TSTP Solution File: NUM454+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM454+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n010.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 : Tue May 21 01:14:02 EDT 2024

% Result   : Theorem 1.54s 0.74s
% Output   : CNFRefutation 1.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   85 (  27 unt;   0 def)
%            Number of atoms       :  310 ( 109 equ)
%            Maximal formula atoms :   46 (   3 avg)
%            Number of connectives :  363 ( 138   ~; 146   |;  55   &)
%                                         (   8 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-3 aty)
%            Number of variables   :  113 (   0 sgn  65   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mArSeq,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & X2 != sz00 )
     => ! [X3] :
          ( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aInteger0(X4)
                  & sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).

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

fof(m__2171,hypothesis,
    ( aInteger0(xp)
    & xp != sz00
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).

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

fof(m__2232,hypothesis,
    ( aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).

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

fof(mEquMod,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
      <=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).

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

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

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

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(c_0_16,plain,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & X2 != sz00 )
     => ! [X3] :
          ( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aInteger0(X4)
                  & sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[mArSeq]) ).

fof(c_0_17,negated_conjecture,
    ~ ( sdtpldt0(sz10,xp) != smndt0(sz10)
      | sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

fof(c_0_18,plain,
    ! [X96,X97,X98,X99,X100,X101] :
      ( ( aSet0(X98)
        | X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
        | ~ aInteger0(X96)
        | ~ aInteger0(X97)
        | X97 = sz00 )
      & ( aInteger0(X99)
        | ~ aElementOf0(X99,X98)
        | X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
        | ~ aInteger0(X96)
        | ~ aInteger0(X97)
        | X97 = sz00 )
      & ( sdteqdtlpzmzozddtrp0(X99,X96,X97)
        | ~ aElementOf0(X99,X98)
        | X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
        | ~ aInteger0(X96)
        | ~ aInteger0(X97)
        | X97 = sz00 )
      & ( ~ aInteger0(X100)
        | ~ sdteqdtlpzmzozddtrp0(X100,X96,X97)
        | aElementOf0(X100,X98)
        | X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
        | ~ aInteger0(X96)
        | ~ aInteger0(X97)
        | X97 = sz00 )
      & ( ~ aElementOf0(esk11_3(X96,X97,X101),X101)
        | ~ aInteger0(esk11_3(X96,X97,X101))
        | ~ sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97)
        | ~ aSet0(X101)
        | X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
        | ~ aInteger0(X96)
        | ~ aInteger0(X97)
        | X97 = sz00 )
      & ( aInteger0(esk11_3(X96,X97,X101))
        | aElementOf0(esk11_3(X96,X97,X101),X101)
        | ~ aSet0(X101)
        | X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
        | ~ aInteger0(X96)
        | ~ aInteger0(X97)
        | X97 = sz00 )
      & ( sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97)
        | aElementOf0(esk11_3(X96,X97,X101),X101)
        | ~ aSet0(X101)
        | X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
        | ~ aInteger0(X96)
        | ~ aInteger0(X97)
        | X97 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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_16])])])])])])]) ).

fof(c_0_19,hypothesis,
    ( aInteger0(xp)
    & xp != sz00
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    inference(fof_simplification,[status(thm)],[m__2171]) ).

fof(c_0_20,plain,
    ! [X17] :
      ( ( sdtpldt0(X17,smndt0(X17)) = sz00
        | ~ aInteger0(X17) )
      & ( sz00 = sdtpldt0(smndt0(X17),X17)
        | ~ aInteger0(X17) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).

fof(c_0_21,negated_conjecture,
    ( sdtpldt0(sz10,xp) = smndt0(sz10)
    & sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
    inference(fof_nnf,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ( aInteger0(X1)
    | X4 = sz00
    | ~ aElementOf0(X1,X2)
    | X2 != szAzrzSzezqlpdtcmdtrp0(X3,X4)
    | ~ aInteger0(X3)
    | ~ aInteger0(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_23,hypothesis,
    ( aInteger0(xp)
    & xp != sz00
    & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
    inference(fof_nnf,[status(thm)],[c_0_19]) ).

fof(c_0_24,plain,
    ! [X11,X12,X13] :
      ( ~ aInteger0(X11)
      | ~ aInteger0(X12)
      | ~ aInteger0(X13)
      | sdtpldt0(X11,sdtpldt0(X12,X13)) = sdtpldt0(sdtpldt0(X11,X12),X13) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).

cnf(c_0_25,plain,
    ( sz00 = sdtpldt0(smndt0(X1),X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    sdtpldt0(sz10,xp) = smndt0(sz10),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,plain,
    aInteger0(sz10),
    inference(split_conjunct,[status(thm)],[mIntOne]) ).

cnf(c_0_28,plain,
    ( X1 = sz00
    | aInteger0(X2)
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
    | ~ aInteger0(X1)
    | ~ aInteger0(X3) ),
    inference(er,[status(thm)],[c_0_22]) ).

cnf(c_0_29,hypothesis,
    aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
    inference(split_conjunct,[status(thm)],[m__2232]) ).

cnf(c_0_30,hypothesis,
    aInteger0(xp),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_31,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_32,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,negated_conjecture,
    sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_34,hypothesis,
    aInteger0(sdtpldt0(sz10,xp)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_27])]),c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_36,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_32,c_0_33]),c_0_27]),c_0_34])]) ).

cnf(c_0_37,negated_conjecture,
    sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
    inference(rw,[status(thm)],[c_0_35,c_0_26]) ).

fof(c_0_38,plain,
    ! [X6] :
      ( ~ aInteger0(X6)
      | aInteger0(smndt0(X6)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).

fof(c_0_39,plain,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
      <=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
    inference(fof_simplification,[status(thm)],[mEquMod]) ).

cnf(c_0_40,plain,
    ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | X3 = sz00
    | ~ aElementOf0(X1,X4)
    | X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_41,negated_conjecture,
    ( sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,smndt0(xp))
    | ~ aInteger0(smndt0(xp)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_42,plain,
    ( aInteger0(smndt0(X1))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

fof(c_0_43,plain,
    ! [X36,X37,X38] :
      ( ( ~ sdteqdtlpzmzozddtrp0(X36,X37,X38)
        | aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37)))
        | ~ aInteger0(X36)
        | ~ aInteger0(X37)
        | ~ aInteger0(X38)
        | X38 = sz00 )
      & ( ~ aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37)))
        | sdteqdtlpzmzozddtrp0(X36,X37,X38)
        | ~ aInteger0(X36)
        | ~ aInteger0(X37)
        | ~ aInteger0(X38)
        | X38 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).

cnf(c_0_44,plain,
    ( X1 = sz00
    | sdteqdtlpzmzozddtrp0(X2,X3,X1)
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
    | ~ aInteger0(X1)
    | ~ aInteger0(X3) ),
    inference(er,[status(thm)],[c_0_40]) ).

fof(c_0_45,plain,
    ! [X16] :
      ( ( sdtpldt0(X16,sz00) = X16
        | ~ aInteger0(X16) )
      & ( X16 = sdtpldt0(sz00,X16)
        | ~ aInteger0(X16) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).

cnf(c_0_46,negated_conjecture,
    sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,smndt0(xp)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_30])]) ).

cnf(c_0_47,plain,
    ( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
    | X3 = sz00
    | ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_48,hypothesis,
    sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_30]),c_0_27])]),c_0_31]) ).

cnf(c_0_49,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_50,negated_conjecture,
    sdtpldt0(sz00,smndt0(xp)) = sdtpldt0(sz00,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_46]),c_0_30])]) ).

fof(c_0_51,plain,
    ! [X28] :
      ( ( sdtasdt0(smndt0(sz10),X28) = smndt0(X28)
        | ~ aInteger0(X28) )
      & ( smndt0(X28) = sdtasdt0(X28,smndt0(sz10))
        | ~ aInteger0(X28) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).

fof(c_0_52,plain,
    ! [X1] :
      ( aInteger0(X1)
     => ! [X2] :
          ( aDivisorOf0(X2,X1)
        <=> ( aInteger0(X2)
            & X2 != sz00
            & ? [X3] :
                ( aInteger0(X3)
                & sdtasdt0(X2,X3) = X1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mDivisor]) ).

cnf(c_0_53,hypothesis,
    aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp))),
    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_47,c_0_48]),c_0_26]),c_0_30]),c_0_27]),c_0_34])]),c_0_31]) ).

cnf(c_0_54,negated_conjecture,
    ( smndt0(xp) = sdtpldt0(sz00,xp)
    | ~ aInteger0(smndt0(xp)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

fof(c_0_55,plain,
    ! [X18,X19,X20] :
      ( ~ aInteger0(X18)
      | ~ aInteger0(X19)
      | ~ aInteger0(X20)
      | sdtasdt0(X18,sdtasdt0(X19,X20)) = sdtasdt0(sdtasdt0(X18,X19),X20) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).

cnf(c_0_56,plain,
    ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

fof(c_0_57,plain,
    ! [X31,X32,X34,X35] :
      ( ( aInteger0(X32)
        | ~ aDivisorOf0(X32,X31)
        | ~ aInteger0(X31) )
      & ( X32 != sz00
        | ~ aDivisorOf0(X32,X31)
        | ~ aInteger0(X31) )
      & ( aInteger0(esk1_2(X31,X32))
        | ~ aDivisorOf0(X32,X31)
        | ~ aInteger0(X31) )
      & ( sdtasdt0(X32,esk1_2(X31,X32)) = X31
        | ~ aDivisorOf0(X32,X31)
        | ~ aInteger0(X31) )
      & ( ~ aInteger0(X34)
        | X34 = sz00
        | ~ aInteger0(X35)
        | sdtasdt0(X34,X35) != X31
        | aDivisorOf0(X34,X31)
        | ~ aInteger0(X31) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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_52])])])])])])]) ).

cnf(c_0_58,hypothesis,
    aDivisorOf0(xp,sdtpldt0(sz00,xp)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_46]),c_0_50]) ).

cnf(c_0_59,negated_conjecture,
    smndt0(xp) = sdtpldt0(sz00,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_30])]) ).

cnf(c_0_60,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_61,plain,
    ( sdtasdt0(sdtpldt0(sz10,xp),X1) = smndt0(X1)
    | ~ aInteger0(X1) ),
    inference(rw,[status(thm)],[c_0_56,c_0_26]) ).

cnf(c_0_62,plain,
    ( sdtasdt0(X1,esk1_2(X2,X1)) = X2
    | ~ aDivisorOf0(X1,X2)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_63,hypothesis,
    aDivisorOf0(xp,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_30])]) ).

cnf(c_0_64,negated_conjecture,
    sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
    inference(rw,[status(thm)],[c_0_50,c_0_59]) ).

cnf(c_0_65,plain,
    ( aInteger0(esk1_2(X1,X2))
    | ~ aDivisorOf0(X2,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

fof(c_0_66,plain,
    ! [X24,X25,X26] :
      ( ( sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26))
        | ~ aInteger0(X24)
        | ~ aInteger0(X25)
        | ~ aInteger0(X26) )
      & ( sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26))
        | ~ aInteger0(X24)
        | ~ aInteger0(X25)
        | ~ aInteger0(X26) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).

cnf(c_0_67,plain,
    ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

fof(c_0_68,plain,
    ! [X21,X22] :
      ( ~ aInteger0(X21)
      | ~ aInteger0(X22)
      | sdtasdt0(X21,X22) = sdtasdt0(X22,X21) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).

cnf(c_0_69,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_60,c_0_61]),c_0_34])]) ).

cnf(c_0_70,hypothesis,
    sdtasdt0(xp,esk1_2(xp,xp)) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_30])]) ).

cnf(c_0_71,negated_conjecture,
    sdtpldt0(sz00,xp) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_49]),c_0_30])]) ).

cnf(c_0_72,hypothesis,
    aInteger0(esk1_2(xp,xp)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_63]),c_0_30])]) ).

cnf(c_0_73,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_66]) ).

cnf(c_0_74,plain,
    ( sdtasdt0(X1,sdtpldt0(sz10,xp)) = smndt0(X1)
    | ~ aInteger0(X1) ),
    inference(rw,[status(thm)],[c_0_67,c_0_26]) ).

cnf(c_0_75,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_76,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_59]),c_0_71]),c_0_70]),c_0_72]),c_0_30])]) ).

cnf(c_0_77,negated_conjecture,
    sdtpldt0(sdtpldt0(sz00,xp),xp) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_59]),c_0_30])]) ).

fof(c_0_78,plain,
    ! [X29,X30] :
      ( ~ aInteger0(X29)
      | ~ aInteger0(X30)
      | sdtasdt0(X29,X30) != sz00
      | X29 = sz00
      | X30 = sz00 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).

cnf(c_0_79,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_73,c_0_74]),c_0_34])]) ).

cnf(c_0_80,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_75,c_0_76]),c_0_30]),c_0_34])]) ).

cnf(c_0_81,negated_conjecture,
    sdtpldt0(xp,xp) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_49]),c_0_30])]) ).

cnf(c_0_82,plain,
    ( X1 = sz00
    | X2 = sz00
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | sdtasdt0(X1,X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_83,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_79,c_0_80]),c_0_59]),c_0_71]),c_0_81]),c_0_46]),c_0_59]),c_0_71]),c_0_71]),c_0_34]),c_0_30])]) ).

cnf(c_0_84,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_30])]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : NUM454+1 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 05:32:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  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/benchmark/theBenchmark.p
% 1.54/0.74  # Version: 3.1.0
% 1.54/0.74  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.54/0.74  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.74  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.54/0.74  # Starting new_bool_3 with 300s (1) cores
% 1.54/0.74  # Starting new_bool_1 with 300s (1) cores
% 1.54/0.74  # Starting sh5l with 300s (1) cores
% 1.54/0.74  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 31598 completed with status 0
% 1.54/0.74  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.54/0.74  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.54/0.74  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.74  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.54/0.74  # No SInE strategy applied
% 1.54/0.74  # Search class: FGHSF-FSLM31-SFFFFFNN
% 1.54/0.74  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.54/0.74  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 666s (1) cores
% 1.54/0.74  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.54/0.74  # Starting new_bool_3 with 194s (1) cores
% 1.54/0.74  # Starting new_bool_1 with 188s (1) cores
% 1.54/0.74  # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.54/0.74  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 31603 completed with status 0
% 1.54/0.74  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.54/0.74  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.54/0.74  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.54/0.74  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.54/0.74  # No SInE strategy applied
% 1.54/0.74  # Search class: FGHSF-FSLM31-SFFFFFNN
% 1.54/0.74  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.54/0.74  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 666s (1) cores
% 1.54/0.74  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.54/0.74  # Preprocessing time       : 0.005 s
% 1.54/0.74  # Presaturation interreduction done
% 1.54/0.74  
% 1.54/0.74  # Proof found!
% 1.54/0.74  # SZS status Theorem
% 1.54/0.74  # SZS output start CNFRefutation
% See solution above
% 1.54/0.74  # Parsed axioms                        : 49
% 1.54/0.74  # Removed by relevancy pruning/SinE    : 0
% 1.54/0.74  # Initial clauses                      : 126
% 1.54/0.74  # Removed in clause preprocessing      : 5
% 1.54/0.74  # Initial clauses in saturation        : 121
% 1.54/0.74  # Processed clauses                    : 1558
% 1.54/0.74  # ...of these trivial                  : 30
% 1.54/0.74  # ...subsumed                          : 851
% 1.54/0.74  # ...remaining for further processing  : 677
% 1.54/0.74  # Other redundant clauses eliminated   : 33
% 1.54/0.74  # Clauses deleted for lack of memory   : 0
% 1.54/0.74  # Backward-subsumed                    : 13
% 1.54/0.74  # Backward-rewritten                   : 68
% 1.54/0.74  # Generated clauses                    : 8951
% 1.54/0.74  # ...of the previous two non-redundant : 6649
% 1.54/0.74  # ...aggressively subsumed             : 0
% 1.54/0.74  # Contextual simplify-reflections      : 79
% 1.54/0.74  # Paramodulations                      : 8918
% 1.54/0.74  # Factorizations                       : 0
% 1.54/0.74  # NegExts                              : 0
% 1.54/0.74  # Equation resolutions                 : 33
% 1.54/0.74  # Disequality decompositions           : 0
% 1.54/0.74  # Total rewrite steps                  : 15970
% 1.54/0.74  # ...of those cached                   : 15884
% 1.54/0.74  # Propositional unsat checks           : 0
% 1.54/0.74  #    Propositional check models        : 0
% 1.54/0.74  #    Propositional check unsatisfiable : 0
% 1.54/0.74  #    Propositional clauses             : 0
% 1.54/0.74  #    Propositional clauses after purity: 0
% 1.54/0.74  #    Propositional unsat core size     : 0
% 1.54/0.74  #    Propositional preprocessing time  : 0.000
% 1.54/0.74  #    Propositional encoding time       : 0.000
% 1.54/0.74  #    Propositional solver time         : 0.000
% 1.54/0.74  #    Success case prop preproc time    : 0.000
% 1.54/0.74  #    Success case prop encoding time   : 0.000
% 1.54/0.74  #    Success case prop solver time     : 0.000
% 1.54/0.74  # Current number of processed clauses  : 445
% 1.54/0.74  #    Positive orientable unit clauses  : 67
% 1.54/0.74  #    Positive unorientable unit clauses: 0
% 1.54/0.74  #    Negative unit clauses             : 10
% 1.54/0.74  #    Non-unit-clauses                  : 368
% 1.54/0.74  # Current number of unprocessed clauses: 5152
% 1.54/0.74  # ...number of literals in the above   : 21341
% 1.54/0.74  # Current number of archived formulas  : 0
% 1.54/0.74  # Current number of archived clauses   : 200
% 1.54/0.74  # Clause-clause subsumption calls (NU) : 33241
% 1.54/0.74  # Rec. Clause-clause subsumption calls : 19653
% 1.54/0.74  # Non-unit clause-clause subsumptions  : 920
% 1.54/0.74  # Unit Clause-clause subsumption calls : 1296
% 1.54/0.74  # Rewrite failures with RHS unbound    : 0
% 1.54/0.74  # BW rewrite match attempts            : 33
% 1.54/0.74  # BW rewrite match successes           : 31
% 1.54/0.74  # Condensation attempts                : 0
% 1.54/0.74  # Condensation successes               : 0
% 1.54/0.74  # Termbank termtop insertions          : 163973
% 1.54/0.74  # Search garbage collected termcells   : 2357
% 1.54/0.74  
% 1.54/0.74  # -------------------------------------------------
% 1.54/0.74  # User time                : 0.224 s
% 1.54/0.74  # System time              : 0.014 s
% 1.54/0.74  # Total time               : 0.238 s
% 1.54/0.74  # Maximum resident set size: 2072 pages
% 1.54/0.74  
% 1.54/0.74  # -------------------------------------------------
% 1.54/0.74  # User time                : 1.131 s
% 1.54/0.74  # System time              : 0.029 s
% 1.54/0.74  # Total time               : 1.160 s
% 1.54/0.74  # Maximum resident set size: 1752 pages
% 1.54/0.74  % E---3.1 exiting
% 1.54/0.74  % E exiting
%------------------------------------------------------------------------------