TSTP Solution File: NUM452+6 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM452+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 : n018.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 10:37:38 EDT 2023

% Result   : Theorem 0.20s 0.68s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   68
% Syntax   : Number of formulae    :  131 (  17 unt;  54 typ;   0 def)
%            Number of atoms       :  398 ( 104 equ)
%            Maximal formula atoms :   44 (   5 avg)
%            Number of connectives :  501 ( 180   ~; 167   |; 126   &)
%                                         (  11 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   74 (  45   >;  29   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   3 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;   7 con; 0-3 aty)
%            Number of variables   :  113 (   0 sgn;  63   !;  13   ?;   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,
    xp: $i ).

tff(decl_47,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk2_1: $i > $i ).

tff(decl_49,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk6_1: $i > $i ).

tff(decl_53,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_57,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk13_1: $i > $i ).

tff(decl_60,type,
    esk14_1: $i > $i ).

tff(decl_61,type,
    esk15_1: $i > $i ).

tff(decl_62,type,
    esk16_1: $i > $i ).

tff(decl_63,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk19_1: $i > $i ).

tff(decl_66,type,
    esk20_1: $i > $i ).

tff(decl_67,type,
    esk21_1: $i > $i ).

tff(decl_68,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk23_1: $i > $i ).

tff(decl_70,type,
    esk24_1: $i > $i ).

tff(decl_71,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk26_1: $i > $i ).

tff(decl_73,type,
    esk27_1: $i > $i ).

tff(decl_74,type,
    epred1_0: $o ).

tff(decl_75,type,
    epred2_0: $o ).

fof(m__2171,hypothesis,
    ( aInteger0(xp)
    & xp != sz00
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & ! [X1] :
        ( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
         => ( aInteger0(X1)
            & ? [X2] :
                ( aInteger0(X2)
                & sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
            & aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
            & sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
        & ( ( aInteger0(X1)
            & ( ? [X2] :
                  ( aInteger0(X2)
                  & sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
              | aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
              | sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
         => aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & 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,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
       => aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).

fof(mEquModRef,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & X2 != sz00 )
     => sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).

fof(mIntOne,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).

fof(mZeroDiv,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => ( sdtasdt0(X1,X2) = sz00
       => ( X1 = sz00
          | X2 = sz00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).

fof(mAddNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).

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__,conjecture,
    ( ( ? [X1] :
          ( aInteger0(X1)
          & sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
      | aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
      | sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
      | aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ( ? [X1] :
          ( aInteger0(X1)
          & sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
      | aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
      | sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
      | aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mAddAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3) )
     => sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).

fof(mIntNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => aInteger0(smndt0(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).

fof(mAddZero,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).

fof(mDivisor,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ! [X2] :
          ( aDivisorOf0(X2,X1)
        <=> ( aInteger0(X2)
            & X2 != sz00
            & ? [X3] :
                ( aInteger0(X3)
                & sdtasdt0(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).

fof(mMulOne,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).

fof(mMulMinOne,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
        & smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).

fof(c_0_14,hypothesis,
    ( aInteger0(xp)
    & xp != sz00
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & ! [X1] :
        ( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
         => ( aInteger0(X1)
            & ? [X2] :
                ( aInteger0(X2)
                & sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
            & aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
            & sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
        & ( ( aInteger0(X1)
            & ( ? [X2] :
                  ( aInteger0(X2)
                  & sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
              | aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
              | sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
         => aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & 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,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
       => aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    inference(fof_simplification,[status(thm)],[m__2171]) ).

fof(c_0_15,hypothesis,
    ! [X155,X157,X158,X159,X161,X162,X163,X164] :
      ( aInteger0(xp)
      & xp != sz00
      & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
      & ( aInteger0(X155)
        | ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( aInteger0(esk26_1(X155))
        | ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( sdtasdt0(xp,esk26_1(X155)) = sdtpldt0(X155,smndt0(sz10))
        | ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( aDivisorOf0(xp,sdtpldt0(X155,smndt0(sz10)))
        | ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( sdteqdtlpzmzozddtrp0(X155,sz10,xp)
        | ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( ~ aInteger0(X158)
        | sdtasdt0(xp,X158) != sdtpldt0(X157,smndt0(sz10))
        | ~ aInteger0(X157)
        | aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( ~ aDivisorOf0(xp,sdtpldt0(X157,smndt0(sz10)))
        | ~ aInteger0(X157)
        | aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( ~ sdteqdtlpzmzozddtrp0(X157,sz10,xp)
        | ~ aInteger0(X157)
        | aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & aSet0(sbsmnsldt0(xS))
      & ( aInteger0(X159)
        | ~ aElementOf0(X159,sbsmnsldt0(xS)) )
      & ( aElementOf0(esk27_1(X159),xS)
        | ~ aElementOf0(X159,sbsmnsldt0(xS)) )
      & ( aElementOf0(X159,esk27_1(X159))
        | ~ aElementOf0(X159,sbsmnsldt0(xS)) )
      & ( ~ aInteger0(X161)
        | ~ aElementOf0(X162,xS)
        | ~ aElementOf0(X161,X162)
        | aElementOf0(X161,sbsmnsldt0(xS)) )
      & ( aInteger0(X163)
        | ~ aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X163,sbsmnsldt0(xS))
        | ~ aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aInteger0(X163)
        | aElementOf0(X163,sbsmnsldt0(xS))
        | aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(X164,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
        | aElementOf0(X164,stldt0(sbsmnsldt0(xS))) )
      & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),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_14])])])])])]) ).

fof(c_0_16,plain,
    ! [X38,X39] :
      ( ~ aInteger0(X38)
      | ~ aInteger0(X39)
      | X39 = sz00
      | sdteqdtlpzmzozddtrp0(X38,X38,X39) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).

cnf(c_0_17,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    | ~ sdteqdtlpzmzozddtrp0(X1,sz10,xp)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,plain,
    ( X2 = sz00
    | sdteqdtlpzmzozddtrp0(X1,X1,X2)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,plain,
    aInteger0(sz10),
    inference(split_conjunct,[status(thm)],[mIntOne]) ).

cnf(c_0_20,hypothesis,
    aInteger0(xp),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_22,plain,
    ! [X28,X29] :
      ( ~ aInteger0(X28)
      | ~ aInteger0(X29)
      | sdtasdt0(X28,X29) != sz00
      | X28 = sz00
      | X29 = sz00 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).

cnf(c_0_23,hypothesis,
    ( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
    | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,hypothesis,
    aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),c_0_21]) ).

cnf(c_0_25,hypothesis,
    ( aInteger0(esk26_1(X1))
    | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_26,plain,
    ( X1 = sz00
    | X2 = sz00
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | sdtasdt0(X1,X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,hypothesis,
    sdtasdt0(xp,esk26_1(sz10)) = sdtpldt0(sz10,smndt0(sz10)),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,hypothesis,
    aInteger0(esk26_1(sz10)),
    inference(spm,[status(thm)],[c_0_25,c_0_24]) ).

fof(c_0_29,plain,
    ! [X16] :
      ( ( sdtpldt0(X16,smndt0(X16)) = sz00
        | ~ aInteger0(X16) )
      & ( sz00 = sdtpldt0(smndt0(X16),X16)
        | ~ aInteger0(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).

fof(c_0_30,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]) ).

cnf(c_0_31,hypothesis,
    ( esk26_1(sz10) = sz00
    | sdtpldt0(sz10,smndt0(sz10)) != sz00 ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_20])]),c_0_21]) ).

cnf(c_0_32,plain,
    ( sdtpldt0(X1,smndt0(X1)) = sz00
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_33,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_30])])])])])]) ).

cnf(c_0_34,hypothesis,
    esk26_1(sz10) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_19])]) ).

cnf(c_0_35,hypothesis,
    ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
    | X1 != smndt0(sz10) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_36,hypothesis,
    stldt0(sbsmnsldt0(xS)) = cS2076,
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

fof(c_0_37,negated_conjecture,
    ~ ( ( ? [X1] :
            ( aInteger0(X1)
            & sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
        | aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
        | sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
        | aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( ? [X1] :
            ( aInteger0(X1)
            & sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
        | aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
        | sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
        | aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_38,hypothesis,
    sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,sz00),
    inference(rw,[status(thm)],[c_0_27,c_0_34]) ).

cnf(c_0_39,hypothesis,
    ( aInteger0(X1)
    | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_40,hypothesis,
    ( aElementOf0(X1,cS2076)
    | X1 != smndt0(sz10) ),
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

fof(c_0_41,negated_conjecture,
    ! [X165,X166] :
      ( ( ~ aInteger0(X166)
        | sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
        | ~ aInteger0(X165)
        | sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
      & ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
        | ~ aInteger0(X165)
        | sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
      & ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
        | ~ aInteger0(X165)
        | sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
      & ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
        | ~ aInteger0(X165)
        | sdtasdt0(xp,X165) != sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
      & ( ~ aInteger0(X166)
        | sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
        | ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
      & ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
        | ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
      & ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
        | ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
      & ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
        | ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) )
      & ( ~ aInteger0(X166)
        | sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
        | ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
      & ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
        | ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
      & ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
        | ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
      & ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
        | ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp) )
      & ( ~ aInteger0(X166)
        | sdtasdt0(xp,X166) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
        | ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
        | ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
        | ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
      & ( ~ aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
        | ~ aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).

fof(c_0_42,plain,
    ! [X10,X11,X12] :
      ( ~ aInteger0(X10)
      | ~ aInteger0(X11)
      | ~ aInteger0(X12)
      | sdtpldt0(X10,sdtpldt0(X11,X12)) = sdtpldt0(sdtpldt0(X10,X11),X12) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

cnf(c_0_43,hypothesis,
    sdtasdt0(xp,sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_38]),c_0_19])]) ).

cnf(c_0_44,hypothesis,
    ( aInteger0(X1)
    | ~ aElementOf0(X1,cS2076) ),
    inference(rw,[status(thm)],[c_0_39,c_0_36]) ).

cnf(c_0_45,hypothesis,
    aElementOf0(smndt0(sz10),cS2076),
    inference(er,[status(thm)],[c_0_40]) ).

cnf(c_0_46,negated_conjecture,
    ( ~ aInteger0(X1)
    | sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
    | ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

fof(c_0_48,plain,
    ! [X5] :
      ( ~ aInteger0(X5)
      | aInteger0(smndt0(X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).

cnf(c_0_49,hypothesis,
    sdtpldt0(sz10,smndt0(sz10)) = sz00,
    inference(rw,[status(thm)],[c_0_38,c_0_43]) ).

cnf(c_0_50,hypothesis,
    aInteger0(smndt0(sz10)),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

fof(c_0_51,plain,
    ! [X13,X14] :
      ( ~ aInteger0(X13)
      | ~ aInteger0(X14)
      | sdtpldt0(X13,X14) = sdtpldt0(X14,X13) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

cnf(c_0_52,negated_conjecture,
    ( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
    | ~ aDivisorOf0(xp,sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))))
    | ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20]),c_0_19])]) ).

cnf(c_0_53,plain,
    ( aInteger0(smndt0(X1))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_54,hypothesis,
    ( sdtpldt0(sz10,sdtpldt0(smndt0(sz10),X1)) = sdtpldt0(sz00,X1)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_49]),c_0_50]),c_0_19])]) ).

cnf(c_0_55,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_56,negated_conjecture,
    ( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
    | ~ aDivisorOf0(xp,sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_19])]) ).

cnf(c_0_57,hypothesis,
    ( sdtpldt0(sz10,sdtpldt0(X1,smndt0(sz10))) = sdtpldt0(sz00,X1)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_50])]) ).

fof(c_0_58,plain,
    ! [X15] :
      ( ( sdtpldt0(X15,sz00) = X15
        | ~ aInteger0(X15) )
      & ( X15 = sdtpldt0(sz00,X15)
        | ~ aInteger0(X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).

fof(c_0_59,plain,
    ! [X30,X31,X33,X34] :
      ( ( aInteger0(X31)
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( X31 != sz00
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( aInteger0(esk1_2(X30,X31))
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( sdtasdt0(X31,esk1_2(X30,X31)) = X30
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( ~ aInteger0(X33)
        | X33 = sz00
        | ~ aInteger0(X34)
        | sdtasdt0(X33,X34) != X30
        | aDivisorOf0(X33,X30)
        | ~ aInteger0(X30) ) ),
    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)],[mDivisor])])])])])]) ).

fof(c_0_60,plain,
    ! [X22] :
      ( ( sdtasdt0(X22,sz10) = X22
        | ~ aInteger0(X22) )
      & ( X22 = sdtasdt0(sz10,X22)
        | ~ aInteger0(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).

cnf(c_0_61,negated_conjecture,
    ( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
    | ~ aDivisorOf0(xp,sdtpldt0(sz00,xp))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_20])]) ).

cnf(c_0_62,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_63,plain,
    ( X1 = sz00
    | aDivisorOf0(X1,X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | sdtasdt0(X1,X2) != X3
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_64,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_65,negated_conjecture,
    ( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
    | ~ aDivisorOf0(xp,xp)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_20])]) ).

cnf(c_0_66,plain,
    ( X1 = sz00
    | aDivisorOf0(X1,X1)
    | ~ aInteger0(X1) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_19])])]) ).

cnf(c_0_67,negated_conjecture,
    ( sdtasdt0(xp,X1) != sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_20])]),c_0_21]) ).

cnf(c_0_68,negated_conjecture,
    ( sdtasdt0(xp,X1) != sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10)))
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_47]),c_0_50]),c_0_19])]) ).

cnf(c_0_69,negated_conjecture,
    ( sdtasdt0(xp,X1) != sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10)))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_53]),c_0_20])]) ).

cnf(c_0_70,hypothesis,
    ( sdtasdt0(xp,X1) != sdtpldt0(sz00,smndt0(xp))
    | ~ aInteger0(smndt0(xp))
    | ~ aInteger0(X1) ),
    inference(spm,[status(thm)],[c_0_69,c_0_57]) ).

fof(c_0_71,plain,
    ! [X27] :
      ( ( sdtasdt0(smndt0(sz10),X27) = smndt0(X27)
        | ~ aInteger0(X27) )
      & ( smndt0(X27) = sdtasdt0(X27,smndt0(sz10))
        | ~ aInteger0(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).

cnf(c_0_72,hypothesis,
    ( sdtasdt0(xp,X1) != sdtpldt0(sz00,smndt0(xp))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_53]),c_0_20])]) ).

cnf(c_0_73,plain,
    ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_74,hypothesis,
    sdtpldt0(sz00,smndt0(xp)) != smndt0(xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_50]),c_0_20])]) ).

cnf(c_0_75,hypothesis,
    ~ aInteger0(smndt0(xp)),
    inference(spm,[status(thm)],[c_0_74,c_0_62]) ).

cnf(c_0_76,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_53]),c_0_20])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM452+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
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 11:26:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.68  % Version  : CSE_E---1.5
% 0.20/0.68  % Problem  : theBenchmark.p
% 0.20/0.68  % Proof found
% 0.20/0.68  % SZS status Theorem for theBenchmark.p
% 0.20/0.68  % SZS output start Proof
% See solution above
% 0.20/0.69  % Total time : 0.094000 s
% 0.20/0.69  % SZS output end Proof
% 0.20/0.69  % Total time : 0.099000 s
%------------------------------------------------------------------------------