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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWC307+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 : n023.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 05:19:07 PM UTC 2026

% Result   : Theorem 1.66s 1.81s
% Output   : CNFRefutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   73 (  29 unt;   0 def)
%            Number of atoms       :  260 (  47 equ)
%            Maximal formula atoms :   30 (   3 avg)
%            Number of connectives :  298 ( 111   ~; 110   |;  28   &)
%                                         (   4 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  10 con; 0-2 aty)
%            Number of variables   :   95 (   0 sgn  65   !;   1   ?)

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

fof(ax82,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).

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

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

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(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).

fof(ax33,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
           => ~ lt(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax33) ).

fof(ax68,axiom,
    ! [X1] :
      ( ssItem(X1)
     => strictorderedP(cons(X1,nil)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax68) ).

fof(ax4,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( singletonP(X1)
      <=> ? [X2] :
            ( ssItem(X2)
            & cons(X2,nil) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

fof(ax12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( strictorderedP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => lt(X2,X3) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax12) ).

fof(ax58,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( segmentP(nil,X1)
      <=> nil = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).

fof(ax69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax69) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ segmentP(X4,X3)
                      | ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssItem(X6)
                             => ! [X7] :
                                  ( ssList(X7)
                                 => ! [X8] :
                                      ( ssList(X8)
                                     => ! [X9] :
                                          ( ssList(X9)
                                         => ( app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
                                            | ~ lt(X6,X5) ) ) ) ) ) )
                      | ( ~ singletonP(X3)
                        & neq(X4,nil) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_14,negated_conjecture,
    ( ssList(esk48_0)
    & ssList(esk49_0)
    & ssList(esk50_0)
    & ssList(esk51_0)
    & esk49_0 = esk51_0
    & esk48_0 = esk50_0
    & segmentP(esk51_0,esk50_0)
    & ssItem(esk52_0)
    & ssItem(esk53_0)
    & ssList(esk54_0)
    & ssList(esk55_0)
    & ssList(esk56_0)
    & app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
    & lt(esk53_0,esk52_0)
    & ( singletonP(esk50_0)
      | ~ neq(esk51_0,nil) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

cnf(c_0_15,negated_conjecture,
    app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_16,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_17,plain,
    ! [X437,X438,X439] :
      ( ~ ssList(X437)
      | ~ ssList(X438)
      | ~ ssList(X439)
      | app(app(X437,X438),X439) = app(X437,app(X438,X439)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_18,negated_conjecture,
    app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk50_0,
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    ssList(esk55_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,negated_conjecture,
    ssList(esk54_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_22,plain,
    ! [X326,X327] :
      ( ~ ssList(X326)
      | ~ ssItem(X327)
      | ssList(cons(X327,X326)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_23,negated_conjecture,
    ( app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0
    | ~ ssList(cons(esk52_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).

cnf(c_0_24,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_25,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_26,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_27,plain,
    ! [X435,X436] :
      ( ~ ssList(X435)
      | ~ ssItem(X436)
      | cons(X436,X435) = app(cons(X436,nil),X435) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_28,negated_conjecture,
    app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_29,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    app(app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]),c_0_26])]) ).

cnf(c_0_31,negated_conjecture,
    ssList(esk56_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_32,negated_conjecture,
    ( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
    | ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
    | ~ ssList(cons(esk53_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_30]),c_0_31])]) ).

cnf(c_0_33,negated_conjecture,
    ssItem(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_34,plain,
    ! [X345,X346] :
      ( ~ ssList(X345)
      | ~ ssList(X346)
      | ssList(app(X345,X346)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_35,negated_conjecture,
    ( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
    | ~ ssList(app(esk54_0,cons(esk52_0,esk55_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_25]),c_0_33])]) ).

cnf(c_0_36,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

fof(c_0_37,plain,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
           => ~ lt(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[ax33]) ).

fof(c_0_38,plain,
    ! [X417] :
      ( ~ ssItem(X417)
      | strictorderedP(cons(X417,nil)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax68])]) ).

fof(c_0_39,plain,
    ! [X232,X234] :
      ( ( ssItem(esk5_1(X232))
        | ~ singletonP(X232)
        | ~ ssList(X232) )
      & ( cons(esk5_1(X232),nil) = X232
        | ~ singletonP(X232)
        | ~ ssList(X232) )
      & ( ~ ssItem(X234)
        | cons(X234,nil) != X232
        | singletonP(X232)
        | ~ ssList(X232) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).

fof(c_0_40,plain,
    ! [X324,X325] :
      ( ( ~ neq(X324,X325)
        | X324 != X325
        | ~ ssList(X325)
        | ~ ssList(X324) )
      & ( X324 = X325
        | neq(X324,X325)
        | ~ ssList(X325)
        | ~ ssList(X324) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_41,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_42,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_43,plain,
    ! [X293,X294,X295,X296,X297,X298] :
      ( ( ~ strictorderedP(X293)
        | ~ ssItem(X294)
        | ~ ssItem(X295)
        | ~ ssList(X296)
        | ~ ssList(X297)
        | ~ ssList(X298)
        | app(app(X296,cons(X294,X297)),cons(X295,X298)) != X293
        | lt(X294,X295)
        | ~ ssList(X293) )
      & ( ssItem(esk30_1(X293))
        | strictorderedP(X293)
        | ~ ssList(X293) )
      & ( ssItem(esk31_1(X293))
        | strictorderedP(X293)
        | ~ ssList(X293) )
      & ( ssList(esk32_1(X293))
        | strictorderedP(X293)
        | ~ ssList(X293) )
      & ( ssList(esk33_1(X293))
        | strictorderedP(X293)
        | ~ ssList(X293) )
      & ( ssList(esk34_1(X293))
        | strictorderedP(X293)
        | ~ ssList(X293) )
      & ( app(app(esk32_1(X293),cons(esk30_1(X293),esk33_1(X293))),cons(esk31_1(X293),esk34_1(X293))) = X293
        | strictorderedP(X293)
        | ~ ssList(X293) )
      & ( ~ lt(esk30_1(X293),esk31_1(X293))
        | strictorderedP(X293)
        | ~ ssList(X293) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])]) ).

cnf(c_0_44,negated_conjecture,
    ( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
    | ~ ssList(cons(esk52_0,esk55_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_21])]) ).

fof(c_0_45,plain,
    ! [X359,X360] :
      ( ~ ssItem(X359)
      | ~ ssItem(X360)
      | ~ lt(X359,X360)
      | ~ lt(X360,X359) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).

cnf(c_0_46,plain,
    ( strictorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_47,plain,
    ( cons(esk5_1(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_48,plain,
    ( ssItem(esk5_1(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_49,negated_conjecture,
    ( singletonP(esk50_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_50,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_51,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_52,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_53,plain,
    ( lt(X2,X3)
    | ~ strictorderedP(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(X6)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_54,negated_conjecture,
    app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_24]),c_0_20]),c_0_26])]) ).

cnf(c_0_55,plain,
    ( ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ lt(X1,X2)
    | ~ lt(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_56,negated_conjecture,
    lt(esk53_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_57,plain,
    ( strictorderedP(X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_58,negated_conjecture,
    ( esk51_0 = nil
    | singletonP(esk50_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_25]),c_0_51])]) ).

cnf(c_0_59,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_52,c_0_16]) ).

cnf(c_0_60,plain,
    ( lt(X1,X2)
    | ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,esk56_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_29]),c_0_31]),c_0_33])]) ).

cnf(c_0_62,negated_conjecture,
    ~ lt(esk52_0,esk53_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_33]),c_0_26])]) ).

cnf(c_0_63,negated_conjecture,
    ( esk51_0 = nil
    | strictorderedP(esk50_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).

cnf(c_0_64,negated_conjecture,
    ~ strictorderedP(esk50_0),
    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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_59]),c_0_31]),c_0_20]),c_0_21]),c_0_33]),c_0_26])]),c_0_62]) ).

fof(c_0_65,plain,
    ! [X410] :
      ( ( ~ segmentP(nil,X410)
        | nil = X410
        | ~ ssList(X410) )
      & ( nil != X410
        | segmentP(nil,X410)
        | ~ ssList(X410) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])]) ).

cnf(c_0_66,negated_conjecture,
    segmentP(esk51_0,esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_67,negated_conjecture,
    esk51_0 = nil,
    inference(sr,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_68,plain,
    ( nil = X1
    | ~ segmentP(nil,X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_69,negated_conjecture,
    segmentP(nil,esk50_0),
    inference(rw,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_70,negated_conjecture,
    esk50_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_59])]) ).

cnf(c_0_71,plain,
    strictorderedP(nil),
    inference(split_conjunct,[status(thm)],[ax69]) ).

cnf(c_0_72,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_70]),c_0_71])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC307+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12  % 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
% 0.16/0.33  % Computer : n023.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Tue May  5 04:43:38 EDT 2026
% 0.16/0.33  % CPUTime    : 
% 0.16/0.34  % start to proof: theBenchmark
% 1.66/1.81  % Version  : CSE_E---1.7
% 1.66/1.81  % Problem  : theBenchmark.p
% 1.66/1.81  % SZS status Theorem for theBenchmark.p
% 1.66/1.81  % SZS output start CNFRefutation
% See solution above
% 1.66/1.81  % Total time : 1.374s
%------------------------------------------------------------------------------