17919,plain,
    ( ~ aElementOf0(xu,xT)
    | ~ isCountable0(xX)
    | aElementOf0(sK65(xu,xX),slbdtsldtrb0(xX,xk))
    | sP23(xX) ),
    inference(instantiation,[status(thm)],[c_17016]) ).

cnf(c_18136,plain,
    ( ~ aSubsetOf0(xX,xY)
    | ~ sP23(xX) ),
    inference(instantiation,[status(thm)],[c_3143]) ).

cnf(c_18401,plain,
    ( ~ aElementOf0(xu,xT)
    | ~ isCountable0(xX)
    | aSet0(sK65(xu,xX))
    | sP23(xX) ),
    inference(instantiation,[status(thm)],[c_17091]) ).

cnf(c_20196,plain,
    ( ~ aElementOf0(sK65(xu,xX),slbdtsldtrb0(xX,xk))
    | ~ aSet0(sK65(xu,xX))
    | sdtlpdtrp0(xd,sK65(xu,xX)) = xu ),
    inference(instantiation,[status(thm)],[c_400]) ).

cnf(c_20197,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_20196,c_18401,c_18136,c_17919,c_17302,c_405,c_408,c_404]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : NUM592+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit : 300
% 0.11/0.30  % WCLimit  : 300
% 0.11/0.30  % DateTime : Fri Aug 25 09:37:42 EDT 2023
% 0.11/0.30  % CPUTime  : 
% 0.15/0.38  Running first-order theorem proving
% 0.15/0.38  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.67/3.04  % SZS status Started for theBenchmark.p
% 16.67/3.04  % SZS status Theorem for theBenchmark.p
% 16.67/3.04  
% 16.67/3.04  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 16.67/3.04  
% 16.67/3.04  ------  iProver source info
% 16.67/3.04  
% 16.67/3.04  git: date: 2023-05-31 18:12:56 +0000
% 16.67/3.04  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 16.67/3.04  git: non_committed_changes: false
% 16.67/3.04  git: last_make_outside_of_git: false
% 16.67/3.04  
% 16.67/3.04  ------ Parsing...
% 16.67/3.04  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 16.67/3.04  
% 16.67/3.04  ------ Preprocessing... sup_sim: 9  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e 
% 16.67/3.04  
% 16.67/3.04  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 16.67/3.04  
% 16.67/3.04  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 16.67/3.04  ------ Proving...
% 16.67/3.04  ------ Problem Properties 
% 16.67/3.04  
% 16.67/3.04  
% 16.67/3.04  clauses                                 346
% 16.67/3.04  conjectures                             5
% 16.67/3.04  EPR                                     63
% 16.67/3.04  Horn                                    267
% 16.67/3.04  unary                                   41
% 16.67/3.04  binary                                  85
% 16.67/3.04  lits                                    1123
% 16.67/3.04  lits eq                                 142
% 16.67/3.04  fd_pure                                 0
% 16.67/3.04  fd_pseudo                               0
% 16.67/3.04  fd_cond                                 11
% 16.67/3.04  fd_pseudo_cond                          39
% 16.67/3.04  AC symbols                              0
% 16.67/3.04  
% 16.67/3.04  ------ Input Options Time Limit: Unbounded
% 16.67/3.04  
% 16.67/3.04  
% 16.67/3.04  ------ 
% 16.67/3.04  Current options:
% 16.67/3.04  ------ 
% 16.67/3.04  
% 16.67/3.04  
% 16.67/3.04  
% 16.67/3.04  
% 16.67/3.04  ------ Proving...
% 16.67/3.04  
% 16.67/3.04  
% 16.67/3.04  % SZS status Theorem for theBenchmark.p
% 16.67/3.04  
% 16.67/3.04  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.67/3.04  
% 16.67/3.05  
%------------------------------------------------------------------------------