TSTP Solution File: SWC072+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC072+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:19:34 EDT 2023

% Result   : Theorem 0.20s 0.78s
% Output   : CNFRefutation 0.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :  100
% Syntax   : Number of formulae    :  251 (  44 unt;  75 typ;   0 def)
%            Number of atoms       :  636 ( 194 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  799 ( 339   ~; 334   |;  63   &)
%                                         (   6 <=>;  57  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   56 (  56 usr;   7 con; 0-2 aty)
%            Number of variables   :  218 (   0 sgn; 105   !;  16   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ssItem: $i > $o ).

tff(decl_23,type,
    neq: ( $i * $i ) > $o ).

tff(decl_24,type,
    ssList: $i > $o ).

tff(decl_25,type,
    memberP: ( $i * $i ) > $o ).

tff(decl_26,type,
    cons: ( $i * $i ) > $i ).

tff(decl_27,type,
    app: ( $i * $i ) > $i ).

tff(decl_28,type,
    singletonP: $i > $o ).

tff(decl_29,type,
    nil: $i ).

tff(decl_30,type,
    frontsegP: ( $i * $i ) > $o ).

tff(decl_31,type,
    rearsegP: ( $i * $i ) > $o ).

tff(decl_32,type,
    segmentP: ( $i * $i ) > $o ).

tff(decl_33,type,
    cyclefreeP: $i > $o ).

tff(decl_34,type,
    leq: ( $i * $i ) > $o ).

tff(decl_35,type,
    totalorderP: $i > $o ).

tff(decl_36,type,
    strictorderP: $i > $o ).

tff(decl_37,type,
    lt: ( $i * $i ) > $o ).

tff(decl_38,type,
    totalorderedP: $i > $o ).

tff(decl_39,type,
    strictorderedP: $i > $o ).

tff(decl_40,type,
    duplicatefreeP: $i > $o ).

tff(decl_41,type,
    equalelemsP: $i > $o ).

tff(decl_42,type,
    hd: $i > $i ).

tff(decl_43,type,
    tl: $i > $i ).

tff(decl_44,type,
    geq: ( $i * $i ) > $o ).

tff(decl_45,type,
    gt: ( $i * $i ) > $o ).

tff(decl_46,type,
    esk1_0: $i ).

tff(decl_47,type,
    esk2_0: $i ).

tff(decl_48,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk5_1: $i > $i ).

tff(decl_51,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk10_1: $i > $i ).

tff(decl_56,type,
    esk11_1: $i > $i ).

tff(decl_57,type,
    esk12_1: $i > $i ).

tff(decl_58,type,
    esk13_1: $i > $i ).

tff(decl_59,type,
    esk14_1: $i > $i ).

tff(decl_60,type,
    esk15_1: $i > $i ).

tff(decl_61,type,
    esk16_1: $i > $i ).

tff(decl_62,type,
    esk17_1: $i > $i ).

tff(decl_63,type,
    esk18_1: $i > $i ).

tff(decl_64,type,
    esk19_1: $i > $i ).

tff(decl_65,type,
    esk20_1: $i > $i ).

tff(decl_66,type,
    esk21_1: $i > $i ).

tff(decl_67,type,
    esk22_1: $i > $i ).

tff(decl_68,type,
    esk23_1: $i > $i ).

tff(decl_69,type,
    esk24_1: $i > $i ).

tff(decl_70,type,
    esk25_1: $i > $i ).

tff(decl_71,type,
    esk26_1: $i > $i ).

tff(decl_72,type,
    esk27_1: $i > $i ).

tff(decl_73,type,
    esk28_1: $i > $i ).

tff(decl_74,type,
    esk29_1: $i > $i ).

tff(decl_75,type,
    esk30_1: $i > $i ).

tff(decl_76,type,
    esk31_1: $i > $i ).

tff(decl_77,type,
    esk32_1: $i > $i ).

tff(decl_78,type,
    esk33_1: $i > $i ).

tff(decl_79,type,
    esk34_1: $i > $i ).

tff(decl_80,type,
    esk35_1: $i > $i ).

tff(decl_81,type,
    esk36_1: $i > $i ).

tff(decl_82,type,
    esk37_1: $i > $i ).

tff(decl_83,type,
    esk38_1: $i > $i ).

tff(decl_84,type,
    esk39_1: $i > $i ).

tff(decl_85,type,
    esk40_1: $i > $i ).

tff(decl_86,type,
    esk41_1: $i > $i ).

tff(decl_87,type,
    esk42_1: $i > $i ).

tff(decl_88,type,
    esk43_1: $i > $i ).

tff(decl_89,type,
    esk44_1: $i > $i ).

tff(decl_90,type,
    esk45_1: $i > $i ).

tff(decl_91,type,
    esk46_1: $i > $i ).

tff(decl_92,type,
    esk47_1: $i > $i ).

tff(decl_93,type,
    esk48_0: $i ).

tff(decl_94,type,
    esk49_0: $i ).

tff(decl_95,type,
    esk50_0: $i ).

tff(decl_96,type,
    esk51_0: $i ).

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

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

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

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

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

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

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

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

fof(ax86,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).

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

fof(ax85,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => hd(app(X1,X2)) = hd(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).

fof(ax5,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).

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/benchmark/Axioms/SWC001+0.ax',ax44) ).

fof(ax20,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).

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/benchmark/Axioms/SWC001+0.ax',ax7) ).

fof(ax6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( rearsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).

fof(ax25,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => tl(cons(X2,X1)) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).

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

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

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

fof(ax43,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( frontsegP(X1,X2)
               => frontsegP(app(X1,X3),X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).

fof(ax45,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax45) ).

fof(ax80,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X2,X3) = app(X2,X1)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).

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/benchmark/Axioms/SWC001+0.ax',ax82) ).

fof(c_0_25,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ~ ssList(X4)
                    | X2 != X4
                    | X1 != X3
                    | ? [X5] :
                        ( ssList(X5)
                        & neq(X5,nil)
                        & segmentP(X2,X5)
                        & segmentP(X1,X5) )
                    | ( nil != X3
                      & nil = X4 )
                    | ( nil = X2
                      & nil = X1 )
                    | ( ? [X6] :
                          ( ssList(X6)
                          & X3 != X6
                          & ? [X7] :
                              ( ssList(X7)
                              & ? [X8] :
                                  ( ssList(X8)
                                  & tl(X4) = X7
                                  & app(X7,X8) = X6
                                  & ? [X9] :
                                      ( ssItem(X9)
                                      & cons(X9,nil) = X8
                                      & hd(X4) = X9
                                      & neq(nil,X4) )
                                  & neq(nil,X4) ) ) )
                      & neq(X4,nil) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_26,negated_conjecture,
    ! [X258,X259,X260,X261,X262] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ( ~ ssList(X258)
        | ~ neq(X258,nil)
        | ~ segmentP(esk49_0,X258)
        | ~ segmentP(esk48_0,X258) )
      & ( nil = esk50_0
        | nil != esk51_0 )
      & ( nil != esk49_0
        | nil != esk48_0 )
      & ( ~ ssList(X259)
        | esk50_0 = X259
        | ~ ssList(X260)
        | ~ ssList(X261)
        | tl(esk51_0) != X260
        | app(X260,X261) != X259
        | ~ ssItem(X262)
        | cons(X262,nil) != X261
        | hd(esk51_0) != X262
        | ~ neq(nil,esk51_0)
        | ~ neq(nil,esk51_0)
        | ~ neq(esk51_0,nil) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).

cnf(c_0_27,negated_conjecture,
    ( esk50_0 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(esk51_0) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(esk51_0) != X4
    | ~ neq(nil,esk51_0)
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_28,plain,
    ! [X133,X134] :
      ( ~ ssList(X133)
      | ~ ssList(X134)
      | ssList(app(X133,X134)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_29,negated_conjecture,
    ( nil != esk49_0
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_30,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    ( esk50_0 = X1
    | hd(esk51_0) != X4
    | tl(esk51_0) != X2
    | app(X2,X3) != X1
    | cons(X4,nil) != X3
    | ~ ssItem(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil) ),
    inference(cn,[status(thm)],[c_0_27]) ).

cnf(c_0_32,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

fof(c_0_34,plain,
    ! [X130] :
      ( ~ ssList(X130)
      | nil = X130
      | ssList(tl(X130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

cnf(c_0_35,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_36,negated_conjecture,
    ( nil = esk50_0
    | nil != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_37,negated_conjecture,
    ( esk48_0 != nil
    | esk51_0 != nil ),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_38,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssList(tl(esk51_0))
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk51_0)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])])])])]),c_0_33]) ).

cnf(c_0_39,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_35,c_0_30]) ).

cnf(c_0_41,negated_conjecture,
    esk51_0 != nil,
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_32]),c_0_37]) ).

fof(c_0_42,plain,
    ! [X114,X115] :
      ( ~ ssList(X114)
      | ~ ssItem(X115)
      | ssList(cons(X115,X114)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_43,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk51_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_44,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_45,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

fof(c_0_46,plain,
    ! [X127] :
      ( ~ ssList(X127)
      | nil = X127
      | ssItem(hd(X127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_47,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_48,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

fof(c_0_49,plain,
    ! [X112,X113] :
      ( ( ~ neq(X112,X113)
        | X112 != X113
        | ~ ssList(X113)
        | ~ ssList(X112) )
      & ( X112 = X113
        | neq(X112,X113)
        | ~ ssList(X113)
        | ~ ssList(X112) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

fof(c_0_50,plain,
    ! [X216] :
      ( ~ ssList(X216)
      | nil = X216
      | cons(hd(X216),tl(X216)) = X216 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

fof(c_0_51,plain,
    ! [X233,X234] :
      ( ~ ssList(X233)
      | ~ ssList(X234)
      | nil = X233
      | tl(app(X233,X234)) = app(tl(X233),X234) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).

fof(c_0_52,plain,
    ! [X228,X229] :
      ( ( nil = X229
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil = X228
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil != X229
        | nil != X228
        | nil = app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_53,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40])]),c_0_41]) ).

cnf(c_0_54,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_55,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_56,plain,
    ( nil = X1
    | tl(app(X1,X2)) = app(tl(X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_57,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
    | ~ neq(esk51_0,nil) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_40]),c_0_45])]),c_0_41]) ).

cnf(c_0_59,plain,
    ( cons(hd(app(X1,X2)),app(tl(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_55,c_0_56]),c_0_33]),c_0_57]) ).

cnf(c_0_60,negated_conjecture,
    app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_54]),c_0_45]),c_0_40])]),c_0_41]) ).

cnf(c_0_61,negated_conjecture,
    ( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk48_0) = app(esk51_0,cons(hd(esk51_0),nil))
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_40])]),c_0_41]) ).

cnf(c_0_62,negated_conjecture,
    ( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk48_0) = app(esk51_0,cons(hd(esk51_0),nil))
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_44]),c_0_45])]) ).

fof(c_0_63,plain,
    ! [X231,X232] :
      ( ~ ssList(X231)
      | ~ ssList(X232)
      | nil = X231
      | hd(app(X231,X232)) = hd(X231) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).

cnf(c_0_64,negated_conjecture,
    cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk48_0) = app(esk51_0,cons(hd(esk51_0),nil)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_48]),c_0_40])]),c_0_41]) ).

cnf(c_0_65,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

fof(c_0_66,plain,
    ! [X125,X126] :
      ( ~ ssList(X125)
      | ~ ssItem(X126)
      | nil != cons(X126,X125) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_67,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk48_0)
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_40])]),c_0_41]) ).

cnf(c_0_68,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_69,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_70,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk48_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_44]),c_0_45])]) ).

cnf(c_0_71,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) != nil
    | ~ ssItem(hd(app(esk51_0,cons(hd(esk51_0),nil)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_64]),c_0_69])]) ).

cnf(c_0_72,negated_conjecture,
    app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk48_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_48]),c_0_40])]),c_0_41]) ).

cnf(c_0_73,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) != nil
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssItem(hd(esk51_0)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_65]),c_0_40])]),c_0_41]) ).

fof(c_0_74,plain,
    ! [X23,X24,X26] :
      ( ( ssList(esk6_2(X23,X24))
        | ~ frontsegP(X23,X24)
        | ~ ssList(X24)
        | ~ ssList(X23) )
      & ( app(X24,esk6_2(X23,X24)) = X23
        | ~ frontsegP(X23,X24)
        | ~ ssList(X24)
        | ~ ssList(X23) )
      & ( ~ ssList(X26)
        | app(X24,X26) != X23
        | frontsegP(X23,X24)
        | ~ ssList(X24)
        | ~ ssList(X23) ) ),
    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_75,negated_conjecture,
    ( hd(cons(hd(esk51_0),esk48_0)) = hd(esk51_0)
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_72]),c_0_40])]),c_0_41]) ).

cnf(c_0_76,negated_conjecture,
    ( ssList(cons(hd(esk51_0),esk48_0))
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_72]),c_0_40])]) ).

cnf(c_0_77,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) != nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_44]),c_0_45])]) ).

cnf(c_0_78,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_79,negated_conjecture,
    ( hd(cons(hd(esk51_0),esk48_0)) = hd(esk51_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_44]),c_0_45])]) ).

cnf(c_0_80,negated_conjecture,
    ( ssList(cons(hd(esk51_0),esk48_0))
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_44]),c_0_45])]) ).

cnf(c_0_81,negated_conjecture,
    app(esk51_0,cons(hd(esk51_0),nil)) != nil,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_48]),c_0_40])]),c_0_41]) ).

cnf(c_0_82,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_78]),c_0_33]) ).

fof(c_0_83,plain,
    ! [X170,X171,X172,X173] :
      ( ( X170 = X171
        | ~ frontsegP(cons(X170,X172),cons(X171,X173))
        | ~ ssList(X173)
        | ~ ssList(X172)
        | ~ ssItem(X171)
        | ~ ssItem(X170) )
      & ( frontsegP(X172,X173)
        | ~ frontsegP(cons(X170,X172),cons(X171,X173))
        | ~ ssList(X173)
        | ~ ssList(X172)
        | ~ ssItem(X171)
        | ~ ssItem(X170) )
      & ( X170 != X171
        | ~ frontsegP(X172,X173)
        | frontsegP(cons(X170,X172),cons(X171,X173))
        | ~ ssList(X173)
        | ~ ssList(X172)
        | ~ ssItem(X171)
        | ~ ssItem(X170) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).

fof(c_0_84,plain,
    ! [X122] :
      ( ( ssList(esk44_1(X122))
        | nil = X122
        | ~ ssList(X122) )
      & ( ssItem(esk45_1(X122))
        | nil = X122
        | ~ ssList(X122) )
      & ( cons(esk45_1(X122),esk44_1(X122)) = X122
        | nil = X122
        | ~ ssList(X122) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).

cnf(c_0_85,negated_conjecture,
    hd(cons(hd(esk51_0),esk48_0)) = hd(esk51_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_48]),c_0_40])]),c_0_41]) ).

cnf(c_0_86,negated_conjecture,
    ssList(cons(hd(esk51_0),esk48_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_48]),c_0_40])]),c_0_41]) ).

cnf(c_0_87,negated_conjecture,
    cons(hd(esk51_0),esk48_0) != nil,
    inference(rw,[status(thm)],[c_0_81,c_0_72]) ).

cnf(c_0_88,negated_conjecture,
    ( frontsegP(esk48_0,tl(esk51_0))
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssList(tl(esk51_0)) ),
    inference(spm,[status(thm)],[c_0_82,c_0_60]) ).

cnf(c_0_89,plain,
    ( X1 = X2
    | ~ frontsegP(cons(X1,X3),cons(X2,X4))
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_83]) ).

cnf(c_0_90,plain,
    ( cons(esk45_1(X1),esk44_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_91,plain,
    ( ssItem(esk45_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_92,plain,
    ( ssList(esk44_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_93,negated_conjecture,
    ( frontsegP(cons(hd(esk51_0),esk48_0),esk51_0)
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_72]),c_0_40])]) ).

cnf(c_0_94,negated_conjecture,
    ssItem(hd(esk51_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_85]),c_0_86])]),c_0_87]) ).

cnf(c_0_95,negated_conjecture,
    ( frontsegP(esk48_0,tl(esk51_0))
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_96,plain,
    ( X1 = esk45_1(X2)
    | nil = X2
    | ~ frontsegP(cons(X1,X3),X2)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]) ).

cnf(c_0_97,negated_conjecture,
    frontsegP(cons(hd(esk51_0),esk48_0),esk51_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_44]),c_0_45]),c_0_94])]) ).

fof(c_0_98,plain,
    ! [X31,X32,X35,X36] :
      ( ( ssList(esk8_2(X31,X32))
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( ssList(esk9_2(X31,X32))
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( app(app(esk8_2(X31,X32),X32),esk9_2(X31,X32)) = X31
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( ~ ssList(X35)
        | ~ ssList(X36)
        | app(app(X35,X32),X36) != X31
        | segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) ) ),
    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_99,negated_conjecture,
    ( frontsegP(esk48_0,tl(esk51_0))
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_44]),c_0_45])]) ).

fof(c_0_100,plain,
    ! [X27,X28,X30] :
      ( ( ssList(esk7_2(X27,X28))
        | ~ rearsegP(X27,X28)
        | ~ ssList(X28)
        | ~ ssList(X27) )
      & ( app(esk7_2(X27,X28),X28) = X27
        | ~ rearsegP(X27,X28)
        | ~ ssList(X28)
        | ~ ssList(X27) )
      & ( ~ ssList(X30)
        | app(X30,X28) != X27
        | rearsegP(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)],[ax6])])])])]) ).

fof(c_0_101,plain,
    ! [X131,X132] :
      ( ~ ssList(X131)
      | ~ ssItem(X132)
      | tl(cons(X132,X131)) = X131 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).

cnf(c_0_102,negated_conjecture,
    esk45_1(esk51_0) = hd(esk51_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_69]),c_0_40]),c_0_94])]),c_0_41]) ).

cnf(c_0_103,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_98]) ).

fof(c_0_104,plain,
    ! [X138] :
      ( ~ ssList(X138)
      | app(nil,X138) = X138 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_105,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_106,negated_conjecture,
    frontsegP(esk48_0,tl(esk51_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_48]),c_0_40])]),c_0_41]) ).

cnf(c_0_107,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_108,plain,
    ( rearsegP(X3,X2)
    | ~ ssList(X1)
    | app(X1,X2) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_100]) ).

fof(c_0_109,plain,
    ! [X223,X224] :
      ( ~ ssList(X223)
      | ~ ssItem(X224)
      | cons(X224,X223) = app(cons(X224,nil),X223) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_110,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_101]) ).

cnf(c_0_111,negated_conjecture,
    cons(hd(esk51_0),esk44_1(esk51_0)) = esk51_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_102]),c_0_40])]),c_0_41]) ).

cnf(c_0_112,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_103]) ).

cnf(c_0_113,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_114,negated_conjecture,
    ( app(tl(esk51_0),esk6_2(esk48_0,tl(esk51_0))) = esk48_0
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_69])]) ).

cnf(c_0_115,negated_conjecture,
    ( ssList(esk6_2(esk48_0,tl(esk51_0)))
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_106]),c_0_69])]) ).

cnf(c_0_116,plain,
    ( rearsegP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_108]),c_0_33]) ).

cnf(c_0_117,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_109]) ).

cnf(c_0_118,negated_conjecture,
    ( esk44_1(esk51_0) = tl(esk51_0)
    | ~ ssList(esk44_1(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_94])]) ).

cnf(c_0_119,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_112,c_0_113]),c_0_45])]),c_0_33]) ).

cnf(c_0_120,negated_conjecture,
    app(tl(esk51_0),esk6_2(esk48_0,tl(esk51_0))) = esk48_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_121,negated_conjecture,
    ssList(esk6_2(esk48_0,tl(esk51_0))),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_122,plain,
    ( rearsegP(cons(X1,X2),X2)
    | ~ ssList(cons(X1,nil))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_116,c_0_117]) ).

cnf(c_0_123,plain,
    ( esk44_1(X1) = tl(X1)
    | nil = X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_90]),c_0_91]),c_0_92]) ).

cnf(c_0_124,negated_conjecture,
    esk44_1(esk51_0) = tl(esk51_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_92]),c_0_40])]),c_0_41]) ).

cnf(c_0_125,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(X1,nil)
    | ~ segmentP(esk49_0,X1)
    | ~ segmentP(esk48_0,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_126,negated_conjecture,
    ( segmentP(esk48_0,tl(esk51_0))
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121])]) ).

fof(c_0_127,plain,
    ! [X230] :
      ( ~ ssList(X230)
      | app(X230,nil) = X230 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_128,plain,
    ( rearsegP(cons(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_44]),c_0_45])]) ).

cnf(c_0_129,negated_conjecture,
    cons(hd(esk51_0),tl(esk51_0)) = esk51_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_123]),c_0_40])]),c_0_41]) ).

cnf(c_0_130,negated_conjecture,
    ssList(tl(esk51_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_124]),c_0_40])]),c_0_41]) ).

cnf(c_0_131,negated_conjecture,
    ( ~ segmentP(esk48_0,X1)
    | ~ segmentP(esk51_0,X1)
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(rw,[status(thm)],[c_0_125,c_0_30]) ).

cnf(c_0_132,negated_conjecture,
    segmentP(esk48_0,tl(esk51_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_133,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_127]) ).

cnf(c_0_134,plain,
    ( app(esk7_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_100]) ).

cnf(c_0_135,negated_conjecture,
    rearsegP(esk51_0,tl(esk51_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]),c_0_94])]) ).

cnf(c_0_136,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_100]) ).

fof(c_0_137,plain,
    ! [X167,X168,X169] :
      ( ~ ssList(X167)
      | ~ ssList(X168)
      | ~ ssList(X169)
      | ~ frontsegP(X167,X168)
      | frontsegP(app(X167,X169),X168) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).

fof(c_0_138,plain,
    ! [X174] :
      ( ~ ssList(X174)
      | frontsegP(X174,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).

cnf(c_0_139,negated_conjecture,
    ( ~ segmentP(esk51_0,tl(esk51_0))
    | ~ ssList(tl(esk51_0))
    | ~ neq(tl(esk51_0),nil) ),
    inference(spm,[status(thm)],[c_0_131,c_0_132]) ).

cnf(c_0_140,plain,
    ( segmentP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_133]),c_0_45])]),c_0_33]) ).

cnf(c_0_141,negated_conjecture,
    app(esk7_2(esk51_0,tl(esk51_0)),tl(esk51_0)) = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_130]),c_0_40])]) ).

cnf(c_0_142,negated_conjecture,
    ssList(esk7_2(esk51_0,tl(esk51_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_135]),c_0_130]),c_0_40])]) ).

cnf(c_0_143,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_137]) ).

cnf(c_0_144,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_138]) ).

fof(c_0_145,plain,
    ! [X220,X221,X222] :
      ( ~ ssList(X220)
      | ~ ssList(X221)
      | ~ ssList(X222)
      | app(X221,X222) != app(X221,X220)
      | X222 = X220 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).

cnf(c_0_146,negated_conjecture,
    ( ~ segmentP(esk51_0,tl(esk51_0))
    | ~ neq(tl(esk51_0),nil) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_147,negated_conjecture,
    segmentP(esk51_0,tl(esk51_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_130]),c_0_142])]) ).

cnf(c_0_148,plain,
    ( frontsegP(app(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_45])]) ).

cnf(c_0_149,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X2,X3) != app(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_145]) ).

cnf(c_0_150,negated_conjecture,
    ~ neq(tl(esk51_0),nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147])]) ).

fof(c_0_151,plain,
    ! [X225,X226,X227] :
      ( ~ ssList(X225)
      | ~ ssList(X226)
      | ~ ssList(X227)
      | app(app(X225,X226),X227) = app(X225,app(X226,X227)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_152,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_153,negated_conjecture,
    ( frontsegP(esk48_0,nil)
    | ~ ssList(tl(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_120]),c_0_121])]) ).

cnf(c_0_154,negated_conjecture,
    ( segmentP(esk48_0,cons(hd(esk51_0),nil))
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssList(tl(esk51_0)) ),
    inference(spm,[status(thm)],[c_0_140,c_0_60]) ).

cnf(c_0_155,negated_conjecture,
    ( X1 = cons(hd(esk51_0),nil)
    | app(tl(esk51_0),X1) != esk48_0
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssList(tl(esk51_0))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_60]) ).

cnf(c_0_156,negated_conjecture,
    tl(esk51_0) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_54]),c_0_45]),c_0_130])]) ).

cnf(c_0_157,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_151]) ).

cnf(c_0_158,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_152])]),c_0_45])]) ).

cnf(c_0_159,negated_conjecture,
    frontsegP(esk48_0,nil),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_160,negated_conjecture,
    ( segmentP(esk48_0,cons(hd(esk51_0),nil))
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_39]),c_0_40])]),c_0_41]) ).

cnf(c_0_161,negated_conjecture,
    ( X1 = cons(hd(esk51_0),nil)
    | app(tl(esk51_0),X1) != esk48_0
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_130])]) ).

cnf(c_0_162,negated_conjecture,
    cons(hd(esk51_0),nil) = esk51_0,
    inference(rw,[status(thm)],[c_0_129,c_0_156]) ).

cnf(c_0_163,plain,
    ( app(nil,app(nil,X1)) = app(nil,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_45])]) ).

cnf(c_0_164,negated_conjecture,
    app(nil,esk6_2(esk48_0,nil)) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_159]),c_0_69]),c_0_45])]) ).

cnf(c_0_165,negated_conjecture,
    ssList(esk6_2(esk48_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_159]),c_0_45]),c_0_69])]) ).

cnf(c_0_166,negated_conjecture,
    segmentP(esk48_0,cons(hd(esk51_0),nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_44]),c_0_45]),c_0_94])]) ).

cnf(c_0_167,negated_conjecture,
    ( X1 = esk51_0
    | app(nil,X1) != esk48_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_156]),c_0_162]),c_0_162]),c_0_40])]) ).

cnf(c_0_168,negated_conjecture,
    app(nil,esk48_0) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_165])]) ).

cnf(c_0_169,negated_conjecture,
    ( ~ segmentP(esk51_0,cons(hd(esk51_0),nil))
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ neq(cons(hd(esk51_0),nil),nil) ),
    inference(spm,[status(thm)],[c_0_131,c_0_166]) ).

cnf(c_0_170,negated_conjecture,
    segmentP(esk48_0,esk51_0),
    inference(rw,[status(thm)],[c_0_166,c_0_162]) ).

cnf(c_0_171,negated_conjecture,
    esk48_0 = esk51_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_69])]) ).

cnf(c_0_172,negated_conjecture,
    ( ~ segmentP(esk51_0,cons(hd(esk51_0),nil))
    | ~ neq(cons(hd(esk51_0),nil),nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_44]),c_0_45]),c_0_94])]) ).

cnf(c_0_173,negated_conjecture,
    segmentP(esk51_0,esk51_0),
    inference(rw,[status(thm)],[c_0_170,c_0_171]) ).

cnf(c_0_174,negated_conjecture,
    ~ neq(esk51_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_162]),c_0_162]),c_0_173])]) ).

cnf(c_0_175,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_54]),c_0_45]),c_0_40])]),c_0_41]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC072+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 19:06:28 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.78  % Version  : CSE_E---1.5
% 0.20/0.78  % Problem  : theBenchmark.p
% 0.20/0.78  % Proof found
% 0.20/0.78  % SZS status Theorem for theBenchmark.p
% 0.20/0.78  % SZS output start Proof
% See solution above
% 0.66/0.80  % Total time : 0.191000 s
% 0.66/0.80  % SZS output end Proof
% 0.66/0.80  % Total time : 0.196000 s
%------------------------------------------------------------------------------