TSTP Solution File: SWC091+1 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : SWC091+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% 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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:39:17 EDT 2023

% Result   : Theorem 0.17s 0.59s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  189 (  45 unt;   0 def)
%            Number of atoms       :  645 ( 168 equ)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  771 ( 315   ~; 333   |;  48   &)
%                                         (   6 <=>;  69  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  232 (   0 sgn; 120   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ neq(X2,nil)
                    | ~ frontsegP(X4,X3)
                    | ~ totalorderedP(X3)
                    | ? [X5] :
                        ( ssList(X5)
                        & neq(X5,nil)
                        & segmentP(X2,X5)
                        & segmentP(X1,X5) )
                    | ? [X6] :
                        ( ssList(X6)
                        & neq(X3,X6)
                        & frontsegP(X4,X6)
                        & segmentP(X6,X3)
                        & totalorderedP(X6) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',co1) ).

fof(ax43,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( frontsegP(X1,X2)
               => frontsegP(app(X1,X3),X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax43) ).

fof(ax45,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,nil) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax45) ).

fof(ax5,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax5) ).

fof(ax17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax17) ).

fof(ax28,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax28) ).

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/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax7) ).

fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax84) ).

fof(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax26) ).

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/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax82) ).

fof(ax50,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( rearsegP(X1,X2)
               => rearsegP(app(X3,X1),X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax50) ).

fof(ax51,axiom,
    ! [X1] :
      ( ssList(X1)
     => rearsegP(X1,nil) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax51) ).

fof(ax55,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax55) ).

fof(ax6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( rearsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax6) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax15) ).

fof(ax78,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax78) ).

fof(ax85,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => hd(app(X1,X2)) = hd(X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax85) ).

fof(ax83,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax83) ).

fof(ax19,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => ! [X4] :
                  ( ssItem(X4)
                 => ( cons(X3,X1) = cons(X4,X2)
                   => ( X3 = X4
                      & X2 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax19) ).

fof(ax20,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax20) ).

fof(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax16) ).

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax21) ).

fof(ax24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax24) ).

fof(ax79,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X3,X2) = app(X1,X2)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax79) ).

fof(ax22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax22) ).

fof(ax23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => hd(cons(X2,X1)) = X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax23) ).

fof(ax44,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( frontsegP(cons(X1,X3),cons(X2,X4))
                  <=> ( X1 = X2
                      & frontsegP(X3,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax44) ).

fof(ax57,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,nil) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax57) ).

fof(ax65,axiom,
    ! [X1] :
      ( ssItem(X1)
     => totalorderedP(cons(X1,nil)) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax65) ).

fof(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p',ax18) ).

fof(c_0_30,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ neq(X2,nil)
                      | ~ frontsegP(X4,X3)
                      | ~ totalorderedP(X3)
                      | ? [X5] :
                          ( ssList(X5)
                          & neq(X5,nil)
                          & segmentP(X2,X5)
                          & segmentP(X1,X5) )
                      | ? [X6] :
                          ( ssList(X6)
                          & neq(X3,X6)
                          & frontsegP(X4,X6)
                          & segmentP(X6,X3)
                          & totalorderedP(X6) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_31,negated_conjecture,
    ! [X11,X12] :
      ( ssList(esk1_0)
      & ssList(esk2_0)
      & ssList(esk3_0)
      & ssList(esk4_0)
      & esk2_0 = esk4_0
      & esk1_0 = esk3_0
      & neq(esk2_0,nil)
      & frontsegP(esk4_0,esk3_0)
      & totalorderedP(esk3_0)
      & ( ~ ssList(X11)
        | ~ neq(X11,nil)
        | ~ segmentP(esk2_0,X11)
        | ~ segmentP(esk1_0,X11) )
      & ( ~ ssList(X12)
        | ~ neq(esk3_0,X12)
        | ~ frontsegP(esk4_0,X12)
        | ~ segmentP(X12,esk3_0)
        | ~ totalorderedP(X12) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).

fof(c_0_32,plain,
    ! [X55,X56,X57] :
      ( ~ ssList(X55)
      | ~ ssList(X56)
      | ~ ssList(X57)
      | ~ frontsegP(X55,X56)
      | frontsegP(app(X55,X57),X56) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).

fof(c_0_33,plain,
    ! [X62] :
      ( ~ ssList(X62)
      | frontsegP(X62,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).

fof(c_0_34,plain,
    ! [X45,X46,X48] :
      ( ( ssList(esk12_2(X45,X46))
        | ~ frontsegP(X45,X46)
        | ~ ssList(X46)
        | ~ ssList(X45) )
      & ( app(X46,esk12_2(X45,X46)) = X45
        | ~ frontsegP(X45,X46)
        | ~ ssList(X46)
        | ~ ssList(X45) )
      & ( ~ ssList(X48)
        | app(X46,X48) != X45
        | frontsegP(X45,X46)
        | ~ ssList(X46)
        | ~ ssList(X45) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).

cnf(c_0_35,negated_conjecture,
    ssList(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_37,negated_conjecture,
    ssList(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_38,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_39,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_40,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_41,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_42,plain,
    ( app(X1,esk12_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_43,negated_conjecture,
    frontsegP(esk4_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_44,negated_conjecture,
    ssList(esk4_0),
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_45,negated_conjecture,
    ssList(esk3_0),
    inference(rw,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_46,plain,
    ( ssList(esk12_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_47,plain,
    ( frontsegP(app(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

cnf(c_0_48,negated_conjecture,
    app(esk3_0,esk12_2(esk4_0,esk3_0)) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).

cnf(c_0_49,negated_conjecture,
    ssList(esk12_2(esk4_0,esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_45]),c_0_44])]) ).

fof(c_0_50,plain,
    ! [X86] :
      ( ~ ssList(X86)
      | app(nil,X86) = X86 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_51,negated_conjecture,
    frontsegP(esk4_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_45])]) ).

fof(c_0_52,plain,
    ! [X27,X28,X31,X32] :
      ( ( ssList(esk10_2(X27,X28))
        | ~ segmentP(X27,X28)
        | ~ ssList(X28)
        | ~ ssList(X27) )
      & ( ssList(esk11_2(X27,X28))
        | ~ segmentP(X27,X28)
        | ~ ssList(X28)
        | ~ ssList(X27) )
      & ( app(app(esk10_2(X27,X28),X28),esk11_2(X27,X28)) = X27
        | ~ segmentP(X27,X28)
        | ~ ssList(X28)
        | ~ ssList(X27) )
      & ( ~ ssList(X31)
        | ~ ssList(X32)
        | app(app(X31,X28),X32) != X27
        | segmentP(X27,X28)
        | ~ ssList(X28)
        | ~ ssList(X27) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).

cnf(c_0_53,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_54,negated_conjecture,
    app(nil,esk12_2(esk4_0,nil)) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_51]),c_0_44]),c_0_41])]) ).

cnf(c_0_55,negated_conjecture,
    ssList(esk12_2(esk4_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_51]),c_0_41]),c_0_44])]) ).

cnf(c_0_56,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_52]) ).

cnf(c_0_57,negated_conjecture,
    esk12_2(esk4_0,nil) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).

cnf(c_0_58,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_56]) ).

cnf(c_0_59,negated_conjecture,
    app(nil,esk4_0) = esk4_0,
    inference(rw,[status(thm)],[c_0_54,c_0_57]) ).

fof(c_0_60,plain,
    ! [X100] :
      ( ~ ssList(X100)
      | app(X100,nil) = X100 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_61,negated_conjecture,
    ( segmentP(app(esk4_0,X1),esk4_0)
    | ~ ssList(app(esk4_0,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_44]),c_0_41])]) ).

cnf(c_0_62,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

fof(c_0_63,plain,
    ! [X81,X82] :
      ( ~ ssList(X81)
      | ~ ssList(X82)
      | ssList(app(X81,X82)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

fof(c_0_64,plain,
    ! [X95,X96,X97] :
      ( ~ ssList(X95)
      | ~ ssList(X96)
      | ~ ssList(X97)
      | app(app(X95,X96),X97) = app(X95,app(X96,X97)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_65,plain,
    ( app(app(esk10_2(X1,X2),X2),esk11_2(X1,X2)) = X1
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_66,negated_conjecture,
    segmentP(esk4_0,esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_44]),c_0_41])]) ).

cnf(c_0_67,plain,
    ( ssList(esk11_2(X1,X2))
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_68,plain,
    ( ssList(esk10_2(X1,X2))
    | ~ segmentP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_69,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_70,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_71,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_72,negated_conjecture,
    app(app(esk10_2(esk4_0,esk4_0),esk4_0),esk11_2(esk4_0,esk4_0)) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_44])]) ).

cnf(c_0_73,negated_conjecture,
    ssList(esk11_2(esk4_0,esk4_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_44])]) ).

cnf(c_0_74,negated_conjecture,
    ssList(esk10_2(esk4_0,esk4_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_66]),c_0_44])]) ).

cnf(c_0_75,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_70]) ).

cnf(c_0_76,negated_conjecture,
    app(esk10_2(esk4_0,esk4_0),app(esk4_0,esk11_2(esk4_0,esk4_0))) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_44]),c_0_74])]) ).

fof(c_0_77,plain,
    ! [X142,X143,X144] :
      ( ~ ssList(X142)
      | ~ ssList(X143)
      | ~ ssList(X144)
      | ~ rearsegP(X142,X143)
      | rearsegP(app(X144,X142),X143) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).

fof(c_0_78,plain,
    ! [X207] :
      ( ~ ssList(X207)
      | rearsegP(X207,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).

cnf(c_0_79,negated_conjecture,
    ( frontsegP(esk4_0,esk10_2(esk4_0,esk4_0))
    | ~ ssList(app(esk4_0,esk11_2(esk4_0,esk4_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_74])]) ).

cnf(c_0_80,plain,
    ( rearsegP(app(X3,X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ rearsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_81,plain,
    ( rearsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_82,negated_conjecture,
    frontsegP(esk4_0,esk10_2(esk4_0,esk4_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_70]),c_0_73]),c_0_44])]) ).

cnf(c_0_83,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(X1,nil)
    | ~ segmentP(esk2_0,X1)
    | ~ segmentP(esk1_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_84,plain,
    ! [X38] :
      ( ~ ssList(X38)
      | segmentP(X38,X38) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).

fof(c_0_85,plain,
    ! [X138,X139,X141] :
      ( ( ssList(esk25_2(X138,X139))
        | ~ rearsegP(X138,X139)
        | ~ ssList(X139)
        | ~ ssList(X138) )
      & ( app(esk25_2(X138,X139),X139) = X138
        | ~ rearsegP(X138,X139)
        | ~ ssList(X139)
        | ~ ssList(X138) )
      & ( ~ ssList(X141)
        | app(X141,X139) != X138
        | rearsegP(X138,X139)
        | ~ ssList(X139)
        | ~ ssList(X138) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).

cnf(c_0_86,plain,
    ( rearsegP(app(X1,X2),nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_41])]) ).

cnf(c_0_87,negated_conjecture,
    app(esk10_2(esk4_0,esk4_0),esk12_2(esk4_0,esk10_2(esk4_0,esk4_0))) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_82]),c_0_44]),c_0_74])]) ).

cnf(c_0_88,negated_conjecture,
    ssList(esk12_2(esk4_0,esk10_2(esk4_0,esk4_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_82]),c_0_74]),c_0_44])]) ).

cnf(c_0_89,negated_conjecture,
    ( ~ segmentP(esk3_0,X1)
    | ~ segmentP(esk4_0,X1)
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_38]),c_0_36]) ).

cnf(c_0_90,plain,
    ( segmentP(X1,X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_91,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_58,c_0_53]),c_0_41])]),c_0_70]) ).

cnf(c_0_92,plain,
    ( app(esk25_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_93,negated_conjecture,
    rearsegP(esk4_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_74]),c_0_88])]) ).

cnf(c_0_94,plain,
    ( ssList(esk25_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_95,negated_conjecture,
    ( ~ segmentP(esk4_0,esk3_0)
    | ~ neq(esk3_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_45])]) ).

cnf(c_0_96,negated_conjecture,
    segmentP(esk4_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_48]),c_0_45]),c_0_49])]) ).

fof(c_0_97,plain,
    ! [X66,X67] :
      ( ( ~ neq(X66,X67)
        | X66 != X67
        | ~ ssList(X67)
        | ~ ssList(X66) )
      & ( X66 = X67
        | neq(X66,X67)
        | ~ ssList(X67)
        | ~ ssList(X66) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

fof(c_0_98,plain,
    ! [X153] :
      ( ~ ssList(X153)
      | nil = X153
      | cons(hd(X153),tl(X153)) = X153 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

fof(c_0_99,plain,
    ! [X145,X146] :
      ( ~ ssList(X145)
      | ~ ssList(X146)
      | nil = X145
      | hd(app(X145,X146)) = hd(X145) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).

fof(c_0_100,plain,
    ! [X98,X99] :
      ( ( nil = X99
        | nil != app(X98,X99)
        | ~ ssList(X99)
        | ~ ssList(X98) )
      & ( nil = X98
        | nil != app(X98,X99)
        | ~ ssList(X99)
        | ~ ssList(X98) )
      & ( nil != X99
        | nil != X98
        | nil = app(X98,X99)
        | ~ ssList(X99)
        | ~ ssList(X98) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_101,negated_conjecture,
    app(esk25_2(esk4_0,nil),nil) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_41]),c_0_44])]) ).

cnf(c_0_102,negated_conjecture,
    ssList(esk25_2(esk4_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_93]),c_0_41]),c_0_44])]) ).

cnf(c_0_103,negated_conjecture,
    ~ neq(esk3_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).

cnf(c_0_104,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

fof(c_0_105,plain,
    ! [X72,X73,X74,X75] :
      ( ( X74 = X75
        | cons(X74,X72) != cons(X75,X73)
        | ~ ssItem(X75)
        | ~ ssItem(X74)
        | ~ ssList(X73)
        | ~ ssList(X72) )
      & ( X73 = X72
        | cons(X74,X72) != cons(X75,X73)
        | ~ ssItem(X75)
        | ~ ssItem(X74)
        | ~ ssList(X73)
        | ~ ssList(X72) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).

fof(c_0_106,plain,
    ! [X76] :
      ( ( ssList(esk13_1(X76))
        | nil = X76
        | ~ ssList(X76) )
      & ( ssItem(esk14_1(X76))
        | nil = X76
        | ~ ssList(X76) )
      & ( cons(esk14_1(X76),esk13_1(X76)) = X76
        | nil = X76
        | ~ ssList(X76) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).

fof(c_0_107,plain,
    ! [X68,X69] :
      ( ~ ssList(X68)
      | ~ ssItem(X69)
      | ssList(cons(X69,X68)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_108,plain,
    ! [X79,X80] :
      ( ~ ssList(X79)
      | ~ ssItem(X80)
      | nil != cons(X80,X79) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_109,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_98]) ).

cnf(c_0_110,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_99]) ).

cnf(c_0_111,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_100]) ).

cnf(c_0_112,negated_conjecture,
    esk25_2(esk4_0,nil) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_101]),c_0_102])]) ).

cnf(c_0_113,negated_conjecture,
    esk3_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_41]),c_0_45])]) ).

cnf(c_0_114,plain,
    ( X1 = X2
    | cons(X3,X2) != cons(X4,X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_105]) ).

cnf(c_0_115,plain,
    ( cons(esk14_1(X1),esk13_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_106]) ).

cnf(c_0_116,plain,
    ( ssItem(esk14_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_106]) ).

cnf(c_0_117,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_107]) ).

cnf(c_0_118,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_108]) ).

cnf(c_0_119,plain,
    ( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
    | nil = X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_70]),c_0_111]) ).

cnf(c_0_120,negated_conjecture,
    app(esk4_0,nil) = esk4_0,
    inference(rw,[status(thm)],[c_0_101,c_0_112]) ).

cnf(c_0_121,negated_conjecture,
    segmentP(esk4_0,nil),
    inference(rw,[status(thm)],[c_0_96,c_0_113]) ).

cnf(c_0_122,plain,
    ( esk13_1(cons(X1,X2)) = X2
    | ~ ssList(esk13_1(cons(X1,X2)))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115])]),c_0_116]),c_0_117]),c_0_118]) ).

cnf(c_0_123,negated_conjecture,
    ( cons(hd(esk4_0),tl(esk4_0)) = esk4_0
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_41]),c_0_44])]) ).

cnf(c_0_124,negated_conjecture,
    app(app(esk10_2(esk4_0,nil),nil),esk11_2(esk4_0,nil)) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_121]),c_0_41]),c_0_44])]) ).

cnf(c_0_125,negated_conjecture,
    ssList(esk10_2(esk4_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_121]),c_0_41]),c_0_44])]) ).

cnf(c_0_126,negated_conjecture,
    ( esk13_1(esk4_0) = tl(esk4_0)
    | esk4_0 = nil
    | ~ ssList(esk13_1(esk4_0))
    | ~ ssList(tl(esk4_0))
    | ~ ssItem(hd(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_122,c_0_123]) ).

cnf(c_0_127,plain,
    ( ssList(esk13_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_106]) ).

fof(c_0_128,plain,
    ! [X209] :
      ( ~ ssList(X209)
      | nil = X209
      | ssList(tl(X209)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

fof(c_0_129,plain,
    ! [X87,X88,X89] :
      ( ~ ssList(X87)
      | ~ ssList(X88)
      | ~ ssList(X89)
      | app(X89,X88) != app(X87,X88)
      | X89 = X87 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).

fof(c_0_130,plain,
    ! [X156] :
      ( ~ ssList(X156)
      | nil = X156
      | ssItem(hd(X156)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_131,negated_conjecture,
    app(esk10_2(esk4_0,nil),esk11_2(esk4_0,nil)) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_62]),c_0_125])]) ).

cnf(c_0_132,negated_conjecture,
    ssList(esk11_2(esk4_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_121]),c_0_41]),c_0_44])]) ).

cnf(c_0_133,negated_conjecture,
    ( esk13_1(esk4_0) = tl(esk4_0)
    | esk4_0 = nil
    | ~ ssList(tl(esk4_0))
    | ~ ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_44])]) ).

cnf(c_0_134,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_128]) ).

cnf(c_0_135,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X3,X2) != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_129]) ).

cnf(c_0_136,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_130]) ).

cnf(c_0_137,negated_conjecture,
    ( hd(esk10_2(esk4_0,nil)) = hd(esk4_0)
    | esk10_2(esk4_0,nil) = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_131]),c_0_132]),c_0_125])]) ).

cnf(c_0_138,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_100]) ).

cnf(c_0_139,negated_conjecture,
    ( esk13_1(esk4_0) = tl(esk4_0)
    | esk4_0 = nil
    | ~ ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_44])]) ).

cnf(c_0_140,plain,
    ( X1 = nil
    | app(X1,X2) != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_53]),c_0_41])]) ).

cnf(c_0_141,negated_conjecture,
    ( esk10_2(esk4_0,nil) = nil
    | ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_125])]) ).

cnf(c_0_142,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_138])]),c_0_41])]) ).

fof(c_0_143,plain,
    ! [X149,X150] :
      ( ~ ssList(X149)
      | ~ ssItem(X150)
      | hd(cons(X150,X149)) = X150 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).

cnf(c_0_144,negated_conjecture,
    ( esk13_1(esk4_0) = tl(esk4_0)
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_136]),c_0_44])]) ).

cnf(c_0_145,negated_conjecture,
    ( app(esk10_2(esk4_0,nil),nil) = nil
    | esk11_2(esk4_0,nil) != esk4_0
    | ~ ssList(app(esk10_2(esk4_0,nil),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_124]),c_0_132])]) ).

cnf(c_0_146,negated_conjecture,
    ( app(nil,esk11_2(esk4_0,nil)) = esk4_0
    | ssItem(hd(esk4_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_141]),c_0_142]) ).

cnf(c_0_147,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_143]) ).

cnf(c_0_148,negated_conjecture,
    ( cons(esk14_1(esk4_0),tl(esk4_0)) = esk4_0
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_144]),c_0_44])]) ).

cnf(c_0_149,negated_conjecture,
    ( esk4_0 = nil
    | ssList(tl(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_144]),c_0_44])]) ).

fof(c_0_150,plain,
    ! [X58,X59,X60,X61] :
      ( ( X58 = X59
        | ~ frontsegP(cons(X58,X60),cons(X59,X61))
        | ~ ssList(X61)
        | ~ ssList(X60)
        | ~ ssItem(X59)
        | ~ ssItem(X58) )
      & ( frontsegP(X60,X61)
        | ~ frontsegP(cons(X58,X60),cons(X59,X61))
        | ~ ssList(X61)
        | ~ ssList(X60)
        | ~ ssItem(X59)
        | ~ ssItem(X58) )
      & ( X58 != X59
        | ~ frontsegP(X60,X61)
        | frontsegP(cons(X58,X60),cons(X59,X61))
        | ~ ssList(X61)
        | ~ ssList(X60)
        | ~ ssItem(X59)
        | ~ ssItem(X58) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).

cnf(c_0_151,negated_conjecture,
    ( app(esk10_2(esk4_0,nil),nil) = nil
    | esk11_2(esk4_0,nil) != esk4_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_70]),c_0_41]),c_0_125])]) ).

cnf(c_0_152,negated_conjecture,
    ( esk11_2(esk4_0,nil) = esk4_0
    | ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_146]),c_0_132])]) ).

cnf(c_0_153,negated_conjecture,
    ( esk14_1(esk4_0) = hd(esk4_0)
    | esk4_0 = nil
    | ~ ssItem(esk14_1(esk4_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]) ).

cnf(c_0_154,plain,
    ( frontsegP(cons(X1,X3),cons(X2,X4))
    | X1 != X2
    | ~ frontsegP(X3,X4)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_150]) ).

cnf(c_0_155,negated_conjecture,
    ( app(esk10_2(esk4_0,nil),nil) = nil
    | ssItem(hd(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_151,c_0_152]) ).

cnf(c_0_156,negated_conjecture,
    ( esk14_1(esk4_0) = hd(esk4_0)
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_116]),c_0_44])]) ).

cnf(c_0_157,plain,
    ( frontsegP(cons(X1,X2),cons(X1,X3))
    | ~ frontsegP(X2,X3)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_154]) ).

cnf(c_0_158,negated_conjecture,
    ( ~ segmentP(nil,X1)
    | ~ segmentP(esk4_0,X1)
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(rw,[status(thm)],[c_0_89,c_0_113]) ).

cnf(c_0_159,negated_conjecture,
    ( segmentP(nil,esk10_2(esk4_0,nil))
    | ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_155]),c_0_125]),c_0_41])]) ).

cnf(c_0_160,negated_conjecture,
    segmentP(esk4_0,esk10_2(esk4_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_131]),c_0_125]),c_0_132])]) ).

cnf(c_0_161,negated_conjecture,
    ( X1 = esk4_0
    | app(X1,nil) != esk4_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_120]),c_0_44]),c_0_41])]) ).

cnf(c_0_162,negated_conjecture,
    ( esk4_0 = nil
    | ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_156]),c_0_44])]) ).

cnf(c_0_163,negated_conjecture,
    neq(esk2_0,nil),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_164,plain,
    ! [X43] :
      ( ~ ssList(X43)
      | segmentP(X43,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).

cnf(c_0_165,plain,
    ( frontsegP(cons(X1,X2),cons(X1,nil))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_40]),c_0_41])]) ).

cnf(c_0_166,negated_conjecture,
    ( ssItem(hd(esk4_0))
    | ~ neq(esk10_2(esk4_0,nil),nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_160]),c_0_125])]) ).

cnf(c_0_167,negated_conjecture,
    ( esk10_2(esk4_0,nil) = esk4_0
    | ssItem(hd(esk4_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_155]),c_0_125])]),c_0_162]) ).

cnf(c_0_168,negated_conjecture,
    neq(esk4_0,nil),
    inference(rw,[status(thm)],[c_0_163,c_0_36]) ).

cnf(c_0_169,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(esk3_0,X1)
    | ~ frontsegP(esk4_0,X1)
    | ~ segmentP(X1,esk3_0)
    | ~ totalorderedP(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_170,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_164]) ).

cnf(c_0_171,negated_conjecture,
    ( esk4_0 = nil
    | frontsegP(esk4_0,cons(esk14_1(esk4_0),nil))
    | ~ ssItem(esk14_1(esk4_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_148]),c_0_149]) ).

cnf(c_0_172,plain,
    ( esk14_1(X1) = hd(X1)
    | nil = X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_115]),c_0_116]),c_0_127]) ).

cnf(c_0_173,negated_conjecture,
    ssItem(hd(esk4_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168])]) ).

cnf(c_0_174,negated_conjecture,
    ( ~ totalorderedP(X1)
    | ~ frontsegP(esk4_0,X1)
    | ~ ssList(X1)
    | ~ neq(nil,X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_113]),c_0_113]),c_0_170]) ).

cnf(c_0_175,negated_conjecture,
    ( esk4_0 = nil
    | frontsegP(esk4_0,cons(hd(esk4_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173]),c_0_44])]) ).

cnf(c_0_176,negated_conjecture,
    ( esk4_0 = nil
    | ~ totalorderedP(cons(hd(esk4_0),nil))
    | ~ ssList(cons(hd(esk4_0),nil))
    | ~ neq(nil,cons(hd(esk4_0),nil)) ),
    inference(spm,[status(thm)],[c_0_174,c_0_175]) ).

fof(c_0_177,plain,
    ! [X24] :
      ( ~ ssItem(X24)
      | totalorderedP(cons(X24,nil)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])]) ).

cnf(c_0_178,negated_conjecture,
    ( esk4_0 = nil
    | ~ totalorderedP(cons(hd(esk4_0),nil))
    | ~ neq(nil,cons(hd(esk4_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_117]),c_0_41]),c_0_173])]) ).

cnf(c_0_179,plain,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_177]) ).

cnf(c_0_180,negated_conjecture,
    ( esk4_0 = nil
    | ~ neq(nil,cons(hd(esk4_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_173])]) ).

fof(c_0_181,plain,
    ! [X70,X71] :
      ( ~ ssList(X70)
      | ~ ssItem(X71)
      | cons(X71,X70) != X70 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_182,negated_conjecture,
    ( cons(hd(esk4_0),nil) = nil
    | esk4_0 = nil
    | ~ ssList(cons(hd(esk4_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_104]),c_0_41])]) ).

cnf(c_0_183,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_181]) ).

cnf(c_0_184,negated_conjecture,
    ( cons(hd(esk4_0),nil) = nil
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_117]),c_0_41]),c_0_173])]) ).

cnf(c_0_185,negated_conjecture,
    ( ~ segmentP(esk4_0,nil)
    | ~ neq(nil,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_170]),c_0_41]),c_0_45])]) ).

cnf(c_0_186,negated_conjecture,
    esk4_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_41]),c_0_173])]) ).

cnf(c_0_187,negated_conjecture,
    ~ neq(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_170]),c_0_44])]) ).

cnf(c_0_188,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_186]),c_0_187]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SWC091+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n005.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 2400
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Tue Oct  3 01:49:34 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.otK7168DFc/E---3.1_9140.p
% 0.17/0.59  # Version: 3.1pre001
% 0.17/0.59  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.59  # Starting sh5l with 300s (1) cores
% 0.17/0.59  # sh5l with pid 9223 completed with status 0
% 0.17/0.59  # Result found by sh5l
% 0.17/0.59  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.59  # Starting sh5l with 300s (1) cores
% 0.17/0.59  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/0.59  # Search class: FGHSF-FSLM21-MFFFFFNN
% 0.17/0.59  # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.59  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 0.17/0.59  # G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 9226 completed with status 0
% 0.17/0.59  # Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 0.17/0.59  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.17/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.17/0.59  # Starting sh5l with 300s (1) cores
% 0.17/0.59  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/0.59  # Search class: FGHSF-FSLM21-MFFFFFNN
% 0.17/0.59  # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.59  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 28s (1) cores
% 0.17/0.59  # Preprocessing time       : 0.003 s
% 0.17/0.59  # Presaturation interreduction done
% 0.17/0.59  
% 0.17/0.59  # Proof found!
% 0.17/0.59  # SZS status Theorem
% 0.17/0.59  # SZS output start CNFRefutation
% See solution above
% 0.17/0.59  # Parsed axioms                        : 96
% 0.17/0.59  # Removed by relevancy pruning/SinE    : 12
% 0.17/0.59  # Initial clauses                      : 167
% 0.17/0.59  # Removed in clause preprocessing      : 2
% 0.17/0.59  # Initial clauses in saturation        : 165
% 0.17/0.59  # Processed clauses                    : 1334
% 0.17/0.59  # ...of these trivial                  : 21
% 0.17/0.59  # ...subsumed                          : 501
% 0.17/0.59  # ...remaining for further processing  : 812
% 0.17/0.59  # Other redundant clauses eliminated   : 63
% 0.17/0.59  # Clauses deleted for lack of memory   : 0
% 0.17/0.59  # Backward-subsumed                    : 76
% 0.17/0.59  # Backward-rewritten                   : 241
% 0.17/0.59  # Generated clauses                    : 3882
% 0.17/0.59  # ...of the previous two non-redundant : 3209
% 0.17/0.59  # ...aggressively subsumed             : 0
% 0.17/0.59  # Contextual simplify-reflections      : 182
% 0.17/0.59  # Paramodulations                      : 3814
% 0.17/0.59  # Factorizations                       : 0
% 0.17/0.59  # NegExts                              : 0
% 0.17/0.59  # Equation resolutions                 : 69
% 0.17/0.59  # Total rewrite steps                  : 4283
% 0.17/0.59  # Propositional unsat checks           : 0
% 0.17/0.59  #    Propositional check models        : 0
% 0.17/0.59  #    Propositional check unsatisfiable : 0
% 0.17/0.59  #    Propositional clauses             : 0
% 0.17/0.59  #    Propositional clauses after purity: 0
% 0.17/0.59  #    Propositional unsat core size     : 0
% 0.17/0.59  #    Propositional preprocessing time  : 0.000
% 0.17/0.59  #    Propositional encoding time       : 0.000
% 0.17/0.59  #    Propositional solver time         : 0.000
% 0.17/0.59  #    Success case prop preproc time    : 0.000
% 0.17/0.59  #    Success case prop encoding time   : 0.000
% 0.17/0.59  #    Success case prop solver time     : 0.000
% 0.17/0.59  # Current number of processed clauses  : 318
% 0.17/0.59  #    Positive orientable unit clauses  : 43
% 0.17/0.59  #    Positive unorientable unit clauses: 0
% 0.17/0.59  #    Negative unit clauses             : 2
% 0.17/0.59  #    Non-unit-clauses                  : 273
% 0.17/0.59  # Current number of unprocessed clauses: 2038
% 0.17/0.59  # ...number of literals in the above   : 11405
% 0.17/0.59  # Current number of archived formulas  : 0
% 0.17/0.59  # Current number of archived clauses   : 476
% 0.17/0.59  # Clause-clause subsumption calls (NU) : 50521
% 0.17/0.59  # Rec. Clause-clause subsumption calls : 17433
% 0.17/0.59  # Non-unit clause-clause subsumptions  : 737
% 0.17/0.59  # Unit Clause-clause subsumption calls : 3332
% 0.17/0.59  # Rewrite failures with RHS unbound    : 0
% 0.17/0.59  # BW rewrite match attempts            : 28
% 0.17/0.59  # BW rewrite match successes           : 22
% 0.17/0.59  # Condensation attempts                : 0
% 0.17/0.59  # Condensation successes               : 0
% 0.17/0.59  # Termbank termtop insertions          : 82958
% 0.17/0.59  
% 0.17/0.59  # -------------------------------------------------
% 0.17/0.59  # User time                : 0.127 s
% 0.17/0.59  # System time              : 0.007 s
% 0.17/0.59  # Total time               : 0.134 s
% 0.17/0.59  # Maximum resident set size: 2472 pages
% 0.17/0.59  
% 0.17/0.59  # -------------------------------------------------
% 0.17/0.59  # User time                : 0.129 s
% 0.17/0.59  # System time              : 0.010 s
% 0.17/0.59  # Total time               : 0.139 s
% 0.17/0.59  # Maximum resident set size: 1796 pages
% 0.17/0.59  % E---3.1 exiting
% 0.17/0.59  % E---3.1 exiting
%------------------------------------------------------------------------------