TSTP Solution File: SWC376+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC376+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 : n004.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 20:22:04 EDT 2023

% Result   : Theorem 115.02s 115.08s
% Output   : CNFRefutation 115.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   44
%            Number of leaves      :  104
% Syntax   : Number of formulae    :  292 (  13 unt;  76 typ;   0 def)
%            Number of atoms       :  830 ( 278 equ)
%            Maximal formula atoms :   27 (   3 avg)
%            Number of connectives : 1015 ( 401   ~; 475   |;  65   &)
%                                         (   8 <=>;  66  =>;   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    :   57 (  57 usr;   8 con; 0-2 aty)
%            Number of variables   :  274 (   0 sgn; 119   !;  14   ?;   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 ).

tff(decl_97,type,
    esk52_0: $i ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssItem(X5)
                       => ( ( ~ memberP(X2,X5)
                            & ~ memberP(X1,X5) )
                          | ( memberP(X2,X5)
                            & memberP(X1,X5) ) ) )
                    | ( nil != X3
                      & nil = X4 )
                    | ( neq(X4,nil)
                      & ( ~ neq(X3,nil)
                        | ? [X6] :
                            ( ssList(X6)
                            & X4 != X6
                            & ? [X7] :
                                ( ssList(X7)
                                & ? [X8] :
                                    ( ssList(X8)
                                    & tl(X3) = X7
                                    & app(X7,X8) = X6
                                    & ? [X9] :
                                        ( ssItem(X9)
                                        & cons(X9,nil) = X8
                                        & hd(X3) = X9
                                        & neq(nil,X3) )
                                    & neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
    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(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).

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

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

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

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(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(ax23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => hd(cons(X2,X1)) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',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/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(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

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

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

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

fof(ax27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).

fof(ax37,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(cons(X2,X3),X1)
              <=> ( X1 = X2
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).

fof(ax38,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).

fof(ax36,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(app(X2,X3),X1)
              <=> ( memberP(X2,X1)
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).

fof(ax3,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( memberP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).

fof(c_0_28,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssItem(X5)
                         => ( ( ~ memberP(X2,X5)
                              & ~ memberP(X1,X5) )
                            | ( memberP(X2,X5)
                              & memberP(X1,X5) ) ) )
                      | ( nil != X3
                        & nil = X4 )
                      | ( neq(X4,nil)
                        & ( ~ neq(X3,nil)
                          | ? [X6] :
                              ( ssList(X6)
                              & X4 != X6
                              & ? [X7] :
                                  ( ssList(X7)
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & tl(X3) = X7
                                      & app(X7,X8) = X6
                                      & ? [X9] :
                                          ( ssItem(X9)
                                          & cons(X9,nil) = X8
                                          & hd(X3) = X9
                                          & neq(nil,X3) )
                                      & neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_29,negated_conjecture,
    ! [X259,X260,X261,X262] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ssItem(esk52_0)
      & ( memberP(esk49_0,esk52_0)
        | memberP(esk48_0,esk52_0) )
      & ( ~ memberP(esk49_0,esk52_0)
        | ~ memberP(esk48_0,esk52_0) )
      & ( nil = esk50_0
        | nil != esk51_0 )
      & ( neq(esk50_0,nil)
        | ~ neq(esk51_0,nil) )
      & ( ~ ssList(X259)
        | esk51_0 = X259
        | ~ ssList(X260)
        | ~ ssList(X261)
        | tl(esk50_0) != X260
        | app(X260,X261) != X259
        | ~ ssItem(X262)
        | cons(X262,nil) != X261
        | hd(esk50_0) != X262
        | ~ neq(nil,esk50_0)
        | ~ neq(nil,esk50_0)
        | ~ neq(esk51_0,nil) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])]) ).

cnf(c_0_30,negated_conjecture,
    ( esk51_0 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(esk50_0) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(esk50_0) != X4
    | ~ neq(nil,esk50_0)
    | ~ neq(nil,esk50_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_31,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_32,negated_conjecture,
    ( esk51_0 = X1
    | hd(esk50_0) != X4
    | tl(esk50_0) != X2
    | app(X2,X3) != X1
    | cons(X4,nil) != X3
    | ~ ssItem(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk50_0)
    | ~ neq(esk51_0,nil) ),
    inference(cn,[status(thm)],[c_0_30]) ).

cnf(c_0_33,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_34,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])])])]) ).

cnf(c_0_35,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_36,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_37,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ ssList(tl(esk50_0))
    | ~ neq(nil,esk50_0)
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk50_0)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_32])])])]),c_0_33]) ).

cnf(c_0_38,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_39,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_35,c_0_36]) ).

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

cnf(c_0_41,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_42,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_43,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ ssList(tl(esk50_0))
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).

cnf(c_0_44,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_45,negated_conjecture,
    ( nil = esk50_0
    | nil != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

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(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ ssList(tl(esk50_0))
    | ~ ssItem(hd(esk50_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_38]),c_0_40]),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,
    ! [X130] :
      ( ~ ssList(X130)
      | nil = X130
      | ssList(tl(X130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

cnf(c_0_50,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ ssList(tl(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_39])]) ).

cnf(c_0_51,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

fof(c_0_52,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])])]) ).

fof(c_0_53,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_54,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_55,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_56,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_39])]) ).

cnf(c_0_57,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_58,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_59,plain,
    ( nil = X1
    | tl(app(X1,X2)) = app(tl(X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_60,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_61,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_40])]) ).

cnf(c_0_62,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_58,c_0_59]),c_0_33]),c_0_60]) ).

cnf(c_0_63,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_48]),c_0_39])]) ).

fof(c_0_64,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])])]) ).

fof(c_0_65,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])])]) ).

fof(c_0_66,plain,
    ! [X20,X22] :
      ( ( ssItem(esk5_1(X20))
        | ~ singletonP(X20)
        | ~ ssList(X20) )
      & ( cons(esk5_1(X20),nil) = X20
        | ~ singletonP(X20)
        | ~ ssList(X20) )
      & ( ~ ssItem(X22)
        | cons(X22,nil) != X20
        | singletonP(X20)
        | ~ ssList(X20) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).

cnf(c_0_67,negated_conjecture,
    ( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_39])]) ).

cnf(c_0_68,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_69,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_70,plain,
    ( singletonP(X2)
    | ~ ssItem(X1)
    | cons(X1,nil) != X2
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_71,negated_conjecture,
    ( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_57]),c_0_40])]) ).

fof(c_0_72,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_73,plain,
    ( cons(hd(cons(X1,X2)),X2) = cons(X1,X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_68]),c_0_57]),c_0_69]) ).

cnf(c_0_74,plain,
    ( cons(esk5_1(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_75,plain,
    ( ssItem(esk5_1(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_76,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_70]) ).

cnf(c_0_77,negated_conjecture,
    ( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_48]),c_0_39])]) ).

cnf(c_0_78,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

cnf(c_0_79,plain,
    ( cons(hd(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_40])]),c_0_75]) ).

cnf(c_0_80,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_57]),c_0_40])]) ).

fof(c_0_81,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_82,negated_conjecture,
    ( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_39])]) ).

cnf(c_0_83,plain,
    ( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_84,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_85,negated_conjecture,
    ( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_57]),c_0_40])]) ).

cnf(c_0_86,plain,
    ( cons(hd(cons(X1,nil)),nil) = cons(X1,nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_57]),c_0_40])]) ).

fof(c_0_87,plain,
    ! [X128,X129] :
      ( ~ ssList(X128)
      | ~ ssItem(X129)
      | hd(cons(X129,X128)) = X129 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).

cnf(c_0_88,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_84]),c_0_33]) ).

cnf(c_0_89,negated_conjecture,
    ( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_48]),c_0_39])]) ).

cnf(c_0_90,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(hd(cons(X1,nil)))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_86]),c_0_40])]) ).

cnf(c_0_91,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

fof(c_0_92,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_93,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_94,negated_conjecture,
    ( esk50_0 = nil
    | frontsegP(cons(hd(esk50_0),esk51_0),esk50_0)
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_39])]) ).

cnf(c_0_95,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_40])]) ).

cnf(c_0_96,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_92]) ).

cnf(c_0_97,plain,
    ( cons(esk45_1(X1),esk44_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_98,plain,
    ( ssItem(esk45_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_99,plain,
    ( ssList(esk44_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_100,negated_conjecture,
    ( esk50_0 = nil
    | frontsegP(cons(hd(esk50_0),esk51_0),esk50_0)
    | ~ ssItem(hd(esk50_0)) ),
    inference(spm,[status(thm)],[c_0_94,c_0_95]) ).

cnf(c_0_101,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_96,c_0_97]),c_0_98]),c_0_99]) ).

cnf(c_0_102,negated_conjecture,
    ( esk50_0 = nil
    | frontsegP(cons(hd(esk50_0),esk51_0),esk50_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_48]),c_0_39])]) ).

fof(c_0_103,plain,
    ! [X230] :
      ( ~ ssList(X230)
      | app(X230,nil) = X230 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

fof(c_0_104,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])])]) ).

fof(c_0_105,plain,
    ! [X138] :
      ( ~ ssList(X138)
      | app(nil,X138) = X138 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_106,negated_conjecture,
    ( esk45_1(esk50_0) = hd(esk50_0)
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_44]),c_0_39])]) ).

cnf(c_0_107,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_103]) ).

cnf(c_0_108,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_109,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_105]) ).

cnf(c_0_110,negated_conjecture,
    ( esk45_1(esk50_0) = hd(esk50_0)
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_48]),c_0_39])]) ).

cnf(c_0_111,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_40])]),c_0_33]) ).

cnf(c_0_112,plain,
    ( app(nil,app(X1,X2)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_40])]) ).

cnf(c_0_113,negated_conjecture,
    ( cons(hd(esk50_0),esk44_1(esk50_0)) = esk50_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_110]),c_0_39])]) ).

cnf(c_0_114,plain,
    ( esk44_1(X1) = tl(X1)
    | nil = X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_97]),c_0_98]),c_0_99]) ).

cnf(c_0_115,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_116,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_117,plain,
    ( app(X1,nil) = app(nil,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_40])]) ).

fof(c_0_118,plain,
    ! [X116,X117] :
      ( ~ ssList(X116)
      | ~ ssItem(X117)
      | cons(X117,X116) != X116 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_119,negated_conjecture,
    ( cons(hd(esk50_0),tl(esk50_0)) = esk50_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_39])]) ).

cnf(c_0_120,plain,
    ( hd(X1) = hd(X2)
    | nil = X2
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_115]),c_0_116]) ).

cnf(c_0_121,plain,
    ( frontsegP(app(nil,X1),X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_117]),c_0_40])]) ).

cnf(c_0_122,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_110]),c_0_39])]) ).

cnf(c_0_123,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_118]) ).

cnf(c_0_124,negated_conjecture,
    ( cons(hd(X1),tl(esk50_0)) = esk50_0
    | esk50_0 = nil
    | ~ frontsegP(X1,esk50_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_39])]) ).

cnf(c_0_125,plain,
    ( frontsegP(app(X1,nil),X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_121,c_0_117]) ).

cnf(c_0_126,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(hd(X1))
    | ~ frontsegP(X1,esk50_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_120]),c_0_39])]) ).

cnf(c_0_127,negated_conjecture,
    ( esk44_1(esk50_0) = tl(esk50_0)
    | esk50_0 = nil
    | ~ ssList(esk44_1(esk50_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_113]),c_0_122]) ).

cnf(c_0_128,plain,
    ( nil = X1
    | tl(X1) != X1
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_58]),c_0_48]),c_0_51]) ).

cnf(c_0_129,negated_conjecture,
    ( cons(hd(app(esk50_0,nil)),tl(esk50_0)) = esk50_0
    | esk50_0 = nil
    | ~ ssList(app(esk50_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_39])]) ).

cnf(c_0_130,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(hd(app(esk50_0,nil)))
    | ~ ssList(app(esk50_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_125]),c_0_39])]) ).

cnf(c_0_131,negated_conjecture,
    ( esk44_1(esk50_0) = tl(esk50_0)
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_99]),c_0_39])]) ).

cnf(c_0_132,plain,
    ( nil = X1
    | app(tl(X1),X2) != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_59]),c_0_33]),c_0_60]) ).

cnf(c_0_133,negated_conjecture,
    ( cons(hd(app(esk50_0,nil)),tl(esk50_0)) = esk50_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_33]),c_0_40]),c_0_39])]) ).

cnf(c_0_134,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(hd(app(esk50_0,nil))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_33]),c_0_40]),c_0_39])]) ).

cnf(c_0_135,negated_conjecture,
    ( esk50_0 = nil
    | ssList(tl(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_131]),c_0_39])]) ).

cnf(c_0_136,plain,
    ( nil = X1
    | tl(X1) != app(X1,nil)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_107]),c_0_40])]),c_0_51]) ).

fof(c_0_137,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_138,negated_conjecture,
    ( cons(hd(cons(hd(esk50_0),esk51_0)),esk51_0) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil ),
    inference(spm,[status(thm)],[c_0_77,c_0_89]) ).

fof(c_0_139,plain,
    ! [X135,X136,X137] :
      ( ~ ssList(X135)
      | ~ ssList(X136)
      | ~ ssItem(X137)
      | cons(X137,app(X136,X135)) = app(cons(X137,X136),X135) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).

cnf(c_0_140,negated_conjecture,
    ( hd(app(esk50_0,nil)) = hd(esk50_0)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_133]),c_0_134]),c_0_135]) ).

fof(c_0_141,plain,
    ! [X157,X158,X159] :
      ( ( ~ memberP(cons(X158,X159),X157)
        | X157 = X158
        | memberP(X159,X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) )
      & ( X157 != X158
        | memberP(cons(X158,X159),X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) )
      & ( ~ memberP(X159,X157)
        | memberP(cons(X158,X159),X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).

cnf(c_0_142,plain,
    ( esk5_1(X1) = hd(X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_74]),c_0_40])]),c_0_75]) ).

cnf(c_0_143,plain,
    ( app(cons(X1,X2),nil) != X2
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_68]),c_0_57]),c_0_69]) ).

cnf(c_0_144,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_137]) ).

cnf(c_0_145,negated_conjecture,
    ( tl(cons(hd(esk50_0),esk51_0)) = esk51_0
    | esk50_0 = nil
    | ~ ssItem(hd(cons(hd(esk50_0),esk51_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_138]),c_0_44])]) ).

cnf(c_0_146,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_139]) ).

cnf(c_0_147,negated_conjecture,
    ( cons(hd(esk50_0),app(tl(esk50_0),nil)) = app(esk50_0,nil)
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_140]),c_0_40]),c_0_39])]) ).

cnf(c_0_148,negated_conjecture,
    ( esk50_0 = nil
    | ssList(cons(hd(esk50_0),esk51_0))
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_89]),c_0_39])]) ).

cnf(c_0_149,plain,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_141]) ).

cnf(c_0_150,plain,
    ( ssItem(hd(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_75,c_0_142]) ).

cnf(c_0_151,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_58,c_0_78]),c_0_33]),c_0_60]) ).

cnf(c_0_152,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_40])]) ).

cnf(c_0_153,negated_conjecture,
    ( tl(cons(hd(esk50_0),esk51_0)) = esk51_0
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_91]),c_0_44])]) ).

cnf(c_0_154,plain,
    ( hd(cons(X1,app(X2,X3))) = hd(cons(X1,X2))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_146]),c_0_57]),c_0_69]) ).

cnf(c_0_155,negated_conjecture,
    ( cons(hd(esk50_0),app(nil,tl(esk50_0))) = app(esk50_0,nil)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_117]),c_0_135]) ).

cnf(c_0_156,negated_conjecture,
    ( esk50_0 = nil
    | ssList(cons(hd(esk50_0),esk51_0))
    | ~ ssItem(hd(esk50_0)) ),
    inference(spm,[status(thm)],[c_0_148,c_0_95]) ).

cnf(c_0_157,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_149]) ).

cnf(c_0_158,plain,
    ( ssItem(hd(cons(X1,nil)))
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_80]),c_0_95]) ).

cnf(c_0_159,plain,
    ( cons(hd(cons(X1,nil)),tl(cons(X1,X2))) = cons(X1,X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_144]),c_0_95]),c_0_152]) ).

cnf(c_0_160,negated_conjecture,
    ( tl(cons(hd(esk50_0),esk51_0)) = esk51_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_48]),c_0_39])]) ).

cnf(c_0_161,negated_conjecture,
    ( hd(cons(hd(esk50_0),nil)) = hd(app(esk50_0,nil))
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_40])]),c_0_122]),c_0_135]) ).

cnf(c_0_162,negated_conjecture,
    ( esk50_0 = nil
    | ssList(cons(hd(esk50_0),esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_48]),c_0_39])]) ).

cnf(c_0_163,plain,
    ( nil = X1
    | memberP(X1,esk45_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_97]),c_0_98]),c_0_99]) ).

cnf(c_0_164,plain,
    ( cons(hd(cons(X1,nil)),X2) = app(cons(X1,nil),X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_73]),c_0_40])]),c_0_158]) ).

cnf(c_0_165,negated_conjecture,
    ( cons(hd(cons(hd(esk50_0),nil)),esk51_0) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_44])]),c_0_122]) ).

fof(c_0_166,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[ax38]) ).

fof(c_0_167,plain,
    ! [X154,X155,X156] :
      ( ( ~ memberP(app(X155,X156),X154)
        | memberP(X155,X154)
        | memberP(X156,X154)
        | ~ ssList(X156)
        | ~ ssList(X155)
        | ~ ssItem(X154) )
      & ( ~ memberP(X155,X154)
        | memberP(app(X155,X156),X154)
        | ~ ssList(X156)
        | ~ ssList(X155)
        | ~ ssItem(X154) )
      & ( ~ memberP(X156,X154)
        | memberP(app(X155,X156),X154)
        | ~ ssList(X156)
        | ~ ssList(X155)
        | ~ ssItem(X154) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).

cnf(c_0_168,negated_conjecture,
    ( cons(hd(app(esk50_0,nil)),nil) = cons(hd(esk50_0),nil)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_161]),c_0_40])]),c_0_122]) ).

cnf(c_0_169,plain,
    ( memberP(cons(X3,X1),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X3)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_141]) ).

cnf(c_0_170,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(hd(cons(hd(esk50_0),esk51_0))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_102]),c_0_162]) ).

cnf(c_0_171,negated_conjecture,
    ( memberP(esk49_0,esk52_0)
    | memberP(esk48_0,esk52_0) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_172,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk50_0,hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_110]),c_0_39])]) ).

cnf(c_0_173,negated_conjecture,
    ( app(cons(hd(esk50_0),nil),esk51_0) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_44])]),c_0_122]) ).

fof(c_0_174,plain,
    ! [X160] :
      ( ~ ssItem(X160)
      | ~ memberP(nil,X160) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_166])]) ).

cnf(c_0_175,plain,
    ( memberP(X1,X3)
    | memberP(X2,X3)
    | ~ memberP(app(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_167]) ).

cnf(c_0_176,negated_conjecture,
    ( esk50_0 = nil
    | ssList(cons(hd(esk50_0),nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_168]),c_0_40])]),c_0_134]) ).

cnf(c_0_177,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),esk51_0),X1)
    | ~ memberP(esk51_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_138]),c_0_44])]),c_0_170]) ).

cnf(c_0_178,negated_conjecture,
    ( memberP(esk51_0,esk52_0)
    | memberP(esk50_0,esk52_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_36]),c_0_42]) ).

cnf(c_0_179,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_180,plain,
    ! [X14,X15,X18,X19] :
      ( ( ssList(esk3_2(X14,X15))
        | ~ memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) )
      & ( ssList(esk4_2(X14,X15))
        | ~ memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) )
      & ( app(esk3_2(X14,X15),cons(X15,esk4_2(X14,X15))) = X14
        | ~ memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) )
      & ( ~ ssList(X18)
        | ~ ssList(X19)
        | app(X18,cons(X15,X19)) != X14
        | memberP(X14,X15)
        | ~ ssItem(X15)
        | ~ ssList(X14) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).

cnf(c_0_181,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk50_0,hd(X1))
    | ~ frontsegP(X1,esk50_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_120]),c_0_39])]) ).

cnf(c_0_182,negated_conjecture,
    ( cons(hd(esk50_0),app(nil,esk51_0)) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_173]),c_0_40]),c_0_44])]),c_0_122]) ).

cnf(c_0_183,plain,
    ( X3 = X1
    | memberP(X2,X3)
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_141]) ).

cnf(c_0_184,plain,
    ( ~ ssItem(X1)
    | ~ memberP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_174]) ).

cnf(c_0_185,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),nil),X1)
    | memberP(esk50_0,X1)
    | ~ memberP(cons(hd(esk50_0),esk51_0),X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_89]),c_0_39])]),c_0_176]) ).

cnf(c_0_186,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),esk51_0),esk52_0)
    | memberP(esk50_0,esk52_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179])]) ).

cnf(c_0_187,plain,
    ( memberP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X1,cons(X3,X2)) != X4
    | ~ ssItem(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_180]) ).

cnf(c_0_188,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk50_0,hd(cons(hd(esk50_0),esk51_0))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_102]),c_0_162]) ).

cnf(c_0_189,negated_conjecture,
    ( hd(cons(hd(esk50_0),esk51_0)) = hd(cons(hd(esk50_0),nil))
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_182]),c_0_44]),c_0_40])]),c_0_122]) ).

cnf(c_0_190,plain,
    ( hd(cons(X1,nil)) = X2
    | ~ memberP(cons(X1,nil),X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_86]),c_0_40])]),c_0_158]),c_0_184]) ).

cnf(c_0_191,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),nil),esk52_0)
    | memberP(esk50_0,esk52_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_179])]) ).

cnf(c_0_192,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(er,[status(thm)],[c_0_187]) ).

cnf(c_0_193,plain,
    ( memberP(app(X1,X3),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_167]) ).

cnf(c_0_194,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk50_0,hd(cons(hd(esk50_0),nil))) ),
    inference(spm,[status(thm)],[c_0_188,c_0_189]) ).

cnf(c_0_195,negated_conjecture,
    ( hd(cons(hd(esk50_0),nil)) = esk52_0
    | esk50_0 = nil
    | memberP(esk50_0,esk52_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_179])]),c_0_122]) ).

cnf(c_0_196,negated_conjecture,
    ( ~ memberP(esk49_0,esk52_0)
    | ~ memberP(esk48_0,esk52_0) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_197,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk51_0,hd(esk50_0))
    | ~ ssList(tl(esk50_0))
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_63]),c_0_44]),c_0_40])]) ).

cnf(c_0_198,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),esk51_0),X1)
    | ~ memberP(esk50_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_89]),c_0_39])]),c_0_176]) ).

cnf(c_0_199,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk50_0,esk52_0) ),
    inference(spm,[status(thm)],[c_0_194,c_0_195]) ).

cnf(c_0_200,negated_conjecture,
    ( ~ memberP(esk50_0,esk52_0)
    | ~ memberP(esk51_0,esk52_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_36]),c_0_42]) ).

cnf(c_0_201,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk51_0,hd(esk50_0))
    | ~ ssList(tl(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_48]),c_0_39])]) ).

cnf(c_0_202,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),esk51_0),esk52_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_179])]) ).

cnf(c_0_203,negated_conjecture,
    ( esk50_0 = nil
    | ~ memberP(esk51_0,esk52_0) ),
    inference(spm,[status(thm)],[c_0_200,c_0_199]) ).

cnf(c_0_204,negated_conjecture,
    ( neq(esk50_0,nil)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_205,negated_conjecture,
    ( esk50_0 = nil
    | memberP(esk51_0,hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_51]),c_0_39])]) ).

cnf(c_0_206,negated_conjecture,
    ( hd(esk50_0) = esk52_0
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_202]),c_0_44]),c_0_179])]),c_0_122]),c_0_203]) ).

cnf(c_0_207,plain,
    ( ~ neq(X1,X2)
    | X1 != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_208,negated_conjecture,
    ( esk51_0 = nil
    | neq(esk50_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_38]),c_0_40]),c_0_44])]) ).

cnf(c_0_209,negated_conjecture,
    esk50_0 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_203]) ).

cnf(c_0_210,plain,
    ( ~ ssList(X1)
    | ~ neq(X1,X1) ),
    inference(er,[status(thm)],[c_0_207]) ).

cnf(c_0_211,negated_conjecture,
    ( esk51_0 = nil
    | neq(nil,nil) ),
    inference(rw,[status(thm)],[c_0_208,c_0_209]) ).

cnf(c_0_212,negated_conjecture,
    ( ~ memberP(nil,esk52_0)
    | ~ memberP(esk51_0,esk52_0) ),
    inference(rw,[status(thm)],[c_0_200,c_0_209]) ).

cnf(c_0_213,negated_conjecture,
    esk51_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_211]),c_0_40])]) ).

cnf(c_0_214,negated_conjecture,
    ~ memberP(nil,esk52_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_213])]) ).

cnf(c_0_215,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_209]),c_0_213])]),c_0_214]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12  % Problem    : SWC376+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n004.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 16:55:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 115.02/115.08  % Version  : CSE_E---1.5
% 115.02/115.08  % Problem  : theBenchmark.p
% 115.02/115.08  % Proof found
% 115.02/115.08  % SZS status Theorem for theBenchmark.p
% 115.02/115.08  % SZS output start Proof
% See solution above
% 115.02/115.10  % Total time : 114.509000 s
% 115.02/115.10  % SZS output end Proof
% 115.02/115.10  % Total time : 114.521000 s
%------------------------------------------------------------------------------