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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWC382+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 : n020.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 05:19:25 PM UTC 2026

% Result   : Theorem 1.49s 1.78s
% Output   : CNFRefutation 1.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   77 (  12 unt;   0 def)
%            Number of atoms       :  293 (  86 equ)
%            Maximal formula atoms :   30 (   3 avg)
%            Number of connectives :  356 ( 140   ~; 149   |;  34   &)
%                                         (   3 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :   93 (   0 sgn  51   !;   7   ?)

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

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(ax22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).

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(ax23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => hd(cons(X2,X1)) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).

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

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(ax7,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).

fof(ax78,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).

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(ax28,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

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

fof(ax24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).

fof(c_0_14,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X3 != X5
                              & ? [X6] :
                                  ( ssItem(X6)
                                  & cons(X6,nil) = X5
                                  & hd(X4) = X6
                                  & neq(nil,X4) ) )
                          | ( singletonP(X1)
                            & segmentP(X2,X1) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_15,negated_conjecture,
    ! [X464,X465] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ( neq(esk49_0,nil)
        | neq(esk49_0,nil) )
      & ( ~ neq(esk51_0,nil)
        | neq(esk49_0,nil) )
      & ( neq(esk49_0,nil)
        | ~ ssList(X464)
        | esk50_0 = X464
        | ~ ssItem(X465)
        | cons(X465,nil) != X464
        | hd(esk51_0) != X465
        | ~ neq(nil,esk51_0) )
      & ( ~ neq(esk51_0,nil)
        | ~ ssList(X464)
        | esk50_0 = X464
        | ~ ssItem(X465)
        | cons(X465,nil) != X464
        | hd(esk51_0) != X465
        | ~ neq(nil,esk51_0) )
      & ( neq(esk49_0,nil)
        | ~ singletonP(esk48_0)
        | ~ segmentP(esk49_0,esk48_0) )
      & ( ~ neq(esk51_0,nil)
        | ~ singletonP(esk48_0)
        | ~ segmentP(esk49_0,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_14])])])])]) ).

cnf(c_0_16,negated_conjecture,
    ( neq(esk49_0,nil)
    | neq(esk49_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_17,negated_conjecture,
    neq(esk49_0,nil),
    inference(cn,[status(thm)],[c_0_16]) ).

cnf(c_0_18,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    ( esk50_0 = X1
    | ~ neq(esk51_0,nil)
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,nil) != X1
    | hd(esk51_0) != X2
    | ~ neq(nil,esk51_0) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    neq(esk51_0,nil),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

fof(c_0_22,plain,
    ! [X320,X321] :
      ( ~ ssList(X320)
      | ~ ssItem(X321)
      | ssList(cons(X321,X320)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_23,negated_conjecture,
    ( cons(hd(esk51_0),nil) = esk48_0
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ neq(nil,esk51_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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]) ).

fof(c_0_26,plain,
    ! [X333] :
      ( ~ ssList(X333)
      | nil = X333
      | ssItem(hd(X333)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_27,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_28,negated_conjecture,
    ( cons(hd(esk51_0),nil) = esk48_0
    | ~ neq(nil,esk51_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_29,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_30,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_27,c_0_18]) ).

fof(c_0_31,plain,
    ! [X318,X319] :
      ( ( ~ neq(X318,X319)
        | X318 != X319
        | ~ ssList(X319)
        | ~ ssList(X318) )
      & ( X318 = X319
        | neq(X318,X319)
        | ~ ssList(X319)
        | ~ ssList(X318) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

fof(c_0_32,plain,
    ! [X334,X335] :
      ( ~ ssList(X334)
      | ~ ssItem(X335)
      | hd(cons(X335,X334)) = X335 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).

cnf(c_0_33,negated_conjecture,
    ( cons(hd(esk51_0),nil) = esk48_0
    | esk51_0 = nil
    | ~ neq(nil,esk51_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).

cnf(c_0_34,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_35,plain,
    ! [X322,X323] :
      ( ~ ssList(X322)
      | ~ ssItem(X323)
      | cons(X323,X322) != X322 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_36,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    ( cons(hd(esk51_0),nil) = esk48_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]),c_0_25])]) ).

cnf(c_0_38,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    ( hd(esk48_0) = hd(esk51_0)
    | esk51_0 = nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_25])]) ).

cnf(c_0_40,negated_conjecture,
    ( esk51_0 = nil
    | esk48_0 != nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_25])]) ).

fof(c_0_41,plain,
    ! [X429,X430] :
      ( ~ ssList(X429)
      | ~ ssItem(X430)
      | cons(X430,X429) = app(cons(X430,nil),X429) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_42,negated_conjecture,
    ( hd(esk48_0) = hd(esk51_0)
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_29]),c_0_30])]) ).

cnf(c_0_43,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_44,negated_conjecture,
    ( esk51_0 = nil
    | esk48_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_29]),c_0_30])]) ).

fof(c_0_45,plain,
    ! [X237,X238,X241,X242] :
      ( ( ssList(esk8_2(X237,X238))
        | ~ segmentP(X237,X238)
        | ~ ssList(X238)
        | ~ ssList(X237) )
      & ( ssList(esk9_2(X237,X238))
        | ~ segmentP(X237,X238)
        | ~ ssList(X238)
        | ~ ssList(X237) )
      & ( app(app(esk8_2(X237,X238),X238),esk9_2(X237,X238)) = X237
        | ~ segmentP(X237,X238)
        | ~ ssList(X238)
        | ~ ssList(X237) )
      & ( ~ ssList(X241)
        | ~ ssList(X242)
        | app(app(X241,X238),X242) != X237
        | segmentP(X237,X238)
        | ~ ssList(X238)
        | ~ ssList(X237) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).

fof(c_0_46,plain,
    ! [X422] :
      ( ~ ssList(X422)
      | nil = X422
      | cons(hd(X422),tl(X422)) = X422 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

cnf(c_0_47,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_48,negated_conjecture,
    ( esk51_0 = nil
    | ssItem(hd(esk51_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42]),c_0_43])]),c_0_44]) ).

fof(c_0_49,plain,
    ! [X226,X228] :
      ( ( ssItem(esk5_1(X226))
        | ~ singletonP(X226)
        | ~ ssList(X226) )
      & ( cons(esk5_1(X226),nil) = X226
        | ~ singletonP(X226)
        | ~ ssList(X226) )
      & ( ~ ssItem(X228)
        | cons(X228,nil) != X226
        | singletonP(X226)
        | ~ ssList(X226) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).

cnf(c_0_50,plain,
    ( segmentP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(app(X1,X3),X2) != X4
    | ~ ssList(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

fof(c_0_51,plain,
    ! [X344] :
      ( ~ ssList(X344)
      | app(nil,X344) = X344 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

fof(c_0_52,plain,
    ! [X339,X340] :
      ( ~ ssList(X339)
      | ~ ssList(X340)
      | ssList(app(X339,X340)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_53,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_54,negated_conjecture,
    ( cons(hd(esk51_0),X1) = app(esk48_0,X1)
    | esk51_0 = nil
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_48]) ).

fof(c_0_55,plain,
    ! [X336] :
      ( ~ ssList(X336)
      | nil = X336
      | ssList(tl(X336)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

cnf(c_0_56,plain,
    ( singletonP(X2)
    | ~ ssItem(X1)
    | cons(X1,nil) != X2
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_57,plain,
    ( segmentP(app(app(X1,X2),X3),X2)
    | ~ ssList(app(app(X1,X2),X3))
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_50]) ).

cnf(c_0_58,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_59,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_60,negated_conjecture,
    ( app(esk48_0,tl(esk51_0)) = esk51_0
    | esk51_0 = nil
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_30])]) ).

cnf(c_0_61,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_62,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_56]) ).

cnf(c_0_63,plain,
    ( segmentP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_25])]),c_0_59]) ).

cnf(c_0_64,negated_conjecture,
    ( app(esk48_0,tl(esk51_0)) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_30])]) ).

cnf(c_0_65,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_24]),c_0_25])]) ).

cnf(c_0_66,negated_conjecture,
    ( ~ neq(esk51_0,nil)
    | ~ singletonP(esk48_0)
    | ~ segmentP(esk49_0,esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_67,negated_conjecture,
    ( esk51_0 = nil
    | segmentP(esk51_0,esk48_0)
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_43])]) ).

cnf(c_0_68,negated_conjecture,
    ( esk51_0 = nil
    | singletonP(esk48_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(spm,[status(thm)],[c_0_65,c_0_37]) ).

cnf(c_0_69,negated_conjecture,
    ( ~ segmentP(esk51_0,esk48_0)
    | ~ singletonP(esk48_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_21]),c_0_18])]) ).

cnf(c_0_70,negated_conjecture,
    ( esk51_0 = nil
    | segmentP(esk51_0,esk48_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_61]),c_0_30])]) ).

cnf(c_0_71,negated_conjecture,
    ( esk51_0 = nil
    | singletonP(esk48_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_29]),c_0_30])]) ).

cnf(c_0_72,plain,
    ( ~ neq(X1,X2)
    | X1 != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_73,negated_conjecture,
    esk51_0 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).

cnf(c_0_74,plain,
    ( ~ ssList(X1)
    | ~ neq(X1,X1) ),
    inference(er,[status(thm)],[c_0_72]) ).

cnf(c_0_75,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[c_0_21,c_0_73]) ).

cnf(c_0_76,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC382+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
% 0.14/0.33  % Computer : n020.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue May  5 04:47:34 EDT 2026
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 1.49/1.78  % Version  : CSE_E---1.7
% 1.49/1.78  % Problem  : theBenchmark.p
% 1.49/1.78  % SZS status Theorem for theBenchmark.p
% 1.49/1.78  % SZS output start CNFRefutation
% See solution above
% 1.49/1.79  % Total time : 1.374s
%------------------------------------------------------------------------------