TSTP Solution File: NUM454+6 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 10:37:39 EDT 2023

% Result   : Theorem 0.71s 0.78s
% Output   : CNFRefutation 0.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   70
% Syntax   : Number of formulae    :  147 (  42 unt;  54 typ;   0 def)
%            Number of atoms       :  302 ( 100 equ)
%            Maximal formula atoms :   44 (   3 avg)
%            Number of connectives :  305 (  96   ~;  94   |;  93   &)
%                                         (   4 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   4 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  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   44 (  44 usr;   9 con; 0-3 aty)
%            Number of variables   :   97 (   0 sgn;  58   !;   8   ?;   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,
    esk28_0: $i ).

tff(decl_75,type,
    esk29_0: $i ).

fof(m__,conjecture,
    ( sdtpldt0(sz10,xp) != smndt0(sz10)
    | sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mAddNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).

fof(mIntNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => aInteger0(smndt0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

fof(m__2232,hypothesis,
    ( ? [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/sandbox2/benchmark/theBenchmark.p',m__2232) ).

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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

fof(mIntOne,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).

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/sandbox2/benchmark/theBenchmark.p',m__2171) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

fof(mAddZero,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

fof(mIntMult,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => aInteger0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).

fof(mIntZero,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(mMulMinOne,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
        & smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3) )
     => sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).

fof(mDistrib,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3) )
     => ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).

fof(mZeroDiv,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => ( sdtasdt0(X1,X2) = sz00
       => ( X1 = sz00
          | X2 = sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).

fof(c_0_16,negated_conjecture,
    ~ ( sdtpldt0(sz10,xp) != smndt0(sz10)
      | sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_17,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_18,negated_conjecture,
    ( sdtpldt0(sz10,xp) = smndt0(sz10)
    & sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
    inference(fof_nnf,[status(thm)],[c_0_16]) ).

fof(c_0_19,plain,
    ! [X5] :
      ( ~ aInteger0(X5)
      | aInteger0(smndt0(X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).

fof(c_0_20,hypothesis,
    ( aInteger0(esk28_0)
    & sdtasdt0(xp,esk28_0) = 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))
    & aInteger0(esk29_0)
    & sdtasdt0(xp,esk29_0) = 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2232])]) ).

fof(c_0_21,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_22,plain,
    ( sz00 = sdtpldt0(smndt0(X1),X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    sdtpldt0(sz10,xp) = smndt0(sz10),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    aInteger0(sz10),
    inference(split_conjunct,[status(thm)],[mIntOne]) ).

cnf(c_0_25,plain,
    ( aInteger0(smndt0(X1))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,negated_conjecture,
    sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,hypothesis,
    sdtasdt0(xp,esk28_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_28,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]) ).

cnf(c_0_29,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,negated_conjecture,
    sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_31,negated_conjecture,
    aInteger0(sdtpldt0(sz10,xp)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_24])]) ).

cnf(c_0_32,hypothesis,
    sdtasdt0(xp,esk29_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_33,negated_conjecture,
    sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
    inference(rw,[status(thm)],[c_0_26,c_0_23]) ).

cnf(c_0_34,hypothesis,
    sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtasdt0(xp,esk28_0),
    inference(rw,[status(thm)],[c_0_27,c_0_23]) ).

fof(c_0_35,plain,
    ! [X20,X21] :
      ( ~ aInteger0(X20)
      | ~ aInteger0(X21)
      | sdtasdt0(X20,X21) = sdtasdt0(X21,X20) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

fof(c_0_36,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_28])])])])])]) ).

fof(c_0_37,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])])]) ).

cnf(c_0_38,negated_conjecture,
    ( sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(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_29,c_0_30]),c_0_24]),c_0_31])]) ).

cnf(c_0_39,plain,
    ( sdtpldt0(X1,smndt0(X1)) = sz00
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_40,hypothesis,
    sdtasdt0(xp,esk29_0) = sdtasdt0(xp,esk28_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_23]),c_0_34]) ).

cnf(c_0_41,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,hypothesis,
    aInteger0(xp),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_43,hypothesis,
    aInteger0(esk29_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_44,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_45,negated_conjecture,
    sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz00,sdtpldt0(sz10,xp)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_23]),c_0_23]),c_0_31]),c_0_24])]) ).

fof(c_0_46,plain,
    ! [X8,X9] :
      ( ~ aInteger0(X8)
      | ~ aInteger0(X9)
      | aInteger0(sdtasdt0(X8,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).

cnf(c_0_47,hypothesis,
    sdtasdt0(xp,esk28_0) = sdtasdt0(esk29_0,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).

cnf(c_0_48,hypothesis,
    aInteger0(esk28_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_49,negated_conjecture,
    sdtpldt0(sz00,sdtpldt0(sz10,xp)) = sdtpldt0(sz10,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_31])]) ).

cnf(c_0_50,plain,
    ( aInteger0(sdtasdt0(X1,X2))
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_51,hypothesis,
    sdtasdt0(esk29_0,xp) = sdtasdt0(esk28_0,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_47]),c_0_48]),c_0_42])]) ).

cnf(c_0_52,negated_conjecture,
    sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz10,xp),
    inference(rw,[status(thm)],[c_0_45,c_0_49]) ).

cnf(c_0_53,plain,
    aInteger0(sz00),
    inference(split_conjunct,[status(thm)],[mIntZero]) ).

fof(c_0_54,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_55,hypothesis,
    aInteger0(sdtasdt0(xp,esk28_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_40]),c_0_43]),c_0_42])]) ).

cnf(c_0_56,hypothesis,
    sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtasdt0(esk28_0,xp),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_47]),c_0_51]) ).

cnf(c_0_57,negated_conjecture,
    sdtpldt0(sz10,sdtpldt0(xp,sz00)) = sdtpldt0(sz10,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_52]),c_0_53]),c_0_42]),c_0_24])]) ).

cnf(c_0_58,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_59,hypothesis,
    aInteger0(sdtasdt0(esk28_0,xp)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_41]),c_0_48]),c_0_42])]) ).

cnf(c_0_60,hypothesis,
    sdtasdt0(esk28_0,xp) = sdtpldt0(sz00,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_38]),c_0_42])]) ).

cnf(c_0_61,negated_conjecture,
    sdtpldt0(sz10,sdtpldt0(sz00,xp)) = sdtpldt0(sz10,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_53]),c_0_42])]) ).

cnf(c_0_62,hypothesis,
    aInteger0(sdtpldt0(sz00,xp)),
    inference(rw,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_63,negated_conjecture,
    sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_61]),c_0_34]),c_0_47]),c_0_51]),c_0_60]),c_0_62])]) ).

cnf(c_0_64,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_65,negated_conjecture,
    sdtpldt0(sz00,xp) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_42])]) ).

fof(c_0_66,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_67,hypothesis,
    sdtasdt0(xp,esk29_0) = sdtasdt0(esk29_0,xp),
    inference(rw,[status(thm)],[c_0_40,c_0_47]) ).

cnf(c_0_68,negated_conjecture,
    ( sdtpldt0(sz00,smndt0(xp)) = xp
    | ~ aInteger0(smndt0(xp)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_33]),c_0_34]),c_0_47]),c_0_51]),c_0_60]),c_0_65]) ).

fof(c_0_69,plain,
    ! [X17,X18,X19] :
      ( ~ aInteger0(X17)
      | ~ aInteger0(X18)
      | ~ aInteger0(X19)
      | sdtasdt0(X17,sdtasdt0(X18,X19)) = sdtasdt0(sdtasdt0(X17,X18),X19) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).

cnf(c_0_70,plain,
    ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_71,hypothesis,
    sdtasdt0(xp,esk29_0) = sdtasdt0(esk28_0,xp),
    inference(rw,[status(thm)],[c_0_67,c_0_51]) ).

cnf(c_0_72,negated_conjecture,
    sdtpldt0(sz00,smndt0(xp)) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_25]),c_0_42])]) ).

cnf(c_0_73,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_74,plain,
    ( sdtasdt0(sdtpldt0(sz10,xp),X1) = smndt0(X1)
    | ~ aInteger0(X1) ),
    inference(rw,[status(thm)],[c_0_70,c_0_23]) ).

cnf(c_0_75,hypothesis,
    sdtasdt0(xp,esk29_0) = sdtpldt0(sz00,xp),
    inference(rw,[status(thm)],[c_0_71,c_0_60]) ).

cnf(c_0_76,negated_conjecture,
    ( smndt0(xp) = xp
    | ~ aInteger0(smndt0(xp)) ),
    inference(spm,[status(thm)],[c_0_64,c_0_72]) ).

fof(c_0_77,plain,
    ! [X23,X24,X25] :
      ( ( sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25))
        | ~ aInteger0(X23)
        | ~ aInteger0(X24)
        | ~ aInteger0(X25) )
      & ( sdtasdt0(sdtpldt0(X23,X24),X25) = sdtpldt0(sdtasdt0(X23,X25),sdtasdt0(X24,X25))
        | ~ aInteger0(X23)
        | ~ aInteger0(X24)
        | ~ aInteger0(X25) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).

cnf(c_0_78,plain,
    ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_79,plain,
    ( sdtasdt0(sdtpldt0(sz10,xp),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2)
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_31])]) ).

cnf(c_0_80,hypothesis,
    sdtasdt0(xp,esk29_0) = xp,
    inference(rw,[status(thm)],[c_0_75,c_0_65]) ).

cnf(c_0_81,negated_conjecture,
    smndt0(xp) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_25]),c_0_42])]) ).

cnf(c_0_82,plain,
    ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_83,plain,
    ( sdtasdt0(X1,sdtpldt0(sz10,xp)) = smndt0(X1)
    | ~ aInteger0(X1) ),
    inference(rw,[status(thm)],[c_0_78,c_0_23]) ).

cnf(c_0_84,hypothesis,
    sdtasdt0(sdtpldt0(sz10,xp),xp) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_80]),c_0_43]),c_0_42])]) ).

fof(c_0_85,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_86,plain,
    ( sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,sdtpldt0(sz10,xp)))
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_31])]) ).

cnf(c_0_87,hypothesis,
    sdtasdt0(xp,sdtpldt0(sz10,xp)) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_84]),c_0_42]),c_0_31])]) ).

cnf(c_0_88,negated_conjecture,
    sdtpldt0(xp,xp) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_81]),c_0_42])]) ).

cnf(c_0_89,plain,
    ( X1 = sz00
    | X2 = sz00
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | sdtasdt0(X1,X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_90,hypothesis,
    sdtasdt0(xp,xp) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_81]),c_0_88]),c_0_34]),c_0_47]),c_0_51]),c_0_60]),c_0_65]),c_0_31]),c_0_42])]) ).

cnf(c_0_91,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_92,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_42])]),c_0_91]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Aug 25 08:47:08 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.71/0.78  % Version  : CSE_E---1.5
% 0.71/0.78  % Problem  : theBenchmark.p
% 0.71/0.78  % Proof found
% 0.71/0.78  % SZS status Theorem for theBenchmark.p
% 0.71/0.78  % SZS output start Proof
% See solution above
% 0.71/0.79  % Total time : 0.187000 s
% 0.71/0.79  % SZS output end Proof
% 0.71/0.79  % Total time : 0.192000 s
%------------------------------------------------------------------------------