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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : NUM582+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n005.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  5 04:57:54 PM UTC 2026

% Result   : Theorem 4.08s 3.47s
% Output   : CNFRefutation 4.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   19 (   7 unt;   0 def)
%            Number of atoms       :  246 (  12 equ)
%            Maximal formula atoms :  181 (  12 avg)
%            Number of connectives :  379 ( 152   ~; 161   |;  54   &)
%                                         (   1 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   45 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn  20   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__3754,hypothesis,
    ! [X1,X2] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0) )
     => ( sdtlseqdt0(X2,X1)
       => ( ! [X3] :
              ( aElementOf0(X3,sdtlpdtrp0(xN,X1))
             => aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
          & aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).

fof(m__3623,hypothesis,
    ( aFunction0(xN)
    & szDzozmdt0(xN) = szNzAzT0
    & sdtlpdtrp0(xN,sz00) = xS
    & ! [X1] :
        ( aElementOf0(X1,szNzAzT0)
       => ( ( ( ( aSet0(sdtlpdtrp0(xN,X1))
                & ! [X2] :
                    ( aElementOf0(X2,sdtlpdtrp0(xN,X1))
                   => aElementOf0(X2,szNzAzT0) ) )
              | aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) )
            & isCountable0(sdtlpdtrp0(xN,X1)) )
         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
            & ! [X2] :
                ( aElementOf0(X2,sdtlpdtrp0(xN,X1))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
            & ! [X2] :
                ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
              <=> ( aElement0(X2)
                  & aElementOf0(X2,sdtlpdtrp0(xN,X1))
                  & X2 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
            & ! [X2] :
                ( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
               => aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).

fof(mZeroLess,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => sdtlseqdt0(sz00,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).

fof(m__,conjecture,
    ( ! [X1] :
        ( aElementOf0(X1,sdtlpdtrp0(xN,xi))
       => aElementOf0(X1,xS) )
    | aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mZeroNum,axiom,
    aElementOf0(sz00,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).

fof(m__3989,hypothesis,
    aElementOf0(xi,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).

fof(c_0_6,hypothesis,
    ! [X386,X387,X388] :
      ( ( ~ aElementOf0(X388,sdtlpdtrp0(xN,X386))
        | aElementOf0(X388,sdtlpdtrp0(xN,X387))
        | ~ sdtlseqdt0(X387,X386)
        | ~ aElementOf0(X386,szNzAzT0)
        | ~ aElementOf0(X387,szNzAzT0) )
      & ( aSubsetOf0(sdtlpdtrp0(xN,X386),sdtlpdtrp0(xN,X387))
        | ~ sdtlseqdt0(X387,X386)
        | ~ aElementOf0(X386,szNzAzT0)
        | ~ aElementOf0(X387,szNzAzT0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3754])])])]) ).

fof(c_0_7,hypothesis,
    ! [X378,X380,X381,X382,X383] :
      ( aFunction0(xN)
      & szDzozmdt0(xN) = szNzAzT0
      & sdtlpdtrp0(xN,sz00) = xS
      & ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X378)),sdtlpdtrp0(xN,X378))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElementOf0(X380,sdtlpdtrp0(xN,X378))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X378)),X380)
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElement0(X381)
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElementOf0(X381,sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( X381 != szmzizndt0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElement0(X382)
        | ~ aElementOf0(X382,sdtlpdtrp0(xN,X378))
        | X382 = szmzizndt0(sdtlpdtrp0(xN,X378))
        | aElementOf0(X382,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElementOf0(X383,sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X378)),sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | aElementOf0(esk31_1(X378),sdtlpdtrp0(xN,X378))
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X378)),sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElementOf0(X380,sdtlpdtrp0(xN,X378))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X378)),X380)
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElement0(X381)
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElementOf0(X381,sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( X381 != szmzizndt0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElement0(X382)
        | ~ aElementOf0(X382,sdtlpdtrp0(xN,X378))
        | X382 = szmzizndt0(sdtlpdtrp0(xN,X378))
        | aElementOf0(X382,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElementOf0(X383,sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X378)),sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | ~ aElementOf0(esk31_1(X378),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,X378))
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X378)),sdtlpdtrp0(xN,X378))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElementOf0(X380,sdtlpdtrp0(xN,X378))
        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X378)),X380)
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElement0(X381)
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aElementOf0(X381,sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( X381 != szmzizndt0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X381,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElement0(X382)
        | ~ aElementOf0(X382,sdtlpdtrp0(xN,X378))
        | X382 = szmzizndt0(sdtlpdtrp0(xN,X378))
        | aElementOf0(X382,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( ~ aElementOf0(X383,sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | aElementOf0(X383,sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X378)),sdtmndt0(sdtlpdtrp0(xN,X378),szmzizndt0(sdtlpdtrp0(xN,X378))))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) )
      & ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X378)))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,X378),szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,X378))
        | ~ aElementOf0(X378,szNzAzT0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3623])])])])])]) ).

fof(c_0_8,plain,
    ! [X242] :
      ( ~ aElementOf0(X242,szNzAzT0)
      | sdtlseqdt0(sz00,X242) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])]) ).

fof(c_0_9,negated_conjecture,
    ~ ( ! [X1] :
          ( aElementOf0(X1,sdtlpdtrp0(xN,xi))
         => aElementOf0(X1,xS) )
      | aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_10,hypothesis,
    ( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    aElementOf0(sz00,szNzAzT0),
    inference(split_conjunct,[status(thm)],[mZeroNum]) ).

cnf(c_0_12,hypothesis,
    sdtlpdtrp0(xN,sz00) = xS,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( sdtlseqdt0(sz00,X1)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_14,negated_conjecture,
    ( aElementOf0(esk33_0,sdtlpdtrp0(xN,xi))
    & ~ aElementOf0(esk33_0,xS)
    & ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_15,hypothesis,
    ( aSubsetOf0(sdtlpdtrp0(xN,X1),xS)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]) ).

cnf(c_0_16,hypothesis,
    aElementOf0(xi,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__3989]) ).

cnf(c_0_17,negated_conjecture,
    ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM582+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32  % Computer : n005.cluster.edu
% 0.15/0.32  % Model    : x86_64 x86_64
% 0.15/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32  % Memory   : 8042.1875MB
% 0.15/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32  % CPULimit   : 300
% 0.15/0.32  % WCLimit    : 300
% 0.15/0.32  % DateTime   : Tue May  5 00:47:45 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 4.08/3.47  % Version  : CSE_E---1.7
% 4.08/3.47  % Problem  : theBenchmark.p
% 4.08/3.47  % SZS status Theorem for theBenchmark.p
% 4.08/3.47  % SZS output start CNFRefutation
% See solution above
% 4.08/3.48  % Total time : 2.769s
%------------------------------------------------------------------------------