TSTP Solution File: NUM437+5 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM437+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 : Wed May 31 12:29:08 EDT 2023

% Result   : Theorem 3.47s 0.91s
% Output   : CNFRefutation 3.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   43 (   5 unt;   1 def)
%            Number of atoms       :  432 (  45 equ)
%            Maximal formula atoms :   31 (  10 avg)
%            Number of connectives :  565 ( 176   ~; 156   |; 206   &)
%                                         (   7 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  10 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :  152 (; 121   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f28,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f37,hypothesis,
    ( aSet0(xS)
    & ! [W0] :
        ( aElementOf0(W0,xS)
       => ( aSet0(cS1395)
          & ! [W1] :
              ( aElementOf0(W1,cS1395)
            <=> aInteger0(W1) )
          & aSet0(W0)
          & ! [W1] :
              ( aElementOf0(W1,W0)
             => aElementOf0(W1,cS1395) )
          & aSubsetOf0(W0,cS1395)
          & ! [W1] :
              ( aElementOf0(W1,W0)
             => ? [W2] :
                  ( aInteger0(W2)
                  & W2 != sz00
                  & aSet0(szAzrzSzezqlpdtcmdtrp0(W1,W2))
                  & ! [W3] :
                      ( ( aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                       => ( aInteger0(W3)
                          & ? [W4] :
                              ( aInteger0(W4)
                              & sdtasdt0(W2,W4) = sdtpldt0(W3,smndt0(W1)) )
                          & aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                          & sdteqdtlpzmzozddtrp0(W3,W1,W2) ) )
                      & ( ( aInteger0(W3)
                          & ( ? [W4] :
                                ( aInteger0(W4)
                                & sdtasdt0(W2,W4) = sdtpldt0(W3,smndt0(W1)) )
                            | aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                            | sdteqdtlpzmzozddtrp0(W3,W1,W2) ) )
                       => aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2)) ) )
                  & ! [W3] :
                      ( aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                     => aElementOf0(W3,W0) )
                  & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0) ) )
          & isOpen0(W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f38,conjecture,
    ( ( aSet0(sbsmnsldt0(xS))
      & ! [W0] :
          ( aElementOf0(W0,sbsmnsldt0(xS))
        <=> ( aInteger0(W0)
            & ? [W1] :
                ( aElementOf0(W1,xS)
                & aElementOf0(W0,W1) ) ) ) )
   => ( ! [W0] :
          ( aElementOf0(W0,sbsmnsldt0(xS))
         => ? [W1] :
              ( aInteger0(W1)
              & W1 != sz00
              & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
                  & ! [W2] :
                      ( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                       => ( aInteger0(W2)
                          & ? [W3] :
                              ( aInteger0(W3)
                              & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
                          & aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                          & sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
                      & ( ( aInteger0(W2)
                          & ( ? [W3] :
                                ( aInteger0(W3)
                                & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
                            | aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                            | sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
                       => aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) )
               => ( ! [W2] :
                      ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                     => aElementOf0(W2,sbsmnsldt0(xS)) )
                  | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),sbsmnsldt0(xS)) ) ) ) )
      | isOpen0(sbsmnsldt0(xS)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f39,negated_conjecture,
    ~ ( ( aSet0(sbsmnsldt0(xS))
        & ! [W0] :
            ( aElementOf0(W0,sbsmnsldt0(xS))
          <=> ( aInteger0(W0)
              & ? [W1] :
                  ( aElementOf0(W1,xS)
                  & aElementOf0(W0,W1) ) ) ) )
     => ( ! [W0] :
            ( aElementOf0(W0,sbsmnsldt0(xS))
           => ? [W1] :
                ( aInteger0(W1)
                & W1 != sz00
                & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
                    & ! [W2] :
                        ( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                         => ( aInteger0(W2)
                            & ? [W3] :
                                ( aInteger0(W3)
                                & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
                            & aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                            & sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
                        & ( ( aInteger0(W2)
                            & ( ? [W3] :
                                  ( aInteger0(W3)
                                  & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
                              | aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                              | sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
                         => aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) ) )
                 => ( ! [W2] :
                        ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                       => aElementOf0(W2,sbsmnsldt0(xS)) )
                    | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),sbsmnsldt0(xS)) ) ) ) )
        | isOpen0(sbsmnsldt0(xS)) ) ),
    inference(negated_conjecture,[status(cth)],[f38]) ).

fof(f116,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( ~ aElementOf0(W2,W1)
                | aElementOf0(W2,W0) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f117,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ! [W1] :
          ( ( ~ aSubsetOf0(W1,W0)
            | ( aSet0(W1)
              & ! [W2] :
                  ( ~ aElementOf0(W2,W1)
                  | aElementOf0(W2,W0) ) ) )
          & ( aSubsetOf0(W1,W0)
            | ~ aSet0(W1)
            | ? [W2] :
                ( aElementOf0(W2,W1)
                & ~ aElementOf0(W2,W0) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f116]) ).

fof(f118,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ( ! [W1] :
            ( ~ aSubsetOf0(W1,W0)
            | ( aSet0(W1)
              & ! [W2] :
                  ( ~ aElementOf0(W2,W1)
                  | aElementOf0(W2,W0) ) ) )
        & ! [W1] :
            ( aSubsetOf0(W1,W0)
            | ~ aSet0(W1)
            | ? [W2] :
                ( aElementOf0(W2,W1)
                & ~ aElementOf0(W2,W0) ) ) ) ),
    inference(miniscoping,[status(esa)],[f117]) ).

fof(f119,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ( ! [W1] :
            ( ~ aSubsetOf0(W1,W0)
            | ( aSet0(W1)
              & ! [W2] :
                  ( ~ aElementOf0(W2,W1)
                  | aElementOf0(W2,W0) ) ) )
        & ! [W1] :
            ( aSubsetOf0(W1,W0)
            | ~ aSet0(W1)
            | ( aElementOf0(sk0_2(W1,W0),W1)
              & ~ aElementOf0(sk0_2(W1,W0),W0) ) ) ) ),
    inference(skolemization,[status(esa)],[f118]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( ~ aSet0(X0)
      | ~ aSubsetOf0(X1,X0)
      | ~ aElementOf0(X2,X1)
      | aElementOf0(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f199,plain,
    ( aSet0(xS)
    & ! [W0] :
        ( ~ aElementOf0(W0,xS)
        | ( aSet0(cS1395)
          & ! [W1] :
              ( aElementOf0(W1,cS1395)
            <=> aInteger0(W1) )
          & aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,cS1395) )
          & aSubsetOf0(W0,cS1395)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ? [W2] :
                  ( aInteger0(W2)
                  & W2 != sz00
                  & aSet0(szAzrzSzezqlpdtcmdtrp0(W1,W2))
                  & ! [W3] :
                      ( ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                        | ( aInteger0(W3)
                          & ? [W4] :
                              ( aInteger0(W4)
                              & sdtasdt0(W2,W4) = sdtpldt0(W3,smndt0(W1)) )
                          & aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                          & sdteqdtlpzmzozddtrp0(W3,W1,W2) ) )
                      & ( ~ aInteger0(W3)
                        | ( ! [W4] :
                              ( ~ aInteger0(W4)
                              | sdtasdt0(W2,W4) != sdtpldt0(W3,smndt0(W1)) )
                          & ~ aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                          & ~ sdteqdtlpzmzozddtrp0(W3,W1,W2) )
                        | aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2)) ) )
                  & ! [W3] :
                      ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                      | aElementOf0(W3,W0) )
                  & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0) ) )
          & isOpen0(W0) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f200,plain,
    ( aSet0(xS)
    & ! [W0] :
        ( ~ aElementOf0(W0,xS)
        | ( aSet0(cS1395)
          & ! [W1] :
              ( ( ~ aElementOf0(W1,cS1395)
                | aInteger0(W1) )
              & ( aElementOf0(W1,cS1395)
                | ~ aInteger0(W1) ) )
          & aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,cS1395) )
          & aSubsetOf0(W0,cS1395)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ? [W2] :
                  ( aInteger0(W2)
                  & W2 != sz00
                  & aSet0(szAzrzSzezqlpdtcmdtrp0(W1,W2))
                  & ! [W3] :
                      ( ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                        | ( aInteger0(W3)
                          & ? [W4] :
                              ( aInteger0(W4)
                              & sdtasdt0(W2,W4) = sdtpldt0(W3,smndt0(W1)) )
                          & aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                          & sdteqdtlpzmzozddtrp0(W3,W1,W2) ) )
                      & ( ~ aInteger0(W3)
                        | ( ! [W4] :
                              ( ~ aInteger0(W4)
                              | sdtasdt0(W2,W4) != sdtpldt0(W3,smndt0(W1)) )
                          & ~ aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                          & ~ sdteqdtlpzmzozddtrp0(W3,W1,W2) )
                        | aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2)) ) )
                  & ! [W3] :
                      ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                      | aElementOf0(W3,W0) )
                  & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0) ) )
          & isOpen0(W0) ) ) ),
    inference(NNF_transformation,[status(esa)],[f199]) ).

fof(f201,plain,
    ( aSet0(xS)
    & ! [W0] :
        ( ~ aElementOf0(W0,xS)
        | ( aSet0(cS1395)
          & ! [W1] :
              ( ~ aElementOf0(W1,cS1395)
              | aInteger0(W1) )
          & ! [W1] :
              ( aElementOf0(W1,cS1395)
              | ~ aInteger0(W1) )
          & aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,cS1395) )
          & aSubsetOf0(W0,cS1395)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ? [W2] :
                  ( aInteger0(W2)
                  & W2 != sz00
                  & aSet0(szAzrzSzezqlpdtcmdtrp0(W1,W2))
                  & ! [W3] :
                      ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                      | ( aInteger0(W3)
                        & ? [W4] :
                            ( aInteger0(W4)
                            & sdtasdt0(W2,W4) = sdtpldt0(W3,smndt0(W1)) )
                        & aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                        & sdteqdtlpzmzozddtrp0(W3,W1,W2) ) )
                  & ! [W3] :
                      ( ~ aInteger0(W3)
                      | ( ! [W4] :
                            ( ~ aInteger0(W4)
                            | sdtasdt0(W2,W4) != sdtpldt0(W3,smndt0(W1)) )
                        & ~ aDivisorOf0(W2,sdtpldt0(W3,smndt0(W1)))
                        & ~ sdteqdtlpzmzozddtrp0(W3,W1,W2) )
                      | aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2)) )
                  & ! [W3] :
                      ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,W2))
                      | aElementOf0(W3,W0) )
                  & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,W2),W0) ) )
          & isOpen0(W0) ) ) ),
    inference(miniscoping,[status(esa)],[f200]) ).

fof(f202,plain,
    ( aSet0(xS)
    & ! [W0] :
        ( ~ aElementOf0(W0,xS)
        | ( aSet0(cS1395)
          & ! [W1] :
              ( ~ aElementOf0(W1,cS1395)
              | aInteger0(W1) )
          & ! [W1] :
              ( aElementOf0(W1,cS1395)
              | ~ aInteger0(W1) )
          & aSet0(W0)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | aElementOf0(W1,cS1395) )
          & aSubsetOf0(W0,cS1395)
          & ! [W1] :
              ( ~ aElementOf0(W1,W0)
              | ( aInteger0(sk0_13(W1,W0))
                & sk0_13(W1,W0) != sz00
                & aSet0(szAzrzSzezqlpdtcmdtrp0(W1,sk0_13(W1,W0)))
                & ! [W3] :
                    ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,sk0_13(W1,W0)))
                    | ( aInteger0(W3)
                      & aInteger0(sk0_14(W3,W1,W0))
                      & sdtasdt0(sk0_13(W1,W0),sk0_14(W3,W1,W0)) = sdtpldt0(W3,smndt0(W1))
                      & aDivisorOf0(sk0_13(W1,W0),sdtpldt0(W3,smndt0(W1)))
                      & sdteqdtlpzmzozddtrp0(W3,W1,sk0_13(W1,W0)) ) )
                & ! [W3] :
                    ( ~ aInteger0(W3)
                    | ( ! [W4] :
                          ( ~ aInteger0(W4)
                          | sdtasdt0(sk0_13(W1,W0),W4) != sdtpldt0(W3,smndt0(W1)) )
                      & ~ aDivisorOf0(sk0_13(W1,W0),sdtpldt0(W3,smndt0(W1)))
                      & ~ sdteqdtlpzmzozddtrp0(W3,W1,sk0_13(W1,W0)) )
                    | aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,sk0_13(W1,W0))) )
                & ! [W3] :
                    ( ~ aElementOf0(W3,szAzrzSzezqlpdtcmdtrp0(W1,sk0_13(W1,W0)))
                    | aElementOf0(W3,W0) )
                & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1,sk0_13(W1,W0)),W0) ) )
          & isOpen0(W0) ) ) ),
    inference(skolemization,[status(esa)],[f201]) ).

fof(f207,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xS)
      | aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f202]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(X1,X0)
      | aInteger0(sk0_13(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f202]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(X1,X0)
      | sk0_13(X1,X0) != sz00 ),
    inference(cnf_transformation,[status(esa)],[f202]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(X1,X0)
      | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,sk0_13(X1,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f202]) ).

fof(f224,plain,
    ( aSet0(sbsmnsldt0(xS))
    & ! [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
      <=> ( aInteger0(W0)
          & ? [W1] :
              ( aElementOf0(W1,xS)
              & aElementOf0(W0,W1) ) ) )
    & ? [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
        & ! [W1] :
            ( ~ aInteger0(W1)
            | W1 = sz00
            | ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
              & ! [W2] :
                  ( ( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                    | ( aInteger0(W2)
                      & ? [W3] :
                          ( aInteger0(W3)
                          & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
                      & aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                      & sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
                  & ( ~ aInteger0(W2)
                    | ( ! [W3] :
                          ( ~ aInteger0(W3)
                          | sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0)) )
                      & ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                      & ~ sdteqdtlpzmzozddtrp0(W2,W0,W1) )
                    | aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
              & ? [W2] :
                  ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                  & ~ aElementOf0(W2,sbsmnsldt0(xS)) )
              & ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),sbsmnsldt0(xS)) ) ) )
    & ~ isOpen0(sbsmnsldt0(xS)) ),
    inference(pre_NNF_transformation,[status(esa)],[f39]) ).

fof(f225,plain,
    ( aSet0(sbsmnsldt0(xS))
    & ! [W0] :
        ( ( ~ aElementOf0(W0,sbsmnsldt0(xS))
          | ( aInteger0(W0)
            & ? [W1] :
                ( aElementOf0(W1,xS)
                & aElementOf0(W0,W1) ) ) )
        & ( aElementOf0(W0,sbsmnsldt0(xS))
          | ~ aInteger0(W0)
          | ! [W1] :
              ( ~ aElementOf0(W1,xS)
              | ~ aElementOf0(W0,W1) ) ) )
    & ? [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
        & ! [W1] :
            ( ~ aInteger0(W1)
            | W1 = sz00
            | ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
              & ! [W2] :
                  ( ( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                    | ( aInteger0(W2)
                      & ? [W3] :
                          ( aInteger0(W3)
                          & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
                      & aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                      & sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
                  & ( ~ aInteger0(W2)
                    | ( ! [W3] :
                          ( ~ aInteger0(W3)
                          | sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0)) )
                      & ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                      & ~ sdteqdtlpzmzozddtrp0(W2,W0,W1) )
                    | aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
              & ? [W2] :
                  ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                  & ~ aElementOf0(W2,sbsmnsldt0(xS)) )
              & ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),sbsmnsldt0(xS)) ) ) )
    & ~ isOpen0(sbsmnsldt0(xS)) ),
    inference(NNF_transformation,[status(esa)],[f224]) ).

fof(f226,plain,
    ( aSet0(sbsmnsldt0(xS))
    & ! [W0] :
        ( ~ aElementOf0(W0,sbsmnsldt0(xS))
        | ( aInteger0(W0)
          & ? [W1] :
              ( aElementOf0(W1,xS)
              & aElementOf0(W0,W1) ) ) )
    & ! [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
        | ~ aInteger0(W0)
        | ! [W1] :
            ( ~ aElementOf0(W1,xS)
            | ~ aElementOf0(W0,W1) ) )
    & ? [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
        & ! [W1] :
            ( ~ aInteger0(W1)
            | W1 = sz00
            | ( aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
              & ! [W2] :
                  ( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                  | ( aInteger0(W2)
                    & ? [W3] :
                        ( aInteger0(W3)
                        & sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
                    & aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                    & sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
              & ! [W2] :
                  ( ~ aInteger0(W2)
                  | ( ! [W3] :
                        ( ~ aInteger0(W3)
                        | sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(W0)) )
                    & ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
                    & ~ sdteqdtlpzmzozddtrp0(W2,W0,W1) )
                  | aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
              & ? [W2] :
                  ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
                  & ~ aElementOf0(W2,sbsmnsldt0(xS)) )
              & ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),sbsmnsldt0(xS)) ) ) )
    & ~ isOpen0(sbsmnsldt0(xS)) ),
    inference(miniscoping,[status(esa)],[f225]) ).

fof(f227,plain,
    ( aSet0(sbsmnsldt0(xS))
    & ! [W0] :
        ( ~ aElementOf0(W0,sbsmnsldt0(xS))
        | ( aInteger0(W0)
          & aElementOf0(sk0_15(W0),xS)
          & aElementOf0(W0,sk0_15(W0)) ) )
    & ! [W0] :
        ( aElementOf0(W0,sbsmnsldt0(xS))
        | ~ aInteger0(W0)
        | ! [W1] :
            ( ~ aElementOf0(W1,xS)
            | ~ aElementOf0(W0,W1) ) )
    & aElementOf0(sk0_16,sbsmnsldt0(xS))
    & ! [W1] :
        ( ~ aInteger0(W1)
        | W1 = sz00
        | ( aSet0(szAzrzSzezqlpdtcmdtrp0(sk0_16,W1))
          & ! [W2] :
              ( ~ aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sk0_16,W1))
              | ( aInteger0(W2)
                & aInteger0(sk0_17(W2,W1))
                & sdtasdt0(W1,sk0_17(W2,W1)) = sdtpldt0(W2,smndt0(sk0_16))
                & aDivisorOf0(W1,sdtpldt0(W2,smndt0(sk0_16)))
                & sdteqdtlpzmzozddtrp0(W2,sk0_16,W1) ) )
          & ! [W2] :
              ( ~ aInteger0(W2)
              | ( ! [W3] :
                    ( ~ aInteger0(W3)
                    | sdtasdt0(W1,W3) != sdtpldt0(W2,smndt0(sk0_16)) )
                & ~ aDivisorOf0(W1,sdtpldt0(W2,smndt0(sk0_16)))
                & ~ sdteqdtlpzmzozddtrp0(W2,sk0_16,W1) )
              | aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(sk0_16,W1)) )
          & aElementOf0(sk0_18(W1),szAzrzSzezqlpdtcmdtrp0(sk0_16,W1))
          & ~ aElementOf0(sk0_18(W1),sbsmnsldt0(xS))
          & ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sk0_16,W1),sbsmnsldt0(xS)) ) )
    & ~ isOpen0(sbsmnsldt0(xS)) ),
    inference(skolemization,[status(esa)],[f226]) ).

fof(f230,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sbsmnsldt0(xS))
      | aElementOf0(sk0_15(X0),xS) ),
    inference(cnf_transformation,[status(esa)],[f227]) ).

fof(f231,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sbsmnsldt0(xS))
      | aElementOf0(X0,sk0_15(X0)) ),
    inference(cnf_transformation,[status(esa)],[f227]) ).

fof(f232,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,sbsmnsldt0(xS))
      | ~ aInteger0(X0)
      | ~ aElementOf0(X1,xS)
      | ~ aElementOf0(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f227]) ).

fof(f233,plain,
    aElementOf0(sk0_16,sbsmnsldt0(xS)),
    inference(cnf_transformation,[status(esa)],[f227]) ).

fof(f235,plain,
    ! [X0,X1] :
      ( ~ aInteger0(X0)
      | X0 = sz00
      | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sk0_16,X0))
      | aInteger0(X1) ),
    inference(cnf_transformation,[status(esa)],[f227]) ).

fof(f243,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | X0 = sz00
      | aElementOf0(sk0_18(X0),szAzrzSzezqlpdtcmdtrp0(sk0_16,X0)) ),
    inference(cnf_transformation,[status(esa)],[f227]) ).

fof(f244,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | X0 = sz00
      | ~ aElementOf0(sk0_18(X0),sbsmnsldt0(xS)) ),
    inference(cnf_transformation,[status(esa)],[f227]) ).

fof(f297,plain,
    aElementOf0(sk0_15(sk0_16),xS),
    inference(resolution,[status(thm)],[f230,f233]) ).

fof(f310,plain,
    aElementOf0(sk0_16,sk0_15(sk0_16)),
    inference(resolution,[status(thm)],[f231,f233]) ).

fof(f312,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | X0 = sz00
      | aInteger0(sk0_18(X0))
      | ~ aInteger0(X0)
      | X0 = sz00 ),
    inference(resolution,[status(thm)],[f235,f243]) ).

fof(f313,plain,
    ! [X0] :
      ( ~ aInteger0(X0)
      | X0 = sz00
      | aInteger0(sk0_18(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f312]) ).

fof(f314,plain,
    ! [X0,X1] :
      ( ~ aInteger0(sk0_18(X0))
      | ~ aElementOf0(X1,xS)
      | ~ aElementOf0(sk0_18(X0),X1)
      | ~ aInteger0(X0)
      | X0 = sz00 ),
    inference(resolution,[status(thm)],[f232,f244]) ).

fof(f315,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(sk0_18(X1),X0)
      | ~ aInteger0(X1)
      | X1 = sz00 ),
    inference(forward_subsumption_resolution,[status(thm)],[f314,f313]) ).

fof(f1504,plain,
    ! [X0,X1,X2] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(X1,X0)
      | ~ aSet0(X0)
      | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,sk0_13(X1,X0)))
      | aElementOf0(X2,X0) ),
    inference(resolution,[status(thm)],[f222,f121]) ).

fof(f1505,plain,
    ! [X0,X1,X2] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(X1,X0)
      | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X1,sk0_13(X1,X0)))
      | aElementOf0(X2,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1504,f207]) ).

fof(f1798,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(sk0_16,X0)
      | aElementOf0(sk0_18(sk0_13(sk0_16,X0)),X0)
      | ~ aInteger0(sk0_13(sk0_16,X0))
      | sk0_13(sk0_16,X0) = sz00 ),
    inference(resolution,[status(thm)],[f1505,f243]) ).

fof(f1799,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(sk0_16,X0)
      | ~ aInteger0(sk0_13(sk0_16,X0))
      | sk0_13(sk0_16,X0) = sz00 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1798,f315]) ).

fof(f1804,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(sk0_16,X0)
      | sk0_13(sk0_16,X0) = sz00 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1799,f210]) ).

fof(f1805,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(sk0_16,X0)
      | ~ aElementOf0(X0,xS)
      | ~ aElementOf0(sk0_16,X0) ),
    inference(resolution,[status(thm)],[f1804,f211]) ).

fof(f1806,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xS)
      | ~ aElementOf0(sk0_16,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f1805]) ).

fof(f1807,plain,
    ~ aElementOf0(sk0_15(sk0_16),xS),
    inference(resolution,[status(thm)],[f1806,f310]) ).

fof(f1808,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f1807,f297]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : NUM437+5 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n013.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 09:48:20 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.5.1
% 3.47/0.91  % Refutation found
% 3.47/0.91  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.47/0.91  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.47/0.94  % Elapsed time: 0.616005 seconds
% 3.47/0.94  % CPU time: 3.848940 seconds
% 3.47/0.94  % Memory used: 85.160 MB
%------------------------------------------------------------------------------