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E---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : NUM448+5 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 01:49:07 PM UTC 2026

% Result   : Theorem 0.15s 0.47s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   44 (   7 unt;   0 def)
%            Number of atoms       :  312 (  72 equ)
%            Maximal formula atoms :  102 (   7 avg)
%            Number of connectives :  404 ( 136   ~; 145   |;  91   &)
%                                         (  11 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   41 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   5 con; 0-2 aty)
%            Number of variables   :   68 (   0 sgn  26   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__,conjecture,
    ( ! [X1] :
        ( aInteger0(X1)
       => ( ( ? [X2] :
                ( isPrime0(X2)
                & ( aDivisorOf0(X2,X1)
                  | ( ? [X3] :
                        ( sdtasdt0(X2,X3) = X1
                        & aInteger0(X3) )
                    & X2 != sz00
                    & aInteger0(X2) ) ) )
           => ( aElementOf0(X1,sbsmnsldt0(xS))
              & ? [X2] :
                  ( aElementOf0(X1,X2)
                  & aElementOf0(X2,xS) ) ) )
          & ( ( aElementOf0(X1,sbsmnsldt0(xS))
              | ? [X2] :
                  ( aElementOf0(X1,X2)
                  & aElementOf0(X2,xS) ) )
           => ? [X2] :
                ( isPrime0(X2)
                & aDivisorOf0(X2,X1)
                & ? [X3] :
                    ( sdtasdt0(X2,X3) = X1
                    & aInteger0(X3) )
                & X2 != sz00
                & aInteger0(X2) ) ) ) )
   => ( ( ! [X1] :
            ( aElementOf0(X1,sbsmnsldt0(xS))
          <=> ( ? [X2] :
                  ( aElementOf0(X1,X2)
                  & aElementOf0(X2,xS) )
              & aInteger0(X1) ) )
        & aSet0(sbsmnsldt0(xS)) )
     => ( ( ! [X1] :
              ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
            <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
                & aInteger0(X1) ) )
          & aSet0(stldt0(sbsmnsldt0(xS))) )
       => ( stldt0(sbsmnsldt0(xS)) = cS2076
          | ! [X1] :
              ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
            <=> ( X1 = smndt0(sz10)
                | X1 = sz10 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mPrimeDivisor,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( ? [X2] :
            ( isPrime0(X2)
            & aDivisorOf0(X2,X1) )
      <=> ( X1 != smndt0(sz10)
          & X1 != sz10 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimeDivisor) ).

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

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

fof(c_0_4,negated_conjecture,
    ~ ( ! [X1] :
          ( aInteger0(X1)
         => ( ( ? [X2] :
                  ( isPrime0(X2)
                  & ( aDivisorOf0(X2,X1)
                    | ( ? [X3] :
                          ( sdtasdt0(X2,X3) = X1
                          & aInteger0(X3) )
                      & X2 != sz00
                      & aInteger0(X2) ) ) )
             => ( aElementOf0(X1,sbsmnsldt0(xS))
                & ? [X2] :
                    ( aElementOf0(X1,X2)
                    & aElementOf0(X2,xS) ) ) )
            & ( ( aElementOf0(X1,sbsmnsldt0(xS))
                | ? [X2] :
                    ( aElementOf0(X1,X2)
                    & aElementOf0(X2,xS) ) )
             => ? [X2] :
                  ( isPrime0(X2)
                  & aDivisorOf0(X2,X1)
                  & ? [X3] :
                      ( sdtasdt0(X2,X3) = X1
                      & aInteger0(X3) )
                  & X2 != sz00
                  & aInteger0(X2) ) ) ) )
     => ( ( ! [X1] :
              ( aElementOf0(X1,sbsmnsldt0(xS))
            <=> ( ? [X2] :
                    ( aElementOf0(X1,X2)
                    & aElementOf0(X2,xS) )
                & aInteger0(X1) ) )
          & aSet0(sbsmnsldt0(xS)) )
       => ( ( ! [X1] :
                ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
              <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
                  & aInteger0(X1) ) )
            & aSet0(stldt0(sbsmnsldt0(xS))) )
         => ( stldt0(sbsmnsldt0(xS)) = cS2076
            | ! [X1] :
                ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
              <=> ( X1 = smndt0(sz10)
                  | X1 = sz10 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_5,negated_conjecture,
    ~ ( ! [X1] :
          ( aInteger0(X1)
         => ( ( ? [X2] :
                  ( isPrime0(X2)
                  & ( aDivisorOf0(X2,X1)
                    | ( ? [X3] :
                          ( sdtasdt0(X2,X3) = X1
                          & aInteger0(X3) )
                      & X2 != sz00
                      & aInteger0(X2) ) ) )
             => ( aElementOf0(X1,sbsmnsldt0(xS))
                & ? [X2] :
                    ( aElementOf0(X1,X2)
                    & aElementOf0(X2,xS) ) ) )
            & ( ( aElementOf0(X1,sbsmnsldt0(xS))
                | ? [X2] :
                    ( aElementOf0(X1,X2)
                    & aElementOf0(X2,xS) ) )
             => ? [X2] :
                  ( isPrime0(X2)
                  & aDivisorOf0(X2,X1)
                  & ? [X3] :
                      ( sdtasdt0(X2,X3) = X1
                      & aInteger0(X3) )
                  & X2 != sz00
                  & aInteger0(X2) ) ) ) )
     => ( ( ! [X1] :
              ( aElementOf0(X1,sbsmnsldt0(xS))
            <=> ( ? [X2] :
                    ( aElementOf0(X1,X2)
                    & aElementOf0(X2,xS) )
                & aInteger0(X1) ) )
          & aSet0(sbsmnsldt0(xS)) )
       => ( ( ! [X1] :
                ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
              <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
                  & aInteger0(X1) ) )
            & aSet0(stldt0(sbsmnsldt0(xS))) )
         => ( stldt0(sbsmnsldt0(xS)) = cS2076
            | ! [X1] :
                ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
              <=> ( X1 = smndt0(sz10)
                  | X1 = sz10 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_6,negated_conjecture,
    ! [X131,X132,X135,X136,X138,X140,X141,X142] :
      ( stldt0(sbsmnsldt0(xS)) != cS2076
      & ( esk23_0 = smndt0(sz10)
        | esk23_0 = sz10
        | aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS))) )
      & ( ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
        | esk23_0 != smndt0(sz10) )
      & ( ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
        | esk23_0 != sz10 )
      & ( aElementOf0(X142,stldt0(sbsmnsldt0(xS)))
        | aElementOf0(X142,sbsmnsldt0(xS))
        | ~ aInteger0(X142) )
      & ( ~ aElementOf0(X142,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X142,sbsmnsldt0(xS)) )
      & ( ~ aElementOf0(X142,stldt0(sbsmnsldt0(xS)))
        | aInteger0(X142) )
      & aSet0(stldt0(sbsmnsldt0(xS)))
      & ( aElementOf0(X140,sbsmnsldt0(xS))
        | ~ aElementOf0(X140,X141)
        | ~ aElementOf0(X141,xS)
        | ~ aInteger0(X140) )
      & ( ~ aElementOf0(X138,sbsmnsldt0(xS))
        | aElementOf0(X138,esk22_1(X138)) )
      & ( ~ aElementOf0(X138,sbsmnsldt0(xS))
        | aElementOf0(esk22_1(X138),xS) )
      & ( ~ aElementOf0(X138,sbsmnsldt0(xS))
        | aInteger0(X138) )
      & aSet0(sbsmnsldt0(xS))
      & ( ~ aInteger0(X131)
        | ~ isPrime0(X135)
        | ~ aDivisorOf0(X135,X131)
        | aElementOf0(X131,sbsmnsldt0(xS)) )
      & ( ~ aInteger0(X131)
        | ~ isPrime0(X135)
        | ~ aDivisorOf0(X135,X131)
        | aElementOf0(X131,esk21_1(X131)) )
      & ( ~ aInteger0(X131)
        | ~ isPrime0(X135)
        | ~ aDivisorOf0(X135,X131)
        | aElementOf0(esk21_1(X131),xS) )
      & ( ~ aInteger0(X131)
        | ~ isPrime0(X135)
        | sdtasdt0(X135,X136) != X131
        | ~ aInteger0(X136)
        | X135 = sz00
        | ~ aInteger0(X135)
        | aElementOf0(X131,sbsmnsldt0(xS)) )
      & ( ~ aInteger0(X131)
        | ~ isPrime0(X135)
        | sdtasdt0(X135,X136) != X131
        | ~ aInteger0(X136)
        | X135 = sz00
        | ~ aInteger0(X135)
        | aElementOf0(X131,esk21_1(X131)) )
      & ( ~ aInteger0(X131)
        | ~ isPrime0(X135)
        | sdtasdt0(X135,X136) != X131
        | ~ aInteger0(X136)
        | X135 = sz00
        | ~ aInteger0(X135)
        | aElementOf0(esk21_1(X131),xS) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,sbsmnsldt0(xS))
        | isPrime0(esk19_1(X131)) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,sbsmnsldt0(xS))
        | aDivisorOf0(esk19_1(X131),X131) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,sbsmnsldt0(xS))
        | sdtasdt0(esk19_1(X131),esk20_1(X131)) = X131 )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,sbsmnsldt0(xS))
        | aInteger0(esk20_1(X131)) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,sbsmnsldt0(xS))
        | esk19_1(X131) != sz00 )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,sbsmnsldt0(xS))
        | aInteger0(esk19_1(X131)) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,X132)
        | ~ aElementOf0(X132,xS)
        | isPrime0(esk19_1(X131)) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,X132)
        | ~ aElementOf0(X132,xS)
        | aDivisorOf0(esk19_1(X131),X131) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,X132)
        | ~ aElementOf0(X132,xS)
        | sdtasdt0(esk19_1(X131),esk20_1(X131)) = X131 )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,X132)
        | ~ aElementOf0(X132,xS)
        | aInteger0(esk20_1(X131)) )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,X132)
        | ~ aElementOf0(X132,xS)
        | esk19_1(X131) != sz00 )
      & ( ~ aInteger0(X131)
        | ~ aElementOf0(X131,X132)
        | ~ aElementOf0(X132,xS)
        | aInteger0(esk19_1(X131)) ) ),
    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_5])])])])])])]) ).

fof(c_0_7,plain,
    ! [X1] :
      ( aInteger0(X1)
     => ( ? [X2] :
            ( isPrime0(X2)
            & aDivisorOf0(X2,X1) )
      <=> ( X1 != smndt0(sz10)
          & X1 != sz10 ) ) ),
    inference(fof_simplification,[status(thm)],[mPrimeDivisor]) ).

fof(c_0_8,plain,
    ! [X6] :
      ( aInteger0(smndt0(X6))
      | ~ aInteger0(X6) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).

cnf(c_0_9,negated_conjecture,
    ( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
    | aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( esk23_0 = smndt0(sz10)
    | esk23_0 = sz10
    | aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS))) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_11,plain,
    ! [X53,X54] :
      ( ( ~ aInteger0(X53)
        | X53 = smndt0(sz10)
        | X53 = sz10
        | isPrime0(esk2_1(X53)) )
      & ( ~ aInteger0(X53)
        | X53 = smndt0(sz10)
        | X53 = sz10
        | aDivisorOf0(esk2_1(X53),X53) )
      & ( ~ aInteger0(X53)
        | ~ isPrime0(X54)
        | ~ aDivisorOf0(X54,X53)
        | X53 != smndt0(sz10) )
      & ( ~ aInteger0(X53)
        | ~ isPrime0(X54)
        | ~ aDivisorOf0(X54,X53)
        | X53 != sz10 ) ),
    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_7])])])])])]) ).

cnf(c_0_12,plain,
    ( ~ aInteger0(X1)
    | aInteger0(smndt0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( aInteger0(esk23_0)
    | esk23_0 = sz10
    | smndt0(sz10) = esk23_0 ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    aInteger0(sz10),
    inference(split_conjunct,[status(thm)],[mIntOne]) ).

cnf(c_0_15,plain,
    ( ~ aInteger0(X1)
    | ~ isPrime0(X2)
    | ~ aDivisorOf0(X2,X1)
    | X1 != smndt0(sz10) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    ( ~ aInteger0(X1)
    | ~ aElementOf0(X1,sbsmnsldt0(xS))
    | aDivisorOf0(esk19_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ aElementOf0(X1,sbsmnsldt0(xS))
    | aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_18,negated_conjecture,
    ( ~ aInteger0(X1)
    | ~ aElementOf0(X1,sbsmnsldt0(xS))
    | isPrime0(esk19_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,plain,
    ( ~ aInteger0(X1)
    | X1 = smndt0(sz10)
    | X1 = sz10
    | aDivisorOf0(esk2_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_20,negated_conjecture,
    ( aInteger0(esk23_0)
    | esk23_0 = sz10 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).

cnf(c_0_21,plain,
    ( ~ aInteger0(X1)
    | X1 = smndt0(sz10)
    | X1 = sz10
    | isPrime0(esk2_1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_22,negated_conjecture,
    ( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
    | ~ aElementOf0(X1,sbsmnsldt0(xS)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ aInteger0(X1)
    | aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
    | aElementOf0(X1,sbsmnsldt0(xS)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_24,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aDivisorOf0(X1,smndt0(sz10))
    | ~ isPrime0(X1) ),
    inference(er,[status(thm)],[c_0_15]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ aElementOf0(X1,sbsmnsldt0(xS))
    | aDivisorOf0(esk19_1(X1),X1) ),
    inference(csr,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ aElementOf0(X1,sbsmnsldt0(xS))
    | isPrime0(esk19_1(X1)) ),
    inference(csr,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_27,negated_conjecture,
    ( ~ aInteger0(X1)
    | ~ isPrime0(X2)
    | ~ aDivisorOf0(X2,X1)
    | aElementOf0(X1,sbsmnsldt0(xS)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_28,negated_conjecture,
    ( aDivisorOf0(esk2_1(esk23_0),esk23_0)
    | esk23_0 = sz10
    | smndt0(sz10) = esk23_0 ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_29,negated_conjecture,
    ( isPrime0(esk2_1(esk23_0))
    | esk23_0 = sz10
    | smndt0(sz10) = esk23_0 ),
    inference(spm,[status(thm)],[c_0_21,c_0_20]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ aElementOf0(esk23_0,sbsmnsldt0(xS))
    | esk23_0 = sz10
    | smndt0(sz10) = esk23_0 ),
    inference(spm,[status(thm)],[c_0_22,c_0_10]) ).

cnf(c_0_31,plain,
    ( ~ aInteger0(X1)
    | ~ isPrime0(X2)
    | ~ aDivisorOf0(X2,X1)
    | X1 != sz10 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_32,negated_conjecture,
    ( ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
    | esk23_0 != smndt0(sz10) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_33,negated_conjecture,
    ( aElementOf0(esk23_0,sbsmnsldt0(xS))
    | aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
    | esk23_0 = sz10 ),
    inference(spm,[status(thm)],[c_0_23,c_0_20]) ).

cnf(c_0_34,negated_conjecture,
    ~ aElementOf0(smndt0(sz10),sbsmnsldt0(xS)),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17]),c_0_26]) ).

cnf(c_0_35,negated_conjecture,
    ( esk23_0 = sz10
    | smndt0(sz10) = esk23_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),c_0_29]),c_0_30]) ).

cnf(c_0_36,plain,
    ( ~ aDivisorOf0(X1,sz10)
    | ~ isPrime0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_14])]) ).

cnf(c_0_37,negated_conjecture,
    ( smndt0(sz10) != esk23_0
    | aElementOf0(esk23_0,sbsmnsldt0(xS))
    | esk23_0 = sz10 ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_38,negated_conjecture,
    ( ~ aElementOf0(esk23_0,sbsmnsldt0(xS))
    | esk23_0 = sz10 ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    ~ aElementOf0(sz10,sbsmnsldt0(xS)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_25]),c_0_26]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ aElementOf0(esk23_0,stldt0(sbsmnsldt0(xS)))
    | esk23_0 != sz10 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_41,negated_conjecture,
    esk23_0 = sz10,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_38]) ).

cnf(c_0_42,negated_conjecture,
    aElementOf0(sz10,stldt0(sbsmnsldt0(xS))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_41]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM448+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37  % Computer : n005.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Mon Sep 21 02:30:19 UTC 2026
% 0.15/0.38  % CPUTime  : 
% 0.15/0.38  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41  Running first-order theorem proving
% 0.15/0.41  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/benchmark/theBenchmark.p
% 0.15/0.47  % Version: 3.5.1
% 0.15/0.47  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.47  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.47  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.47  % Starting new_bool_3 with 300s (1) cores
% 0.15/0.47  % Starting new_bool_1 with 300s (1) cores
% 0.15/0.47  % Starting sh5l with 300s (1) cores
% 0.15/0.47  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2355384 completed with status 0
% 0.15/0.47  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.47  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.47  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.47  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.47  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.47  % No SInE strategy applied
% 0.15/0.47  % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.15/0.47  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.47  % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.47  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.47  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 0.15/0.47  % Starting new_bool_3 with 194s (1) cores
% 0.15/0.47  % Starting new_bool_1 with 188s (1) cores
% 0.15/0.47  % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2355393 completed with status 0
% 0.15/0.47  % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.47  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.47  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.47  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.47  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.47  % No SInE strategy applied
% 0.15/0.47  % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.15/0.47  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.47  % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.47  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.47  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 0.15/0.47  % Preprocessing time       : 0.004 s
% 0.15/0.47  % Presaturation interreduction done
% 0.15/0.47  
% 0.15/0.47  % Proof found!
% 0.15/0.47  % SZS status Theorem
% 0.15/0.47  % SZS output start CNFRefutation
% See solution above
% 0.15/0.47  % Parsed axioms                        : 43
% 0.15/0.47  % Removed by relevancy pruning/SinE    : 0
% 0.15/0.47  % Initial clauses                      : 168
% 0.15/0.47  % Removed in clause preprocessing      : 5
% 0.15/0.47  % Initial clauses in saturation        : 163
% 0.15/0.47  % Processed clauses                    : 315
% 0.15/0.47  % ...of these trivial                  : 1
% 0.15/0.47  % ...subsumed                          : 13
% 0.15/0.47  % ...remaining for further processing  : 301
% 0.15/0.47  % Other redundant clauses eliminated   : 36
% 0.15/0.47  % Clauses deleted for lack of memory   : 0
% 0.15/0.47  % Backward-subsumed                    : 6
% 0.15/0.47  % Backward-rewritten                   : 23
% 0.15/0.47  % Generated clauses                    : 206
% 0.15/0.47  % ...of the previous two non-redundant : 169
% 0.15/0.47  % ...aggressively subsumed             : 0
% 0.15/0.47  % Contextual simplify-reflections      : 20
% 0.15/0.47  % Paramodulations                      : 170
% 0.15/0.47  % Factorizations                       : 0
% 0.15/0.47  % NegExts                              : 0
% 0.15/0.47  % Equation resolutions                 : 36
% 0.15/0.47  % Disequality decompositions           : 0
% 0.15/0.47  % Total rewrite steps                  : 117
% 0.15/0.47  % ...of those cached                   : 110
% 0.15/0.47  % Propositional unsat checks           : 0
% 0.15/0.47  %    Propositional check models        : 0
% 0.15/0.47  %    Propositional check unsatisfiable : 0
% 0.15/0.47  %    Propositional clauses             : 0
% 0.15/0.47  %    Propositional clauses after purity: 0
% 0.15/0.47  %    Propositional unsat core size     : 0
% 0.15/0.47  %    Propositional preprocessing time  : 0.000
% 0.15/0.47  %    Propositional encoding time       : 0.000
% 0.15/0.47  %    Propositional solver time         : 0.000
% 0.15/0.47  %    Success case prop preproc time    : 0.000
% 0.15/0.47  %    Success case prop encoding time   : 0.000
% 0.15/0.47  %    Success case prop solver time     : 0.000
% 0.15/0.47  % Current number of processed clauses  : 73
% 0.15/0.47  %    Positive orientable unit clauses  : 10
% 0.15/0.47  %    Positive unorientable unit clauses: 0
% 0.15/0.47  %    Negative unit clauses             : 3
% 0.15/0.47  %    Non-unit-clauses                  : 60
% 0.15/0.47  % Current number of unprocessed clauses: 179
% 0.15/0.47  % ...number of literals in the above   : 769
% 0.15/0.47  % Current number of archived formulas  : 0
% 0.15/0.47  % Current number of archived clauses   : 192
% 0.15/0.47  % Clause-clause subsumption calls (NU) : 6512
% 0.15/0.47  % Rec. Clause-clause subsumption calls : 1272
% 0.15/0.47  % Non-unit clause-clause subsumptions  : 37
% 0.15/0.47  % Unit Clause-clause subsumption calls : 81
% 0.15/0.47  % Rewrite failures with RHS unbound    : 0
% 0.15/0.47  % BW rewrite match attempts            : 2
% 0.15/0.47  % BW rewrite match successes           : 2
% 0.15/0.47  % Condensation attempts                : 0
% 0.15/0.47  % Condensation successes               : 0
% 0.15/0.47  % Termbank termtop insertions          : 18570
% 0.15/0.47  % Search garbage collected termcells   : 3363
% 0.15/0.47  
% 0.15/0.47  % -------------------------------------------------
% 0.15/0.47  % User time                : 0.034 s
% 0.15/0.47  % System time              : 0.008 s
% 0.15/0.47  % Total time               : 0.042 s
% 0.15/0.47  % Maximum resident set size: 3900 pages
% 0.15/0.47  
% 0.15/0.47  % -------------------------------------------------
% 0.15/0.47  % User time                : 0.140 s
% 0.15/0.47  % System time              : 0.031 s
% 0.15/0.47  % Total time               : 0.171 s
% 0.15/0.47  % Maximum resident set size: 4608 pages
% 0.15/0.47  % E exiting
%------------------------------------------------------------------------------