%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO500^1.005 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 08:46:26 EDT 2024

% Result   : Theorem 1.21s 0.57s
% Output   : CNFRefutation 1.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   43
% Syntax   : Number of formulae    :  471 (   9 unt;  24 typ;   0 def)
%            Number of atoms       : 22539 (   0 equ;   0 cnn)
%            Maximal formula atoms : 5117 (  50 avg)
%            Number of connectives : 29395 (7303   ~;9714   |;3957   &;8387   @)
%                                         (  34 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (   7 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;  21 con; 0-1 aty)
%            Number of variables   :    0 (   0   ^   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    x: $o ).

thf(decl_23,type,
    f0: $o > $o ).

thf(decl_24,type,
    f1: $o > $o ).

thf(decl_25,type,
    f2: $o > $o ).

thf(decl_26,type,
    f3: $o > $o ).

thf(decl_27,type,
    f4: $o > $o ).

thf(decl_28,type,
    epred1_0: $o ).

thf(decl_29,type,
    epred2_0: $o ).

thf(decl_30,type,
    epred3_0: $o ).

thf(decl_31,type,
    epred4_0: $o ).

thf(decl_32,type,
    epred5_0: $o ).

thf(decl_33,type,
    epred6_0: $o ).

thf(decl_34,type,
    epred7_0: $o ).

thf(decl_35,type,
    epred8_0: $o ).

thf(decl_36,type,
    epred9_0: $o ).

thf(decl_37,type,
    epred10_0: $o ).

thf(decl_38,type,
    epred11_0: $o ).

thf(decl_39,type,
    epred12_0: $o ).

thf(decl_40,type,
    epred13_0: $o ).

thf(decl_41,type,
    epred14_0: $o ).

thf(decl_42,type,
    epred15_0: $o ).

thf(decl_43,type,
    epred16_0: $o ).

thf(decl_44,type,
    epred17_0: $o ).

thf(decl_45,type,
    epred18_0: $o ).

thf(kaminski5,conjecture,
    ( ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ ( f4 @ x ) ) ) ) ) ) ) ) )
  <=> ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ ( f4 @ ( f4 @ ( f4 @ x ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kaminski5) ).

thf(c_0_1,plain,
    ( epred2_0
  <=> ( ( ( ( ~ x
            | ~ ( f4 @ $true ) )
          & ( x
            | ~ ( f4 @ $false ) ) )
        | ( f3 @ $true ) )
      & ( ( ( ~ x
            | ( f4 @ $true ) )
          & ( x
            | ( f4 @ $false ) ) )
        | ( f3 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_2,plain,
    ( epred1_0
  <=> ( ( ( ( ~ x
            | ~ ( f4 @ $true ) )
          & ( x
            | ~ ( f4 @ $false ) ) )
        | ~ ( f3 @ $true ) )
      & ( ( ( ~ x
            | ( f4 @ $true ) )
          & ( x
            | ( f4 @ $false ) ) )
        | ~ ( f3 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_3,plain,
    ( ( ~ x
      | ~ ( f4 @ $true )
      | ( f3 @ $true )
      | ~ epred2_0 )
    & ( x
      | ~ ( f4 @ $false )
      | ( f3 @ $true )
      | ~ epred2_0 )
    & ( ~ x
      | ( f4 @ $true )
      | ( f3 @ $false )
      | ~ epred2_0 )
    & ( x
      | ( f4 @ $false )
      | ( f3 @ $false )
      | ~ epred2_0 )
    & ( ~ x
      | x
      | ~ x
      | x
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | x
      | epred2_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred2_0 )
    & ( ~ ( f3 @ $false )
      | ~ x
      | x
      | epred2_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | x
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | x
      | epred2_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred2_0 )
    & ( ~ ( f3 @ $false )
      | ( f4 @ $false )
      | x
      | epred2_0 )
    & ( ~ x
      | x
      | ~ x
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ ( f3 @ $false )
      | ~ x
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ ( f3 @ $false )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred2_0 )
    & ( ~ x
      | x
      | ~ ( f3 @ $true )
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ ( f3 @ $true )
      | epred2_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ ( f3 @ $true )
      | epred2_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ ( f3 @ $true )
      | epred2_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | epred2_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).

thf(c_0_4,plain,
    ( epred7_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ~ ( f1 @ $false ) ) )
            | ~ ( f1 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f1 @ $false ) ) )
            | ~ ( f1 @ $false ) ) )
        | ~ ( f1 @ $true ) )
      & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ~ ( f1 @ $false ) ) )
            | ( f1 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f1 @ $false ) ) )
            | ( f1 @ $false ) ) )
        | ~ ( f1 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_5,plain,
    ( epred5_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ~ ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ~ ( f2 @ $false ) ) )
        | ~ ( f1 @ $true ) )
      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ( f2 @ $false ) ) )
        | ~ ( f1 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_6,plain,
    ( epred6_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ~ ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ~ ( f2 @ $false ) ) )
        | ( f1 @ $true ) )
      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f3 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f3 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f3 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ( f2 @ $false ) ) )
        | ( f1 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_7,plain,
    ( epred18_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ~ ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ~ ( f2 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ( f2 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ~ ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ~ ( f2 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
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                                      & ( ( ( ~ x
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                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
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                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
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                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ( f2 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
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                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
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                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
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                                      & ( ( ( ~ x
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                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
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                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
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                            | ~ ( f2 @ $false ) ) )
                        | ~ ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
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                                  & ( ( ( ( ( ~ x
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                              & ( ( ( ( ( ( ( ~ x
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                                  & ( ( ( ( ( ~ x
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                                          & ( x
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                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
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                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
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                              & ( ( ( ( ( ( ( ~ x
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                        | ~ ( f2 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
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                              & ( ( ( ( ( ( ( ~ x
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                          & ( ( ( ( ( ( ( ( ( ~ x
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                              & ( ( ( ( ( ( ( ~ x
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                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
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                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
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                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
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                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
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                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ( f2 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f1 @ $false ) ) )
            | ( f0 @ $false ) ) )
        | ( f0 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_8,plain,
    ( epred15_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f2 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
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                              & ( ( ( ~ x
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                                    | ( f4 @ $false ) ) )
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                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ~ ( f2 @ $false ) ) )
            | ~ ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
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                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
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                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
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                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
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                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ( f2 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f2 @ $false ) ) )
            | ~ ( f2 @ $false ) ) )
        | ~ ( f1 @ $true ) )
      & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
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                          & ( ( ( ( ( ~ x
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                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
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                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f2 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
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                                | ~ ( f4 @ $false ) ) )
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                          & ( ( ( ( ( ~ x
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                                  & ( x
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                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
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                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
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                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
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                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
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                                  & ( x
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                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
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                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
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                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
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                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
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                          & ( ( ( ( ( ~ x
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                                  & ( x
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                      & ( ( ( ( ( ( ( ~ x
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                                  & ( x
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                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
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                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ~ ( f2 @ $false ) ) )
            | ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
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                                  & ( x
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                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
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                                    | ( f4 @ $false ) ) )
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                          & ( ( ( ( ( ~ x
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                                  & ( x
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                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
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                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
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                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
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                                    | ( f4 @ $false ) ) )
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                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
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                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
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                                    | ( f4 @ $false ) ) )
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                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
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                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
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                                  & ( x
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                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
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                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
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                    | ~ ( f2 @ $false ) ) )
                | ( f2 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
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                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f2 @ $false ) ) )
            | ( f2 @ $false ) ) )
        | ~ ( f1 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_9,plain,
    ( epred16_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
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                                    | ( f4 @ $true ) )
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                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ~ ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ~ ( f4 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f4 @ $false ) ) )
                            | ( f4 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f4 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f4 @ $false ) ) )
                            | ( f4 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f2 @ $false ) ) )
            | ( f2 @ $false ) ) )
        | ( f1 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_10,plain,
    ( epred8_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ~ ( f1 @ $false ) ) )
            | ~ ( f1 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f1 @ $false ) ) )
            | ~ ( f1 @ $false ) ) )
        | ( f1 @ $true ) )
      & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ~ ( f1 @ $false ) ) )
            | ( f1 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ~ ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ~ ( f3 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f3 @ $false ) ) )
                        | ( f3 @ $true ) )
                      & ( ( ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f3 @ $true ) )
                          & ( ( ( ( ( ~ x
                                    | ~ ( f4 @ $true ) )
                                  & ( x
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ~ x
                                    | ( f4 @ $true ) )
                                  & ( x
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f3 @ $false ) ) )
                        | ( f3 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f1 @ $false ) ) )
            | ( f1 @ $false ) ) )
        | ( f1 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_11,plain,
    ( epred17_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ~ ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ~ ( f2 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ( f2 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ~ ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ~ ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
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                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ~ ( f2 @ $false ) ) )
                    | ~ ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ( f2 @ $false ) ) )
                    | ~ ( f2 @ $false ) ) )
                | ( f1 @ $true ) )
              & ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ~ ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ~ ( f2 @ $false ) ) )
                    | ( f2 @ $true ) )
                  & ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ~ ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ~ ( f2 @ $false ) ) )
                        | ( f2 @ $true ) )
                      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ~ ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ~ ( f3 @ $false ) ) )
                            | ( f2 @ $true ) )
                          & ( ( ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ~ ( f4 @ $false ) ) )
                                | ( f3 @ $true ) )
                              & ( ( ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ~ ( f4 @ $false ) ) )
                                    | ( f4 @ $true ) )
                                  & ( ( ( ( ( ~ x
                                            | ~ ( f4 @ $true ) )
                                          & ( x
                                            | ~ ( f4 @ $false ) ) )
                                        | ( f4 @ $true ) )
                                      & ( ( ( ~ x
                                            | ( f4 @ $true ) )
                                          & ( x
                                            | ( f4 @ $false ) ) )
                                        | ( f4 @ $false ) ) )
                                    | ( f4 @ $false ) ) )
                                | ( f3 @ $false ) ) )
                            | ( f2 @ $false ) ) )
                        | ( f2 @ $false ) ) )
                    | ( f2 @ $false ) ) )
                | ( f1 @ $false ) ) )
            | ( f0 @ $false ) ) )
        | ~ ( f0 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_12,plain,
    ( epred9_0
  <=> ( ( ( ( ~ x
            | ~ ( f4 @ $true ) )
          & ( x
            | ~ ( f4 @ $false ) ) )
        | ~ ( f4 @ $true ) )
      & ( ( ( ~ x
            | ( f4 @ $true ) )
          & ( x
            | ( f4 @ $false ) ) )
        | ~ ( f4 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_13,plain,
    ( ( ~ x
      | ~ ( f4 @ $true )
      | ~ ( f3 @ $true )
      | ~ epred1_0 )
    & ( x
      | ~ ( f4 @ $false )
      | ~ ( f3 @ $true )
      | ~ epred1_0 )
    & ( ~ x
      | ( f4 @ $true )
      | ~ ( f3 @ $false )
      | ~ epred1_0 )
    & ( x
      | ( f4 @ $false )
      | ~ ( f3 @ $false )
      | ~ epred1_0 )
    & ( ~ x
      | x
      | ~ x
      | x
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | x
      | epred1_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred1_0 )
    & ( ( f3 @ $false )
      | ~ x
      | x
      | epred1_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | x
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | x
      | epred1_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred1_0 )
    & ( ( f3 @ $false )
      | ( f4 @ $false )
      | x
      | epred1_0 )
    & ( ~ x
      | x
      | ~ x
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred1_0 )
    & ( ( f3 @ $false )
      | ~ x
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred1_0 )
    & ( ( f3 @ $false )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred1_0 )
    & ( ~ x
      | x
      | ( f3 @ $true )
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f3 @ $true )
      | epred1_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f3 @ $true )
      | epred1_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f3 @ $true )
      | epred1_0 )
    & ( ( f3 @ $false )
      | ( f3 @ $true )
      | epred1_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

thf(c_0_14,plain,
    ( ( f3 @ $true )
    | ~ x
    | ~ ( f4 @ $true )
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_15,plain,
    ( ( f4 @ $true )
    | ( f3 @ ~ $true )
    | ~ x
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_16,plain,
    ( epred7_0
  <=> ( ( ( ( epred5_0
            | ~ ( f1 @ $true ) )
          & ( epred6_0
            | ~ ( f1 @ $false ) ) )
        | ~ ( f1 @ $true ) )
      & ( ( ( epred5_0
            | ( f1 @ $true ) )
          & ( epred6_0
            | ( f1 @ $false ) ) )
        | ~ ( f1 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]),c_0_5]),c_0_6]) ).

thf(c_0_17,plain,
    ( epred18_0
  <=> ( ( ( ( epred15_0
            | ~ ( f0 @ $true ) )
          & ( epred16_0
            | ~ ( f0 @ $false ) ) )
        | ( f0 @ $true ) )
      & ( ( ( epred15_0
            | ( f0 @ $true ) )
          & ( epred16_0
            | ( f0 @ $false ) ) )
        | ( f0 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_8]),c_0_9]) ).

thf(c_0_18,plain,
    ( epred3_0
  <=> ( ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ~ ( f3 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ~ ( f3 @ $false ) ) )
        | ~ ( f3 @ $true ) )
      & ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ( f3 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ( f3 @ $false ) ) )
        | ~ ( f3 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_19,plain,
    ( epred4_0
  <=> ( ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ~ ( f3 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ~ ( f3 @ $false ) ) )
        | ( f3 @ $true ) )
      & ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ( f3 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ( f3 @ $false ) ) )
        | ( f3 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_20,negated_conjecture,
    ~ ( ( ( epred7_0
          | ( f0 @ $true ) )
        & ( epred8_0
          | ( f0 @ $false ) ) )
    <=> ( ( epred17_0
          | ( f0 @ $true ) )
        & ( epred18_0
          | ( f0 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[kaminski5])]),c_0_4]),c_0_10]),c_0_11]),c_0_7]) ).

thf(c_0_21,plain,
    ( epred8_0
  <=> ( ( ( ( epred5_0
            | ~ ( f1 @ $true ) )
          & ( epred6_0
            | ~ ( f1 @ $false ) ) )
        | ( f1 @ $true ) )
      & ( ( ( epred5_0
            | ( f1 @ $true ) )
          & ( epred6_0
            | ( f1 @ $false ) ) )
        | ( f1 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_5]),c_0_6]),c_0_5]),c_0_6]) ).

thf(c_0_22,plain,
    ( epred11_0
  <=> ( ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f4 @ $false ) ) )
            | ~ ( f4 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f4 @ $false ) ) )
            | ~ ( f4 @ $false ) ) )
        | ~ ( f3 @ $true ) )
      & ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f4 @ $false ) ) )
            | ( f4 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f4 @ $false ) ) )
            | ( f4 @ $false ) ) )
        | ~ ( f3 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_23,plain,
    ( epred10_0
  <=> ( ( ( ( ~ x
            | ~ ( f4 @ $true ) )
          & ( x
            | ~ ( f4 @ $false ) ) )
        | ( f4 @ $true ) )
      & ( ( ( ~ x
            | ( f4 @ $true ) )
          & ( x
            | ( f4 @ $false ) ) )
        | ( f4 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_24,plain,
    ( epred12_0
  <=> ( ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f4 @ $false ) ) )
            | ~ ( f4 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f4 @ $false ) ) )
            | ~ ( f4 @ $false ) ) )
        | ( f3 @ $true ) )
      & ( ( ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ~ ( f4 @ $false ) ) )
            | ( f4 @ $true ) )
          & ( ( ( ( ( ~ x
                    | ~ ( f4 @ $true ) )
                  & ( x
                    | ~ ( f4 @ $false ) ) )
                | ( f4 @ $true ) )
              & ( ( ( ~ x
                    | ( f4 @ $true ) )
                  & ( x
                    | ( f4 @ $false ) ) )
                | ( f4 @ $false ) ) )
            | ( f4 @ $false ) ) )
        | ( f3 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_25,plain,
    ( ( ~ x
      | ~ ( f4 @ $true )
      | ~ ( f4 @ $true )
      | ~ epred9_0 )
    & ( x
      | ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ epred9_0 )
    & ( ~ x
      | ( f4 @ $true )
      | ~ ( f4 @ $false )
      | ~ epred9_0 )
    & ( x
      | ( f4 @ $false )
      | ~ ( f4 @ $false )
      | ~ epred9_0 )
    & ( ~ x
      | x
      | ~ x
      | x
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | x
      | epred9_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred9_0 )
    & ( ( f4 @ $false )
      | ~ x
      | x
      | epred9_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | x
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | x
      | epred9_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred9_0 )
    & ( ( f4 @ $false )
      | ( f4 @ $false )
      | x
      | epred9_0 )
    & ( ~ x
      | x
      | ~ x
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred9_0 )
    & ( ( f4 @ $false )
      | ~ x
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred9_0 )
    & ( ( f4 @ $false )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ x
      | x
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $true )
      | epred9_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $true )
      | epred9_0 )
    & ( ( f4 @ $false )
      | ( f4 @ $true )
      | epred9_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

thf(c_0_26,plain,
    ( ~ x
    | ~ ( f4 @ $true )
    | ~ ( f3 @ $true )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_27,plain,
    ( ( f4 @ $true )
    | ~ x
    | ~ ( f3 @ ~ $true )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_28,plain,
    ( ( f3 @ ~ $true )
    | ( f3 @ $true )
    | ~ x
    | ~ epred2_0 ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_29,plain,
    ( ( epred5_0
      | ~ ( f1 @ $true )
      | ~ ( f1 @ $true )
      | ~ epred7_0 )
    & ( epred6_0
      | ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ~ epred7_0 )
    & ( epred5_0
      | ( f1 @ $true )
      | ~ ( f1 @ $false )
      | ~ epred7_0 )
    & ( epred6_0
      | ( f1 @ $false )
      | ~ ( f1 @ $false )
      | ~ epred7_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ~ epred6_0
      | ~ epred5_0
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ~ epred6_0
      | ~ epred5_0
      | epred7_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ~ epred5_0
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ~ epred5_0
      | epred7_0 )
    & ( ( f1 @ $false )
      | ~ epred6_0
      | ~ epred5_0
      | epred7_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ( f1 @ $false )
      | ~ epred5_0
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ( f1 @ $false )
      | ~ epred5_0
      | epred7_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ~ epred5_0
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ~ epred5_0
      | epred7_0 )
    & ( ( f1 @ $false )
      | ( f1 @ $false )
      | ~ epred5_0
      | epred7_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ~ epred6_0
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ~ epred6_0
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ( f1 @ $true )
      | epred7_0 )
    & ( ( f1 @ $false )
      | ~ epred6_0
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred7_0 )
    & ( ( f1 @ $false )
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ( f1 @ $true )
      | epred7_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ( f1 @ $true )
      | epred7_0 )
    & ( ( f1 @ $false )
      | ( f1 @ $true )
      | epred7_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

thf(c_0_30,plain,
    ( ( epred15_0
      | ~ ( f0 @ $true )
      | ( f0 @ $true )
      | ~ epred18_0 )
    & ( epred16_0
      | ~ ( f0 @ $false )
      | ( f0 @ $true )
      | ~ epred18_0 )
    & ( epred15_0
      | ( f0 @ $true )
      | ( f0 @ $false )
      | ~ epred18_0 )
    & ( epred16_0
      | ( f0 @ $false )
      | ( f0 @ $false )
      | ~ epred18_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ~ epred16_0
      | ~ epred15_0
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ~ epred16_0
      | ~ epred15_0
      | epred18_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ~ epred15_0
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ~ epred15_0
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred16_0
      | ~ epred15_0
      | epred18_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ( f0 @ $false )
      | ~ epred15_0
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ( f0 @ $false )
      | ~ epred15_0
      | epred18_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ~ epred15_0
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ~ epred15_0
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ( f0 @ $false )
      | ~ epred15_0
      | epred18_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ~ epred16_0
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ~ epred16_0
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred16_0
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred18_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ~ ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ~ ( f0 @ $true )
      | epred18_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ~ ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ ( f0 @ $true )
      | epred18_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | epred18_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).

thf(c_0_31,plain,
    ( epred5_0
  <=> ( ( ( ( epred3_0
            | ~ ( f2 @ $true ) )
          & ( epred4_0
            | ~ ( f2 @ $false ) ) )
        | ~ ( f1 @ $true ) )
      & ( ( ( epred3_0
            | ( f2 @ $true ) )
          & ( epred4_0
            | ( f2 @ $false ) ) )
        | ~ ( f1 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_18]),c_0_19]),c_0_18]),c_0_19]) ).

thf(c_0_32,negated_conjecture,
    ( ( ~ epred18_0
      | ~ epred17_0
      | ~ epred8_0
      | ~ epred7_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred17_0
      | ~ epred8_0
      | ~ epred7_0 )
    & ( ~ epred18_0
      | ~ ( f0 @ $true )
      | ~ epred8_0
      | ~ epred7_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ epred8_0
      | ~ epred7_0 )
    & ( ~ epred18_0
      | ~ epred17_0
      | ~ ( f0 @ $false )
      | ~ epred7_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred17_0
      | ~ ( f0 @ $false )
      | ~ epred7_0 )
    & ( ~ epred18_0
      | ~ ( f0 @ $true )
      | ~ ( f0 @ $false )
      | ~ epred7_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ ( f0 @ $false )
      | ~ epred7_0 )
    & ( ~ epred18_0
      | ~ epred17_0
      | ~ epred8_0
      | ~ ( f0 @ $true ) )
    & ( ~ ( f0 @ $false )
      | ~ epred17_0
      | ~ epred8_0
      | ~ ( f0 @ $true ) )
    & ( ~ epred18_0
      | ~ ( f0 @ $true )
      | ~ epred8_0
      | ~ ( f0 @ $true ) )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ epred8_0
      | ~ ( f0 @ $true ) )
    & ( ~ epred18_0
      | ~ epred17_0
      | ~ ( f0 @ $false )
      | ~ ( f0 @ $true ) )
    & ( ~ ( f0 @ $false )
      | ~ epred17_0
      | ~ ( f0 @ $false )
      | ~ ( f0 @ $true ) )
    & ( ~ epred18_0
      | ~ ( f0 @ $true )
      | ~ ( f0 @ $false )
      | ~ ( f0 @ $true ) )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ ( f0 @ $false )
      | ~ ( f0 @ $true ) )
    & ( epred17_0
      | ( f0 @ $true )
      | epred7_0
      | ( f0 @ $true ) )
    & ( epred18_0
      | ( f0 @ $false )
      | epred7_0
      | ( f0 @ $true ) )
    & ( epred17_0
      | ( f0 @ $true )
      | epred8_0
      | ( f0 @ $false ) )
    & ( epred18_0
      | ( f0 @ $false )
      | epred8_0
      | ( f0 @ $false ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).

thf(c_0_33,plain,
    ( ( epred5_0
      | ~ ( f1 @ $true )
      | ( f1 @ $true )
      | ~ epred8_0 )
    & ( epred6_0
      | ~ ( f1 @ $false )
      | ( f1 @ $true )
      | ~ epred8_0 )
    & ( epred5_0
      | ( f1 @ $true )
      | ( f1 @ $false )
      | ~ epred8_0 )
    & ( epred6_0
      | ( f1 @ $false )
      | ( f1 @ $false )
      | ~ epred8_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ~ epred6_0
      | ~ epred5_0
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ~ epred6_0
      | ~ epred5_0
      | epred8_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ~ epred5_0
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ~ epred5_0
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred6_0
      | ~ epred5_0
      | epred8_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ( f1 @ $false )
      | ~ epred5_0
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ( f1 @ $false )
      | ~ epred5_0
      | epred8_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ~ epred5_0
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ~ epred5_0
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ( f1 @ $false )
      | ~ epred5_0
      | epred8_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ~ epred6_0
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ~ epred6_0
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ~ epred6_0
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred6_0
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ( f1 @ $false )
      | ( f1 @ $true )
      | epred8_0 )
    & ( ~ epred6_0
      | ~ epred5_0
      | ~ ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred5_0
      | ~ ( f1 @ $true )
      | epred8_0 )
    & ( ~ epred6_0
      | ~ ( f1 @ $true )
      | ~ ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | ~ ( f1 @ $true )
      | epred8_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | epred8_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).

thf(c_0_34,plain,
    ( epred11_0
  <=> ( ( ( ( epred9_0
            | ~ ( f4 @ $true ) )
          & ( epred10_0
            | ~ ( f4 @ $false ) ) )
        | ~ ( f3 @ $true ) )
      & ( ( ( epred9_0
            | ( f4 @ $true ) )
          & ( epred10_0
            | ( f4 @ $false ) ) )
        | ~ ( f3 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22,c_0_12]),c_0_23]),c_0_12]),c_0_23]) ).

thf(c_0_35,plain,
    ( epred12_0
  <=> ( ( ( ( epred9_0
            | ~ ( f4 @ $true ) )
          & ( epred10_0
            | ~ ( f4 @ $false ) ) )
        | ( f3 @ $true ) )
      & ( ( ( epred9_0
            | ( f4 @ $true ) )
          & ( epred10_0
            | ( f4 @ $false ) ) )
        | ( f3 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_24,c_0_12]),c_0_23]),c_0_12]),c_0_23]) ).

thf(c_0_36,plain,
    ( ( f4 @ ~ $true )
    | ( f4 @ ~ $true )
    | x
    | epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_37,plain,
    ( epred13_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ~ ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ~ ( f2 @ $false ) ) )
        | ~ ( f2 @ $true ) )
      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ( f2 @ $false ) ) )
        | ~ ( f2 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_38,plain,
    ( x
    | ~ ( f4 @ ~ $true )
    | ~ ( f3 @ $true )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_39,plain,
    ( x
    | ( f4 @ ~ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_40,plain,
    ( ~ ( f3 @ $true )
    | ~ ( f3 @ ~ $true )
    | ~ x
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

thf(c_0_41,plain,
    ( ( f3 @ $true )
    | ~ x
    | ~ epred2_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_27]),c_0_28]) ).

thf(c_0_42,plain,
    ( epred4_0
  <=> ( ( ( ( epred1_0
            | ~ ( f3 @ $true ) )
          & ( epred2_0
            | ~ ( f3 @ $false ) ) )
        | ( f3 @ $true ) )
      & ( ( ( epred1_0
            | ( f3 @ $true ) )
          & ( epred2_0
            | ( f3 @ $false ) ) )
        | ( f3 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19,c_0_2]),c_0_1]),c_0_2]),c_0_1]) ).

thf(c_0_43,plain,
    ( x
    | epred2_0
    | ~ ( f4 @ ~ $true )
    | ~ ( f3 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_44,plain,
    ( ( f3 @ ~ $true )
    | ( f4 @ ~ $true )
    | x
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_45,plain,
    ( ( f3 @ ~ $true )
    | ( f3 @ $true )
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_46,plain,
    ( ( f1 @ ~ $true )
    | ( f1 @ ~ $true )
    | epred7_0
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_47,plain,
    ( ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $true )
      | ~ epred10_0 )
    & ( x
      | ~ ( f4 @ $false )
      | ( f4 @ $true )
      | ~ epred10_0 )
    & ( ~ x
      | ( f4 @ $true )
      | ( f4 @ $false )
      | ~ epred10_0 )
    & ( x
      | ( f4 @ $false )
      | ( f4 @ $false )
      | ~ epred10_0 )
    & ( ~ x
      | x
      | ~ x
      | x
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | x
      | epred10_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | x
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ x
      | x
      | epred10_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | x
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | x
      | epred10_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | x
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ( f4 @ $false )
      | x
      | epred10_0 )
    & ( ~ x
      | x
      | ~ x
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ x
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ x
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ x
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ x
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred10_0 )
    & ( ~ x
      | x
      | ~ ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | x
      | ~ ( f4 @ $true )
      | epred10_0 )
    & ( ~ x
      | ~ ( f4 @ $true )
      | ~ ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ ( f4 @ $true )
      | epred10_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | epred10_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).

thf(c_0_48,plain,
    ( epred17_0
  <=> ( ( ( ( epred15_0
            | ~ ( f0 @ $true ) )
          & ( epred16_0
            | ~ ( f0 @ $false ) ) )
        | ~ ( f0 @ $true ) )
      & ( ( ( epred15_0
            | ( f0 @ $true ) )
          & ( epred16_0
            | ( f0 @ $false ) ) )
        | ~ ( f0 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_8]),c_0_9]),c_0_8]),c_0_9]) ).

thf(c_0_49,plain,
    ( epred18_0
    | ~ epred16_0
    | ~ ( f0 @ $true )
    | ~ ( f0 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_50,plain,
    ( ( epred3_0
      | ~ ( f2 @ $true )
      | ~ ( f1 @ $true )
      | ~ epred5_0 )
    & ( epred4_0
      | ~ ( f2 @ $false )
      | ~ ( f1 @ $true )
      | ~ epred5_0 )
    & ( epred3_0
      | ( f2 @ $true )
      | ~ ( f1 @ $false )
      | ~ epred5_0 )
    & ( epred4_0
      | ( f2 @ $false )
      | ~ ( f1 @ $false )
      | ~ epred5_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ~ epred4_0
      | ~ epred3_0
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ~ epred4_0
      | ~ epred3_0
      | epred5_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ~ epred3_0
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ~ epred3_0
      | epred5_0 )
    & ( ( f1 @ $false )
      | ~ epred4_0
      | ~ epred3_0
      | epred5_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ( f2 @ $false )
      | ~ epred3_0
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ( f2 @ $false )
      | ~ epred3_0
      | epred5_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred3_0
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred3_0
      | epred5_0 )
    & ( ( f1 @ $false )
      | ( f2 @ $false )
      | ~ epred3_0
      | epred5_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ~ epred4_0
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ~ epred4_0
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ( f2 @ $true )
      | epred5_0 )
    & ( ( f1 @ $false )
      | ~ epred4_0
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred5_0 )
    & ( ( f1 @ $false )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred5_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ( f1 @ $true )
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ( f1 @ $true )
      | epred5_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ( f1 @ $true )
      | epred5_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f1 @ $true )
      | epred5_0 )
    & ( ( f1 @ $false )
      | ( f1 @ $true )
      | epred5_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).

thf(c_0_51,plain,
    ( epred5_0
    | ~ ( f1 @ $true )
    | ~ ( f1 @ $true )
    | ~ epred7_0 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_52,negated_conjecture,
    ( ~ epred18_0
    | ~ ( f0 @ $true )
    | ~ epred8_0
    | ~ ( f0 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_53,negated_conjecture,
    ( epred17_0
    | ( f0 @ $true )
    | epred7_0
    | ( f0 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_54,plain,
    ( epred8_0
    | ~ epred6_0
    | ~ ( f1 @ $true )
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_55,plain,
    ( epred14_0
  <=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ~ ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ~ ( f2 @ $false ) ) )
        | ( f2 @ $true ) )
      & ( ( ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ~ ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ~ ( f3 @ $false ) ) )
            | ( f2 @ $true ) )
          & ( ( ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ~ ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ~ ( f4 @ $false ) ) )
                | ( f3 @ $true ) )
              & ( ( ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ~ ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ~ ( f4 @ $false ) ) )
                    | ( f4 @ $true ) )
                  & ( ( ( ( ( ~ x
                            | ~ ( f4 @ $true ) )
                          & ( x
                            | ~ ( f4 @ $false ) ) )
                        | ( f4 @ $true ) )
                      & ( ( ( ~ x
                            | ( f4 @ $true ) )
                          & ( x
                            | ( f4 @ $false ) ) )
                        | ( f4 @ $false ) ) )
                    | ( f4 @ $false ) ) )
                | ( f3 @ $false ) ) )
            | ( f2 @ $false ) ) )
        | ( f2 @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_56,plain,
    ( ( epred9_0
      | ~ ( f4 @ $true )
      | ~ ( f3 @ $true )
      | ~ epred11_0 )
    & ( epred10_0
      | ~ ( f4 @ $false )
      | ~ ( f3 @ $true )
      | ~ epred11_0 )
    & ( epred9_0
      | ( f4 @ $true )
      | ~ ( f3 @ $false )
      | ~ epred11_0 )
    & ( epred10_0
      | ( f4 @ $false )
      | ~ ( f3 @ $false )
      | ~ epred11_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ~ epred10_0
      | ~ epred9_0
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ~ epred10_0
      | ~ epred9_0
      | epred11_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ~ epred9_0
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ~ epred9_0
      | epred11_0 )
    & ( ( f3 @ $false )
      | ~ epred10_0
      | ~ epred9_0
      | epred11_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ( f4 @ $false )
      | ~ epred9_0
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ( f4 @ $false )
      | ~ epred9_0
      | epred11_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ~ epred9_0
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ~ epred9_0
      | epred11_0 )
    & ( ( f3 @ $false )
      | ( f4 @ $false )
      | ~ epred9_0
      | epred11_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ~ epred10_0
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ~ epred10_0
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ( f4 @ $true )
      | epred11_0 )
    & ( ( f3 @ $false )
      | ~ epred10_0
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred11_0 )
    & ( ( f3 @ $false )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred11_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ( f3 @ $true )
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ( f3 @ $true )
      | epred11_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ( f3 @ $true )
      | epred11_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f3 @ $true )
      | epred11_0 )
    & ( ( f3 @ $false )
      | ( f3 @ $true )
      | epred11_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).

thf(c_0_57,plain,
    ( ( epred9_0
      | ~ ( f4 @ $true )
      | ( f3 @ $true )
      | ~ epred12_0 )
    & ( epred10_0
      | ~ ( f4 @ $false )
      | ( f3 @ $true )
      | ~ epred12_0 )
    & ( epred9_0
      | ( f4 @ $true )
      | ( f3 @ $false )
      | ~ epred12_0 )
    & ( epred10_0
      | ( f4 @ $false )
      | ( f3 @ $false )
      | ~ epred12_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ~ epred10_0
      | ~ epred9_0
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ~ epred10_0
      | ~ epred9_0
      | epred12_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ~ epred9_0
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ~ epred9_0
      | epred12_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred10_0
      | ~ epred9_0
      | epred12_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ( f4 @ $false )
      | ~ epred9_0
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ( f4 @ $false )
      | ~ epred9_0
      | epred12_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ~ epred9_0
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ~ epred9_0
      | epred12_0 )
    & ( ~ ( f3 @ $false )
      | ( f4 @ $false )
      | ~ epred9_0
      | epred12_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ~ epred10_0
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ~ epred10_0
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ epred10_0
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred10_0
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ ( f3 @ $false )
      | ( f4 @ $false )
      | ( f4 @ $true )
      | epred12_0 )
    & ( ~ epred10_0
      | ~ epred9_0
      | ~ ( f3 @ $true )
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ epred9_0
      | ~ ( f3 @ $true )
      | epred12_0 )
    & ( ~ epred10_0
      | ~ ( f4 @ $true )
      | ~ ( f3 @ $true )
      | epred12_0 )
    & ( ~ ( f4 @ $false )
      | ~ ( f4 @ $true )
      | ~ ( f3 @ $true )
      | epred12_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | epred12_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).

thf(c_0_58,plain,
    ( x
    | ( f4 @ $true )
    | epred9_0
    | ~ ( f4 @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_59,plain,
    ( x
    | epred9_0
    | ( f4 @ ~ $true ) ),
    inference(cn,[status(thm)],[c_0_36]) ).

thf(c_0_60,plain,
    ( epred13_0
  <=> ( ( ( ( epred11_0
            | ~ ( f2 @ $true ) )
          & ( epred12_0
            | ~ ( f2 @ $false ) ) )
        | ~ ( f2 @ $true ) )
      & ( ( ( epred11_0
            | ( f2 @ $true ) )
          & ( epred12_0
            | ( f2 @ $false ) ) )
        | ~ ( f2 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_37,c_0_22]),c_0_24]),c_0_22]),c_0_24]) ).

thf(c_0_61,plain,
    ( x
    | ( f3 @ $true )
    | ~ ( f4 @ ~ $true )
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_62,plain,
    ( x
    | ( f4 @ ~ $true )
    | ( f3 @ ~ $true )
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_63,plain,
    ( ~ ( f3 @ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).

thf(c_0_64,plain,
    ( ( f3 @ ~ $true )
    | ~ x
    | ~ epred1_0
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_15]),c_0_41]) ).

thf(c_0_65,plain,
    ( ( epred1_0
      | ~ ( f3 @ $true )
      | ( f3 @ $true )
      | ~ epred4_0 )
    & ( epred2_0
      | ~ ( f3 @ $false )
      | ( f3 @ $true )
      | ~ epred4_0 )
    & ( epred1_0
      | ( f3 @ $true )
      | ( f3 @ $false )
      | ~ epred4_0 )
    & ( epred2_0
      | ( f3 @ $false )
      | ( f3 @ $false )
      | ~ epred4_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ~ epred2_0
      | ~ epred1_0
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ~ epred2_0
      | ~ epred1_0
      | epred4_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ~ epred1_0
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ~ epred1_0
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred2_0
      | ~ epred1_0
      | epred4_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ( f3 @ $false )
      | ~ epred1_0
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ( f3 @ $false )
      | ~ epred1_0
      | epred4_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ~ epred1_0
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ~ epred1_0
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ( f3 @ $false )
      | ~ epred1_0
      | epred4_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ~ epred2_0
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ~ epred2_0
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred2_0
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred4_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ~ ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ~ ( f3 @ $true )
      | epred4_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ~ ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ~ ( f3 @ $true )
      | epred4_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | epred4_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).

thf(c_0_66,plain,
    ( epred2_0
    | ~ ( f3 @ ~ $true )
    | ~ ( f3 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_67,plain,
    ( ( f3 @ ~ $true )
    | epred1_0
    | epred2_0
    | x ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).

thf(c_0_68,plain,
    ( epred16_0
    | ( f0 @ ~ $true )
    | ( f0 @ ~ $true )
    | ~ epred18_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_69,negated_conjecture,
    ( ~ ( f0 @ ~ $true )
    | ~ epred17_0
    | ~ ( f0 @ ~ $true )
    | ~ epred7_0 ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_70,negated_conjecture,
    ( epred18_0
    | ( f0 @ ~ $true )
    | epred8_0
    | ( f0 @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_71,plain,
    ( ( f1 @ $true )
    | epred7_0
    | ~ ( f1 @ ~ $true )
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_72,plain,
    ( epred7_0
    | ( f1 @ ~ $true )
    | ~ epred5_0 ),
    inference(cn,[status(thm)],[c_0_46]) ).

thf(c_0_73,plain,
    ( x
    | ( f4 @ ~ $true )
    | ( f4 @ ~ $true )
    | ~ epred10_0 ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_74,plain,
    ( ( epred15_0
      | ~ ( f0 @ $true )
      | ~ ( f0 @ $true )
      | ~ epred17_0 )
    & ( epred16_0
      | ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ epred17_0 )
    & ( epred15_0
      | ( f0 @ $true )
      | ~ ( f0 @ $false )
      | ~ epred17_0 )
    & ( epred16_0
      | ( f0 @ $false )
      | ~ ( f0 @ $false )
      | ~ epred17_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ~ epred16_0
      | ~ epred15_0
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ~ epred16_0
      | ~ epred15_0
      | epred17_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ~ epred15_0
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ~ epred15_0
      | epred17_0 )
    & ( ( f0 @ $false )
      | ~ epred16_0
      | ~ epred15_0
      | epred17_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ( f0 @ $false )
      | ~ epred15_0
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ( f0 @ $false )
      | ~ epred15_0
      | epred17_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ~ epred15_0
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ~ epred15_0
      | epred17_0 )
    & ( ( f0 @ $false )
      | ( f0 @ $false )
      | ~ epred15_0
      | epred17_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ~ epred16_0
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ~ epred16_0
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ epred16_0
      | ( f0 @ $true )
      | epred17_0 )
    & ( ( f0 @ $false )
      | ~ epred16_0
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred17_0 )
    & ( ( f0 @ $false )
      | ( f0 @ $false )
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ epred16_0
      | ~ epred15_0
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ epred15_0
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ epred16_0
      | ~ ( f0 @ $true )
      | ( f0 @ $true )
      | epred17_0 )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ( f0 @ $true )
      | epred17_0 )
    & ( ( f0 @ $false )
      | ( f0 @ $true )
      | epred17_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])]) ).

thf(c_0_75,negated_conjecture,
    ( ~ ( f0 @ ~ $true )
    | ~ ( f0 @ $true )
    | ~ ( f0 @ ~ $true )
    | ~ ( f0 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_76,plain,
    ( ( f0 @ $true )
    | epred18_0
    | ~ ( f0 @ ~ $true )
    | ~ epred16_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_77,plain,
    ( epred18_0
    | ~ epred16_0
    | ~ ( f0 @ $true ) ),
    inference(cn,[status(thm)],[c_0_49]) ).

thf(c_0_78,plain,
    ( epred5_0
    | ( f1 @ $true )
    | ~ ( f1 @ ~ $true )
    | ~ epred7_0 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_79,plain,
    ( ( f1 @ ~ $true )
    | ( f1 @ $true )
    | epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_80,plain,
    ( epred5_0
    | ~ epred7_0
    | ~ ( f1 @ $true ) ),
    inference(cn,[status(thm)],[c_0_51]) ).

thf(c_0_81,negated_conjecture,
    ( ~ epred8_0
    | ~ epred18_0
    | ~ ( f0 @ $true ) ),
    inference(cn,[status(thm)],[c_0_52]) ).

thf(c_0_82,negated_conjecture,
    ( epred7_0
    | epred17_0
    | ( f0 @ $true ) ),
    inference(cn,[status(thm)],[c_0_53]) ).

thf(c_0_83,plain,
    ( ( f1 @ $true )
    | epred8_0
    | ~ ( f1 @ ~ $true )
    | ~ epred6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_84,plain,
    ( epred8_0
    | ~ epred6_0
    | ~ ( f1 @ $true ) ),
    inference(cn,[status(thm)],[c_0_54]) ).

thf(c_0_85,plain,
    ( epred16_0
  <=> ( ( ( ( epred13_0
            | ~ ( f2 @ $true ) )
          & ( epred14_0
            | ~ ( f2 @ $false ) ) )
        | ( f1 @ $true ) )
      & ( ( ( epred13_0
            | ( f2 @ $true ) )
          & ( epred14_0
            | ( f2 @ $false ) ) )
        | ( f1 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_37]),c_0_55]),c_0_37]),c_0_55]) ).

thf(c_0_86,plain,
    ( epred15_0
  <=> ( ( ( ( epred13_0
            | ~ ( f2 @ $true ) )
          & ( epred14_0
            | ~ ( f2 @ $false ) ) )
        | ~ ( f1 @ $true ) )
      & ( ( ( epred13_0
            | ( f2 @ $true ) )
          & ( epred14_0
            | ( f2 @ $false ) ) )
        | ~ ( f1 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_37]),c_0_55]),c_0_37]),c_0_55]) ).

thf(c_0_87,plain,
    ( epred14_0
  <=> ( ( ( ( epred11_0
            | ~ ( f2 @ $true ) )
          & ( epred12_0
            | ~ ( f2 @ $false ) ) )
        | ( f2 @ $true ) )
      & ( ( ( epred11_0
            | ( f2 @ $true ) )
          & ( epred12_0
            | ( f2 @ $false ) ) )
        | ( f2 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_55,c_0_22]),c_0_24]),c_0_22]),c_0_24]) ).

thf(c_0_88,plain,
    ( ( f3 @ $true )
    | epred11_0
    | ~ epred10_0
    | ~ ( f4 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_89,plain,
    ( ( f4 @ $true )
    | epred12_0
    | ~ ( f3 @ ~ $true )
    | ~ epred10_0 ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_90,plain,
    ( ( f3 @ ~ $true )
    | ( f3 @ $true )
    | epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_91,plain,
    ( ( f4 @ $true )
    | epred10_0
    | ~ ( f4 @ ~ $true )
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_92,plain,
    ( epred10_0
    | ~ ( f4 @ ~ $true )
    | ~ ( f4 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_93,plain,
    ( ( f4 @ $true )
    | epred9_0
    | x ),
    inference(csr,[status(thm)],[c_0_58,c_0_59]) ).

thf(c_0_94,plain,
    ( ( epred11_0
      | ~ ( f2 @ $true )
      | ~ ( f2 @ $true )
      | ~ epred13_0 )
    & ( epred12_0
      | ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred13_0 )
    & ( epred11_0
      | ( f2 @ $true )
      | ~ ( f2 @ $false )
      | ~ epred13_0 )
    & ( epred12_0
      | ( f2 @ $false )
      | ~ ( f2 @ $false )
      | ~ epred13_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ~ epred12_0
      | ~ epred11_0
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ~ epred12_0
      | ~ epred11_0
      | epred13_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ~ epred11_0
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ~ epred11_0
      | epred13_0 )
    & ( ( f2 @ $false )
      | ~ epred12_0
      | ~ epred11_0
      | epred13_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ( f2 @ $false )
      | ~ epred11_0
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ( f2 @ $false )
      | ~ epred11_0
      | epred13_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred11_0
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred11_0
      | epred13_0 )
    & ( ( f2 @ $false )
      | ( f2 @ $false )
      | ~ epred11_0
      | epred13_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ~ epred12_0
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ~ epred12_0
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ( f2 @ $true )
      | epred13_0 )
    & ( ( f2 @ $false )
      | ~ epred12_0
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred13_0 )
    & ( ( f2 @ $false )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ( f2 @ $true )
      | epred13_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $true )
      | epred13_0 )
    & ( ( f2 @ $false )
      | ( f2 @ $true )
      | epred13_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).

thf(c_0_95,plain,
    ( ( f3 @ ~ $true )
    | ( f3 @ $true )
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_28]) ).

thf(c_0_96,plain,
    ( ~ epred1_0
    | ~ x
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_41]) ).

thf(c_0_97,plain,
    ( epred2_0
    | ( f3 @ ~ $true )
    | ( f3 @ ~ $true )
    | ~ epred4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

thf(c_0_98,plain,
    ( epred3_0
  <=> ( ( ( ( epred1_0
            | ~ ( f3 @ $true ) )
          & ( epred2_0
            | ~ ( f3 @ $false ) ) )
        | ~ ( f3 @ $true ) )
      & ( ( ( epred1_0
            | ( f3 @ $true ) )
          & ( epred2_0
            | ( f3 @ $false ) ) )
        | ~ ( f3 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_2]),c_0_1]),c_0_2]),c_0_1]) ).

thf(c_0_99,plain,
    ( epred2_0
    | ~ x
    | ~ ( f4 @ $true )
    | ~ ( f3 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_100,plain,
    ( ( f3 @ ~ $true )
    | ( f4 @ $true )
    | epred1_0
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_101,plain,
    ( x
    | epred1_0
    | epred2_0
    | ~ ( f3 @ $true ) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

thf(c_0_102,plain,
    ( epred6_0
  <=> ( ( ( ( epred3_0
            | ~ ( f2 @ $true ) )
          & ( epred4_0
            | ~ ( f2 @ $false ) ) )
        | ( f1 @ $true ) )
      & ( ( ( epred3_0
            | ( f2 @ $true ) )
          & ( epred4_0
            | ( f2 @ $false ) ) )
        | ( f1 @ $false ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_18]),c_0_19]),c_0_18]),c_0_19]) ).

thf(c_0_103,plain,
    ( epred6_0
    | ( f1 @ ~ $true )
    | ( f1 @ ~ $true )
    | ~ epred8_0 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_104,plain,
    ( epred16_0
    | ( f0 @ $true )
    | ~ ( f0 @ ~ $true )
    | ~ epred18_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_105,plain,
    ( epred16_0
    | ( f0 @ ~ $true )
    | ~ epred18_0 ),
    inference(cn,[status(thm)],[c_0_68]) ).

thf(c_0_106,negated_conjecture,
    ( ~ epred7_0
    | ~ epred17_0
    | ~ ( f0 @ ~ $true ) ),
    inference(cn,[status(thm)],[c_0_69]) ).

thf(c_0_107,negated_conjecture,
    ( epred8_0
    | epred18_0
    | ( f0 @ ~ $true ) ),
    inference(cn,[status(thm)],[c_0_70]) ).

thf(c_0_108,plain,
    ( epred8_0
    | ~ ( f1 @ ~ $true )
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_109,plain,
    ( ( f1 @ $true )
    | epred7_0
    | ~ epred5_0 ),
    inference(csr,[status(thm)],[c_0_71,c_0_72]) ).

thf(c_0_110,plain,
    ( x
    | ( f4 @ $true )
    | ~ ( f4 @ ~ $true )
    | ~ epred10_0 ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_111,plain,
    ( x
    | ( f4 @ ~ $true )
    | ~ epred10_0 ),
    inference(cn,[status(thm)],[c_0_73]) ).

thf(c_0_112,plain,
    ( epred15_0
    | ( f0 @ $true )
    | ~ ( f0 @ ~ $true )
    | ~ epred17_0 ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

thf(c_0_113,negated_conjecture,
    ( ~ ( f0 @ $true )
    | ~ ( f0 @ ~ $true ) ),
    inference(cn,[status(thm)],[c_0_75]) ).

thf(c_0_114,plain,
    ( epred15_0
    | ~ ( f0 @ $true )
    | ~ ( f0 @ $true )
    | ~ epred17_0 ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

thf(c_0_115,plain,
    ( epred18_0
    | ~ ( f0 @ ~ $true )
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[c_0_76,c_0_77]) ).

thf(c_0_116,negated_conjecture,
    ( epred18_0
    | ( f0 @ ~ $true )
    | epred7_0
    | ( f0 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_117,plain,
    ( epred5_0
    | ~ epred7_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).

thf(c_0_118,negated_conjecture,
    ( epred17_0
    | epred7_0
    | ~ epred8_0
    | ~ epred18_0 ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

thf(c_0_119,negated_conjecture,
    ( epred17_0
    | epred7_0
    | epred18_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_77,c_0_82]) ).

thf(c_0_120,plain,
    ( epred8_0
    | ~ ( f1 @ ~ $true )
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[c_0_83,c_0_84]) ).

thf(c_0_121,plain,
    ( ( f1 @ ~ $true )
    | ( f1 @ $true )
    | epred7_0 ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

thf(c_0_122,plain,
    ( epred8_0
    | ~ epred6_0
    | ~ epred5_0
    | ~ epred6_0
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_123,plain,
    ( ( epred13_0
      | ~ ( f2 @ $true )
      | ( f1 @ $true )
      | ~ epred16_0 )
    & ( epred14_0
      | ~ ( f2 @ $false )
      | ( f1 @ $true )
      | ~ epred16_0 )
    & ( epred13_0
      | ( f2 @ $true )
      | ( f1 @ $false )
      | ~ epred16_0 )
    & ( epred14_0
      | ( f2 @ $false )
      | ( f1 @ $false )
      | ~ epred16_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ~ epred14_0
      | ~ epred13_0
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ~ epred14_0
      | ~ epred13_0
      | epred16_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ~ epred13_0
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ~ epred13_0
      | epred16_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred14_0
      | ~ epred13_0
      | epred16_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ( f2 @ $false )
      | ~ epred13_0
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ( f2 @ $false )
      | ~ epred13_0
      | epred16_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred13_0
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred13_0
      | epred16_0 )
    & ( ~ ( f1 @ $false )
      | ( f2 @ $false )
      | ~ epred13_0
      | epred16_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ~ epred14_0
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ~ epred14_0
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred14_0
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ ( f1 @ $false )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred16_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ~ ( f1 @ $true )
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ~ ( f1 @ $true )
      | epred16_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ~ ( f1 @ $true )
      | epred16_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ ( f1 @ $true )
      | epred16_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | epred16_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])]) ).

thf(c_0_124,plain,
    ( ( epred13_0
      | ~ ( f2 @ $true )
      | ~ ( f1 @ $true )
      | ~ epred15_0 )
    & ( epred14_0
      | ~ ( f2 @ $false )
      | ~ ( f1 @ $true )
      | ~ epred15_0 )
    & ( epred13_0
      | ( f2 @ $true )
      | ~ ( f1 @ $false )
      | ~ epred15_0 )
    & ( epred14_0
      | ( f2 @ $false )
      | ~ ( f1 @ $false )
      | ~ epred15_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ~ epred14_0
      | ~ epred13_0
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ~ epred14_0
      | ~ epred13_0
      | epred15_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ~ epred13_0
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ~ epred13_0
      | epred15_0 )
    & ( ( f1 @ $false )
      | ~ epred14_0
      | ~ epred13_0
      | epred15_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ( f2 @ $false )
      | ~ epred13_0
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ( f2 @ $false )
      | ~ epred13_0
      | epred15_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred13_0
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred13_0
      | epred15_0 )
    & ( ( f1 @ $false )
      | ( f2 @ $false )
      | ~ epred13_0
      | epred15_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ~ epred14_0
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ~ epred14_0
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred14_0
      | ( f2 @ $true )
      | epred15_0 )
    & ( ( f1 @ $false )
      | ~ epred14_0
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred15_0 )
    & ( ( f1 @ $false )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred15_0 )
    & ( ~ epred14_0
      | ~ epred13_0
      | ( f1 @ $true )
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred13_0
      | ( f1 @ $true )
      | epred15_0 )
    & ( ~ epred14_0
      | ~ ( f2 @ $true )
      | ( f1 @ $true )
      | epred15_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f1 @ $true )
      | epred15_0 )
    & ( ( f1 @ $false )
      | ( f1 @ $true )
      | epred15_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])]) ).

thf(c_0_125,plain,
    ( ( epred11_0
      | ~ ( f2 @ $true )
      | ( f2 @ $true )
      | ~ epred14_0 )
    & ( epred12_0
      | ~ ( f2 @ $false )
      | ( f2 @ $true )
      | ~ epred14_0 )
    & ( epred11_0
      | ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred14_0 )
    & ( epred12_0
      | ( f2 @ $false )
      | ( f2 @ $false )
      | ~ epred14_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ~ epred12_0
      | ~ epred11_0
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ~ epred12_0
      | ~ epred11_0
      | epred14_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ~ epred11_0
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ~ epred11_0
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred12_0
      | ~ epred11_0
      | epred14_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ( f2 @ $false )
      | ~ epred11_0
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ( f2 @ $false )
      | ~ epred11_0
      | epred14_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred11_0
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred11_0
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ( f2 @ $false )
      | ~ epred11_0
      | epred14_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ~ epred12_0
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ~ epred12_0
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred12_0
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred12_0
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred14_0 )
    & ( ~ epred12_0
      | ~ epred11_0
      | ~ ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred11_0
      | ~ ( f2 @ $true )
      | epred14_0 )
    & ( ~ epred12_0
      | ~ ( f2 @ $true )
      | ~ ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ ( f2 @ $true )
      | epred14_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | epred14_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])]) ).

thf(c_0_126,plain,
    ( epred12_0
    | ~ epred10_0
    | ~ ( f4 @ $true )
    | ~ ( f3 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_127,plain,
    ( ( f3 @ ~ $true )
    | ( f4 @ $true )
    | epred11_0
    | ~ epred10_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_128,plain,
    ( ( f3 @ $true )
    | epred12_0
    | epred11_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).

thf(c_0_129,plain,
    ( epred10_0
    | ~ x
    | ~ ( f4 @ $true )
    | ~ ( f4 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_130,plain,
    ( epred10_0
    | ~ ( f4 @ ~ $true )
    | ~ x ),
    inference(csr,[status(thm)],[c_0_91,c_0_92]) ).

thf(c_0_131,plain,
    ( ( f4 @ ~ $true )
    | ( f4 @ $true )
    | epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_132,plain,
    ( epred9_0
    | x
    | epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_59]),c_0_93]) ).

thf(c_0_133,plain,
    ( ( f2 @ ~ $true )
    | ( f2 @ ~ $true )
    | epred13_0
    | ~ epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

thf(c_0_134,plain,
    ( ( f3 @ $true )
    | ~ epred2_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_39]),c_0_95]),c_0_96]) ).

thf(c_0_135,plain,
    ( epred2_0
    | ( f3 @ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

thf(c_0_136,plain,
    ( epred2_0
    | ( f3 @ ~ $true )
    | ~ epred4_0 ),
    inference(cn,[status(thm)],[c_0_97]) ).

thf(c_0_137,plain,
    ( ( epred1_0
      | ~ ( f3 @ $true )
      | ~ ( f3 @ $true )
      | ~ epred3_0 )
    & ( epred2_0
      | ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ~ epred3_0 )
    & ( epred1_0
      | ( f3 @ $true )
      | ~ ( f3 @ $false )
      | ~ epred3_0 )
    & ( epred2_0
      | ( f3 @ $false )
      | ~ ( f3 @ $false )
      | ~ epred3_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ~ epred2_0
      | ~ epred1_0
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ~ epred2_0
      | ~ epred1_0
      | epred3_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ~ epred1_0
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ~ epred1_0
      | epred3_0 )
    & ( ( f3 @ $false )
      | ~ epred2_0
      | ~ epred1_0
      | epred3_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ( f3 @ $false )
      | ~ epred1_0
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ( f3 @ $false )
      | ~ epred1_0
      | epred3_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ~ epred1_0
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ~ epred1_0
      | epred3_0 )
    & ( ( f3 @ $false )
      | ( f3 @ $false )
      | ~ epred1_0
      | epred3_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ~ epred2_0
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ~ epred2_0
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ~ epred2_0
      | ( f3 @ $true )
      | epred3_0 )
    & ( ( f3 @ $false )
      | ~ epred2_0
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred3_0 )
    & ( ( f3 @ $false )
      | ( f3 @ $false )
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ epred2_0
      | ~ epred1_0
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ epred1_0
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ epred2_0
      | ~ ( f3 @ $true )
      | ( f3 @ $true )
      | epred3_0 )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | ( f3 @ $true )
      | epred3_0 )
    & ( ( f3 @ $false )
      | ( f3 @ $true )
      | epred3_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])]) ).

thf(c_0_138,plain,
    ( epred4_0
    | ~ epred2_0
    | ~ ( f3 @ $true )
    | ~ ( f3 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

thf(c_0_139,plain,
    ( ( f3 @ ~ $true )
    | epred1_0
    | epred2_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_45]) ).

thf(c_0_140,plain,
    ( ( f3 @ $true )
    | epred1_0
    | ~ x
    | ~ ( f4 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_141,plain,
    ( ( f4 @ $true )
    | epred2_0
    | ~ ( f3 @ ~ $true )
    | ~ x ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_142,plain,
    ( ~ x
    | ~ ( f4 @ $true )
    | ~ ( f4 @ $true )
    | ~ epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_143,plain,
    ( epred11_0
    | ~ ( f2 @ $true )
    | ~ ( f2 @ $true )
    | ~ epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

thf(c_0_144,plain,
    ( ( epred3_0
      | ~ ( f2 @ $true )
      | ( f1 @ $true )
      | ~ epred6_0 )
    & ( epred4_0
      | ~ ( f2 @ $false )
      | ( f1 @ $true )
      | ~ epred6_0 )
    & ( epred3_0
      | ( f2 @ $true )
      | ( f1 @ $false )
      | ~ epred6_0 )
    & ( epred4_0
      | ( f2 @ $false )
      | ( f1 @ $false )
      | ~ epred6_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ~ epred4_0
      | ~ epred3_0
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ~ epred4_0
      | ~ epred3_0
      | epred6_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ~ epred3_0
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ~ epred3_0
      | epred6_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred4_0
      | ~ epred3_0
      | epred6_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ( f2 @ $false )
      | ~ epred3_0
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ( f2 @ $false )
      | ~ epred3_0
      | epred6_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred3_0
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ~ epred3_0
      | epred6_0 )
    & ( ~ ( f1 @ $false )
      | ( f2 @ $false )
      | ~ epred3_0
      | epred6_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ~ epred4_0
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ~ epred4_0
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ epred4_0
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ ( f1 @ $false )
      | ~ epred4_0
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ ( f1 @ $false )
      | ( f2 @ $false )
      | ( f2 @ $true )
      | epred6_0 )
    & ( ~ epred4_0
      | ~ epred3_0
      | ~ ( f1 @ $true )
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ epred3_0
      | ~ ( f1 @ $true )
      | epred6_0 )
    & ( ~ epred4_0
      | ~ ( f2 @ $true )
      | ~ ( f1 @ $true )
      | epred6_0 )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ ( f1 @ $true )
      | epred6_0 )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | epred6_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_102])])]) ).

thf(c_0_145,plain,
    ( epred6_0
    | ( f1 @ $true )
    | ~ ( f1 @ ~ $true )
    | ~ epred8_0 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_146,plain,
    ( epred6_0
    | ( f1 @ ~ $true )
    | ~ epred8_0 ),
    inference(cn,[status(thm)],[c_0_103]) ).

thf(c_0_147,plain,
    ( ( f0 @ $true )
    | epred16_0
    | ~ epred18_0 ),
    inference(csr,[status(thm)],[c_0_104,c_0_105]) ).

thf(c_0_148,negated_conjecture,
    ( epred18_0
    | epred8_0
    | ~ epred7_0
    | ~ epred17_0 ),
    inference(spm,[status(thm)],[c_0_106,c_0_107]) ).

thf(c_0_149,plain,
    ( epred7_0
    | epred8_0
    | ~ epred5_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_72]),c_0_109]) ).

thf(c_0_150,plain,
    ( ( f0 @ ~ $true )
    | ( f0 @ ~ $true )
    | epred17_0
    | ~ epred15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

thf(c_0_151,plain,
    ( ( f4 @ $true )
    | x
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[c_0_110,c_0_111]) ).

thf(c_0_152,plain,
    ( epred15_0
    | ~ ( f0 @ ~ $true )
    | ~ epred17_0 ),
    inference(csr,[status(thm)],[c_0_112,c_0_113]) ).

thf(c_0_153,plain,
    ( epred15_0
    | ( f0 @ $true )
    | ( f0 @ ~ $true )
    | ~ epred18_0 ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_154,plain,
    ( epred15_0
    | ~ epred17_0
    | ~ ( f0 @ $true ) ),
    inference(cn,[status(thm)],[c_0_114]) ).

thf(c_0_155,negated_conjecture,
    ( epred7_0
    | epred18_0
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_77]) ).

thf(c_0_156,plain,
    ( epred17_0
    | epred5_0
    | ~ epred8_0
    | ~ epred18_0 ),
    inference(spm,[status(thm)],[c_0_117,c_0_118]) ).

thf(c_0_157,plain,
    ( epred18_0
    | epred17_0
    | epred5_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_117,c_0_119]) ).

thf(c_0_158,plain,
    ( epred7_0
    | epred8_0
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_84]) ).

thf(c_0_159,plain,
    ( epred8_0
    | ~ epred5_0
    | ~ epred6_0 ),
    inference(cn,[status(thm)],[c_0_122]) ).

thf(c_0_160,plain,
    ( epred16_0
    | ~ epred14_0
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_161,plain,
    ( ( f1 @ $true )
    | epred15_0
    | ~ epred14_0
    | ~ ( f2 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_162,plain,
    ( ( f2 @ $true )
    | epred14_0
    | ~ ( f2 @ ~ $true )
    | ~ epred12_0 ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

thf(c_0_163,plain,
    ( epred14_0
    | ~ ( f2 @ ~ $true )
    | ~ ( f2 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

thf(c_0_164,plain,
    ( epred14_0
    | ~ epred12_0
    | ~ ( f2 @ $true )
    | ~ ( f2 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

thf(c_0_165,plain,
    ( epred16_0
    | ~ ( f2 @ ~ $true )
    | ~ epred13_0
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_166,plain,
    ( ( f1 @ $true )
    | epred15_0
    | ~ ( f2 @ ~ $true )
    | ~ epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_167,plain,
    ( ( f3 @ $true )
    | epred11_0
    | ~ ( f4 @ ~ $true )
    | ~ epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_168,plain,
    ( ( f4 @ ~ $true )
    | epred12_0
    | ~ ( f3 @ ~ $true )
    | ~ epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_169,plain,
    ( epred12_0
    | ~ ( f3 @ ~ $true )
    | ~ ( f3 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_170,plain,
    ( ( f3 @ ~ $true )
    | epred11_0
    | epred12_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).

thf(c_0_171,plain,
    ( epred10_0
    | ~ x
    | ~ ( f4 @ $true ) ),
    inference(cn,[status(thm)],[c_0_129]) ).

thf(c_0_172,plain,
    ( ( f4 @ $true )
    | epred9_0
    | epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_132]) ).

thf(c_0_173,plain,
    ( ( f2 @ $true )
    | epred13_0
    | ~ ( f2 @ ~ $true )
    | ~ epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

thf(c_0_174,plain,
    ( epred13_0
    | ( f2 @ ~ $true )
    | ~ epred11_0 ),
    inference(cn,[status(thm)],[c_0_133]) ).

thf(c_0_175,plain,
    ( ( f3 @ ~ $true )
    | ~ epred1_0
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_62]),c_0_134]),c_0_96]) ).

thf(c_0_176,plain,
    ( ( f3 @ $true )
    | epred2_0
    | ~ epred4_0 ),
    inference(csr,[status(thm)],[c_0_135,c_0_136]) ).

thf(c_0_177,plain,
    ( epred2_0
    | ~ ( f3 @ $true )
    | ~ epred4_0 ),
    inference(spm,[status(thm)],[c_0_66,c_0_136]) ).

thf(c_0_178,plain,
    ( epred1_0
    | ~ ( f3 @ $true )
    | ~ ( f3 @ $true )
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_137]) ).

thf(c_0_179,plain,
    ( ( f3 @ ~ $true )
    | ( f3 @ ~ $true )
    | epred3_0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_137]) ).

thf(c_0_180,plain,
    ( ( f3 @ $true )
    | epred4_0
    | ~ ( f3 @ ~ $true )
    | ~ epred2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

thf(c_0_181,plain,
    ( epred4_0
    | ~ epred2_0
    | ~ ( f3 @ $true ) ),
    inference(cn,[status(thm)],[c_0_138]) ).

thf(c_0_182,plain,
    ( epred4_0
    | ~ epred2_0
    | ~ epred1_0
    | ~ epred2_0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

thf(c_0_183,plain,
    ( epred1_0
    | epred2_0
    | ~ ( f3 @ $true ) ),
    inference(spm,[status(thm)],[c_0_66,c_0_139]) ).

thf(c_0_184,plain,
    ( ( f3 @ $true )
    | epred2_0
    | epred1_0
    | ~ x ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_45]) ).

thf(c_0_185,plain,
    ( x
    | ~ ( f4 @ ~ $true )
    | ~ ( f4 @ $true )
    | ~ epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_186,plain,
    ( ~ x
    | ~ epred9_0
    | ~ ( f4 @ $true ) ),
    inference(cn,[status(thm)],[c_0_142]) ).

thf(c_0_187,plain,
    ( epred10_0
    | ( f3 @ $true )
    | ~ ( f4 @ ~ $true )
    | ~ epred12_0 ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_188,plain,
    ( epred10_0
    | ( f4 @ ~ $true )
    | ( f3 @ ~ $true )
    | ~ epred12_0 ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_189,plain,
    ( epred9_0
    | ( f3 @ $true )
    | ~ ( f4 @ $true )
    | ~ epred12_0 ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_190,plain,
    ( epred9_0
    | ( f4 @ $true )
    | ( f3 @ ~ $true )
    | ~ epred12_0 ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_191,plain,
    ( epred12_0
    | ( f2 @ ~ $true )
    | ( f2 @ ~ $true )
    | ~ epred14_0 ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

thf(c_0_192,plain,
    ( epred11_0
    | ( f2 @ $true )
    | ~ ( f2 @ ~ $true )
    | ~ epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

thf(c_0_193,plain,
    ( epred11_0
    | ~ epred13_0
    | ~ ( f2 @ $true ) ),
    inference(cn,[status(thm)],[c_0_143]) ).

thf(c_0_194,plain,
    ( epred14_0
    | ~ ( f2 @ ~ $true )
    | ~ ( f1 @ $true )
    | ~ epred15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_195,plain,
    ( epred14_0
    | ( f1 @ $true )
    | ~ ( f2 @ ~ $true )
    | ~ epred16_0 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_196,plain,
    ( epred13_0
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true )
    | ~ epred15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_197,plain,
    ( epred13_0
    | ( f1 @ $true )
    | ~ ( f2 @ $true )
    | ~ epred16_0 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_198,plain,
    ( epred6_0
    | ~ ( f1 @ ~ $true )
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_199,plain,
    ( ( f1 @ $true )
    | epred6_0
    | ~ epred8_0 ),
    inference(csr,[status(thm)],[c_0_145,c_0_146]) ).

thf(c_0_200,negated_conjecture,
    ( epred16_0
    | ~ epred18_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_105]),c_0_147]) ).

thf(c_0_201,negated_conjecture,
    ( epred8_0
    | epred18_0
    | ~ epred17_0
    | ~ epred5_0 ),
    inference(spm,[status(thm)],[c_0_148,c_0_149]) ).

thf(c_0_202,plain,
    ( ( f0 @ $true )
    | epred17_0
    | ~ ( f0 @ ~ $true )
    | ~ epred15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

thf(c_0_203,plain,
    ( epred17_0
    | ( f0 @ ~ $true )
    | ~ epred15_0 ),
    inference(cn,[status(thm)],[c_0_150]) ).

thf(c_0_204,plain,
    ( x
    | ~ ( f3 @ $true )
    | ~ epred1_0
    | ~ epred10_0 ),
    inference(spm,[status(thm)],[c_0_38,c_0_111]) ).

thf(c_0_205,plain,
    ( ( f3 @ $true )
    | x
    | epred11_0
    | ~ epred10_0 ),
    inference(spm,[status(thm)],[c_0_88,c_0_151]) ).

thf(c_0_206,plain,
    ( epred15_0
    | ~ epred17_0
    | ~ epred18_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).

thf(c_0_207,plain,
    ( epred18_0
    | epred5_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_117,c_0_155]) ).

thf(c_0_208,plain,
    ( epred5_0
    | epred17_0
    | ~ epred8_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_156,c_0_157]) ).

thf(c_0_209,plain,
    ( epred8_0
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_158]),c_0_159]) ).

thf(c_0_210,plain,
    ( ( f2 @ $true )
    | epred16_0
    | ~ ( f1 @ ~ $true )
    | ~ epred14_0 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_211,plain,
    ( ( f1 @ ~ $true )
    | ( f2 @ $true )
    | epred15_0
    | ~ epred14_0 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_212,plain,
    ( epred15_0
    | epred16_0
    | ~ ( f2 @ $true )
    | ~ epred14_0 ),
    inference(spm,[status(thm)],[c_0_160,c_0_161]) ).

thf(c_0_213,plain,
    ( epred14_0
    | ~ ( f2 @ ~ $true )
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[c_0_162,c_0_163]) ).

thf(c_0_214,plain,
    ( ( f2 @ ~ $true )
    | ( f2 @ $true )
    | epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

thf(c_0_215,plain,
    ( epred14_0
    | ~ epred12_0
    | ~ ( f2 @ $true ) ),
    inference(cn,[status(thm)],[c_0_164]) ).

thf(c_0_216,plain,
    ( ( f2 @ ~ $true )
    | epred16_0
    | ~ ( f1 @ ~ $true )
    | ~ epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_217,plain,
    ( ( f1 @ ~ $true )
    | ( f2 @ ~ $true )
    | epred15_0
    | ~ epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_218,plain,
    ( epred15_0
    | epred16_0
    | ~ ( f2 @ ~ $true )
    | ~ epred13_0 ),
    inference(spm,[status(thm)],[c_0_165,c_0_166]) ).

thf(c_0_219,plain,
    ( epred12_0
    | ~ ( f4 @ ~ $true )
    | ~ epred9_0
    | ~ ( f3 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_220,plain,
    ( ( f3 @ ~ $true )
    | ( f4 @ ~ $true )
    | epred11_0
    | ~ epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_221,plain,
    ( ( f3 @ $true )
    | epred12_0
    | epred11_0
    | ~ epred9_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_90]) ).

thf(c_0_222,plain,
    ( epred11_0
    | epred12_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_128]) ).

thf(c_0_223,plain,
    ( epred9_0
    | epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_132]) ).

thf(c_0_224,plain,
    ( ( f2 @ $true )
    | epred13_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[c_0_173,c_0_174]) ).

thf(c_0_225,plain,
    ( ~ epred1_0
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_175]),c_0_134]) ).

thf(c_0_226,plain,
    ( epred2_0
    | ~ epred4_0 ),
    inference(csr,[status(thm)],[c_0_176,c_0_177]) ).

thf(c_0_227,plain,
    ( epred1_0
    | ( f3 @ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_137]) ).

thf(c_0_228,plain,
    ( epred1_0
    | ~ epred3_0
    | ~ ( f3 @ $true ) ),
    inference(cn,[status(thm)],[c_0_178]) ).

thf(c_0_229,plain,
    ( epred4_0
    | ~ ( f2 @ ~ $true )
    | ~ ( f1 @ $true )
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_230,plain,
    ( epred4_0
    | ( f1 @ $true )
    | ~ ( f2 @ ~ $true )
    | ~ epred6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_231,plain,
    ( epred3_0
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true )
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_232,plain,
    ( epred3_0
    | ( f1 @ $true )
    | ~ ( f2 @ $true )
    | ~ epred6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_233,plain,
    ( ( f3 @ $true )
    | epred3_0
    | ~ ( f3 @ ~ $true )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_137]) ).

thf(c_0_234,plain,
    ( epred3_0
    | ( f3 @ ~ $true )
    | ~ epred1_0 ),
    inference(cn,[status(thm)],[c_0_179]) ).

thf(c_0_235,plain,
    ( epred3_0
    | ~ epred2_0
    | ~ epred1_0
    | ~ epred2_0
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_137]) ).

thf(c_0_236,plain,
    ( epred4_0
    | ~ ( f3 @ ~ $true )
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[c_0_180,c_0_181]) ).

thf(c_0_237,plain,
    ( epred4_0
    | ~ epred1_0
    | ~ epred2_0 ),
    inference(cn,[status(thm)],[c_0_182]) ).

thf(c_0_238,plain,
    ( x
    | ( f3 @ $true )
    | epred1_0
    | ~ ( f4 @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_239,plain,
    ( ( f4 @ ~ $true )
    | x
    | epred2_0
    | ~ ( f3 @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_240,plain,
    ( epred2_0
    | epred1_0
    | ~ x ),
    inference(spm,[status(thm)],[c_0_183,c_0_184]) ).

thf(c_0_241,plain,
    ( ( f4 @ $true )
    | ~ x
    | ~ ( f4 @ ~ $true )
    | ~ epred9_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_242,plain,
    ( ~ ( f4 @ $true )
    | ~ ( f4 @ ~ $true )
    | ~ epred9_0 ),
    inference(csr,[status(thm)],[c_0_185,c_0_186]) ).

thf(c_0_243,plain,
    ( ( f4 @ $true )
    | ( f4 @ ~ $true )
    | ~ x
    | ~ epred10_0 ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

thf(c_0_244,plain,
    ( epred10_0
    | ( f4 @ ~ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_245,plain,
    ( ( f3 @ ~ $true )
    | ( f3 @ $true )
    | epred10_0
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_187,c_0_188]) ).

thf(c_0_246,plain,
    ( epred9_0
    | ( f4 @ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_247,plain,
    ( ( f3 @ ~ $true )
    | ( f3 @ $true )
    | epred9_0
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_189,c_0_190]) ).

thf(c_0_248,plain,
    ( epred12_0
    | ( f2 @ $true )
    | ~ ( f2 @ ~ $true )
    | ~ epred14_0 ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

thf(c_0_249,plain,
    ( epred12_0
    | ( f2 @ ~ $true )
    | ~ epred14_0 ),
    inference(cn,[status(thm)],[c_0_191]) ).

thf(c_0_250,plain,
    ( epred11_0
    | ~ ( f2 @ ~ $true )
    | ~ epred13_0 ),
    inference(csr,[status(thm)],[c_0_192,c_0_193]) ).

thf(c_0_251,plain,
    ( epred11_0
    | ( f2 @ $true )
    | ( f2 @ ~ $true )
    | ~ epred14_0 ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

thf(c_0_252,plain,
    ( epred14_0
    | ( f2 @ ~ $true )
    | ~ ( f1 @ ~ $true )
    | ~ epred15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_253,plain,
    ( epred14_0
    | ( f2 @ ~ $true )
    | ( f1 @ ~ $true )
    | ~ epred16_0 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_254,plain,
    ( epred14_0
    | ~ ( f2 @ ~ $true )
    | ~ epred15_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_194,c_0_195]) ).

thf(c_0_255,plain,
    ( epred13_0
    | ( f2 @ $true )
    | ~ ( f1 @ ~ $true )
    | ~ epred15_0 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_256,plain,
    ( epred13_0
    | ( f2 @ $true )
    | ( f1 @ ~ $true )
    | ~ epred16_0 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_257,plain,
    ( epred13_0
    | ~ ( f2 @ $true )
    | ~ epred15_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_196,c_0_197]) ).

thf(c_0_258,plain,
    ( epred6_0
    | ~ epred8_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_146]),c_0_199]) ).

thf(c_0_259,negated_conjecture,
    ( epred8_0
    | epred16_0
    | ~ epred17_0
    | ~ epred5_0 ),
    inference(spm,[status(thm)],[c_0_200,c_0_201]) ).

thf(c_0_260,plain,
    ( ( f0 @ $true )
    | epred17_0
    | ~ epred15_0 ),
    inference(csr,[status(thm)],[c_0_202,c_0_203]) ).

thf(c_0_261,plain,
    ( epred11_0
    | x
    | ~ epred1_0
    | ~ epred10_0 ),
    inference(spm,[status(thm)],[c_0_204,c_0_205]) ).

thf(c_0_262,plain,
    ( epred5_0
    | epred15_0
    | ~ epred17_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_206,c_0_207]) ).

thf(c_0_263,plain,
    ( epred17_0
    | epred5_0
    | ~ epred16_0
    | ~ epred6_0 ),
    inference(spm,[status(thm)],[c_0_208,c_0_209]) ).

thf(c_0_264,plain,
    ( epred15_0
    | epred16_0
    | ~ epred14_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_211]),c_0_212]) ).

thf(c_0_265,plain,
    ( epred13_0
    | epred14_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_215]) ).

thf(c_0_266,plain,
    ( epred15_0
    | epred16_0
    | ~ epred13_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_218]) ).

thf(c_0_267,plain,
    ( ( f3 @ ~ $true )
    | epred11_0
    | epred12_0
    | ~ epred9_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_221]) ).

thf(c_0_268,plain,
    ( epred9_0
    | epred12_0
    | epred11_0 ),
    inference(spm,[status(thm)],[c_0_222,c_0_223]) ).

thf(c_0_269,plain,
    ( epred13_0
    | epred14_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_174]),c_0_224]) ).

thf(c_0_270,plain,
    ( ~ epred1_0
    | ~ epred4_0 ),
    inference(spm,[status(thm)],[c_0_225,c_0_226]) ).

thf(c_0_271,plain,
    ( epred1_0
    | ~ epred3_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_227,c_0_45]),c_0_228]) ).

thf(c_0_272,plain,
    ( epred4_0
    | ( f2 @ ~ $true )
    | ~ ( f1 @ ~ $true )
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_273,plain,
    ( epred4_0
    | ( f2 @ ~ $true )
    | ( f1 @ ~ $true )
    | ~ epred6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_274,plain,
    ( epred4_0
    | ~ ( f2 @ ~ $true )
    | ~ epred5_0
    | ~ epred6_0 ),
    inference(spm,[status(thm)],[c_0_229,c_0_230]) ).

thf(c_0_275,plain,
    ( epred3_0
    | ( f2 @ $true )
    | ~ ( f1 @ ~ $true )
    | ~ epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_276,plain,
    ( epred3_0
    | ( f2 @ $true )
    | ( f1 @ ~ $true )
    | ~ epred6_0 ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_277,plain,
    ( epred3_0
    | ~ ( f2 @ $true )
    | ~ epred5_0
    | ~ epred6_0 ),
    inference(spm,[status(thm)],[c_0_231,c_0_232]) ).

thf(c_0_278,plain,
    ( epred6_0
    | ~ epred4_0
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_279,plain,
    ( ( f1 @ $true )
    | epred5_0
    | ~ epred4_0
    | ~ ( f2 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_280,plain,
    ( ( f3 @ $true )
    | epred3_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[c_0_233,c_0_234]) ).

thf(c_0_281,plain,
    ( epred3_0
    | ~ epred1_0
    | ~ epred2_0 ),
    inference(cn,[status(thm)],[c_0_235]) ).

thf(c_0_282,plain,
    ( epred4_0
    | ~ epred2_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_45]),c_0_237]),c_0_181]) ).

thf(c_0_283,plain,
    ( epred2_0
    | epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_139]),c_0_240]),c_0_183]) ).

thf(c_0_284,plain,
    ( epred6_0
    | ~ ( f2 @ ~ $true )
    | ~ epred3_0
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_285,plain,
    ( ( f1 @ $true )
    | epred5_0
    | ~ ( f2 @ ~ $true )
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_286,plain,
    ( ~ ( f4 @ ~ $true )
    | ~ x
    | ~ epred9_0 ),
    inference(csr,[status(thm)],[c_0_241,c_0_242]) ).

thf(c_0_287,plain,
    ( ( f4 @ ~ $true )
    | ( f4 @ $true )
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[c_0_243,c_0_151]) ).

thf(c_0_288,plain,
    ( x
    | ~ epred9_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_111]),c_0_151]) ).

thf(c_0_289,plain,
    ( epred10_0
    | ~ ( f4 @ ~ $true )
    | ~ ( f3 @ $true )
    | ~ epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_290,plain,
    ( ( f3 @ $true )
    | epred10_0
    | ~ epred12_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_244]),c_0_245]) ).

thf(c_0_291,plain,
    ( epred9_0
    | ~ ( f4 @ $true )
    | ~ ( f3 @ $true )
    | ~ epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_292,plain,
    ( ( f3 @ $true )
    | epred9_0
    | ~ epred12_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_246]),c_0_247]) ).

thf(c_0_293,plain,
    ( epred12_0
    | ~ ( f2 @ ~ $true )
    | ~ ( f2 @ $true )
    | ~ epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

thf(c_0_294,plain,
    ( ( f2 @ $true )
    | epred12_0
    | ~ epred14_0 ),
    inference(csr,[status(thm)],[c_0_248,c_0_249]) ).

thf(c_0_295,plain,
    ( epred11_0
    | ~ epred13_0
    | ~ epred14_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_251]),c_0_193]) ).

thf(c_0_296,plain,
    ( epred14_0
    | ~ epred15_0
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_254]) ).

thf(c_0_297,plain,
    ( epred13_0
    | ~ epred15_0
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_257]) ).

thf(c_0_298,plain,
    ( epred16_0
    | epred6_0
    | ~ epred17_0
    | ~ epred5_0 ),
    inference(spm,[status(thm)],[c_0_258,c_0_259]) ).

thf(c_0_299,negated_conjecture,
    ( epred17_0
    | ~ epred15_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_203]),c_0_260]) ).

thf(c_0_300,plain,
    ( ( f3 @ $true )
    | epred11_0
    | ~ epred10_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_27]),c_0_261]),c_0_90]) ).

thf(c_0_301,plain,
    ( ( f3 @ ~ $true )
    | ( f4 @ ~ $true )
    | ( f4 @ $true )
    | epred11_0 ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

thf(c_0_302,plain,
    ( epred15_0
    | epred5_0
    | ~ epred16_0
    | ~ epred6_0 ),
    inference(spm,[status(thm)],[c_0_262,c_0_263]) ).

thf(c_0_303,plain,
    ( epred16_0
    | epred15_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_265]),c_0_266]) ).

thf(c_0_304,plain,
    ( epred11_0
    | epred12_0
    | ~ ( f3 @ $true ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_267]),c_0_268]) ).

thf(c_0_305,plain,
    ( epred16_0
    | epred15_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_269]),c_0_266]) ).

thf(c_0_306,plain,
    ( ~ epred4_0
    | ~ epred3_0 ),
    inference(spm,[status(thm)],[c_0_270,c_0_271]) ).

thf(c_0_307,plain,
    ( epred4_0
    | ~ epred5_0
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_274]) ).

thf(c_0_308,plain,
    ( epred3_0
    | ~ epred5_0
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_277]) ).

thf(c_0_309,plain,
    ( ( f2 @ $true )
    | epred6_0
    | ~ ( f1 @ ~ $true )
    | ~ epred4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_310,plain,
    ( ( f1 @ ~ $true )
    | ( f2 @ $true )
    | epred5_0
    | ~ epred4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_311,plain,
    ( epred5_0
    | epred6_0
    | ~ ( f2 @ $true )
    | ~ epred4_0 ),
    inference(spm,[status(thm)],[c_0_278,c_0_279]) ).

thf(c_0_312,plain,
    ( epred3_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_234]),c_0_280]),c_0_281]) ).

thf(c_0_313,plain,
    ( epred1_0
    | epred4_0 ),
    inference(spm,[status(thm)],[c_0_282,c_0_283]) ).

thf(c_0_314,plain,
    ( ( f2 @ ~ $true )
    | epred6_0
    | ~ ( f1 @ ~ $true )
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_315,plain,
    ( ( f1 @ ~ $true )
    | ( f2 @ ~ $true )
    | epred5_0
    | ~ epred3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_316,plain,
    ( epred5_0
    | epred6_0
    | ~ ( f2 @ ~ $true )
    | ~ epred3_0 ),
    inference(spm,[status(thm)],[c_0_284,c_0_285]) ).

thf(c_0_317,plain,
    ( ( f4 @ $true )
    | ~ epred9_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_287]),c_0_288]) ).

thf(c_0_318,plain,
    ( epred10_0
    | ~ ( f3 @ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_289,c_0_244]) ).

thf(c_0_319,plain,
    ( ( f3 @ ~ $true )
    | epred10_0
    | ~ epred11_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_188]),c_0_290]) ).

thf(c_0_320,plain,
    ( epred9_0
    | ~ ( f3 @ $true )
    | ~ ( f3 @ ~ $true )
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_291,c_0_246]) ).

thf(c_0_321,plain,
    ( ( f3 @ ~ $true )
    | epred9_0
    | ~ epred11_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_190]),c_0_292]) ).

thf(c_0_322,plain,
    ( epred12_0
    | ~ epred13_0
    | ~ epred14_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_249]),c_0_294]) ).

thf(c_0_323,plain,
    ( epred11_0
    | ~ epred15_0
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_296]),c_0_297]) ).

thf(c_0_324,negated_conjecture,
    ( epred6_0
    | epred16_0
    | ~ epred5_0
    | ~ epred15_0 ),
    inference(spm,[status(thm)],[c_0_298,c_0_299]) ).

thf(c_0_325,plain,
    ( ( f3 @ ~ $true )
    | epred11_0
    | ~ epred1_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_127]),c_0_261]),c_0_300]) ).

thf(c_0_326,plain,
    ( ( f3 @ ~ $true )
    | ( f4 @ $true )
    | epred11_0
    | ~ x ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_301]),c_0_127]) ).

thf(c_0_327,plain,
    ( epred5_0
    | epred15_0
    | ~ epred6_0
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_302,c_0_303]) ).

thf(c_0_328,plain,
    ( epred12_0
    | epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_221]),c_0_268]) ).

thf(c_0_329,plain,
    ( epred5_0
    | epred15_0
    | ~ epred6_0
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_302,c_0_305]) ).

thf(c_0_330,plain,
    ( ~ epred5_0
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_306,c_0_307]),c_0_308]) ).

thf(c_0_331,plain,
    ( epred5_0
    | epred6_0
    | ~ epred4_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_310]),c_0_311]) ).

thf(c_0_332,plain,
    ( epred4_0
    | epred3_0 ),
    inference(spm,[status(thm)],[c_0_312,c_0_313]) ).

thf(c_0_333,plain,
    ( epred5_0
    | epred6_0
    | ~ epred3_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_315]),c_0_316]) ).

thf(c_0_334,plain,
    ( ~ epred9_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_317]),c_0_288]) ).

thf(c_0_335,plain,
    ( epred10_0
    | ~ epred11_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_318,c_0_319]),c_0_290]) ).

thf(c_0_336,plain,
    ( epred9_0
    | ~ epred11_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_321]),c_0_292]) ).

thf(c_0_337,plain,
    ( epred12_0
    | ~ epred15_0
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_296]),c_0_297]) ).

thf(c_0_338,negated_conjecture,
    ( epred6_0
    | epred11_0
    | ~ epred15_0
    | ~ epred5_0 ),
    inference(spm,[status(thm)],[c_0_323,c_0_324]) ).

thf(c_0_339,plain,
    ( epred11_0
    | ~ epred1_0
    | ~ epred10_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_325]),c_0_300]) ).

thf(c_0_340,plain,
    ( epred10_0
    | ~ ( f3 @ ~ $true )
    | ~ x
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_171,c_0_27]) ).

thf(c_0_341,plain,
    ( ( f3 @ ~ $true )
    | epred11_0
    | epred10_0
    | ~ x ),
    inference(spm,[status(thm)],[c_0_171,c_0_326]) ).

thf(c_0_342,plain,
    ( epred15_0
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_328]),c_0_329]),c_0_330]) ).

thf(c_0_343,plain,
    ( epred6_0
    | epred5_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_332]),c_0_333]) ).

thf(c_0_344,plain,
    ( ~ epred11_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_335]),c_0_336]) ).

thf(c_0_345,negated_conjecture,
    ( epred6_0
    | epred12_0
    | ~ epred15_0
    | ~ epred5_0 ),
    inference(spm,[status(thm)],[c_0_337,c_0_324]) ).

thf(c_0_346,negated_conjecture,
    ( epred11_0
    | ~ epred5_0
    | ~ epred15_0 ),
    inference(spm,[status(thm)],[c_0_330,c_0_338]) ).

thf(c_0_347,plain,
    ( epred9_0
    | epred11_0
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_339,c_0_223]) ).

thf(c_0_348,plain,
    ( epred11_0
    | ~ x
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_340,c_0_341]),c_0_339]) ).

thf(c_0_349,plain,
    ( ( f1 @ ~ $true )
    | ( f2 @ ~ $true )
    | ( f2 @ $true )
    | epred5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_350,plain,
    ( epred5_0
    | epred15_0 ),
    inference(spm,[status(thm)],[c_0_342,c_0_343]) ).

thf(c_0_351,negated_conjecture,
    ( ~ epred15_0
    | ~ epred5_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_344,c_0_345]),c_0_346]),c_0_330]) ).

thf(c_0_352,plain,
    ( epred10_0
    | ~ ( f3 @ ~ $true )
    | ~ x
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_130,c_0_244]) ).

thf(c_0_353,plain,
    ( ( f3 @ ~ $true )
    | epred1_0
    | epred10_0
    | ~ x ),
    inference(spm,[status(thm)],[c_0_171,c_0_100]) ).

thf(c_0_354,plain,
    ( x
    | epred9_0
    | ~ ( f3 @ $true )
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_151]),c_0_132]) ).

thf(c_0_355,plain,
    ( ( f3 @ $true )
    | epred9_0
    | epred1_0
    | x ),
    inference(spm,[status(thm)],[c_0_238,c_0_59]) ).

thf(c_0_356,plain,
    ( ( f3 @ $true )
    | epred11_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_39]),c_0_347]),c_0_90]),c_0_348]) ).

thf(c_0_357,plain,
    ( ( f2 @ $true )
    | ( f2 @ ~ $true )
    | epred5_0
    | epred14_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_349]),c_0_350]) ).

thf(c_0_358,plain,
    ( epred5_0
    | epred13_0
    | ~ ( f2 @ $true )
    | ~ epred15_0
    | ~ epred4_0 ),
    inference(spm,[status(thm)],[c_0_196,c_0_279]) ).

thf(c_0_359,plain,
    ( ( f2 @ $true )
    | epred13_0
    | ~ epred15_0
    | ~ epred4_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_310]),c_0_351]) ).

thf(c_0_360,plain,
    ( epred1_0
    | epred10_0
    | ~ x
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_352,c_0_353]) ).

thf(c_0_361,plain,
    ( epred1_0
    | epred9_0
    | x
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_354,c_0_355]) ).

thf(c_0_362,plain,
    ( ( f3 @ $true )
    | epred9_0
    | x
    | ~ epred2_0 ),
    inference(spm,[status(thm)],[c_0_61,c_0_59]) ).

thf(c_0_363,plain,
    ( ( f3 @ ~ $true )
    | epred11_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_220]),c_0_347]),c_0_356]),c_0_348]) ).

thf(c_0_364,plain,
    ( epred5_0
    | epred14_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_357]),c_0_215]) ).

thf(c_0_365,plain,
    ( epred13_0
    | ~ epred15_0
    | ~ epred4_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_358,c_0_359]),c_0_351]) ).

thf(c_0_366,plain,
    ( ( f3 @ ~ $true )
    | epred1_0
    | epred10_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_44]),c_0_45]),c_0_360]) ).

thf(c_0_367,plain,
    ( ( f3 @ $true )
    | epred1_0
    | x
    | ~ epred10_0 ),
    inference(spm,[status(thm)],[c_0_238,c_0_111]) ).

thf(c_0_368,plain,
    ( ( f3 @ ~ $true )
    | epred1_0
    | epred9_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_100]),c_0_361]),c_0_45]) ).

thf(c_0_369,plain,
    ( epred9_0
    | x
    | ~ epred11_0
    | ~ epred2_0 ),
    inference(spm,[status(thm)],[c_0_354,c_0_362]) ).

thf(c_0_370,plain,
    ( epred11_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_363]),c_0_356]) ).

thf(c_0_371,plain,
    ( epred5_0
    | epred11_0
    | ~ epred13_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_364]),c_0_328]) ).

thf(c_0_372,plain,
    ( epred3_0
    | epred13_0
    | ~ epred15_0 ),
    inference(spm,[status(thm)],[c_0_365,c_0_332]) ).

thf(c_0_373,plain,
    ( epred1_0
    | epred10_0
    | ~ ( f3 @ $true )
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_318,c_0_366]) ).

thf(c_0_374,plain,
    ( ( f3 @ $true )
    | epred1_0
    | x
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_244]),c_0_366]),c_0_367]) ).

thf(c_0_375,plain,
    ( epred1_0
    | epred9_0
    | ~ ( f3 @ $true )
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_320,c_0_368]) ).

thf(c_0_376,plain,
    ( ( f3 @ $true )
    | epred9_0
    | ~ epred2_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_246]),c_0_369]),c_0_95]) ).

thf(c_0_377,plain,
    ( epred13_0
    | epred6_0
    | ~ ( f2 @ $true )
    | ~ epred4_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_278,c_0_197]) ).

thf(c_0_378,plain,
    ( epred4_0
    | epred11_0 ),
    inference(spm,[status(thm)],[c_0_370,c_0_313]) ).

thf(c_0_379,plain,
    ( ( f1 @ $true )
    | epred5_0
    | ~ ( f2 @ ~ $true )
    | ~ ( f2 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_380,plain,
    ( epred11_0
    | ~ epred3_0 ),
    inference(spm,[status(thm)],[c_0_370,c_0_271]) ).

thf(c_0_381,plain,
    ( epred3_0
    | epred11_0
    | epred5_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_371,c_0_372]),c_0_350]) ).

thf(c_0_382,plain,
    ( epred10_0
    | epred1_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_373,c_0_374]),c_0_360]) ).

thf(c_0_383,plain,
    ( epred9_0
    | epred1_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_375,c_0_376]),c_0_283]) ).

thf(c_0_384,plain,
    ( epred6_0
    | ~ ( f2 @ ~ $true )
    | ~ ( f2 @ $true )
    | ~ ( f1 @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_144]) ).

thf(c_0_385,plain,
    ( epred13_0
    | epred6_0
    | ~ epred4_0
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_256]),c_0_377]) ).

thf(c_0_386,plain,
    ( epred13_0
    | ~ ( f2 @ $true )
    | ~ ( f2 @ ~ $true )
    | ~ epred15_0
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_230]),c_0_365]) ).

thf(c_0_387,plain,
    ( epred11_0
    | epred13_0
    | ~ epred15_0 ),
    inference(spm,[status(thm)],[c_0_365,c_0_378]) ).

thf(c_0_388,plain,
    ( epred16_0
    | ~ epred14_0
    | ~ epred13_0
    | ~ epred14_0
    | ~ epred13_0 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_389,plain,
    ( epred5_0
    | epred14_0
    | ~ ( f2 @ ~ $true )
    | ~ epred15_0
    | ~ epred3_0 ),
    inference(spm,[status(thm)],[c_0_194,c_0_285]) ).

thf(c_0_390,plain,
    ( ( f2 @ ~ $true )
    | epred14_0
    | ~ epred15_0
    | ~ epred3_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_315]),c_0_351]) ).

thf(c_0_391,plain,
    ( epred5_0
    | epred13_0
    | ~ ( f2 @ $true )
    | ~ ( f2 @ ~ $true )
    | ~ epred15_0 ),
    inference(spm,[status(thm)],[c_0_196,c_0_379]) ).

thf(c_0_392,plain,
    ( epred5_0
    | epred11_0 ),
    inference(spm,[status(thm)],[c_0_380,c_0_381]) ).

thf(c_0_393,plain,
    ( epred1_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_382]),c_0_383]) ).

thf(c_0_394,plain,
    ( epred15_0
    | epred4_0
    | ~ ( f2 @ ~ $true )
    | ~ epred5_0
    | ~ epred13_0 ),
    inference(spm,[status(thm)],[c_0_229,c_0_166]) ).

thf(c_0_395,plain,
    ( ( f2 @ ~ $true )
    | epred4_0
    | ~ epred5_0
    | ~ epred13_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_217]),c_0_351]) ).

thf(c_0_396,plain,
    ( epred13_0
    | epred6_0
    | ~ ( f2 @ $true )
    | ~ ( f2 @ ~ $true )
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_384,c_0_197]) ).

thf(c_0_397,plain,
    ( epred11_0
    | epred6_0
    | epred13_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_385,c_0_378]) ).

thf(c_0_398,plain,
    ( epred13_0
    | ~ ( f2 @ $true )
    | ~ epred6_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_386,c_0_174]),c_0_387]),c_0_342]) ).

thf(c_0_399,plain,
    ( epred16_0
    | ~ epred13_0
    | ~ epred14_0 ),
    inference(cn,[status(thm)],[c_0_388]) ).

thf(c_0_400,plain,
    ( epred14_0
    | ~ epred15_0
    | ~ epred3_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_389,c_0_390]),c_0_351]) ).

thf(c_0_401,plain,
    ( epred13_0
    | epred5_0
    | ~ ( f2 @ $true ) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_391,c_0_174]),c_0_392]),c_0_350]) ).

thf(c_0_402,plain,
    ( ~ epred4_0
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_270,c_0_393]) ).

thf(c_0_403,plain,
    ( epred4_0
    | ~ epred5_0
    | ~ epred13_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_394,c_0_395]),c_0_351]) ).

thf(c_0_404,plain,
    ( epred13_0
    | ~ ( f2 @ $true )
    | ~ epred16_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_396,c_0_174]),c_0_397]),c_0_398]) ).

thf(c_0_405,plain,
    ( epred16_0
    | ~ epred13_0
    | ~ epred3_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_399,c_0_400]),c_0_266]) ).

thf(c_0_406,plain,
    ( epred5_0
    | epred13_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_401,c_0_224]),c_0_392]) ).

thf(c_0_407,plain,
    ( ( f3 @ ~ $true )
    | epred10_0
    | ~ x
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_130,c_0_188]) ).

thf(c_0_408,plain,
    ( epred9_0
    | x
    | ~ ( f3 @ $true )
    | ~ epred1_0 ),
    inference(spm,[status(thm)],[c_0_38,c_0_59]) ).

thf(c_0_409,plain,
    ( ( f3 @ $true )
    | x
    | epred9_0
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_189,c_0_93]) ).

thf(c_0_410,plain,
    ( ~ epred11_0
    | ~ epred5_0
    | ~ epred13_0 ),
    inference(spm,[status(thm)],[c_0_402,c_0_403]) ).

thf(c_0_411,plain,
    ( epred13_0
    | ~ epred16_0
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_404,c_0_224]) ).

thf(c_0_412,plain,
    ( epred5_0
    | epred16_0
    | ~ epred3_0 ),
    inference(spm,[status(thm)],[c_0_405,c_0_406]) ).

thf(c_0_413,plain,
    ( epred3_0
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_312,c_0_393]) ).

thf(c_0_414,plain,
    ( epred10_0
    | ~ x
    | ~ epred1_0
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_340,c_0_407]) ).

thf(c_0_415,plain,
    ( x
    | epred9_0
    | ~ epred1_0
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_408,c_0_409]) ).

thf(c_0_416,plain,
    ( ~ epred11_0
    | ~ epred5_0
    | ~ epred16_0 ),
    inference(spm,[status(thm)],[c_0_410,c_0_411]) ).

thf(c_0_417,plain,
    ( epred16_0
    | epred5_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_412,c_0_413]),c_0_392]) ).

thf(c_0_418,plain,
    ( ( f3 @ $true )
    | epred10_0
    | ~ epred12_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_39]),c_0_245]),c_0_414]) ).

thf(c_0_419,plain,
    ( ( f3 @ $true )
    | epred9_0
    | ~ epred12_0
    | ~ epred1_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_27]),c_0_415]),c_0_247]) ).

thf(c_0_420,plain,
    ( epred15_0
    | ~ epred11_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_416,c_0_305]),c_0_350]) ).

thf(c_0_421,plain,
    ( epred5_0
    | epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_337,c_0_417]),c_0_350]) ).

thf(c_0_422,plain,
    ( ( f3 @ ~ $true )
    | epred10_0
    | ~ epred1_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_188]),c_0_418]),c_0_414]) ).

thf(c_0_423,plain,
    ( ( f3 @ ~ $true )
    | epred9_0
    | ~ epred1_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_190]),c_0_408]),c_0_419]) ).

thf(c_0_424,plain,
    ( epred15_0
    | epred3_0
    | ~ ( f2 @ $true )
    | ~ epred5_0
    | ~ epred14_0 ),
    inference(spm,[status(thm)],[c_0_231,c_0_161]) ).

thf(c_0_425,plain,
    ( ( f2 @ $true )
    | epred3_0
    | ~ epred5_0
    | ~ epred14_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_211]),c_0_351]) ).

thf(c_0_426,negated_conjecture,
    ( ~ epred5_0
    | ~ epred11_0 ),
    inference(spm,[status(thm)],[c_0_351,c_0_420]) ).

thf(c_0_427,plain,
    epred5_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_344,c_0_421]),c_0_392]) ).

thf(c_0_428,plain,
    ( epred10_0
    | ~ epred1_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_422]),c_0_418]) ).

thf(c_0_429,plain,
    ( epred9_0
    | ~ epred1_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_423]),c_0_419]) ).

thf(c_0_430,plain,
    ( epred3_0
    | ~ epred5_0
    | ~ epred14_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_425]),c_0_351]) ).

thf(c_0_431,negated_conjecture,
    ~ epred11_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_426,c_0_427])]) ).

thf(c_0_432,plain,
    ( ~ epred1_0
    | ~ epred12_0 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_428]),c_0_429]) ).

thf(c_0_433,plain,
    ( epred13_0
    | epred3_0
    | ~ epred5_0
    | ~ epred12_0 ),
    inference(spm,[status(thm)],[c_0_430,c_0_265]) ).

thf(c_0_434,plain,
    epred12_0,
    inference(sr,[status(thm)],[c_0_328,c_0_431]) ).

thf(c_0_435,plain,
    ( ~ epred12_0
    | ~ epred3_0 ),
    inference(spm,[status(thm)],[c_0_432,c_0_271]) ).

thf(c_0_436,plain,
    ( epred3_0
    | epred13_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_433,c_0_427])]),c_0_434])]) ).

thf(c_0_437,plain,
    ~ epred3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_435,c_0_434])]) ).

thf(c_0_438,plain,
    epred13_0,
    inference(sr,[status(thm)],[c_0_436,c_0_437]) ).

thf(c_0_439,plain,
    epred4_0,
    inference(sr,[status(thm)],[c_0_378,c_0_431]) ).

thf(c_0_440,plain,
    ~ epred6_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_330,c_0_427])]) ).

thf(c_0_441,negated_conjecture,
    ~ epred15_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_351,c_0_427])]) ).

thf(c_0_442,plain,
    ~ ( f2 @ ~ $true ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_438])]),c_0_431]) ).

thf(c_0_443,plain,
    ( ( f2 @ $true )
    | ~ ( f1 @ ~ $true ) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_309,c_0_439])]),c_0_440]) ).

thf(c_0_444,plain,
    f1 @ ~ $true,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_217,c_0_438])]),c_0_441]),c_0_442]) ).

thf(c_0_445,plain,
    ~ ( f2 @ $true ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_438])]),c_0_431]) ).

thf(c_0_446,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_443,c_0_444])]),c_0_445]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem    : SYO500^1.005 : TPTP v8.2.0. Released v4.1.0.
% 0.02/0.10  % Command    : run_E %s %d THM
% 0.10/0.30  % Computer : n002.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Mon May 20 10:23:07 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.15/0.42  Running higher-order theorem proving
% 0.15/0.42  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/0.57  # Version: 3.1.0-ho
% 1.21/0.57  # Preprocessing class: HSSSSMSSSSSNFFN.
% 1.21/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.57  # Starting new_ho_10 with 1500s (5) cores
% 1.21/0.57  # Starting ho_unfolding_6 with 300s (1) cores
% 1.21/0.57  # Starting sh4l with 300s (1) cores
% 1.21/0.57  # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.21/0.57  # ho_unfolding_6 with pid 20425 completed with status 0
% 1.21/0.57  # Result found by ho_unfolding_6
% 1.21/0.57  # Preprocessing class: HSSSSMSSSSSNFFN.
% 1.21/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.57  # Starting new_ho_10 with 1500s (5) cores
% 1.21/0.57  # Starting ho_unfolding_6 with 300s (1) cores
% 1.21/0.57  # No SInE strategy applied
% 1.21/0.57  # Search class: HGHNF-FSLM00-SFFFFFNN
% 1.21/0.57  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.21/0.57  # Starting new_ho_10 with 163s (1) cores
% 1.21/0.57  # new_ho_10 with pid 20429 completed with status 0
% 1.21/0.57  # Result found by new_ho_10
% 1.21/0.57  # Preprocessing class: HSSSSMSSSSSNFFN.
% 1.21/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.57  # Starting new_ho_10 with 1500s (5) cores
% 1.21/0.57  # Starting ho_unfolding_6 with 300s (1) cores
% 1.21/0.57  # No SInE strategy applied
% 1.21/0.57  # Search class: HGHNF-FSLM00-SFFFFFNN
% 1.21/0.57  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.21/0.57  # Starting new_ho_10 with 163s (1) cores
% 1.21/0.57  # Preprocessing time       : 0.003 s
% 1.21/0.57  # Presaturation interreduction done
% 1.21/0.57  
% 1.21/0.57  # Proof found!
% 1.21/0.57  # SZS status Theorem
% 1.21/0.57  # SZS output start CNFRefutation
% See solution above
% 1.21/0.57  # Parsed axioms                        : 7
% 1.21/0.57  # Removed by relevancy pruning/SinE    : 0
% 1.21/0.57  # Initial clauses                      : 548
% 1.21/0.57  # Removed in clause preprocessing      : 206
% 1.21/0.57  # Initial clauses in saturation        : 342
% 1.21/0.57  # Processed clauses                    : 1516
% 1.21/0.57  # ...of these trivial                  : 6
% 1.21/0.57  # ...subsumed                          : 705
% 1.21/0.57  # ...remaining for further processing  : 805
% 1.21/0.57  # Other redundant clauses eliminated   : 0
% 1.21/0.57  # Clauses deleted for lack of memory   : 0
% 1.21/0.57  # Backward-subsumed                    : 386
% 1.21/0.57  # Backward-rewritten                   : 170
% 1.21/0.57  # Generated clauses                    : 3745
% 1.21/0.57  # ...of the previous two non-redundant : 2179
% 1.21/0.57  # ...aggressively subsumed             : 0
% 1.21/0.57  # Contextual simplify-reflections      : 262
% 1.21/0.57  # Paramodulations                      : 3726
% 1.21/0.57  # Factorizations                       : 0
% 1.21/0.57  # NegExts                              : 0
% 1.21/0.57  # Equation resolutions                 : 0
% 1.21/0.57  # Disequality decompositions           : 0
% 1.21/0.57  # Total rewrite steps                  : 176
% 1.21/0.57  # ...of those cached                   : 168
% 1.21/0.57  # Propositional unsat checks           : 0
% 1.21/0.57  #    Propositional check models        : 0
% 1.21/0.57  #    Propositional check unsatisfiable : 0
% 1.21/0.57  #    Propositional clauses             : 0
% 1.21/0.57  #    Propositional clauses after purity: 0
% 1.21/0.57  #    Propositional unsat core size     : 0
% 1.21/0.57  #    Propositional preprocessing time  : 0.000
% 1.21/0.57  #    Propositional encoding time       : 0.000
% 1.21/0.57  #    Propositional solver time         : 0.000
% 1.21/0.57  #    Success case prop preproc time    : 0.000
% 1.21/0.57  #    Success case prop encoding time   : 0.000
% 1.21/0.57  #    Success case prop solver time     : 0.000
% 1.21/0.57  # Current number of processed clauses  : 69
% 1.21/0.57  #    Positive orientable unit clauses  : 8
% 1.21/0.57  #    Positive unorientable unit clauses: 0
% 1.21/0.57  #    Negative unit clauses             : 8
% 1.21/0.57  #    Non-unit-clauses                  : 53
% 1.21/0.57  # Current number of unprocessed clauses: 985
% 1.21/0.57  # ...number of literals in the above   : 5332
% 1.21/0.57  # Current number of archived formulas  : 0
% 1.21/0.57  # Current number of archived clauses   : 736
% 1.21/0.57  # Clause-clause subsumption calls (NU) : 80408
% 1.21/0.57  # Rec. Clause-clause subsumption calls : 28323
% 1.21/0.57  # Non-unit clause-clause subsumptions  : 1250
% 1.21/0.57  # Unit Clause-clause subsumption calls : 1633
% 1.21/0.57  # Rewrite failures with RHS unbound    : 0
% 1.21/0.57  # BW rewrite match attempts            : 8
% 1.21/0.57  # BW rewrite match successes           : 8
% 1.21/0.57  # Condensation attempts                : 1516
% 1.21/0.57  # Condensation successes               : 0
% 1.21/0.57  # Termbank termtop insertions          : 86224
% 1.21/0.57  # Search garbage collected termcells   : 2931
% 1.21/0.57  
% 1.21/0.57  # -------------------------------------------------
% 1.21/0.57  # User time                : 0.129 s
% 1.21/0.57  # System time              : 0.008 s
% 1.21/0.57  # Total time               : 0.137 s
% 1.21/0.57  # Maximum resident set size: 2892 pages
% 1.21/0.57  
% 1.21/0.57  # -------------------------------------------------
% 1.21/0.57  # User time                : 0.131 s
% 1.21/0.57  # System time              : 0.009 s
% 1.21/0.57  # Total time               : 0.140 s
% 1.21/0.57  # Maximum resident set size: 2012 pages
% 1.21/0.57  % E---3.1 exiting
% 1.21/0.57  % E exiting
%------------------------------------------------------------------------------