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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : RNG112+4 : 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 : n026.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 05:05:23 PM UTC 2026

% Result   : Theorem 1.36s 1.75s
% Output   : CNFRefutation 1.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   35 (  13 unt;   0 def)
%            Number of atoms       :  307 ( 117 equ)
%            Maximal formula atoms :   68 (   8 avg)
%            Number of connectives :  408 ( 136   ~; 153   |; 105   &)
%                                         (   5 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  10 con; 0-2 aty)
%            Number of variables   :   92 (   0 sgn  40   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__,conjecture,
    ? [X1] :
      ( ( ? [X2,X3] :
            ( aElementOf0(X2,slsdtgt0(xa))
            & aElementOf0(X3,slsdtgt0(xb))
            & sdtpldt0(X2,X3) = X1 )
        | aElementOf0(X1,xI) )
      & X1 != sz00
      & ! [X2] :
          ( ( ? [X3,X4] :
                ( aElementOf0(X3,slsdtgt0(xa))
                & aElementOf0(X4,slsdtgt0(xb))
                & sdtpldt0(X3,X4) = X2 )
            & aElementOf0(X2,xI)
            & X2 != sz00 )
         => ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__2351,hypothesis,
    ! [X1] :
      ( ( ( ? [X2,X3] :
              ( aElementOf0(X2,slsdtgt0(xa))
              & aElementOf0(X3,slsdtgt0(xb))
              & sdtpldt0(X2,X3) = X1 )
          | aElementOf0(X1,xI) )
        & X1 != sz00 )
     => ? [X2] :
          ( ? [X3,X4] :
              ( aElementOf0(X3,slsdtgt0(xa))
              & aElementOf0(X4,slsdtgt0(xb))
              & sdtpldt0(X3,X4) = X2 )
          & aElementOf0(X2,xI)
          & X2 != sz00
          & ! [X3] :
              ( ( ( ? [X4,X5] :
                      ( aElementOf0(X4,slsdtgt0(xa))
                      & aElementOf0(X5,slsdtgt0(xb))
                      & sdtpldt0(X4,X5) = X3 )
                  | aElementOf0(X3,xI) )
                & X3 != sz00 )
             => ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2351) ).

fof(m__2228,hypothesis,
    ? [X1] :
      ( ! [X2] :
          ( aElementOf0(X2,slsdtgt0(xa))
        <=> ? [X3] :
              ( aElement0(X3)
              & sdtasdt0(xa,X3) = X2 ) )
      & ! [X2] :
          ( aElementOf0(X2,slsdtgt0(xb))
        <=> ? [X3] :
              ( aElement0(X3)
              & sdtasdt0(xb,X3) = X2 ) )
      & ? [X2,X3] :
          ( aElementOf0(X2,slsdtgt0(xa))
          & aElementOf0(X3,slsdtgt0(xb))
          & sdtpldt0(X2,X3) = X1 )
      & aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
      & X1 != sz00 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2228) ).

fof(m__2174,hypothesis,
    ( aSet0(xI)
    & ! [X1] :
        ( aElementOf0(X1,xI)
       => ( ! [X2] :
              ( aElementOf0(X2,xI)
             => aElementOf0(sdtpldt0(X1,X2),xI) )
          & ! [X2] :
              ( aElement0(X2)
             => aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
    & aIdeal0(xI)
    & ! [X1] :
        ( aElementOf0(X1,slsdtgt0(xa))
      <=> ? [X2] :
            ( aElement0(X2)
            & sdtasdt0(xa,X2) = X1 ) )
    & ! [X1] :
        ( aElementOf0(X1,slsdtgt0(xb))
      <=> ? [X2] :
            ( aElement0(X2)
            & sdtasdt0(xb,X2) = X1 ) )
    & ! [X1] :
        ( aElementOf0(X1,xI)
      <=> ? [X2,X3] :
            ( aElementOf0(X2,slsdtgt0(xa))
            & aElementOf0(X3,slsdtgt0(xb))
            & sdtpldt0(X2,X3) = X1 ) )
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).

fof(c_0_4,negated_conjecture,
    ~ ? [X1] :
        ( ( ? [X2,X3] :
              ( aElementOf0(X2,slsdtgt0(xa))
              & aElementOf0(X3,slsdtgt0(xb))
              & sdtpldt0(X2,X3) = X1 )
          | aElementOf0(X1,xI) )
        & X1 != sz00
        & ! [X2] :
            ( ( ? [X3,X4] :
                  ( aElementOf0(X3,slsdtgt0(xa))
                  & aElementOf0(X4,slsdtgt0(xb))
                  & sdtpldt0(X3,X4) = X2 )
              & aElementOf0(X2,xI)
              & X2 != sz00 )
           => ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

fof(c_0_5,hypothesis,
    ! [X1] :
      ( ( ( ? [X2,X3] :
              ( aElementOf0(X2,slsdtgt0(xa))
              & aElementOf0(X3,slsdtgt0(xb))
              & sdtpldt0(X2,X3) = X1 )
          | aElementOf0(X1,xI) )
        & X1 != sz00 )
     => ? [X2] :
          ( ? [X3,X4] :
              ( aElementOf0(X3,slsdtgt0(xa))
              & aElementOf0(X4,slsdtgt0(xb))
              & sdtpldt0(X3,X4) = X2 )
          & aElementOf0(X2,xI)
          & X2 != sz00
          & ! [X3] :
              ( ( ( ? [X4,X5] :
                      ( aElementOf0(X4,slsdtgt0(xa))
                      & aElementOf0(X5,slsdtgt0(xb))
                      & sdtpldt0(X4,X5) = X3 )
                  | aElementOf0(X3,xI) )
                & X3 != sz00 )
             => ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[m__2351]) ).

fof(c_0_6,hypothesis,
    ! [X265,X267,X268,X270] :
      ( ( aElement0(esk33_1(X265))
        | ~ aElementOf0(X265,slsdtgt0(xa)) )
      & ( sdtasdt0(xa,esk33_1(X265)) = X265
        | ~ aElementOf0(X265,slsdtgt0(xa)) )
      & ( ~ aElement0(X267)
        | sdtasdt0(xa,X267) != X265
        | aElementOf0(X265,slsdtgt0(xa)) )
      & ( aElement0(esk34_1(X268))
        | ~ aElementOf0(X268,slsdtgt0(xb)) )
      & ( sdtasdt0(xb,esk34_1(X268)) = X268
        | ~ aElementOf0(X268,slsdtgt0(xb)) )
      & ( ~ aElement0(X270)
        | sdtasdt0(xb,X270) != X268
        | aElementOf0(X268,slsdtgt0(xb)) )
      & aElementOf0(esk35_0,slsdtgt0(xa))
      & aElementOf0(esk36_0,slsdtgt0(xb))
      & sdtpldt0(esk35_0,esk36_0) = esk32_0
      & aElementOf0(esk32_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
      & esk32_0 != sz00 ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2228])])])])]) ).

fof(c_0_7,hypothesis,
    ! [X243,X244,X245,X246,X248,X249,X250,X252,X253,X254,X257,X258,X259] :
      ( aSet0(xI)
      & ( ~ aElementOf0(X244,xI)
        | aElementOf0(sdtpldt0(X243,X244),xI)
        | ~ aElementOf0(X243,xI) )
      & ( ~ aElement0(X245)
        | aElementOf0(sdtasdt0(X245,X243),xI)
        | ~ aElementOf0(X243,xI) )
      & aIdeal0(xI)
      & ( aElement0(esk24_1(X246))
        | ~ aElementOf0(X246,slsdtgt0(xa)) )
      & ( sdtasdt0(xa,esk24_1(X246)) = X246
        | ~ aElementOf0(X246,slsdtgt0(xa)) )
      & ( ~ aElement0(X249)
        | sdtasdt0(xa,X249) != X248
        | aElementOf0(X248,slsdtgt0(xa)) )
      & ( aElement0(esk25_1(X250))
        | ~ aElementOf0(X250,slsdtgt0(xb)) )
      & ( sdtasdt0(xb,esk25_1(X250)) = X250
        | ~ aElementOf0(X250,slsdtgt0(xb)) )
      & ( ~ aElement0(X253)
        | sdtasdt0(xb,X253) != X252
        | aElementOf0(X252,slsdtgt0(xb)) )
      & ( aElementOf0(esk26_1(X254),slsdtgt0(xa))
        | ~ aElementOf0(X254,xI) )
      & ( aElementOf0(esk27_1(X254),slsdtgt0(xb))
        | ~ aElementOf0(X254,xI) )
      & ( sdtpldt0(esk26_1(X254),esk27_1(X254)) = X254
        | ~ aElementOf0(X254,xI) )
      & ( ~ aElementOf0(X258,slsdtgt0(xa))
        | ~ aElementOf0(X259,slsdtgt0(xb))
        | sdtpldt0(X258,X259) != X257
        | aElementOf0(X257,xI) )
      & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    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__2174])])])])])]) ).

fof(c_0_8,negated_conjecture,
    ! [X282,X283,X284] :
      ( ( aElementOf0(esk41_1(X282),slsdtgt0(xa))
        | ~ aElementOf0(X283,slsdtgt0(xa))
        | ~ aElementOf0(X284,slsdtgt0(xb))
        | sdtpldt0(X283,X284) != X282
        | X282 = sz00 )
      & ( aElementOf0(esk42_1(X282),slsdtgt0(xb))
        | ~ aElementOf0(X283,slsdtgt0(xa))
        | ~ aElementOf0(X284,slsdtgt0(xb))
        | sdtpldt0(X283,X284) != X282
        | X282 = sz00 )
      & ( sdtpldt0(esk41_1(X282),esk42_1(X282)) = esk40_1(X282)
        | ~ aElementOf0(X283,slsdtgt0(xa))
        | ~ aElementOf0(X284,slsdtgt0(xb))
        | sdtpldt0(X283,X284) != X282
        | X282 = sz00 )
      & ( aElementOf0(esk40_1(X282),xI)
        | ~ aElementOf0(X283,slsdtgt0(xa))
        | ~ aElementOf0(X284,slsdtgt0(xb))
        | sdtpldt0(X283,X284) != X282
        | X282 = sz00 )
      & ( esk40_1(X282) != sz00
        | ~ aElementOf0(X283,slsdtgt0(xa))
        | ~ aElementOf0(X284,slsdtgt0(xb))
        | sdtpldt0(X283,X284) != X282
        | X282 = sz00 )
      & ( iLess0(sbrdtbr0(esk40_1(X282)),sbrdtbr0(X282))
        | ~ aElementOf0(X283,slsdtgt0(xa))
        | ~ aElementOf0(X284,slsdtgt0(xb))
        | sdtpldt0(X283,X284) != X282
        | X282 = sz00 )
      & ( aElementOf0(esk41_1(X282),slsdtgt0(xa))
        | ~ aElementOf0(X282,xI)
        | X282 = sz00 )
      & ( aElementOf0(esk42_1(X282),slsdtgt0(xb))
        | ~ aElementOf0(X282,xI)
        | X282 = sz00 )
      & ( sdtpldt0(esk41_1(X282),esk42_1(X282)) = esk40_1(X282)
        | ~ aElementOf0(X282,xI)
        | X282 = sz00 )
      & ( aElementOf0(esk40_1(X282),xI)
        | ~ aElementOf0(X282,xI)
        | X282 = sz00 )
      & ( esk40_1(X282) != sz00
        | ~ aElementOf0(X282,xI)
        | X282 = sz00 )
      & ( iLess0(sbrdtbr0(esk40_1(X282)),sbrdtbr0(X282))
        | ~ aElementOf0(X282,xI)
        | X282 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).

fof(c_0_9,hypothesis,
    ! [X273,X274,X275,X279,X280,X281] :
      ( ( aElementOf0(esk38_0,slsdtgt0(xa))
        | ~ aElementOf0(X274,slsdtgt0(xa))
        | ~ aElementOf0(X275,slsdtgt0(xb))
        | sdtpldt0(X274,X275) != X273
        | X273 = sz00 )
      & ( aElementOf0(esk39_0,slsdtgt0(xb))
        | ~ aElementOf0(X274,slsdtgt0(xa))
        | ~ aElementOf0(X275,slsdtgt0(xb))
        | sdtpldt0(X274,X275) != X273
        | X273 = sz00 )
      & ( sdtpldt0(esk38_0,esk39_0) = esk37_0
        | ~ aElementOf0(X274,slsdtgt0(xa))
        | ~ aElementOf0(X275,slsdtgt0(xb))
        | sdtpldt0(X274,X275) != X273
        | X273 = sz00 )
      & ( aElementOf0(esk37_0,xI)
        | ~ aElementOf0(X274,slsdtgt0(xa))
        | ~ aElementOf0(X275,slsdtgt0(xb))
        | sdtpldt0(X274,X275) != X273
        | X273 = sz00 )
      & ( esk37_0 != sz00
        | ~ aElementOf0(X274,slsdtgt0(xa))
        | ~ aElementOf0(X275,slsdtgt0(xb))
        | sdtpldt0(X274,X275) != X273
        | X273 = sz00 )
      & ( ~ aElementOf0(X280,slsdtgt0(xa))
        | ~ aElementOf0(X281,slsdtgt0(xb))
        | sdtpldt0(X280,X281) != X279
        | X279 = sz00
        | ~ iLess0(sbrdtbr0(X279),sbrdtbr0(esk37_0))
        | ~ aElementOf0(X274,slsdtgt0(xa))
        | ~ aElementOf0(X275,slsdtgt0(xb))
        | sdtpldt0(X274,X275) != X273
        | X273 = sz00 )
      & ( ~ aElementOf0(X279,xI)
        | X279 = sz00
        | ~ iLess0(sbrdtbr0(X279),sbrdtbr0(esk37_0))
        | ~ aElementOf0(X274,slsdtgt0(xa))
        | ~ aElementOf0(X275,slsdtgt0(xb))
        | sdtpldt0(X274,X275) != X273
        | X273 = sz00 )
      & ( aElementOf0(esk38_0,slsdtgt0(xa))
        | ~ aElementOf0(X273,xI)
        | X273 = sz00 )
      & ( aElementOf0(esk39_0,slsdtgt0(xb))
        | ~ aElementOf0(X273,xI)
        | X273 = sz00 )
      & ( sdtpldt0(esk38_0,esk39_0) = esk37_0
        | ~ aElementOf0(X273,xI)
        | X273 = sz00 )
      & ( aElementOf0(esk37_0,xI)
        | ~ aElementOf0(X273,xI)
        | X273 = sz00 )
      & ( esk37_0 != sz00
        | ~ aElementOf0(X273,xI)
        | X273 = sz00 )
      & ( ~ aElementOf0(X280,slsdtgt0(xa))
        | ~ aElementOf0(X281,slsdtgt0(xb))
        | sdtpldt0(X280,X281) != X279
        | X279 = sz00
        | ~ iLess0(sbrdtbr0(X279),sbrdtbr0(esk37_0))
        | ~ aElementOf0(X273,xI)
        | X273 = sz00 )
      & ( ~ aElementOf0(X279,xI)
        | X279 = sz00
        | ~ iLess0(sbrdtbr0(X279),sbrdtbr0(esk37_0))
        | ~ aElementOf0(X273,xI)
        | X273 = sz00 ) ),
    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)],[c_0_5])])])])])]) ).

cnf(c_0_10,hypothesis,
    aElementOf0(esk32_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,hypothesis,
    xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,negated_conjecture,
    ( iLess0(sbrdtbr0(esk40_1(X1)),sbrdtbr0(X1))
    | X1 = sz00
    | ~ aElementOf0(X2,slsdtgt0(xa))
    | ~ aElementOf0(X3,slsdtgt0(xb))
    | sdtpldt0(X2,X3) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,hypothesis,
    ( sdtpldt0(esk38_0,esk39_0) = esk37_0
    | X1 = sz00
    | ~ aElementOf0(X1,xI) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,hypothesis,
    aElementOf0(esk32_0,xI),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,hypothesis,
    esk32_0 != sz00,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_16,hypothesis,
    ( aElementOf0(esk39_0,slsdtgt0(xb))
    | X1 = sz00
    | ~ aElementOf0(X1,xI) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,hypothesis,
    ( aElementOf0(esk38_0,slsdtgt0(xa))
    | X1 = sz00
    | ~ aElementOf0(X1,xI) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,hypothesis,
    ( X1 = sz00
    | esk37_0 != sz00
    | ~ aElementOf0(X1,xI) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    ( aElementOf0(esk40_1(X1),xI)
    | X1 = sz00
    | ~ aElementOf0(X2,slsdtgt0(xa))
    | ~ aElementOf0(X3,slsdtgt0(xb))
    | sdtpldt0(X2,X3) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,hypothesis,
    ( aElementOf0(esk37_0,xI)
    | X1 = sz00
    | ~ aElementOf0(X1,xI) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_21,negated_conjecture,
    ( sdtpldt0(X1,X2) = sz00
    | iLess0(sbrdtbr0(esk40_1(sdtpldt0(X1,X2))),sbrdtbr0(sdtpldt0(X1,X2)))
    | ~ aElementOf0(X2,slsdtgt0(xb))
    | ~ aElementOf0(X1,slsdtgt0(xa)) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_22,hypothesis,
    sdtpldt0(esk38_0,esk39_0) = esk37_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

cnf(c_0_23,hypothesis,
    aElementOf0(esk39_0,slsdtgt0(xb)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_15]) ).

cnf(c_0_24,hypothesis,
    aElementOf0(esk38_0,slsdtgt0(xa)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]) ).

cnf(c_0_25,hypothesis,
    esk37_0 != sz00,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15]) ).

cnf(c_0_26,negated_conjecture,
    ( sdtpldt0(X1,X2) = sz00
    | aElementOf0(esk40_1(sdtpldt0(X1,X2)),xI)
    | ~ aElementOf0(X2,slsdtgt0(xb))
    | ~ aElementOf0(X1,slsdtgt0(xa)) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_27,negated_conjecture,
    ( X1 = sz00
    | esk40_1(X1) != sz00
    | ~ aElementOf0(X1,xI) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_28,hypothesis,
    aElementOf0(esk37_0,xI),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_15]) ).

cnf(c_0_29,hypothesis,
    ( X1 = sz00
    | X2 = sz00
    | ~ aElementOf0(X1,xI)
    | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk37_0))
    | ~ aElementOf0(X2,xI) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_30,hypothesis,
    iLess0(sbrdtbr0(esk40_1(esk37_0)),sbrdtbr0(esk37_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).

cnf(c_0_31,hypothesis,
    aElementOf0(esk40_1(esk37_0),xI),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).

cnf(c_0_32,negated_conjecture,
    esk40_1(esk37_0) != sz00,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]) ).

cnf(c_0_33,hypothesis,
    ( X1 = sz00
    | ~ aElementOf0(X1,xI) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).

cnf(c_0_34,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_32]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : RNG112+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11  % 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 : n026.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 01:50:53 EDT 2026
% 0.15/0.32  % CPUTime    : 
% 0.15/0.33  % start to proof: theBenchmark
% 1.36/1.75  % Version  : CSE_E---1.7
% 1.36/1.75  % Problem  : theBenchmark.p
% 1.36/1.75  % SZS status Theorem for theBenchmark.p
% 1.36/1.75  % SZS output start CNFRefutation
% See solution above
% 1.36/1.76  % Total time : 1.371s
%------------------------------------------------------------------------------