TSTP Solution File: NUM450+6 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 10:37:37 EDT 2023

% Result   : Theorem 0.20s 0.65s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   75 (   4 unt;  52 typ;   0 def)
%            Number of atoms       :  441 (  65 equ)
%            Maximal formula atoms :  116 (  19 avg)
%            Number of connectives :  578 ( 160   ~; 176   |; 196   &)
%                                         (  18 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   65 (  11 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   77 (  46   >;  31   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;   6 con; 0-3 aty)
%            Number of variables   :  101 (   0 sgn;  66   !;  26   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aInteger0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    sz10: $i ).

tff(decl_25,type,
    smndt0: $i > $i ).

tff(decl_26,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_28,type,
    aDivisorOf0: ( $i * $i ) > $o ).

tff(decl_29,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

tff(decl_30,type,
    isPrime0: $i > $o ).

tff(decl_31,type,
    aSet0: $i > $o ).

tff(decl_32,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_33,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(decl_34,type,
    isFinite0: $i > $o ).

tff(decl_35,type,
    cS1395: $i ).

tff(decl_36,type,
    sdtbsmnsldt0: ( $i * $i ) > $i ).

tff(decl_37,type,
    sdtslmnbsdt0: ( $i * $i ) > $i ).

tff(decl_38,type,
    sbsmnsldt0: $i > $i ).

tff(decl_39,type,
    stldt0: $i > $i ).

tff(decl_40,type,
    szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).

tff(decl_41,type,
    isOpen0: $i > $o ).

tff(decl_42,type,
    isClosed0: $i > $o ).

tff(decl_43,type,
    xS: $i ).

tff(decl_44,type,
    cS2043: $i ).

tff(decl_45,type,
    cS2076: $i ).

tff(decl_46,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk2_1: $i > $i ).

tff(decl_48,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk6_1: $i > $i ).

tff(decl_52,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk13_1: $i > $i ).

tff(decl_59,type,
    esk14_1: $i > $i ).

tff(decl_60,type,
    esk15_1: $i > $i ).

tff(decl_61,type,
    esk16_1: $i > $i ).

tff(decl_62,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk19_1: $i > $i ).

tff(decl_65,type,
    esk20_1: $i > $i ).

tff(decl_66,type,
    esk21_1: $i > $i ).

tff(decl_67,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk23_1: $i > $i ).

tff(decl_69,type,
    esk24_1: $i > $i ).

tff(decl_70,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk26_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_73,type,
    esk28_1: $i > $i ).

fof(m__,conjecture,
    ? [X1] :
      ( aInteger0(X1)
      & X1 != sz00
      & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X1))
          & ! [X2] :
              ( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
               => ( aInteger0(X2)
                  & ? [X3] :
                      ( aInteger0(X3)
                      & sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
                  & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
                  & sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
              & ( ( aInteger0(X2)
                  & ( ? [X3] :
                        ( aInteger0(X3)
                        & sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
                    | aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
                    | sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
               => aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1)) ) ) )
       => ( ( aSet0(sbsmnsldt0(xS))
            & ! [X2] :
                ( aElementOf0(X2,sbsmnsldt0(xS))
              <=> ( aInteger0(X2)
                  & ? [X3] :
                      ( aElementOf0(X3,xS)
                      & aElementOf0(X2,X3) ) ) ) )
         => ( ! [X2] :
                ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
              <=> ( aInteger0(X2)
                  & ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
           => ( ! [X2] :
                  ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
                 => aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
              | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__2079,hypothesis,
    ( aSet0(sbsmnsldt0(xS))
    & ! [X1] :
        ( aElementOf0(X1,sbsmnsldt0(xS))
      <=> ( aInteger0(X1)
          & ? [X2] :
              ( aElementOf0(X2,xS)
              & aElementOf0(X1,X2) ) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(X1)
          & ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( X1 = sz10
          | X1 = smndt0(sz10) ) )
    & stldt0(sbsmnsldt0(xS)) = cS2076 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).

fof(m__2144,hypothesis,
    ( aSet0(sbsmnsldt0(xS))
    & ! [X1] :
        ( aElementOf0(X1,sbsmnsldt0(xS))
      <=> ( aInteger0(X1)
          & ? [X2] :
              ( aElementOf0(X2,xS)
              & aElementOf0(X1,X2) ) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(X1)
          & ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
       => ? [X2] :
            ( aInteger0(X2)
            & X2 != sz00
            & aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
            & ! [X3] :
                ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
                 => ( aInteger0(X3)
                    & ? [X4] :
                        ( aInteger0(X4)
                        & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                    & aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                    & sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                & ( ( aInteger0(X3)
                    & ( ? [X4] :
                          ( aInteger0(X4)
                          & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                      | aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                      | sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                 => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
            & ! [X3] :
                ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
               => aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
            & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) )
    & isOpen0(stldt0(sbsmnsldt0(xS)))
    & isClosed0(sbsmnsldt0(xS))
    & aSet0(sbsmnsldt0(xS))
    & ! [X1] :
        ( aElementOf0(X1,sbsmnsldt0(xS))
      <=> ( aInteger0(X1)
          & ? [X2] :
              ( aElementOf0(X2,xS)
              & aElementOf0(X1,X2) ) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(X1)
          & ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
       => ? [X2] :
            ( aInteger0(X2)
            & X2 != sz00
            & aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
            & ! [X3] :
                ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
                 => ( aInteger0(X3)
                    & ? [X4] :
                        ( aInteger0(X4)
                        & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                    & aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                    & sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                & ( ( aInteger0(X3)
                    & ( ? [X4] :
                          ( aInteger0(X4)
                          & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                      | aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                      | sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                 => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
            & ! [X3] :
                ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
               => aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
            & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).

fof(c_0_3,negated_conjecture,
    ~ ? [X1] :
        ( aInteger0(X1)
        & X1 != sz00
        & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X1))
            & ! [X2] :
                ( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
                 => ( aInteger0(X2)
                    & ? [X3] :
                        ( aInteger0(X3)
                        & sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
                    & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
                    & sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
                & ( ( aInteger0(X2)
                    & ( ? [X3] :
                          ( aInteger0(X3)
                          & sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
                      | aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
                      | sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
                 => aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1)) ) ) )
         => ( ( aSet0(sbsmnsldt0(xS))
              & ! [X2] :
                  ( aElementOf0(X2,sbsmnsldt0(xS))
                <=> ( aInteger0(X2)
                    & ? [X3] :
                        ( aElementOf0(X3,xS)
                        & aElementOf0(X2,X3) ) ) ) )
           => ( ! [X2] :
                  ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
                <=> ( aInteger0(X2)
                    & ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
             => ( ! [X2] :
                    ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
                   => aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
                | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

fof(c_0_4,hypothesis,
    ( aSet0(sbsmnsldt0(xS))
    & ! [X1] :
        ( aElementOf0(X1,sbsmnsldt0(xS))
      <=> ( aInteger0(X1)
          & ? [X2] :
              ( aElementOf0(X2,xS)
              & aElementOf0(X1,X2) ) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(X1)
          & ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( X1 = sz10
          | X1 = smndt0(sz10) ) )
    & stldt0(sbsmnsldt0(xS)) = cS2076 ),
    inference(fof_simplification,[status(thm)],[m__2079]) ).

fof(c_0_5,hypothesis,
    ( aSet0(sbsmnsldt0(xS))
    & ! [X1] :
        ( aElementOf0(X1,sbsmnsldt0(xS))
      <=> ( aInteger0(X1)
          & ? [X2] :
              ( aElementOf0(X2,xS)
              & aElementOf0(X1,X2) ) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(X1)
          & ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
       => ? [X2] :
            ( aInteger0(X2)
            & X2 != sz00
            & aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
            & ! [X3] :
                ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
                 => ( aInteger0(X3)
                    & ? [X4] :
                        ( aInteger0(X4)
                        & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                    & aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                    & sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                & ( ( aInteger0(X3)
                    & ( ? [X4] :
                          ( aInteger0(X4)
                          & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                      | aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                      | sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                 => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
            & ! [X3] :
                ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
               => aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
            & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) )
    & isOpen0(stldt0(sbsmnsldt0(xS)))
    & isClosed0(sbsmnsldt0(xS))
    & aSet0(sbsmnsldt0(xS))
    & ! [X1] :
        ( aElementOf0(X1,sbsmnsldt0(xS))
      <=> ( aInteger0(X1)
          & ? [X2] :
              ( aElementOf0(X2,xS)
              & aElementOf0(X1,X2) ) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( aInteger0(X1)
          & ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
       => ? [X2] :
            ( aInteger0(X2)
            & X2 != sz00
            & aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
            & ! [X3] :
                ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
                 => ( aInteger0(X3)
                    & ? [X4] :
                        ( aInteger0(X4)
                        & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                    & aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                    & sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                & ( ( aInteger0(X3)
                    & ( ? [X4] :
                          ( aInteger0(X4)
                          & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
                      | aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
                      | sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
                 => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
            & ! [X3] :
                ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
               => aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
            & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) ) ),
    inference(fof_simplification,[status(thm)],[m__2144]) ).

fof(c_0_6,negated_conjecture,
    ! [X155,X156,X158,X159,X160,X162,X163,X164,X165] :
      ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aInteger0(X156)
        | ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aInteger0(esk26_2(X155,X156))
        | ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( sdtasdt0(X155,esk26_2(X155,X156)) = sdtpldt0(X156,smndt0(sz10))
        | ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aDivisorOf0(X155,sdtpldt0(X156,smndt0(sz10)))
        | ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( sdteqdtlpzmzozddtrp0(X156,sz10,X155)
        | ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ aInteger0(X159)
        | sdtasdt0(X155,X159) != sdtpldt0(X158,smndt0(sz10))
        | ~ aInteger0(X158)
        | aElementOf0(X158,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ aDivisorOf0(X155,sdtpldt0(X158,smndt0(sz10)))
        | ~ aInteger0(X158)
        | aElementOf0(X158,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ sdteqdtlpzmzozddtrp0(X158,sz10,X155)
        | ~ aInteger0(X158)
        | aElementOf0(X158,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aSet0(sbsmnsldt0(xS))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aInteger0(X160)
        | ~ aElementOf0(X160,sbsmnsldt0(xS))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aElementOf0(esk27_2(X155,X160),xS)
        | ~ aElementOf0(X160,sbsmnsldt0(xS))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aElementOf0(X160,esk27_2(X155,X160))
        | ~ aElementOf0(X160,sbsmnsldt0(xS))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ aInteger0(X162)
        | ~ aElementOf0(X163,xS)
        | ~ aElementOf0(X162,X163)
        | aElementOf0(X162,sbsmnsldt0(xS))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aInteger0(X164)
        | ~ aElementOf0(X164,stldt0(sbsmnsldt0(xS)))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ aElementOf0(X164,sbsmnsldt0(xS))
        | ~ aElementOf0(X164,stldt0(sbsmnsldt0(xS)))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ aInteger0(X165)
        | aElementOf0(X165,sbsmnsldt0(xS))
        | aElementOf0(X165,stldt0(sbsmnsldt0(xS)))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( aElementOf0(esk28_1(X155),szAzrzSzezqlpdtcmdtrp0(sz10,X155))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ aElementOf0(esk28_1(X155),stldt0(sbsmnsldt0(xS)))
        | ~ aInteger0(X155)
        | X155 = sz00 )
      & ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X155),stldt0(sbsmnsldt0(xS)))
        | ~ aInteger0(X155)
        | X155 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])]) ).

fof(c_0_7,hypothesis,
    ! [X125,X127,X128,X129,X130] :
      ( aSet0(sbsmnsldt0(xS))
      & ( aInteger0(X125)
        | ~ aElementOf0(X125,sbsmnsldt0(xS)) )
      & ( aElementOf0(esk19_1(X125),xS)
        | ~ aElementOf0(X125,sbsmnsldt0(xS)) )
      & ( aElementOf0(X125,esk19_1(X125))
        | ~ aElementOf0(X125,sbsmnsldt0(xS)) )
      & ( ~ aInteger0(X127)
        | ~ aElementOf0(X128,xS)
        | ~ aElementOf0(X127,X128)
        | aElementOf0(X127,sbsmnsldt0(xS)) )
      & aSet0(stldt0(sbsmnsldt0(xS)))
      & ( aInteger0(X129)
        | ~ aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X129,sbsmnsldt0(xS))
        | ~ aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aInteger0(X129)
        | aElementOf0(X129,sbsmnsldt0(xS))
        | aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X130,stldt0(sbsmnsldt0(xS)))
        | X130 = sz10
        | X130 = smndt0(sz10) )
      & ( X130 != sz10
        | aElementOf0(X130,stldt0(sbsmnsldt0(xS))) )
      & ( X130 != smndt0(sz10)
        | aElementOf0(X130,stldt0(sbsmnsldt0(xS))) )
      & stldt0(sbsmnsldt0(xS)) = cS2076 ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).

fof(c_0_8,hypothesis,
    ! [X131,X133,X134,X135,X136,X138,X140,X141,X142,X143,X145,X146,X147,X148,X150,X152,X153,X154] :
      ( aSet0(sbsmnsldt0(xS))
      & ( aInteger0(X131)
        | ~ aElementOf0(X131,sbsmnsldt0(xS)) )
      & ( aElementOf0(esk20_1(X131),xS)
        | ~ aElementOf0(X131,sbsmnsldt0(xS)) )
      & ( aElementOf0(X131,esk20_1(X131))
        | ~ aElementOf0(X131,sbsmnsldt0(xS)) )
      & ( ~ aInteger0(X133)
        | ~ aElementOf0(X134,xS)
        | ~ aElementOf0(X133,X134)
        | aElementOf0(X133,sbsmnsldt0(xS)) )
      & ( aInteger0(X135)
        | ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X135,sbsmnsldt0(xS))
        | ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aInteger0(X135)
        | aElementOf0(X135,sbsmnsldt0(xS))
        | aElementOf0(X135,stldt0(sbsmnsldt0(xS))) )
      & ( aInteger0(esk21_1(X136))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( esk21_1(X136) != sz00
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( aSet0(szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( aInteger0(X138)
        | ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( aInteger0(esk22_2(X136,X138))
        | ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( sdtasdt0(esk21_1(X136),esk22_2(X136,X138)) = sdtpldt0(X138,smndt0(X136))
        | ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( aDivisorOf0(esk21_1(X136),sdtpldt0(X138,smndt0(X136)))
        | ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( sdteqdtlpzmzozddtrp0(X138,X136,esk21_1(X136))
        | ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aInteger0(X141)
        | sdtasdt0(esk21_1(X136),X141) != sdtpldt0(X140,smndt0(X136))
        | ~ aInteger0(X140)
        | aElementOf0(X140,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aDivisorOf0(esk21_1(X136),sdtpldt0(X140,smndt0(X136)))
        | ~ aInteger0(X140)
        | aElementOf0(X140,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( ~ sdteqdtlpzmzozddtrp0(X140,X136,esk21_1(X136))
        | ~ aInteger0(X140)
        | aElementOf0(X140,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
        | aElementOf0(X142,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)),stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
      & isOpen0(stldt0(sbsmnsldt0(xS)))
      & isClosed0(sbsmnsldt0(xS))
      & aSet0(sbsmnsldt0(xS))
      & ( aInteger0(X143)
        | ~ aElementOf0(X143,sbsmnsldt0(xS)) )
      & ( aElementOf0(esk23_1(X143),xS)
        | ~ aElementOf0(X143,sbsmnsldt0(xS)) )
      & ( aElementOf0(X143,esk23_1(X143))
        | ~ aElementOf0(X143,sbsmnsldt0(xS)) )
      & ( ~ aInteger0(X145)
        | ~ aElementOf0(X146,xS)
        | ~ aElementOf0(X145,X146)
        | aElementOf0(X145,sbsmnsldt0(xS)) )
      & ( aInteger0(X147)
        | ~ aElementOf0(X147,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X147,sbsmnsldt0(xS))
        | ~ aElementOf0(X147,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aInteger0(X147)
        | aElementOf0(X147,sbsmnsldt0(xS))
        | aElementOf0(X147,stldt0(sbsmnsldt0(xS))) )
      & ( aInteger0(esk24_1(X148))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( esk24_1(X148) != sz00
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( aSet0(szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( aInteger0(X150)
        | ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( aInteger0(esk25_2(X148,X150))
        | ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( sdtasdt0(esk24_1(X148),esk25_2(X148,X150)) = sdtpldt0(X150,smndt0(X148))
        | ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( aDivisorOf0(esk24_1(X148),sdtpldt0(X150,smndt0(X148)))
        | ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( sdteqdtlpzmzozddtrp0(X150,X148,esk24_1(X148))
        | ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aInteger0(X153)
        | sdtasdt0(esk24_1(X148),X153) != sdtpldt0(X152,smndt0(X148))
        | ~ aInteger0(X152)
        | aElementOf0(X152,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aDivisorOf0(esk24_1(X148),sdtpldt0(X152,smndt0(X148)))
        | ~ aInteger0(X152)
        | aElementOf0(X152,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( ~ sdteqdtlpzmzozddtrp0(X152,X148,esk24_1(X148))
        | ~ aInteger0(X152)
        | aElementOf0(X152,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X154,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
        | aElementOf0(X154,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
      & ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)),stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).

cnf(c_0_9,negated_conjecture,
    ( X1 = sz00
    | ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS)))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,hypothesis,
    stldt0(sbsmnsldt0(xS)) = cS2076,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,hypothesis,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,esk21_1(X1)),stldt0(sbsmnsldt0(xS)))
    | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,hypothesis,
    ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
    | X1 != sz10 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    ( X1 = sz00
    | ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),cS2076)
    | ~ aInteger0(X1) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,hypothesis,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,esk21_1(X1)),cS2076)
    | ~ aElementOf0(X1,cS2076) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).

cnf(c_0_15,hypothesis,
    aElementOf0(sz10,cS2076),
    inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_10])]) ).

cnf(c_0_16,hypothesis,
    ( aInteger0(esk21_1(X1))
    | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,hypothesis,
    ( esk21_1(X1) != sz00
    | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    ( esk21_1(sz10) = sz00
    | ~ aInteger0(esk21_1(sz10)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_19,hypothesis,
    ( aInteger0(esk21_1(X1))
    | ~ aElementOf0(X1,cS2076) ),
    inference(rw,[status(thm)],[c_0_16,c_0_10]) ).

cnf(c_0_20,hypothesis,
    ( esk21_1(X1) != sz00
    | ~ aElementOf0(X1,cS2076) ),
    inference(rw,[status(thm)],[c_0_17,c_0_10]) ).

cnf(c_0_21,hypothesis,
    esk21_1(sz10) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15])]) ).

cnf(c_0_22,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n026.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   : Fri Aug 25 15:11:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.59  start to proof: theBenchmark
% 0.20/0.65  % Version  : CSE_E---1.5
% 0.20/0.65  % Problem  : theBenchmark.p
% 0.20/0.65  % Proof found
% 0.20/0.65  % SZS status Theorem for theBenchmark.p
% 0.20/0.65  % SZS output start Proof
% See solution above
% 0.20/0.66  % Total time : 0.056000 s
% 0.20/0.66  % SZS output end Proof
% 0.20/0.66  % Total time : 0.061000 s
%------------------------------------------------------------------------------