TSTP Solution File: NUM527+3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM527+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n020.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 08:55:10 EDT 2024

% Result   : Theorem 5.97s 1.20s
% Output   : CNFRefutation 5.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  101 (  33 unt;   0 def)
%            Number of atoms       :  375 ( 131 equ)
%            Maximal formula atoms :   28 (   3 avg)
%            Number of connectives :  438 ( 164   ~; 162   |;  87   &)
%                                         (   3 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-2 aty)
%            Number of variables   :  112 (   0 sgn  58   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
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/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mDefQuot) ).

fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mDefDiv) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mSortsB_02) ).

fof(m__2987,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & xn != sz00
    & xm != sz00
    & xp != sz00 ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m__2987) ).

fof(m__3046,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
    & doDivides0(xp,sdtasdt0(xn,xn))
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xn = sdtasdt0(xp,X1) )
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m__3046) ).

fof(m__3082,hypothesis,
    sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m__3082) ).

fof(m__,conjecture,
    ( ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xn,X1) = xm )
      & sdtlseqdt0(xn,xm) )
   => ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
      | sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m__) ).

fof(m__3059,hypothesis,
    ( aNaturalNumber0(xq)
    & xn = sdtasdt0(xp,xq)
    & xq = sdtsldt0(xn,xp) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m__3059) ).

fof(m__3014,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m__3014) ).

fof(mLETotal,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( X2 != X1
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mLETotal) ).

fof(mMonMul,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( X1 != sz00
          & X2 != X3
          & sdtlseqdt0(X2,X3) )
       => ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
          & sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
          & sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
          & sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mMonMul) ).

fof(mLETran,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mLETran) ).

fof(mSortsC_01,axiom,
    ( aNaturalNumber0(sz10)
    & sz10 != sz00 ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mSortsC_01) ).

fof(m_MulUnit,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m_MulUnit) ).

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mMulAsso) ).

fof(mLEAsym,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mLEAsym) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mMulComm) ).

fof(m_AddZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',m_AddZero) ).

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p',mSortsC) ).

fof(c_0_19,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_20,plain,
    ! [X65,X66,X68] :
      ( ( aNaturalNumber0(esk2_2(X65,X66))
        | ~ doDivides0(X65,X66)
        | ~ aNaturalNumber0(X65)
        | ~ aNaturalNumber0(X66) )
      & ( X66 = sdtasdt0(X65,esk2_2(X65,X66))
        | ~ doDivides0(X65,X66)
        | ~ aNaturalNumber0(X65)
        | ~ aNaturalNumber0(X66) )
      & ( ~ aNaturalNumber0(X68)
        | X66 != sdtasdt0(X65,X68)
        | doDivides0(X65,X66)
        | ~ aNaturalNumber0(X65)
        | ~ aNaturalNumber0(X66) ) ),
    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])])])])])]) ).

fof(c_0_21,plain,
    ! [X9,X10] :
      ( ~ aNaturalNumber0(X9)
      | ~ aNaturalNumber0(X10)
      | aNaturalNumber0(sdtasdt0(X9,X10)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).

fof(c_0_22,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & xn != sz00
    & xm != sz00
    & xp != sz00 ),
    inference(fof_simplification,[status(thm)],[m__2987]) ).

fof(c_0_23,plain,
    ! [X69,X70,X71] :
      ( ( aNaturalNumber0(X71)
        | X71 != sdtsldt0(X70,X69)
        | X69 = sz00
        | ~ doDivides0(X69,X70)
        | ~ aNaturalNumber0(X69)
        | ~ aNaturalNumber0(X70) )
      & ( X70 = sdtasdt0(X69,X71)
        | X71 != sdtsldt0(X70,X69)
        | X69 = sz00
        | ~ doDivides0(X69,X70)
        | ~ aNaturalNumber0(X69)
        | ~ aNaturalNumber0(X70) )
      & ( ~ aNaturalNumber0(X71)
        | X70 != sdtasdt0(X69,X71)
        | X71 = sdtsldt0(X70,X69)
        | X69 = sz00
        | ~ doDivides0(X69,X70)
        | ~ aNaturalNumber0(X69)
        | ~ aNaturalNumber0(X70) ) ),
    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_19])])])])]) ).

cnf(c_0_24,plain,
    ( doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_26,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & xn != sz00
    & xm != sz00
    & xp != sz00 ),
    inference(fof_nnf,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( X1 = sdtsldt0(X2,X3)
    | X3 = sz00
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_28,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).

fof(c_0_29,hypothesis,
    ( aNaturalNumber0(esk7_0)
    & sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
    & doDivides0(xp,sdtasdt0(xn,xn))
    & aNaturalNumber0(esk8_0)
    & xn = sdtasdt0(xp,esk8_0)
    & doDivides0(xp,xn) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__3046])]) ).

cnf(c_0_30,hypothesis,
    sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
    inference(split_conjunct,[status(thm)],[m__3082]) ).

cnf(c_0_31,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_32,negated_conjecture,
    ~ ( ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xn,X1) = xm )
        & sdtlseqdt0(xn,xm) )
     => ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
        | sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_33,plain,
    ( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
    | X1 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_25]),c_0_28]) ).

cnf(c_0_34,hypothesis,
    sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,hypothesis,
    aNaturalNumber0(esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_36,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_37,hypothesis,
    ( aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_31])]) ).

cnf(c_0_38,hypothesis,
    aNaturalNumber0(xq),
    inference(split_conjunct,[status(thm)],[m__3059]) ).

fof(c_0_39,negated_conjecture,
    ! [X104] :
      ( aNaturalNumber0(esk9_0)
      & sdtpldt0(xn,esk9_0) = xm
      & sdtlseqdt0(xn,xm)
      & ( ~ aNaturalNumber0(X104)
        | sdtpldt0(sdtasdt0(xn,xn),X104) != sdtasdt0(xm,xm) )
      & ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
    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_32])])])])]) ).

cnf(c_0_40,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(split_conjunct,[status(thm)],[m__3014]) ).

cnf(c_0_41,hypothesis,
    sdtsldt0(sdtasdt0(xn,xn),xp) = esk7_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_31]),c_0_35])]),c_0_36]) ).

cnf(c_0_42,hypothesis,
    aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_25]),c_0_38])]) ).

fof(c_0_43,plain,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( X2 != X1
          & sdtlseqdt0(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[mLETotal]) ).

fof(c_0_44,plain,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( X1 != sz00
          & X2 != X3
          & sdtlseqdt0(X2,X3) )
       => ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
          & sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
          & sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
          & sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
    inference(fof_simplification,[status(thm)],[mMonMul]) ).

cnf(c_0_45,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_46,hypothesis,
    sdtasdt0(xm,xm) = esk7_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_31])]),c_0_36]),c_0_41]),c_0_42])]) ).

fof(c_0_47,plain,
    ! [X50,X51] :
      ( ( X51 != X50
        | sdtlseqdt0(X50,X51)
        | ~ aNaturalNumber0(X50)
        | ~ aNaturalNumber0(X51) )
      & ( sdtlseqdt0(X51,X50)
        | sdtlseqdt0(X50,X51)
        | ~ aNaturalNumber0(X50)
        | ~ aNaturalNumber0(X51) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).

fof(c_0_48,plain,
    ! [X55,X56,X57] :
      ( ( sdtasdt0(X55,X56) != sdtasdt0(X55,X57)
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) )
      & ( sdtlseqdt0(sdtasdt0(X55,X56),sdtasdt0(X55,X57))
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) )
      & ( sdtasdt0(X56,X55) != sdtasdt0(X57,X55)
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) )
      & ( sdtlseqdt0(sdtasdt0(X56,X55),sdtasdt0(X57,X55))
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])]) ).

fof(c_0_49,plain,
    ! [X47,X48,X49] :
      ( ~ aNaturalNumber0(X47)
      | ~ aNaturalNumber0(X48)
      | ~ aNaturalNumber0(X49)
      | ~ sdtlseqdt0(X47,X48)
      | ~ sdtlseqdt0(X48,X49)
      | sdtlseqdt0(X47,X49) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).

cnf(c_0_50,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(xn,xn),esk7_0),
    inference(rw,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_51,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_52,hypothesis,
    aNaturalNumber0(sdtasdt0(xn,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_34]),c_0_35]),c_0_31])]) ).

cnf(c_0_53,plain,
    ( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
    | X1 = sz00
    | X2 = X3
    | ~ sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_54,negated_conjecture,
    sdtlseqdt0(xn,xm),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_55,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_56,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_57,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_58,negated_conjecture,
    sdtlseqdt0(esk7_0,sdtasdt0(xn,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_35])]) ).

cnf(c_0_59,negated_conjecture,
    ( xm = xn
    | X1 = sz00
    | sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xm))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56])]) ).

cnf(c_0_60,hypothesis,
    xm != sz00,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_61,plain,
    ( aNaturalNumber0(sz10)
    & sz10 != sz00 ),
    inference(fof_simplification,[status(thm)],[mSortsC_01]) ).

cnf(c_0_62,negated_conjecture,
    ( sdtlseqdt0(X1,sdtasdt0(xn,xn))
    | ~ sdtlseqdt0(X1,esk7_0)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_52]),c_0_35])]) ).

cnf(c_0_63,hypothesis,
    ( xm = xn
    | sdtlseqdt0(sdtasdt0(xm,xn),esk7_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_46]),c_0_55])]),c_0_60]) ).

fof(c_0_64,plain,
    ! [X22] :
      ( ( sdtasdt0(X22,sz10) = X22
        | ~ aNaturalNumber0(X22) )
      & ( X22 = sdtasdt0(sz10,X22)
        | ~ aNaturalNumber0(X22) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).

fof(c_0_65,plain,
    ! [X19,X20,X21] :
      ( ~ aNaturalNumber0(X19)
      | ~ aNaturalNumber0(X20)
      | ~ aNaturalNumber0(X21)
      | sdtasdt0(sdtasdt0(X19,X20),X21) = sdtasdt0(X19,sdtasdt0(X20,X21)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).

fof(c_0_66,plain,
    ( aNaturalNumber0(sz10)
    & sz10 != sz00 ),
    inference(fof_nnf,[status(thm)],[c_0_61]) ).

fof(c_0_67,plain,
    ! [X45,X46] :
      ( ~ aNaturalNumber0(X45)
      | ~ aNaturalNumber0(X46)
      | ~ sdtlseqdt0(X45,X46)
      | ~ sdtlseqdt0(X46,X45)
      | X45 = X46 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).

cnf(c_0_68,hypothesis,
    ( xm = xn
    | sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_69,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_70,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_71,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_72,hypothesis,
    xn = sdtasdt0(xp,xq),
    inference(split_conjunct,[status(thm)],[m__3059]) ).

cnf(c_0_73,plain,
    ( X1 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_74,hypothesis,
    ( xm = xn
    | sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_25]),c_0_56]),c_0_55])]) ).

cnf(c_0_75,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

fof(c_0_76,plain,
    ! [X17,X18] :
      ( ~ aNaturalNumber0(X17)
      | ~ aNaturalNumber0(X18)
      | sdtasdt0(X17,X18) = sdtasdt0(X18,X17) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).

cnf(c_0_77,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]),c_0_25]) ).

cnf(c_0_78,hypothesis,
    ( sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_72]),c_0_38]),c_0_31])]) ).

cnf(c_0_79,hypothesis,
    ( sdtasdt0(xm,xn) = sdtasdt0(xn,xn)
    | xm = xn
    | ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_52])]) ).

cnf(c_0_80,plain,
    ( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2))
    | X2 = sz00
    | X1 = X3
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_81,plain,
    ( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_75]),c_0_71])]) ).

cnf(c_0_82,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_76]) ).

cnf(c_0_83,hypothesis,
    sdtasdt0(xn,sz10) = xn,
    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_77,c_0_78]),c_0_72]),c_0_38]),c_0_31]),c_0_71])]) ).

fof(c_0_84,plain,
    ! [X16] :
      ( ( sdtpldt0(X16,sz00) = X16
        | ~ aNaturalNumber0(X16) )
      & ( X16 = sdtpldt0(sz00,X16)
        | ~ aNaturalNumber0(X16) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).

cnf(c_0_85,hypothesis,
    ( sdtasdt0(xm,xn) = sdtasdt0(xn,xn)
    | xm = xn
    | ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_25]),c_0_56]),c_0_55])]) ).

cnf(c_0_86,negated_conjecture,
    ( xm = xn
    | X1 = sz00
    | sdtlseqdt0(sdtasdt0(xn,X1),sdtasdt0(xm,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_54]),c_0_55]),c_0_56])]) ).

cnf(c_0_87,hypothesis,
    xn != sz00,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_88,plain,
    ( sdtsldt0(sdtasdt0(X1,sdtasdt0(X2,X3)),sdtasdt0(X1,X2)) = X3
    | sdtasdt0(X1,X2) = sz00
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_70]),c_0_25]) ).

cnf(c_0_89,hypothesis,
    sdtasdt0(sz10,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_34]),c_0_35]),c_0_31])]) ).

cnf(c_0_90,hypothesis,
    sdtasdt0(sz10,xn) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_71]),c_0_56])]) ).

cnf(c_0_91,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(sdtasdt0(xn,xn),X1) != sdtasdt0(xm,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_92,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_93,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_94,plain,
    ( sdtsldt0(sdtasdt0(X1,X2),X2) = X1
    | X2 = sz00
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_82]) ).

cnf(c_0_95,negated_conjecture,
    ( sdtasdt0(xm,xn) = sdtasdt0(xn,xn)
    | xm = xn ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_56])]),c_0_87]) ).

cnf(c_0_96,hypothesis,
    sdtsldt0(sdtasdt0(xn,xn),xn) = xn,
    inference(sr,[status(thm)],[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_88,c_0_89]),c_0_90]),c_0_90]),c_0_56]),c_0_71])]),c_0_87]) ).

cnf(c_0_97,negated_conjecture,
    sdtasdt0(xm,xm) != sdtasdt0(xn,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]),c_0_52])]) ).

cnf(c_0_98,negated_conjecture,
    xm = xn,
    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_94,c_0_95]),c_0_96]),c_0_56]),c_0_55])]),c_0_87]) ).

cnf(c_0_99,negated_conjecture,
    sdtasdt0(xn,xn) != esk7_0,
    inference(rw,[status(thm)],[c_0_97,c_0_46]) ).

cnf(c_0_100,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_98]),c_0_98]),c_0_99]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : NUM527+3 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n020.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 09:12:31 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.18/0.44  Running first-order theorem proving
% 0.18/0.44  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.BhKIYynu9Q/E---3.1_30341.p
% 5.97/1.20  # Version: 3.1.0
% 5.97/1.20  # Preprocessing class: FSLSSMSSSSSNFFN.
% 5.97/1.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.97/1.20  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.97/1.20  # Starting new_bool_3 with 300s (1) cores
% 5.97/1.20  # Starting new_bool_1 with 300s (1) cores
% 5.97/1.20  # Starting sh5l with 300s (1) cores
% 5.97/1.20  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 30420 completed with status 0
% 5.97/1.20  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 5.97/1.20  # Preprocessing class: FSLSSMSSSSSNFFN.
% 5.97/1.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.97/1.20  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.97/1.20  # No SInE strategy applied
% 5.97/1.20  # Search class: FGHSF-FSMM32-SFFFFFNN
% 5.97/1.20  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 5.97/1.20  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 811s (1) cores
% 5.97/1.20  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.97/1.20  # Starting new_bool_3 with 136s (1) cores
% 5.97/1.20  # Starting new_bool_1 with 136s (1) cores
% 5.97/1.20  # Starting sh5l with 136s (1) cores
% 5.97/1.20  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 30428 completed with status 0
% 5.97/1.20  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 5.97/1.20  # Preprocessing class: FSLSSMSSSSSNFFN.
% 5.97/1.20  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.97/1.20  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.97/1.20  # No SInE strategy applied
% 5.97/1.20  # Search class: FGHSF-FSMM32-SFFFFFNN
% 5.97/1.20  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 5.97/1.20  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 811s (1) cores
% 5.97/1.20  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.97/1.20  # Preprocessing time       : 0.002 s
% 5.97/1.20  # Presaturation interreduction done
% 5.97/1.20  
% 5.97/1.20  # Proof found!
% 5.97/1.20  # SZS status Theorem
% 5.97/1.20  # SZS output start CNFRefutation
% See solution above
% 5.97/1.20  # Parsed axioms                        : 47
% 5.97/1.20  # Removed by relevancy pruning/SinE    : 0
% 5.97/1.20  # Initial clauses                      : 104
% 5.97/1.20  # Removed in clause preprocessing      : 3
% 5.97/1.20  # Initial clauses in saturation        : 101
% 5.97/1.20  # Processed clauses                    : 4805
% 5.97/1.20  # ...of these trivial                  : 226
% 5.97/1.20  # ...subsumed                          : 2557
% 5.97/1.20  # ...remaining for further processing  : 2022
% 5.97/1.20  # Other redundant clauses eliminated   : 114
% 5.97/1.20  # Clauses deleted for lack of memory   : 0
% 5.97/1.20  # Backward-subsumed                    : 68
% 5.97/1.20  # Backward-rewritten                   : 618
% 5.97/1.20  # Generated clauses                    : 38450
% 5.97/1.20  # ...of the previous two non-redundant : 34196
% 5.97/1.20  # ...aggressively subsumed             : 0
% 5.97/1.20  # Contextual simplify-reflections      : 143
% 5.97/1.20  # Paramodulations                      : 38321
% 5.97/1.20  # Factorizations                       : 5
% 5.97/1.20  # NegExts                              : 0
% 5.97/1.20  # Equation resolutions                 : 122
% 5.97/1.20  # Disequality decompositions           : 0
% 5.97/1.20  # Total rewrite steps                  : 51421
% 5.97/1.20  # ...of those cached                   : 50850
% 5.97/1.20  # Propositional unsat checks           : 0
% 5.97/1.20  #    Propositional check models        : 0
% 5.97/1.20  #    Propositional check unsatisfiable : 0
% 5.97/1.20  #    Propositional clauses             : 0
% 5.97/1.20  #    Propositional clauses after purity: 0
% 5.97/1.20  #    Propositional unsat core size     : 0
% 5.97/1.20  #    Propositional preprocessing time  : 0.000
% 5.97/1.20  #    Propositional encoding time       : 0.000
% 5.97/1.20  #    Propositional solver time         : 0.000
% 5.97/1.20  #    Success case prop preproc time    : 0.000
% 5.97/1.20  #    Success case prop encoding time   : 0.000
% 5.97/1.20  #    Success case prop solver time     : 0.000
% 5.97/1.20  # Current number of processed clauses  : 1227
% 5.97/1.20  #    Positive orientable unit clauses  : 416
% 5.97/1.20  #    Positive unorientable unit clauses: 0
% 5.97/1.20  #    Negative unit clauses             : 226
% 5.97/1.20  #    Non-unit-clauses                  : 585
% 5.97/1.20  # Current number of unprocessed clauses: 28929
% 5.97/1.20  # ...number of literals in the above   : 124128
% 5.97/1.20  # Current number of archived formulas  : 0
% 5.97/1.20  # Current number of archived clauses   : 784
% 5.97/1.20  # Clause-clause subsumption calls (NU) : 74767
% 5.97/1.20  # Rec. Clause-clause subsumption calls : 29423
% 5.97/1.20  # Non-unit clause-clause subsumptions  : 1329
% 5.97/1.20  # Unit Clause-clause subsumption calls : 17922
% 5.97/1.20  # Rewrite failures with RHS unbound    : 0
% 5.97/1.20  # BW rewrite match attempts            : 167
% 5.97/1.20  # BW rewrite match successes           : 108
% 5.97/1.20  # Condensation attempts                : 0
% 5.97/1.20  # Condensation successes               : 0
% 5.97/1.20  # Termbank termtop insertions          : 728477
% 5.97/1.20  # Search garbage collected termcells   : 1695
% 5.97/1.20  
% 5.97/1.20  # -------------------------------------------------
% 5.97/1.20  # User time                : 0.721 s
% 5.97/1.20  # System time              : 0.021 s
% 5.97/1.20  # Total time               : 0.743 s
% 5.97/1.20  # Maximum resident set size: 2004 pages
% 5.97/1.20  
% 5.97/1.20  # -------------------------------------------------
% 5.97/1.20  # User time                : 3.649 s
% 5.97/1.20  # System time              : 0.051 s
% 5.97/1.20  # Total time               : 3.700 s
% 5.97/1.20  # Maximum resident set size: 1752 pages
% 5.97/1.20  % E---3.1 exiting
% 5.97/1.20  % E exiting
%------------------------------------------------------------------------------