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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWC327+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n019.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 05:19:12 PM UTC 2026

% Result   : Theorem 1.46s 1.79s
% Output   : CNFRefutation 1.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   67 (  19 unt;   0 def)
%            Number of atoms       :  302 ( 149 equ)
%            Maximal formula atoms :   66 (   4 avg)
%            Number of connectives :  390 ( 155   ~; 168   |;  41   &)
%                                         (   1 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   78 (   0 sgn  38   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssList(X5)
                       => ( app(X3,X5) != X4
                          | ~ equalelemsP(X3)
                          | ? [X6] :
                              ( ssItem(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(cons(X6,nil),X7) = X5
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                    | ( nil != X4
                      & nil = X3 )
                    | ( ? [X9] :
                          ( ssList(X9)
                          & app(X1,X9) = X2
                          & ! [X10] :
                              ( ssItem(X10)
                             => ! [X11] :
                                  ( ssList(X11)
                                 => ( app(cons(X10,nil),X11) != X9
                                    | ! [X12] :
                                        ( ssList(X12)
                                       => app(X12,cons(X10,nil)) != X1 ) ) ) )
                          & equalelemsP(X1) )
                      & ( nil != X1
                        | nil = X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).

fof(ax17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

fof(ax83,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).

fof(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).

fof(ax81,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).

fof(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssList(X5)
                         => ( app(X3,X5) != X4
                            | ~ equalelemsP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssList(X8)
                                        & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                      | ( nil != X4
                        & nil = X3 )
                      | ( ? [X9] :
                            ( ssList(X9)
                            & app(X1,X9) = X2
                            & ! [X10] :
                                ( ssItem(X10)
                               => ! [X11] :
                                    ( ssList(X11)
                                   => ( app(cons(X10,nil),X11) != X9
                                      | ! [X12] :
                                          ( ssList(X12)
                                         => app(X12,cons(X10,nil)) != X1 ) ) ) )
                            & equalelemsP(X1) )
                        & ( nil != X1
                          | nil = X2 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_8,negated_conjecture,
    ! [X477,X478,X479,X480] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ssList(esk52_0)
      & app(esk50_0,esk52_0) = esk51_0
      & equalelemsP(esk50_0)
      & ( ~ ssItem(X477)
        | ~ ssList(X478)
        | app(cons(X477,nil),X478) != esk52_0
        | ~ ssList(X479)
        | app(X479,cons(X477,nil)) != esk50_0 )
      & ( nil = esk51_0
        | nil != esk50_0 )
      & ( nil = esk48_0
        | ssItem(esk53_1(X480))
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil != esk49_0
        | ssItem(esk53_1(X480))
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil = esk48_0
        | ssList(esk54_1(X480))
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil != esk49_0
        | ssList(esk54_1(X480))
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil = esk48_0
        | app(cons(esk53_1(X480),nil),esk54_1(X480)) = X480
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil != esk49_0
        | app(cons(esk53_1(X480),nil),esk54_1(X480)) = X480
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil = esk48_0
        | ssList(esk55_1(X480))
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil != esk49_0
        | ssList(esk55_1(X480))
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil = esk48_0
        | app(esk55_1(X480),cons(esk53_1(X480),nil)) = esk48_0
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) )
      & ( nil != esk49_0
        | app(esk55_1(X480),cons(esk53_1(X480),nil)) = esk48_0
        | ~ ssList(X480)
        | app(esk48_0,X480) != esk49_0
        | ~ equalelemsP(esk48_0) ) ),
    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_7])])])])]) ).

cnf(c_0_9,negated_conjecture,
    equalelemsP(esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_10,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    ( nil = esk48_0
    | app(esk55_1(X1),cons(esk53_1(X1),nil)) = esk48_0
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    equalelemsP(esk48_0),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    app(esk50_0,esk52_0) = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,negated_conjecture,
    ( nil = esk48_0
    | ssItem(esk53_1(X1))
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_16,negated_conjecture,
    ( nil = esk48_0
    | ssList(esk55_1(X1))
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != esk52_0
    | ~ ssList(X3)
    | app(X3,cons(X1,nil)) != esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_18,negated_conjecture,
    ( app(esk55_1(X1),cons(esk53_1(X1),nil)) = esk48_0
    | esk48_0 = nil
    | app(esk48_0,X1) != esk49_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).

cnf(c_0_19,negated_conjecture,
    app(esk48_0,esk52_0) = esk49_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_10]),c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    ssList(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,negated_conjecture,
    ( esk48_0 = nil
    | ssItem(esk53_1(X1))
    | app(esk48_0,X1) != esk49_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_12])]) ).

cnf(c_0_22,negated_conjecture,
    ( esk48_0 = nil
    | ssList(esk55_1(X1))
    | app(esk48_0,X1) != esk49_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_12])]) ).

cnf(c_0_23,negated_conjecture,
    ( nil = esk48_0
    | app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_24,negated_conjecture,
    ( nil = esk48_0
    | ssList(esk54_1(X1))
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_25,negated_conjecture,
    ( app(X1,cons(X2,nil)) != esk48_0
    | app(cons(X2,nil),X3) != esk52_0
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssItem(X2) ),
    inference(rw,[status(thm)],[c_0_17,c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    ( app(esk55_1(esk52_0),cons(esk53_1(esk52_0),nil)) = esk48_0
    | esk48_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).

cnf(c_0_27,negated_conjecture,
    ( esk48_0 = nil
    | ssItem(esk53_1(esk52_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_20])]) ).

cnf(c_0_28,negated_conjecture,
    ( esk48_0 = nil
    | ssList(esk55_1(esk52_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_20])]) ).

cnf(c_0_29,negated_conjecture,
    ( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
    | esk48_0 = nil
    | app(esk48_0,X1) != esk49_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_12])]) ).

cnf(c_0_30,negated_conjecture,
    ( esk48_0 = nil
    | ssList(esk54_1(X1))
    | app(esk48_0,X1) != esk49_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_12])]) ).

cnf(c_0_31,negated_conjecture,
    ( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
    | nil != esk49_0
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_32,plain,
    ! [X448] :
      ( ~ ssList(X448)
      | app(X448,nil) = X448 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_33,negated_conjecture,
    ( nil = esk51_0
    | nil != esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_34,negated_conjecture,
    ( esk48_0 = nil
    | app(cons(esk53_1(esk52_0),nil),X1) != esk52_0
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ( app(cons(esk53_1(esk52_0),nil),esk54_1(esk52_0)) = esk52_0
    | esk48_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_20])]) ).

cnf(c_0_36,negated_conjecture,
    ( esk48_0 = nil
    | ssList(esk54_1(esk52_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_20])]) ).

cnf(c_0_37,negated_conjecture,
    ( ssList(esk54_1(X1))
    | nil != esk49_0
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_38,negated_conjecture,
    ( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
    | app(esk48_0,X1) != esk49_0
    | esk49_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_12])]) ).

cnf(c_0_39,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_40,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_41,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_42,negated_conjecture,
    ( esk49_0 = nil
    | esk48_0 != nil ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_14]),c_0_10]) ).

cnf(c_0_43,negated_conjecture,
    esk48_0 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_44,negated_conjecture,
    ( ssList(esk54_1(X1))
    | app(esk48_0,X1) != esk49_0
    | esk49_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_12])]) ).

cnf(c_0_45,negated_conjecture,
    ( ssItem(esk53_1(X1))
    | nil != esk49_0
    | ~ ssList(X1)
    | app(esk48_0,X1) != esk49_0
    | ~ equalelemsP(esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_46,plain,
    ! [X446,X447] :
      ( ( nil = X447
        | nil != app(X446,X447)
        | ~ ssList(X447)
        | ~ ssList(X446) )
      & ( nil = X446
        | nil != app(X446,X447)
        | ~ ssList(X447)
        | ~ ssList(X446) )
      & ( nil != X447
        | nil != X446
        | nil = app(X446,X447)
        | ~ ssList(X447)
        | ~ ssList(X446) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_47,negated_conjecture,
    ( app(cons(esk53_1(nil),nil),esk54_1(nil)) = nil
    | esk49_0 != esk48_0
    | esk49_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).

cnf(c_0_48,negated_conjecture,
    esk49_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).

cnf(c_0_49,negated_conjecture,
    ( ssList(esk54_1(nil))
    | esk49_0 != esk48_0
    | esk49_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_40]),c_0_41])]) ).

cnf(c_0_50,negated_conjecture,
    ( ssItem(esk53_1(X1))
    | app(esk48_0,X1) != esk49_0
    | esk49_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_12])]) ).

cnf(c_0_51,plain,
    ( nil = X1
    | nil != app(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_52,negated_conjecture,
    app(cons(esk53_1(nil),nil),esk54_1(nil)) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_43])]),c_0_48])]) ).

cnf(c_0_53,negated_conjecture,
    ssList(esk54_1(nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_43])]),c_0_48])]) ).

fof(c_0_54,plain,
    ! [X332,X333] :
      ( ~ ssList(X332)
      | ~ ssItem(X333)
      | ssList(cons(X333,X332)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_55,negated_conjecture,
    ( ssItem(esk53_1(nil))
    | esk49_0 != esk48_0
    | esk49_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_39]),c_0_40]),c_0_41])]) ).

cnf(c_0_56,negated_conjecture,
    ( esk54_1(nil) = nil
    | ~ ssList(cons(esk53_1(nil),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).

cnf(c_0_57,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_58,negated_conjecture,
    ssItem(esk53_1(nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_43])]),c_0_48])]) ).

fof(c_0_59,plain,
    ! [X441,X442] :
      ( ~ ssList(X441)
      | ~ ssItem(X442)
      | cons(X442,X441) = app(cons(X442,nil),X441) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_60,negated_conjecture,
    esk54_1(nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_40]),c_0_58])]) ).

fof(c_0_61,plain,
    ! [X334,X335] :
      ( ~ ssList(X334)
      | ~ ssItem(X335)
      | cons(X335,X334) != X334 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_62,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_63,negated_conjecture,
    app(cons(esk53_1(nil),nil),nil) = nil,
    inference(rw,[status(thm)],[c_0_52,c_0_60]) ).

cnf(c_0_64,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_65,negated_conjecture,
    cons(esk53_1(nil),nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_40]),c_0_58])]) ).

cnf(c_0_66,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_40]),c_0_58])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : SWC327+1 : TPTP v9.2.1. Released v2.4.0.
% 0.12/0.14  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.35  % Computer : n019.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit   : 300
% 0.16/0.35  % WCLimit    : 300
% 0.16/0.35  % DateTime   : Tue May  5 04:44:14 EDT 2026
% 0.16/0.35  % CPUTime    : 
% 0.20/0.36  % start to proof: theBenchmark
% 1.46/1.79  % Version  : CSE_E---1.7
% 1.46/1.79  % Problem  : theBenchmark.p
% 1.46/1.79  % SZS status Theorem for theBenchmark.p
% 1.46/1.79  % SZS output start CNFRefutation
% See solution above
% 1.46/1.79  % Total time : 1.376s
%------------------------------------------------------------------------------