TSTP Solution File: NUM511+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM511+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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 : Sat May  4 08:55:04 EDT 2024

% Result   : Theorem 25.63s 3.68s
% Output   : CNFRefutation 25.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   66 (  27 unt;   0 def)
%            Number of atoms       :  230 (  80 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  269 ( 105   ~; 107   |;  35   &)
%                                         (   5 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   70 (   2 sgn  37   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mDefPrime,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( isPrime0(X1)
      <=> ( X1 != sz00
          & X1 != sz10
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & doDivides0(X2,X1) )
             => ( X2 = sz10
                | X2 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',mDefPrime) ).

fof(mDefQuot,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != sz00
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( X3 = sdtsldt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & X2 = sdtasdt0(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',mDefQuot) ).

fof(m__1860,hypothesis,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',m__1860) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',m__1837) ).

fof(mDivAsso,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != sz00
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( aNaturalNumber0(X3)
           => sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',mDivAsso) ).

fof(m__2306,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',m__2306) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',mSortsB_02) ).

fof(m__2342,hypothesis,
    ( aNaturalNumber0(xr)
    & doDivides0(xr,xk)
    & isPrime0(xr) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',m__2342) ).

fof(m__2487,hypothesis,
    doDivides0(xr,xn),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',m__2487) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',mMulComm) ).

fof(m__,conjecture,
    doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',m__) ).

fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p',mDefDiv) ).

fof(c_0_12,plain,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( isPrime0(X1)
      <=> ( X1 != sz00
          & X1 != sz10
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & doDivides0(X2,X1) )
             => ( X2 = sz10
                | X2 = X1 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[mDefPrime]) ).

fof(c_0_13,plain,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != sz00
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( X3 = sdtsldt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & X2 = sdtasdt0(X1,X3) ) ) ) ),
    inference(fof_simplification,[status(thm)],[mDefQuot]) ).

fof(c_0_14,plain,
    ! [X84,X85] :
      ( ( X84 != sz00
        | ~ isPrime0(X84)
        | ~ aNaturalNumber0(X84) )
      & ( X84 != sz10
        | ~ isPrime0(X84)
        | ~ aNaturalNumber0(X84) )
      & ( ~ aNaturalNumber0(X85)
        | ~ doDivides0(X85,X84)
        | X85 = sz10
        | X85 = X84
        | ~ isPrime0(X84)
        | ~ aNaturalNumber0(X84) )
      & ( aNaturalNumber0(esk3_1(X84))
        | X84 = sz00
        | X84 = sz10
        | isPrime0(X84)
        | ~ aNaturalNumber0(X84) )
      & ( doDivides0(esk3_1(X84),X84)
        | X84 = sz00
        | X84 = sz10
        | isPrime0(X84)
        | ~ aNaturalNumber0(X84) )
      & ( esk3_1(X84) != sz10
        | X84 = sz00
        | X84 = sz10
        | isPrime0(X84)
        | ~ aNaturalNumber0(X84) )
      & ( esk3_1(X84) != X84
        | X84 = sz00
        | X84 = sz10
        | isPrime0(X84)
        | ~ aNaturalNumber0(X84) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])])]) ).

fof(c_0_15,plain,
    ! [X67,X68,X69] :
      ( ( aNaturalNumber0(X69)
        | X69 != sdtsldt0(X68,X67)
        | X67 = sz00
        | ~ doDivides0(X67,X68)
        | ~ aNaturalNumber0(X67)
        | ~ aNaturalNumber0(X68) )
      & ( X68 = sdtasdt0(X67,X69)
        | X69 != sdtsldt0(X68,X67)
        | X67 = sz00
        | ~ doDivides0(X67,X68)
        | ~ aNaturalNumber0(X67)
        | ~ aNaturalNumber0(X68) )
      & ( ~ aNaturalNumber0(X69)
        | X68 != sdtasdt0(X67,X69)
        | X69 = sdtsldt0(X68,X67)
        | X67 = sz00
        | ~ doDivides0(X67,X68)
        | ~ aNaturalNumber0(X67)
        | ~ aNaturalNumber0(X68) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).

cnf(c_0_16,plain,
    ( X1 != sz00
    | ~ isPrime0(X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,hypothesis,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_18,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_19,plain,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != sz00
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( aNaturalNumber0(X3)
           => sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
    inference(fof_simplification,[status(thm)],[mDivAsso]) ).

cnf(c_0_20,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X2 = sz00
    | X3 != sdtsldt0(X1,X2)
    | ~ doDivides0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_22,hypothesis,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_23,hypothesis,
    xp != sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).

fof(c_0_24,plain,
    ! [X7,X8] :
      ( ~ aNaturalNumber0(X7)
      | ~ aNaturalNumber0(X8)
      | aNaturalNumber0(sdtasdt0(X7,X8)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).

cnf(c_0_25,plain,
    ( aNaturalNumber0(X1)
    | X3 = sz00
    | X1 != sdtsldt0(X2,X3)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_26,plain,
    ! [X81,X82,X83] :
      ( ~ aNaturalNumber0(X81)
      | ~ aNaturalNumber0(X82)
      | X81 = sz00
      | ~ doDivides0(X81,X82)
      | ~ aNaturalNumber0(X83)
      | sdtasdt0(X83,sdtsldt0(X82,X81)) = sdtsldt0(sdtasdt0(X83,X82),X81) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).

cnf(c_0_27,hypothesis,
    isPrime0(xr),
    inference(split_conjunct,[status(thm)],[m__2342]) ).

cnf(c_0_28,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[m__2342]) ).

cnf(c_0_29,hypothesis,
    ( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
    | X1 != xk
    | ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_18])]),c_0_23]) ).

cnf(c_0_30,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_32,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_33,hypothesis,
    ( aNaturalNumber0(X1)
    | X1 != xk
    | ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_22]),c_0_18])]),c_0_23]) ).

cnf(c_0_34,plain,
    ( X1 = sz00
    | sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_35,hypothesis,
    doDivides0(xr,xn),
    inference(split_conjunct,[status(thm)],[m__2487]) ).

cnf(c_0_36,hypothesis,
    xr != sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_27]),c_0_28])]) ).

fof(c_0_37,plain,
    ! [X15,X16] :
      ( ~ aNaturalNumber0(X15)
      | ~ aNaturalNumber0(X16)
      | sdtasdt0(X15,X16) = sdtasdt0(X16,X15) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).

cnf(c_0_38,hypothesis,
    ( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
    | X1 != xk ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).

cnf(c_0_39,hypothesis,
    ( aNaturalNumber0(X1)
    | X1 != xk ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_31]),c_0_32])]) ).

cnf(c_0_40,hypothesis,
    ( sdtsldt0(sdtasdt0(X1,xn),xr) = sdtasdt0(X1,sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_32]),c_0_28])]),c_0_36]) ).

cnf(c_0_41,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

fof(c_0_42,negated_conjecture,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_43,hypothesis,
    ( aNaturalNumber0(sdtasdt0(xn,xm))
    | X1 != xk ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_38]),c_0_18])]),c_0_39]) ).

cnf(c_0_44,hypothesis,
    ( sdtsldt0(sdtasdt0(xn,X1),xr) = sdtasdt0(X1,sdtsldt0(xn,xr))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32])]) ).

cnf(c_0_45,hypothesis,
    ( sdtasdt0(xn,xm) = sdtasdt0(X1,xp)
    | X1 != xk ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_18])]),c_0_39]) ).

fof(c_0_46,negated_conjecture,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    inference(fof_nnf,[status(thm)],[c_0_42]) ).

cnf(c_0_47,plain,
    ( X1 = sz00
    | aNaturalNumber0(sdtsldt0(X2,X1))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[c_0_25]) ).

cnf(c_0_48,hypothesis,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(er,[status(thm)],[c_0_43]) ).

cnf(c_0_49,hypothesis,
    ( sdtsldt0(sdtasdt0(X1,xp),xr) = sdtasdt0(xm,sdtsldt0(xn,xr))
    | X1 != xk ),
    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,negated_conjecture,
    ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_51,hypothesis,
    doDivides0(xr,xk),
    inference(split_conjunct,[status(thm)],[m__2342]) ).

cnf(c_0_52,hypothesis,
    aNaturalNumber0(xk),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_22]),c_0_21]),c_0_18]),c_0_48])]),c_0_23]) ).

cnf(c_0_53,hypothesis,
    ( sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xm,sdtsldt0(xn,xr))
    | X1 != xk ),
    inference(spm,[status(thm)],[c_0_49,c_0_45]) ).

cnf(c_0_54,negated_conjecture,
    ( ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr)))
    | ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_31])]) ).

cnf(c_0_55,hypothesis,
    aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_28]),c_0_32])]),c_0_36]) ).

cnf(c_0_56,hypothesis,
    ( sdtsldt0(sdtasdt0(X1,xk),xr) = sdtasdt0(X1,sdtsldt0(xk,xr))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_51]),c_0_28])]),c_0_36]),c_0_52])]) ).

cnf(c_0_57,hypothesis,
    sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xm,sdtsldt0(xn,xr)),
    inference(er,[status(thm)],[c_0_53]) ).

fof(c_0_58,plain,
    ! [X63,X64,X66] :
      ( ( aNaturalNumber0(esk2_2(X63,X64))
        | ~ doDivides0(X63,X64)
        | ~ aNaturalNumber0(X63)
        | ~ aNaturalNumber0(X64) )
      & ( X64 = sdtasdt0(X63,esk2_2(X63,X64))
        | ~ doDivides0(X63,X64)
        | ~ aNaturalNumber0(X63)
        | ~ aNaturalNumber0(X64) )
      & ( ~ aNaturalNumber0(X66)
        | X64 != sdtasdt0(X63,X66)
        | doDivides0(X63,X64)
        | ~ aNaturalNumber0(X63)
        | ~ aNaturalNumber0(X64) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])])]) ).

cnf(c_0_59,negated_conjecture,
    ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).

cnf(c_0_60,hypothesis,
    sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(xp,sdtsldt0(xk,xr)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_38]),c_0_57]),c_0_18])]) ).

cnf(c_0_61,plain,
    ( doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_62,negated_conjecture,
    ~ doDivides0(xp,sdtasdt0(xp,sdtsldt0(xk,xr))),
    inference(rw,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_63,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_61]),c_0_30]) ).

cnf(c_0_64,hypothesis,
    aNaturalNumber0(sdtsldt0(xk,xr)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_51]),c_0_28])]),c_0_36]),c_0_52])]) ).

cnf(c_0_65,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_18]),c_0_64])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : NUM511+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n002.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Fri May  3 09:41:57 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.m4l2yF3dwF/E---3.1_28724.p
% 25.63/3.68  # Version: 3.1.0
% 25.63/3.68  # Preprocessing class: FSLSSMSSSSSNFFN.
% 25.63/3.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.63/3.68  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 25.63/3.68  # Starting new_bool_3 with 300s (1) cores
% 25.63/3.68  # Starting new_bool_1 with 300s (1) cores
% 25.63/3.68  # Starting sh5l with 300s (1) cores
% 25.63/3.68  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 28803 completed with status 0
% 25.63/3.68  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 25.63/3.68  # Preprocessing class: FSLSSMSSSSSNFFN.
% 25.63/3.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.63/3.68  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 25.63/3.68  # No SInE strategy applied
% 25.63/3.68  # Search class: FGHSF-FFMM21-SFFFFFNN
% 25.63/3.68  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 25.63/3.68  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 25.63/3.68  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 25.63/3.68  # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 25.63/3.68  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 25.63/3.68  # Starting G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 25.63/3.68  # G-E--_208_C18_F1_AE_CS_SP_PS_S3S with pid 28809 completed with status 0
% 25.63/3.68  # Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S3S
% 25.63/3.68  # Preprocessing class: FSLSSMSSSSSNFFN.
% 25.63/3.68  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.63/3.68  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 25.63/3.68  # No SInE strategy applied
% 25.63/3.68  # Search class: FGHSF-FFMM21-SFFFFFNN
% 25.63/3.68  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 25.63/3.68  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 25.63/3.68  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 25.63/3.68  # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 25.63/3.68  # Preprocessing time       : 0.002 s
% 25.63/3.68  # Presaturation interreduction done
% 25.63/3.68  
% 25.63/3.68  # Proof found!
% 25.63/3.68  # SZS status Theorem
% 25.63/3.68  # SZS output start CNFRefutation
% See solution above
% 25.63/3.68  # Parsed axioms                        : 54
% 25.63/3.68  # Removed by relevancy pruning/SinE    : 0
% 25.63/3.68  # Initial clauses                      : 99
% 25.63/3.68  # Removed in clause preprocessing      : 3
% 25.63/3.68  # Initial clauses in saturation        : 96
% 25.63/3.68  # Processed clauses                    : 14723
% 25.63/3.68  # ...of these trivial                  : 453
% 25.63/3.68  # ...subsumed                          : 11041
% 25.63/3.68  # ...remaining for further processing  : 3229
% 25.63/3.68  # Other redundant clauses eliminated   : 546
% 25.63/3.68  # Clauses deleted for lack of memory   : 0
% 25.63/3.68  # Backward-subsumed                    : 957
% 25.63/3.68  # Backward-rewritten                   : 409
% 25.63/3.68  # Generated clauses                    : 145110
% 25.63/3.68  # ...of the previous two non-redundant : 137641
% 25.63/3.68  # ...aggressively subsumed             : 0
% 25.63/3.68  # Contextual simplify-reflections      : 698
% 25.63/3.68  # Paramodulations                      : 144344
% 25.63/3.68  # Factorizations                       : 12
% 25.63/3.68  # NegExts                              : 0
% 25.63/3.68  # Equation resolutions                 : 717
% 25.63/3.68  # Disequality decompositions           : 0
% 25.63/3.68  # Total rewrite steps                  : 143408
% 25.63/3.68  # ...of those cached                   : 143143
% 25.63/3.68  # Propositional unsat checks           : 0
% 25.63/3.68  #    Propositional check models        : 0
% 25.63/3.68  #    Propositional check unsatisfiable : 0
% 25.63/3.68  #    Propositional clauses             : 0
% 25.63/3.68  #    Propositional clauses after purity: 0
% 25.63/3.68  #    Propositional unsat core size     : 0
% 25.63/3.68  #    Propositional preprocessing time  : 0.000
% 25.63/3.68  #    Propositional encoding time       : 0.000
% 25.63/3.68  #    Propositional solver time         : 0.000
% 25.63/3.68  #    Success case prop preproc time    : 0.000
% 25.63/3.68  #    Success case prop encoding time   : 0.000
% 25.63/3.68  #    Success case prop solver time     : 0.000
% 25.63/3.68  # Current number of processed clauses  : 1737
% 25.63/3.68  #    Positive orientable unit clauses  : 253
% 25.63/3.68  #    Positive unorientable unit clauses: 0
% 25.63/3.68  #    Negative unit clauses             : 156
% 25.63/3.68  #    Non-unit-clauses                  : 1328
% 25.63/3.68  # Current number of unprocessed clauses: 121563
% 25.63/3.68  # ...number of literals in the above   : 704941
% 25.63/3.68  # Current number of archived formulas  : 0
% 25.63/3.68  # Current number of archived clauses   : 1491
% 25.63/3.68  # Clause-clause subsumption calls (NU) : 1159213
% 25.63/3.68  # Rec. Clause-clause subsumption calls : 313331
% 25.63/3.68  # Non-unit clause-clause subsumptions  : 5036
% 25.63/3.68  # Unit Clause-clause subsumption calls : 52393
% 25.63/3.68  # Rewrite failures with RHS unbound    : 0
% 25.63/3.68  # BW rewrite match attempts            : 91
% 25.63/3.68  # BW rewrite match successes           : 91
% 25.63/3.68  # Condensation attempts                : 0
% 25.63/3.68  # Condensation successes               : 0
% 25.63/3.68  # Termbank termtop insertions          : 3172424
% 25.63/3.68  # Search garbage collected termcells   : 1364
% 25.63/3.68  
% 25.63/3.68  # -------------------------------------------------
% 25.63/3.68  # User time                : 3.092 s
% 25.63/3.68  # System time              : 0.098 s
% 25.63/3.68  # Total time               : 3.190 s
% 25.63/3.68  # Maximum resident set size: 1968 pages
% 25.63/3.68  
% 25.63/3.68  # -------------------------------------------------
% 25.63/3.68  # User time                : 15.477 s
% 25.63/3.68  # System time              : 0.448 s
% 25.63/3.68  # Total time               : 15.924 s
% 25.63/3.68  # Maximum resident set size: 1752 pages
% 25.63/3.68  % E---3.1 exiting
% 25.63/3.68  % E exiting
%------------------------------------------------------------------------------