TSTP Solution File: SYO873^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO873^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 08:50:17 EDT 2024

% Result   : Theorem 85.27s 17.73s
% Output   : CNFRefutation 85.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   76 (  12 unt;  28 typ;   0 def)
%            Number of atoms       : 2525 (  43 equ;   0 cnn)
%            Maximal formula atoms :  695 (  52 avg)
%            Number of connectives : 11126 ( 752   ~;1233   |; 492   &;8561   @)
%                                         (  10 <=>;  78  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   79 (  15 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  118 ( 118   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  28 usr;   6 con; 0-3 aty)
%            Number of variables   :  162 (   3   ^  91   !;  68   ?; 162   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_23,type,
    c_False: $o ).

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

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

thf(decl_29,type,
    c_In: $i > $i > $o ).

thf(decl_30,type,
    c_Subq: $i > $i > $o ).

thf(decl_31,type,
    c_Empty: $i ).

thf(decl_33,type,
    c_Power: $i > $i ).

thf(decl_35,type,
    c_TransSet: $i > $o ).

thf(decl_41,type,
    c_exactly2: $i > $o ).

thf(decl_71,type,
    c_binintersect: $i > $i > $i ).

thf(decl_79,type,
    c_ordsucc: $i > $i ).

thf(decl_93,type,
    c_binrep: $i > $i > $i ).

thf(decl_95,type,
    c_setprod: $i > $i > $i ).

thf(decl_113,type,
    c_SNo: $i > $o ).

thf(decl_268,type,
    epred143_2: ( $i > $i ) > $i > $o ).

thf(decl_271,type,
    epred146_3: $i > ( $i > $i ) > ( $i > $o ) > $o ).

thf(decl_272,type,
    epred147_3: $i > ( $i > $i ) > ( $i > $o ) > $o ).

thf(decl_274,type,
    epred149_0: $o ).

thf(decl_275,type,
    epred150_2: ( $i > $i ) > ( $i > $o ) > $o ).

thf(decl_276,type,
    epred151_2: ( $i > $i ) > ( $i > $o ) > $o ).

thf(decl_277,type,
    esk1_0: $i ).

thf(decl_290,type,
    epred153_2: $o > $o > $o ).

thf(decl_335,type,
    epred159_0: $i > $o ).

thf(decl_336,type,
    esk52_0: $i > $i ).

thf(decl_505,type,
    esk219_2: ( $i > $o ) > ( $i > $i ) > $i ).

thf(decl_506,type,
    esk220_2: ( $i > $o ) > ( $i > $i ) > $i ).

thf(decl_507,type,
    esk221_2: ( $i > $o ) > ( $i > $i ) > $i ).

thf(decl_508,type,
    esk222_2: ( $i > $o ) > ( $i > $i ) > $i ).

thf(conj,conjecture,
    ( c_not
    @ ! [X1: $i > $o,X201: $i > $i] :
        ( c_and
        @ ( ( ( X1 @ ( X201 @ ( c_binintersect @ ( X201 @ ( c_Power @ c_Empty ) ) @ ( X201 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
           => ( ( c_TransSet @ ( X201 @ c_Empty ) )
             => ! [X9: $i] :
                  ( ( c_In @ X9 @ c_Empty )
                 => ? [X13: $i] : ( c_and @ ( c_Subq @ X13 @ X9 ) @ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) ) ) ) ) )
         => ? [X9: $i] :
              ( c_and
              @ ? [X13: $i] :
                  ( c_and @ ( c_Subq @ X13 @ X9 )
                  @ ( ( X9
                      = ( X201 @ X9 ) )
                   => ? [X66: $i] : ( c_and @ ( c_Subq @ X66 @ X9 ) @ ( c_not @ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) ) ) ) ) )
              @ ( c_not @ ( c_SNo @ X9 ) ) ) )
        @ ( c_not @ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(ax13,axiom,
    ( c_not
    = ( ^ [X17: $o] :
          ( X17
         => c_False ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).

thf(ax5,axiom,
    ( c_not
    @ ? [X7: $i] : ( c_In @ X7 @ c_Empty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

thf(ax14,axiom,
    ( c_and
    = ( ^ [X18: $o,X19: $o] :
        ! [X20: $o] :
          ( ( X18
           => ( X19
             => X20 ) )
         => X20 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).

thf(c_0_4,plain,
    ( epred149_0
  <=> ( ~ ! [X1: $i > $o,X201: $i > $i] :
            ( ( ~ ( ( ( X1 @ ( X201 @ ( c_binintersect @ ( X201 @ ( c_Power @ c_Empty ) ) @ ( X201 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
                   => ( ( c_TransSet @ ( X201 @ c_Empty ) )
                     => ! [X9: $i] :
                          ( ( c_In @ X9 @ c_Empty )
                         => ? [X13: $i] :
                              ( ( ~ ( c_Subq @ X13 @ X9 )
                                | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                    | ( c_and @ $true @ $true ) )
                                  & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                    | ( c_and @ $true @ $false ) ) ) )
                              & ( ( c_Subq @ X13 @ X9 )
                                | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                    | ( c_and @ $false @ $true ) )
                                  & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                    | ( c_and @ $false @ $false ) ) ) ) ) ) ) )
                 => ? [X9: $i] :
                      ( ( ~ ? [X13: $i] :
                              ( ( ~ ( c_Subq @ X13 @ X9 )
                                | ( ( ~ ( ( X9
                                          = ( X201 @ X9 ) )
                                       => ? [X66: $i] :
                                            ( ( ~ ( c_Subq @ X66 @ X9 )
                                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $false ) ) )
                                                  | ( c_and @ $true @ $true ) )
                                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $false ) ) )
                                                  | ( c_and @ $true @ $false ) ) ) )
                                            & ( ( c_Subq @ X66 @ X9 )
                                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $false ) ) )
                                                  | ( c_and @ $false @ $true ) )
                                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $false ) ) )
                                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                                    | ( c_and @ $true @ $true ) )
                                  & ( ( ( X9
                                        = ( X201 @ X9 ) )
                                     => ? [X66: $i] :
                                          ( ( ~ ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $false ) ) ) )
                                          & ( ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $false ) ) ) ) ) )
                                    | ( c_and @ $true @ $false ) ) ) )
                              & ( ( c_Subq @ X13 @ X9 )
                                | ( ( ~ ( ( X9
                                          = ( X201 @ X9 ) )
                                       => ? [X66: $i] :
                                            ( ( ~ ( c_Subq @ X66 @ X9 )
                                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $false ) ) )
                                                  | ( c_and @ $true @ $true ) )
                                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $false ) ) )
                                                  | ( c_and @ $true @ $false ) ) ) )
                                            & ( ( c_Subq @ X66 @ X9 )
                                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ~ ( c_not @ $false ) ) )
                                                  | ( c_and @ $false @ $true ) )
                                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $true ) )
                                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                      | ( c_not @ $false ) ) )
                                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                                    | ( c_and @ $false @ $true ) )
                                  & ( ( ( X9
                                        = ( X201 @ X9 ) )
                                     => ? [X66: $i] :
                                          ( ( ~ ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $false ) ) ) )
                                          & ( ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $false ) ) ) ) ) )
                                    | ( c_and @ $false @ $false ) ) ) ) )
                        | ( ( ( ( ~ ( c_SNo @ X9 )
                                | ~ ( c_not @ $true ) )
                              & ( ( c_SNo @ X9 )
                                | ~ ( c_not @ $false ) ) )
                            | ( c_and @ $true @ $true ) )
                          & ( ( ( ~ ( c_SNo @ X9 )
                                | ( c_not @ $true ) )
                              & ( ( c_SNo @ X9 )
                                | ( c_not @ $false ) ) )
                            | ( c_and @ $true @ $false ) ) ) )
                      & ( ? [X13: $i] :
                            ( ( ~ ( c_Subq @ X13 @ X9 )
                              | ( ( ~ ( ( X9
                                        = ( X201 @ X9 ) )
                                     => ? [X66: $i] :
                                          ( ( ~ ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $false ) ) ) )
                                          & ( ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $true @ $true ) )
                                & ( ( ( X9
                                      = ( X201 @ X9 ) )
                                   => ? [X66: $i] :
                                        ( ( ~ ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $false ) ) ) )
                                        & ( ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ( c_Subq @ X13 @ X9 )
                              | ( ( ~ ( ( X9
                                        = ( X201 @ X9 ) )
                                     => ? [X66: $i] :
                                          ( ( ~ ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $false ) ) ) )
                                          & ( ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $false @ $true ) )
                                & ( ( ( X9
                                      = ( X201 @ X9 ) )
                                   => ? [X66: $i] :
                                        ( ( ~ ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $false ) ) ) )
                                        & ( ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $false @ $false ) ) ) ) )
                        | ( ( ( ( ~ ( c_SNo @ X9 )
                                | ~ ( c_not @ $true ) )
                              & ( ( c_SNo @ X9 )
                                | ~ ( c_not @ $false ) ) )
                            | ( c_and @ $false @ $true ) )
                          & ( ( ( ~ ( c_SNo @ X9 )
                                | ( c_not @ $true ) )
                              & ( ( c_SNo @ X9 )
                                | ( c_not @ $false ) ) )
                            | ( c_and @ $false @ $false ) ) ) ) ) )
              | ( ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ~ ( c_not @ $true ) )
                    & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ~ ( c_not @ $false ) ) )
                  | ( c_and @ $true @ $true ) )
                & ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ( c_not @ $true ) )
                    & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ( c_not @ $false ) ) )
                  | ( c_and @ $true @ $false ) ) ) )
            & ( ( ( ( X1 @ ( X201 @ ( c_binintersect @ ( X201 @ ( c_Power @ c_Empty ) ) @ ( X201 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
                 => ( ( c_TransSet @ ( X201 @ c_Empty ) )
                   => ! [X9: $i] :
                        ( ( c_In @ X9 @ c_Empty )
                       => ? [X13: $i] :
                            ( ( ~ ( c_Subq @ X13 @ X9 )
                              | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                  | ( c_and @ $true @ $true ) )
                                & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ( c_Subq @ X13 @ X9 )
                              | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                  | ( c_and @ $false @ $true ) )
                                & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                                  | ( c_and @ $false @ $false ) ) ) ) ) ) ) )
               => ? [X9: $i] :
                    ( ( ~ ? [X13: $i] :
                            ( ( ~ ( c_Subq @ X13 @ X9 )
                              | ( ( ~ ( ( X9
                                        = ( X201 @ X9 ) )
                                     => ? [X66: $i] :
                                          ( ( ~ ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $false ) ) ) )
                                          & ( ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $true @ $true ) )
                                & ( ( ( X9
                                      = ( X201 @ X9 ) )
                                   => ? [X66: $i] :
                                        ( ( ~ ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $false ) ) ) )
                                        & ( ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ( c_Subq @ X13 @ X9 )
                              | ( ( ~ ( ( X9
                                        = ( X201 @ X9 ) )
                                     => ? [X66: $i] :
                                          ( ( ~ ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $true @ $false ) ) ) )
                                          & ( ( c_Subq @ X66 @ X9 )
                                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ~ ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $true ) )
                                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $true ) )
                                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                    | ( c_not @ $false ) ) )
                                                | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $false @ $true ) )
                                & ( ( ( X9
                                      = ( X201 @ X9 ) )
                                   => ? [X66: $i] :
                                        ( ( ~ ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $false ) ) ) )
                                        & ( ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $false ) ) ) ) ) )
                                  | ( c_and @ $false @ $false ) ) ) ) )
                      | ( ( ( ( ~ ( c_SNo @ X9 )
                              | ~ ( c_not @ $true ) )
                            & ( ( c_SNo @ X9 )
                              | ~ ( c_not @ $false ) ) )
                          | ( c_and @ $true @ $true ) )
                        & ( ( ( ~ ( c_SNo @ X9 )
                              | ( c_not @ $true ) )
                            & ( ( c_SNo @ X9 )
                              | ( c_not @ $false ) ) )
                          | ( c_and @ $true @ $false ) ) ) )
                    & ( ? [X13: $i] :
                          ( ( ~ ( c_Subq @ X13 @ X9 )
                            | ( ( ~ ( ( X9
                                      = ( X201 @ X9 ) )
                                   => ? [X66: $i] :
                                        ( ( ~ ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $false ) ) ) )
                                        & ( ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $false ) ) ) ) ) )
                                | ( c_and @ $true @ $true ) )
                              & ( ( ( X9
                                    = ( X201 @ X9 ) )
                                 => ? [X66: $i] :
                                      ( ( ~ ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $false ) ) ) )
                                      & ( ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $false ) ) ) ) ) )
                                | ( c_and @ $true @ $false ) ) ) )
                          & ( ( c_Subq @ X13 @ X9 )
                            | ( ( ~ ( ( X9
                                      = ( X201 @ X9 ) )
                                   => ? [X66: $i] :
                                        ( ( ~ ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $true @ $false ) ) ) )
                                        & ( ( c_Subq @ X66 @ X9 )
                                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ~ ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $true ) )
                                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $true ) )
                                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                  | ( c_not @ $false ) ) )
                                              | ( c_and @ $false @ $false ) ) ) ) ) )
                                | ( c_and @ $false @ $true ) )
                              & ( ( ( X9
                                    = ( X201 @ X9 ) )
                                 => ? [X66: $i] :
                                      ( ( ~ ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $false ) ) ) )
                                      & ( ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $false ) ) ) ) ) )
                                | ( c_and @ $false @ $false ) ) ) ) )
                      | ( ( ( ( ~ ( c_SNo @ X9 )
                              | ~ ( c_not @ $true ) )
                            & ( ( c_SNo @ X9 )
                              | ~ ( c_not @ $false ) ) )
                          | ( c_and @ $false @ $true ) )
                        & ( ( ( ~ ( c_SNo @ X9 )
                              | ( c_not @ $true ) )
                            & ( ( c_SNo @ X9 )
                              | ( c_not @ $false ) ) )
                          | ( c_and @ $false @ $false ) ) ) ) ) )
              | ( ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ~ ( c_not @ $true ) )
                    & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ~ ( c_not @ $false ) ) )
                  | ( c_and @ $false @ $true ) )
                & ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ( c_not @ $true ) )
                    & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                      | ( c_not @ $false ) ) )
                  | ( c_and @ $false @ $false ) ) ) ) )
      | ( c_not @ $true ) ) ),
    introduced(definition) ).

thf(c_0_5,plain,
    ! [X1: $i > $o,X201: $i > $i] :
      ( ( epred150_2 @ X201 @ X1 )
    <=> ( ~ ( ( ( X1 @ ( X201 @ ( c_binintersect @ ( X201 @ ( c_Power @ c_Empty ) ) @ ( X201 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
             => ( ( c_TransSet @ ( X201 @ c_Empty ) )
               => ! [X9: $i] :
                    ( ( c_In @ X9 @ c_Empty )
                   => ? [X13: $i] :
                        ( ( ~ ( c_Subq @ X13 @ X9 )
                          | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                              | ( c_and @ $true @ $true ) )
                            & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                              | ( c_and @ $true @ $false ) ) ) )
                        & ( ( c_Subq @ X13 @ X9 )
                          | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                              | ( c_and @ $false @ $true ) )
                            & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                              | ( c_and @ $false @ $false ) ) ) ) ) ) ) )
           => ? [X9: $i] :
                ( ( ~ ? [X13: $i] :
                        ( ( ~ ( c_Subq @ X13 @ X9 )
                          | ( ( ~ ( ( X9
                                    = ( X201 @ X9 ) )
                                 => ? [X66: $i] :
                                      ( ( ~ ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $false ) ) ) )
                                      & ( ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $false ) ) ) ) ) )
                              | ( c_and @ $true @ $true ) )
                            & ( ( ( X9
                                  = ( X201 @ X9 ) )
                               => ? [X66: $i] :
                                    ( ( ~ ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $false ) ) ) )
                                    & ( ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $false ) ) ) ) ) )
                              | ( c_and @ $true @ $false ) ) ) )
                        & ( ( c_Subq @ X13 @ X9 )
                          | ( ( ~ ( ( X9
                                    = ( X201 @ X9 ) )
                                 => ? [X66: $i] :
                                      ( ( ~ ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $true @ $false ) ) ) )
                                      & ( ( c_Subq @ X66 @ X9 )
                                        | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ~ ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $true ) )
                                          & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $true ) )
                                              & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                                | ( c_not @ $false ) ) )
                                            | ( c_and @ $false @ $false ) ) ) ) ) )
                              | ( c_and @ $false @ $true ) )
                            & ( ( ( X9
                                  = ( X201 @ X9 ) )
                               => ? [X66: $i] :
                                    ( ( ~ ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $false ) ) ) )
                                    & ( ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $false ) ) ) ) ) )
                              | ( c_and @ $false @ $false ) ) ) ) )
                  | ( ( ( ( ~ ( c_SNo @ X9 )
                          | ~ ( c_not @ $true ) )
                        & ( ( c_SNo @ X9 )
                          | ~ ( c_not @ $false ) ) )
                      | ( c_and @ $true @ $true ) )
                    & ( ( ( ~ ( c_SNo @ X9 )
                          | ( c_not @ $true ) )
                        & ( ( c_SNo @ X9 )
                          | ( c_not @ $false ) ) )
                      | ( c_and @ $true @ $false ) ) ) )
                & ( ? [X13: $i] :
                      ( ( ~ ( c_Subq @ X13 @ X9 )
                        | ( ( ~ ( ( X9
                                  = ( X201 @ X9 ) )
                               => ? [X66: $i] :
                                    ( ( ~ ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $false ) ) ) )
                                    & ( ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $true @ $true ) )
                          & ( ( ( X9
                                = ( X201 @ X9 ) )
                             => ? [X66: $i] :
                                  ( ( ~ ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $false ) ) ) )
                                  & ( ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $true @ $false ) ) ) )
                      & ( ( c_Subq @ X13 @ X9 )
                        | ( ( ~ ( ( X9
                                  = ( X201 @ X9 ) )
                               => ? [X66: $i] :
                                    ( ( ~ ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $false ) ) ) )
                                    & ( ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $false @ $true ) )
                          & ( ( ( X9
                                = ( X201 @ X9 ) )
                             => ? [X66: $i] :
                                  ( ( ~ ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $false ) ) ) )
                                  & ( ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $false @ $false ) ) ) ) )
                  | ( ( ( ( ~ ( c_SNo @ X9 )
                          | ~ ( c_not @ $true ) )
                        & ( ( c_SNo @ X9 )
                          | ~ ( c_not @ $false ) ) )
                      | ( c_and @ $false @ $true ) )
                    & ( ( ( ~ ( c_SNo @ X9 )
                          | ( c_not @ $true ) )
                        & ( ( c_SNo @ X9 )
                          | ( c_not @ $false ) ) )
                      | ( c_and @ $false @ $false ) ) ) ) ) )
        | ( ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $true @ $true ) )
          & ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $true @ $false ) ) ) ) ),
    introduced(definition) ).

thf(c_0_6,plain,
    ! [X1: $i > $o,X201: $i > $i] :
      ( ( epred151_2 @ X201 @ X1 )
    <=> ( ( ( ( X1 @ ( X201 @ ( c_binintersect @ ( X201 @ ( c_Power @ c_Empty ) ) @ ( X201 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
           => ( ( c_TransSet @ ( X201 @ c_Empty ) )
             => ! [X9: $i] :
                  ( ( c_In @ X9 @ c_Empty )
                 => ? [X13: $i] :
                      ( ( ~ ( c_Subq @ X13 @ X9 )
                        | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                            | ( c_and @ $true @ $true ) )
                          & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                            | ( c_and @ $true @ $false ) ) ) )
                      & ( ( c_Subq @ X13 @ X9 )
                        | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                            | ( c_and @ $false @ $true ) )
                          & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                            | ( c_and @ $false @ $false ) ) ) ) ) ) ) )
         => ? [X9: $i] :
              ( ( ~ ? [X13: $i] :
                      ( ( ~ ( c_Subq @ X13 @ X9 )
                        | ( ( ~ ( ( X9
                                  = ( X201 @ X9 ) )
                               => ? [X66: $i] :
                                    ( ( ~ ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $false ) ) ) )
                                    & ( ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $true @ $true ) )
                          & ( ( ( X9
                                = ( X201 @ X9 ) )
                             => ? [X66: $i] :
                                  ( ( ~ ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $false ) ) ) )
                                  & ( ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $true @ $false ) ) ) )
                      & ( ( c_Subq @ X13 @ X9 )
                        | ( ( ~ ( ( X9
                                  = ( X201 @ X9 ) )
                               => ? [X66: $i] :
                                    ( ( ~ ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $true @ $false ) ) ) )
                                    & ( ( c_Subq @ X66 @ X9 )
                                      | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ~ ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $true ) )
                                        & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $true ) )
                                            & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                              | ( c_not @ $false ) ) )
                                          | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $false @ $true ) )
                          & ( ( ( X9
                                = ( X201 @ X9 ) )
                             => ? [X66: $i] :
                                  ( ( ~ ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $false ) ) ) )
                                  & ( ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $false ) ) ) ) ) )
                            | ( c_and @ $false @ $false ) ) ) ) )
                | ( ( ( ( ~ ( c_SNo @ X9 )
                        | ~ ( c_not @ $true ) )
                      & ( ( c_SNo @ X9 )
                        | ~ ( c_not @ $false ) ) )
                    | ( c_and @ $true @ $true ) )
                  & ( ( ( ~ ( c_SNo @ X9 )
                        | ( c_not @ $true ) )
                      & ( ( c_SNo @ X9 )
                        | ( c_not @ $false ) ) )
                    | ( c_and @ $true @ $false ) ) ) )
              & ( ? [X13: $i] :
                    ( ( ~ ( c_Subq @ X13 @ X9 )
                      | ( ( ~ ( ( X9
                                = ( X201 @ X9 ) )
                             => ? [X66: $i] :
                                  ( ( ~ ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $false ) ) ) )
                                  & ( ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $false ) ) ) ) ) )
                          | ( c_and @ $true @ $true ) )
                        & ( ( ( X9
                              = ( X201 @ X9 ) )
                           => ? [X66: $i] :
                                ( ( ~ ( c_Subq @ X66 @ X9 )
                                  | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $false ) ) )
                                      | ( c_and @ $true @ $true ) )
                                    & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $false ) ) )
                                      | ( c_and @ $true @ $false ) ) ) )
                                & ( ( c_Subq @ X66 @ X9 )
                                  | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $false ) ) )
                                      | ( c_and @ $false @ $true ) )
                                    & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $false ) ) )
                                      | ( c_and @ $false @ $false ) ) ) ) ) )
                          | ( c_and @ $true @ $false ) ) ) )
                    & ( ( c_Subq @ X13 @ X9 )
                      | ( ( ~ ( ( X9
                                = ( X201 @ X9 ) )
                             => ? [X66: $i] :
                                  ( ( ~ ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $true @ $false ) ) ) )
                                  & ( ( c_Subq @ X66 @ X9 )
                                    | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ~ ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $true ) )
                                      & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $true ) )
                                          & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                            | ( c_not @ $false ) ) )
                                        | ( c_and @ $false @ $false ) ) ) ) ) )
                          | ( c_and @ $false @ $true ) )
                        & ( ( ( X9
                              = ( X201 @ X9 ) )
                           => ? [X66: $i] :
                                ( ( ~ ( c_Subq @ X66 @ X9 )
                                  | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $false ) ) )
                                      | ( c_and @ $true @ $true ) )
                                    & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $false ) ) )
                                      | ( c_and @ $true @ $false ) ) ) )
                                & ( ( c_Subq @ X66 @ X9 )
                                  | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ~ ( c_not @ $false ) ) )
                                      | ( c_and @ $false @ $true ) )
                                    & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $true ) )
                                        & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                          | ( c_not @ $false ) ) )
                                      | ( c_and @ $false @ $false ) ) ) ) ) )
                          | ( c_and @ $false @ $false ) ) ) ) )
                | ( ( ( ( ~ ( c_SNo @ X9 )
                        | ~ ( c_not @ $true ) )
                      & ( ( c_SNo @ X9 )
                        | ~ ( c_not @ $false ) ) )
                    | ( c_and @ $false @ $true ) )
                  & ( ( ( ~ ( c_SNo @ X9 )
                        | ( c_not @ $true ) )
                      & ( ( c_SNo @ X9 )
                        | ( c_not @ $false ) ) )
                    | ( c_and @ $false @ $false ) ) ) ) ) )
        | ( ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $false @ $true ) )
          & ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $false @ $false ) ) ) ) ),
    introduced(definition) ).

thf(c_0_7,negated_conjecture,
    ~ ( epred149_0
      & ( ! [X1: $i > $o,X201: $i > $i] :
            ( ( epred150_2 @ X201 @ X1 )
            & ( epred151_2 @ X201 @ X1 ) )
        | ( c_not @ $false ) ) ),
    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)],[conj])]),c_0_4]),c_0_5]),c_0_6]) ).

thf(c_0_8,plain,
    ! [X231: $o] :
      ( ( c_not @ X231 )
    <=> ( X231
       => c_False ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax13])]) ).

thf(c_0_9,plain,
    ( ( ~ ! [X1: $i > $o,X201: $i > $i] :
            ( ( epred150_2 @ X201 @ X1 )
            & ( epred151_2 @ X201 @ X1 ) )
      | ( c_not @ $true ) )
   => epred149_0 ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_4]),c_0_5]),c_0_6]) ).

thf(c_0_10,negated_conjecture,
    ( ( ~ ( epred150_2 @ esk52_0 @ epred159_0 )
      | ~ ( epred151_2 @ esk52_0 @ epred159_0 )
      | ~ epred149_0 )
    & ( ~ ( c_not @ $false )
      | ~ epred149_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).

thf(c_0_11,plain,
    ! [X479: $o] :
      ( ( ~ ( c_not @ X479 )
        | ~ X479
        | c_False )
      & ( X479
        | ( c_not @ X479 ) )
      & ( ~ c_False
        | ( c_not @ X479 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

thf(c_0_12,plain,
    ! [X9: $i,X201: $i > $i] :
      ( ( epred143_2 @ X201 @ X9 )
    <=> ? [X13: $i] :
          ( ( ~ ( c_Subq @ X13 @ X9 )
            | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                | ( c_and @ $true @ $true ) )
              & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                | ( c_and @ $true @ $false ) ) ) )
          & ( ( c_Subq @ X13 @ X9 )
            | ( ( ~ ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                | ( c_and @ $false @ $true ) )
              & ( ( c_exactly2 @ ( c_ordsucc @ ( X201 @ X13 ) ) )
                | ( c_and @ $false @ $false ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_13,plain,
    ! [X1: $i > $o,X201: $i > $i,X9: $i] :
      ( ( epred146_3 @ X9 @ X201 @ X1 )
    <=> ( ~ ? [X13: $i] :
              ( ( ~ ( c_Subq @ X13 @ X9 )
                | ( ( ~ ( ( X9
                          = ( X201 @ X9 ) )
                       => ? [X66: $i] :
                            ( ( ~ ( c_Subq @ X66 @ X9 )
                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $false ) ) )
                                  | ( c_and @ $true @ $true ) )
                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $false ) ) )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ( c_Subq @ X66 @ X9 )
                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $false ) ) )
                                  | ( c_and @ $false @ $true ) )
                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $false ) ) )
                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                    | ( c_and @ $true @ $true ) )
                  & ( ( ( X9
                        = ( X201 @ X9 ) )
                     => ? [X66: $i] :
                          ( ( ~ ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $false ) ) ) )
                          & ( ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $false ) ) ) ) ) )
                    | ( c_and @ $true @ $false ) ) ) )
              & ( ( c_Subq @ X13 @ X9 )
                | ( ( ~ ( ( X9
                          = ( X201 @ X9 ) )
                       => ? [X66: $i] :
                            ( ( ~ ( c_Subq @ X66 @ X9 )
                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $false ) ) )
                                  | ( c_and @ $true @ $true ) )
                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $false ) ) )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ( c_Subq @ X66 @ X9 )
                              | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ~ ( c_not @ $false ) ) )
                                  | ( c_and @ $false @ $true ) )
                                & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $true ) )
                                    & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                      | ( c_not @ $false ) ) )
                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                    | ( c_and @ $false @ $true ) )
                  & ( ( ( X9
                        = ( X201 @ X9 ) )
                     => ? [X66: $i] :
                          ( ( ~ ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $false ) ) ) )
                          & ( ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $false ) ) ) ) ) )
                    | ( c_and @ $false @ $false ) ) ) ) )
        | ( ( ( ( ~ ( c_SNo @ X9 )
                | ~ ( c_not @ $true ) )
              & ( ( c_SNo @ X9 )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $true @ $true ) )
          & ( ( ( ~ ( c_SNo @ X9 )
                | ( c_not @ $true ) )
              & ( ( c_SNo @ X9 )
                | ( c_not @ $false ) ) )
            | ( c_and @ $true @ $false ) ) ) ) ),
    introduced(definition) ).

thf(c_0_14,plain,
    ! [X1: $i > $o,X201: $i > $i,X9: $i] :
      ( ( epred147_3 @ X9 @ X201 @ X1 )
    <=> ( ? [X13: $i] :
            ( ( ~ ( c_Subq @ X13 @ X9 )
              | ( ( ~ ( ( X9
                        = ( X201 @ X9 ) )
                     => ? [X66: $i] :
                          ( ( ~ ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $false ) ) ) )
                          & ( ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $false ) ) ) ) ) )
                  | ( c_and @ $true @ $true ) )
                & ( ( ( X9
                      = ( X201 @ X9 ) )
                   => ? [X66: $i] :
                        ( ( ~ ( c_Subq @ X66 @ X9 )
                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $false ) ) )
                              | ( c_and @ $true @ $true ) )
                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $false ) ) )
                              | ( c_and @ $true @ $false ) ) ) )
                        & ( ( c_Subq @ X66 @ X9 )
                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $false ) ) )
                              | ( c_and @ $false @ $true ) )
                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $false ) ) )
                              | ( c_and @ $false @ $false ) ) ) ) ) )
                  | ( c_and @ $true @ $false ) ) ) )
            & ( ( c_Subq @ X13 @ X9 )
              | ( ( ~ ( ( X9
                        = ( X201 @ X9 ) )
                     => ? [X66: $i] :
                          ( ( ~ ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $true @ $false ) ) ) )
                          & ( ( c_Subq @ X66 @ X9 )
                            | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ~ ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $true ) )
                              & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $true ) )
                                  & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                    | ( c_not @ $false ) ) )
                                | ( c_and @ $false @ $false ) ) ) ) ) )
                  | ( c_and @ $false @ $true ) )
                & ( ( ( X9
                      = ( X201 @ X9 ) )
                   => ? [X66: $i] :
                        ( ( ~ ( c_Subq @ X66 @ X9 )
                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $false ) ) )
                              | ( c_and @ $true @ $true ) )
                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $false ) ) )
                              | ( c_and @ $true @ $false ) ) ) )
                        & ( ( c_Subq @ X66 @ X9 )
                          | ( ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ~ ( c_not @ $false ) ) )
                              | ( c_and @ $false @ $true ) )
                            & ( ( ( ~ ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $true ) )
                                & ( ( X1 @ ( c_setprod @ X13 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) )
                                  | ( c_not @ $false ) ) )
                              | ( c_and @ $false @ $false ) ) ) ) ) )
                  | ( c_and @ $false @ $false ) ) ) ) )
        | ( ( ( ( ~ ( c_SNo @ X9 )
                | ~ ( c_not @ $true ) )
              & ( ( c_SNo @ X9 )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $false @ $true ) )
          & ( ( ( ~ ( c_SNo @ X9 )
                | ( c_not @ $true ) )
              & ( ( c_SNo @ X9 )
                | ( c_not @ $false ) ) )
            | ( c_and @ $false @ $false ) ) ) ) ),
    introduced(definition) ).

thf(c_0_15,axiom,
    ( ( ~ ? [X7: $i] : ( c_In @ X7 @ c_Empty )
      | ( c_not @ $true ) )
    & ( ? [X7: $i] : ( c_In @ X7 @ c_Empty )
      | ( c_not @ $false ) ) ),
    inference(fool_unroll,[status(thm)],[ax5]) ).

thf(c_0_16,plain,
    ! [X1932: $i > $o,X1933: $i > $i] :
      ( ( ( epred150_2 @ X1933 @ X1932 )
        | epred149_0 )
      & ( ( epred151_2 @ X1933 @ X1932 )
        | epred149_0 )
      & ( ~ ( c_not @ $true )
        | epred149_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).

thf(c_0_17,negated_conjecture,
    ( ~ ( c_not @ ~ $true )
    | ~ epred149_0 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_18,plain,
    c_not @ ~ $true,
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11])])]) ).

thf(c_0_19,plain,
    ! [X1: $i > $o,X201: $i > $i] :
      ( ( epred151_2 @ X201 @ X1 )
    <=> ( ( ( ( X1 @ ( X201 @ ( c_binintersect @ ( X201 @ ( c_Power @ c_Empty ) ) @ ( X201 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
           => ( ( c_TransSet @ ( X201 @ c_Empty ) )
             => ! [X9: $i] :
                  ( ( c_In @ X9 @ c_Empty )
                 => ( epred143_2 @ X201 @ X9 ) ) ) )
         => ? [X9: $i] :
              ( ( epred146_3 @ X9 @ X201 @ X1 )
              & ( epred147_3 @ X9 @ X201 @ X1 ) ) )
        | ( ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $false @ $true ) )
          & ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $false @ $false ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_12]),c_0_13]),c_0_14]) ).

thf(c_0_20,plain,
    ! [X446: $i] :
      ( ( ~ ( c_In @ X446 @ c_Empty )
        | ( c_not @ $true ) )
      & ( ( c_In @ esk1_0 @ c_Empty )
        | ( c_not @ $false ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).

thf(c_0_21,plain,
    ( epred149_0
    | ~ ( c_not @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_22,negated_conjecture,
    ~ epred149_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).

thf(c_0_23,plain,
    ! [X232: $o,X233: $o] :
      ( ( c_and @ X232 @ X233 )
    <=> ! [X20: $o] :
          ( ( X232
           => ( X233
             => X20 ) )
         => X20 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax14])]) ).

thf(c_0_24,plain,
    ! [X1: $i > $o,X201: $i > $i] :
      ( ( epred150_2 @ X201 @ X1 )
    <=> ( ~ ( ( ( X1 @ ( X201 @ ( c_binintersect @ ( X201 @ ( c_Power @ c_Empty ) ) @ ( X201 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
             => ( ( c_TransSet @ ( X201 @ c_Empty ) )
               => ! [X9: $i] :
                    ( ( c_In @ X9 @ c_Empty )
                   => ( epred143_2 @ X201 @ X9 ) ) ) )
           => ? [X9: $i] :
                ( ( epred146_3 @ X9 @ X201 @ X1 )
                & ( epred147_3 @ X9 @ X201 @ X1 ) ) )
        | ( ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $true @ $true ) )
          & ( ( ( ~ ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X1 @ ( X201 @ ( X201 @ ( X201 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $true @ $false ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_12]),c_0_13]),c_0_14]) ).

thf(c_0_25,plain,
    ! [X1942: $i > $o,X1943: $i > $i,X1946: $i > $o,X1947: $i > $i,X1948: $i,X1949: $i] :
      ( ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( X1942 @ ( X1943 @ ( c_binintersect @ ( X1943 @ ( c_Power @ c_Empty ) ) @ ( X1943 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_TransSet @ ( X1943 @ c_Empty ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ( c_In @ ( esk221_2 @ X1942 @ X1943 ) @ c_Empty )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred146_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1943 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( epred147_3 @ ( esk222_2 @ X1942 @ X1943 ) @ X1943 @ X1942 )
        | ~ ( epred143_2 @ X1943 @ ( esk221_2 @ X1942 @ X1943 ) )
        | ~ ( epred151_2 @ X1943 @ X1942 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( c_binintersect @ ( X1947 @ ( c_Power @ c_Empty ) ) @ ( X1947 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_TransSet @ ( X1947 @ c_Empty ) )
        | ~ ( c_In @ X1948 @ c_Empty )
        | ( epred143_2 @ X1947 @ X1948 )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( epred146_3 @ X1949 @ X1947 @ X1946 )
        | ~ ( epred147_3 @ X1949 @ X1947 @ X1946 )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_and @ $false @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_and @ $false @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( X1946 @ ( X1947 @ ( X1947 @ ( X1947 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $false @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $false @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ( epred151_2 @ X1947 @ X1946 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])])]) ).

thf(c_0_26,plain,
    ! [X12: $i > $i,X1: $i > $o] :
      ( ( epred151_2 @ X12 @ X1 )
      | epred149_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_27,plain,
    ! [X2: $i] :
      ( ( c_not @ $true )
      | ~ ( c_In @ X2 @ c_Empty ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_28,plain,
    ~ ( c_not @ $true ),
    inference(sr,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_29,plain,
    ! [X480: $o,X481: $o,X482: $o,X483: $o,X484: $o] :
      ( ( X480
        | X482
        | ~ ( c_and @ X480 @ X481 ) )
      & ( X481
        | X482
        | ~ ( c_and @ X480 @ X481 ) )
      & ( ~ X482
        | X482
        | ~ ( c_and @ X480 @ X481 ) )
      & ( ~ X483
        | ~ X484
        | ( epred153_2 @ X483 @ X484 )
        | ( c_and @ X483 @ X484 ) )
      & ( ~ ( epred153_2 @ X483 @ X484 )
        | ( c_and @ X483 @ X484 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])])])]) ).

thf(c_0_30,plain,
    ! [X1934: $i > $o,X1935: $i > $i,X1936: $i,X1937: $i,X1938: $i > $o,X1939: $i > $i] :
      ( ( ~ ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $true @ $true )
        | ~ ( X1934 @ ( X1935 @ ( c_binintersect @ ( X1935 @ ( c_Power @ c_Empty ) ) @ ( X1935 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_TransSet @ ( X1935 @ c_Empty ) )
        | ~ ( c_In @ X1936 @ c_Empty )
        | ( epred143_2 @ X1935 @ X1936 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $true @ $true )
        | ~ ( X1934 @ ( X1935 @ ( c_binintersect @ ( X1935 @ ( c_Power @ c_Empty ) ) @ ( X1935 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_TransSet @ ( X1935 @ c_Empty ) )
        | ~ ( c_In @ X1936 @ c_Empty )
        | ( epred143_2 @ X1935 @ X1936 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ~ ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $true @ $false )
        | ~ ( X1934 @ ( X1935 @ ( c_binintersect @ ( X1935 @ ( c_Power @ c_Empty ) ) @ ( X1935 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_TransSet @ ( X1935 @ c_Empty ) )
        | ~ ( c_In @ X1936 @ c_Empty )
        | ( epred143_2 @ X1935 @ X1936 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $true @ $false )
        | ~ ( X1934 @ ( X1935 @ ( c_binintersect @ ( X1935 @ ( c_Power @ c_Empty ) ) @ ( X1935 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_TransSet @ ( X1935 @ c_Empty ) )
        | ~ ( c_In @ X1936 @ c_Empty )
        | ( epred143_2 @ X1935 @ X1936 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ~ ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $true @ $true )
        | ~ ( epred146_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred147_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $true @ $true )
        | ~ ( epred146_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred147_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ~ ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $true @ $false )
        | ~ ( epred146_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred147_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ( X1934 @ ( X1935 @ ( X1935 @ ( X1935 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $true @ $false )
        | ~ ( epred146_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred147_3 @ X1937 @ X1935 @ X1934 )
        | ~ ( epred150_2 @ X1935 @ X1934 ) )
      & ( ( epred146_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ( X1938 @ ( X1939 @ ( c_binintersect @ ( X1939 @ ( c_Power @ c_Empty ) ) @ ( X1939 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ( epred147_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ( X1938 @ ( X1939 @ ( c_binintersect @ ( X1939 @ ( c_Power @ c_Empty ) ) @ ( X1939 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ( epred146_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ( c_TransSet @ ( X1939 @ c_Empty ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ( epred147_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ( c_TransSet @ ( X1939 @ c_Empty ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ( epred146_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ( c_In @ ( esk219_2 @ X1938 @ X1939 ) @ c_Empty )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ( epred147_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ( c_In @ ( esk219_2 @ X1938 @ X1939 ) @ c_Empty )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ( epred146_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ~ ( epred143_2 @ X1939 @ ( esk219_2 @ X1938 @ X1939 ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ( epred147_3 @ ( esk220_2 @ X1938 @ X1939 ) @ X1939 @ X1938 )
        | ~ ( epred143_2 @ X1939 @ ( esk219_2 @ X1938 @ X1939 ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_and @ $true @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_and @ $true @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( X1938 @ ( X1939 @ ( X1939 @ ( X1939 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $true @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $true @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ~ ( c_and @ $true @ $true )
        | ( epred150_2 @ X1939 @ X1938 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])])])]) ).

thf(c_0_31,plain,
    ! [X12: $i > $i,X1: $i > $o] :
      ( ( epred150_2 @ X12 @ X1 )
      | epred149_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_32,plain,
    ! [X12: $i > $i,X1: $i > $o] :
      ( ( c_not @ $true )
      | ( c_and @ ~ $true @ ~ $true )
      | ( epred146_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 )
      | ( c_In @ ( esk221_2 @ X1 @ X12 ) @ c_Empty )
      | ~ ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
      | ~ ( epred151_2 @ X12 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_33,plain,
    ! [X12: $i > $i,X1: $i > $o] : ( epred151_2 @ X12 @ X1 ),
    inference(sr,[status(thm)],[c_0_26,c_0_22]) ).

thf(c_0_34,plain,
    ! [X2: $i] :
      ~ ( c_In @ X2 @ c_Empty ),
    inference(sr,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_35,plain,
    ! [X5: $o] :
      ~ ( c_and @ X5 @ ~ $true ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_29])])]) ).

thf(c_0_36,plain,
    ! [X12: $i > $i,X1: $i > $o] :
      ( ( c_not @ $true )
      | ( c_and @ ~ $true @ ~ $true )
      | ( epred147_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 )
      | ( c_In @ ( esk221_2 @ X1 @ X12 ) @ c_Empty )
      | ~ ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
      | ~ ( epred151_2 @ X12 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_37,plain,
    ! [X12: $i > $i,X2: $i,X1: $i > $o] :
      ( ( c_not @ $true )
      | ( c_and @ $true @ ~ $true )
      | ~ ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
      | ~ ( epred146_3 @ X2 @ X12 @ X1 )
      | ~ ( epred147_3 @ X2 @ X12 @ X1 )
      | ~ ( epred150_2 @ X12 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_38,plain,
    ! [X12: $i > $i,X1: $i > $o] : ( epred150_2 @ X12 @ X1 ),
    inference(sr,[status(thm)],[c_0_31,c_0_22]) ).

thf(c_0_39,plain,
    ! [X12: $i > $i,X1: $i > $o] :
      ( ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
      | ( c_and @ ~ $true @ $true )
      | ( epred146_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 )
      | ( c_In @ ( esk221_2 @ X1 @ X12 ) @ c_Empty )
      | ~ ( c_not @ ~ $true )
      | ~ ( epred151_2 @ X12 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_40,plain,
    ! [X5: $o] :
      ~ ( c_and @ ~ $true @ X5 ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_29])])]) ).

thf(c_0_41,plain,
    ! [X1: $i > $o,X12: $i > $i] :
      ( ( epred146_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 )
      | ~ ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) ) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),c_0_34]),c_0_35]),c_0_28]) ).

thf(c_0_42,plain,
    ! [X12: $i > $i,X1: $i > $o] :
      ( ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
      | ( c_and @ ~ $true @ $true )
      | ( epred147_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 )
      | ( c_In @ ( esk221_2 @ X1 @ X12 ) @ c_Empty )
      | ~ ( c_not @ ~ $true )
      | ~ ( epred151_2 @ X12 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_43,plain,
    ! [X1: $i > $o,X12: $i > $i] :
      ( ( epred147_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 )
      | ~ ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) ) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_33])]),c_0_34]),c_0_35]),c_0_28]) ).

thf(c_0_44,plain,
    ! [X12: $i > $i,X2: $i,X1: $i > $o] :
      ( ~ ( X1 @ ( X12 @ ( X12 @ ( X12 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) )
      | ~ ( epred146_3 @ X2 @ X12 @ X1 )
      | ~ ( epred147_3 @ X2 @ X12 @ X1 ) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),c_0_35]),c_0_28]) ).

thf(c_0_45,plain,
    ! [X12: $i > $i,X1: $i > $o] : ( epred146_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_18]),c_0_33])]),c_0_34]),c_0_40]),c_0_41]) ).

thf(c_0_46,plain,
    ! [X12: $i > $i,X1: $i > $o] : ( epred147_3 @ ( esk222_2 @ X1 @ X12 ) @ X12 @ X1 ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_18]),c_0_33])]),c_0_34]),c_0_40]),c_0_43]) ).

thf(c_0_47,plain,
    $false,
    inference(flex_resolve,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYO873^1 : TPTP v8.2.0. Released v7.5.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 09:55:22 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.46  Running higher-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 85.27/17.73  # Version: 3.1.0-ho
% 85.27/17.73  # partial match(1): HSLMSMSSSSLCHSA
% 85.27/17.73  # Preprocessing class: HSLMSLSSSSLCHSA.
% 85.27/17.73  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.27/17.73  # Starting pre_casc_6 with 1500s (5) cores
% 85.27/17.73  # Starting ehoh_best7 with 300s (1) cores
% 85.27/17.73  # Starting new_bool_8 with 300s (1) cores
% 85.27/17.73  # Starting new_ho_11 with 300s (1) cores
% 85.27/17.73  # new_ho_11 with pid 31255 completed with status 0
% 85.27/17.73  # Result found by new_ho_11
% 85.27/17.73  # partial match(1): HSLMSMSSSSLCHSA
% 85.27/17.73  # Preprocessing class: HSLMSLSSSSLCHSA.
% 85.27/17.73  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.27/17.73  # Starting pre_casc_6 with 1500s (5) cores
% 85.27/17.73  # Starting ehoh_best7 with 300s (1) cores
% 85.27/17.73  # Starting new_bool_8 with 300s (1) cores
% 85.27/17.73  # Starting new_ho_11 with 300s (1) cores
% 85.27/17.73  # No SInE strategy applied
% 85.27/17.73  # Search class: HGHSM-SMLM33-DHSFFSBC
% 85.27/17.73  # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 85.27/17.73  # Scheduled 6 strats onto 1 cores with 288 seconds (288 total)
% 85.27/17.73  # Starting new_ho_10 with 87s (1) cores
% 85.27/17.73  # new_ho_10 with pid 31261 completed with status 0
% 85.27/17.73  # Result found by new_ho_10
% 85.27/17.73  # partial match(1): HSLMSMSSSSLCHSA
% 85.27/17.73  # Preprocessing class: HSLMSLSSSSLCHSA.
% 85.27/17.73  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 85.27/17.73  # Starting pre_casc_6 with 1500s (5) cores
% 85.27/17.73  # Starting ehoh_best7 with 300s (1) cores
% 85.27/17.73  # Starting new_bool_8 with 300s (1) cores
% 85.27/17.73  # Starting new_ho_11 with 300s (1) cores
% 85.27/17.73  # No SInE strategy applied
% 85.27/17.73  # Search class: HGHSM-SMLM33-DHSFFSBC
% 85.27/17.73  # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 85.27/17.73  # Scheduled 6 strats onto 1 cores with 288 seconds (288 total)
% 85.27/17.73  # Starting new_ho_10 with 87s (1) cores
% 85.27/17.73  # Preprocessing time       : 0.088 s
% 85.27/17.73  # Presaturation interreduction done
% 85.27/17.73  
% 85.27/17.73  # Proof found!
% 85.27/17.73  # SZS status Theorem
% 85.27/17.73  # SZS output start CNFRefutation
% See solution above
% 85.27/17.73  # Parsed axioms                        : 213
% 85.27/17.73  # Removed by relevancy pruning/SinE    : 0
% 85.27/17.73  # Initial clauses                      : 469172
% 85.27/17.73  # Removed in clause preprocessing      : 464072
% 85.27/17.73  # Initial clauses in saturation        : 5100
% 85.27/17.73  # Processed clauses                    : 9692
% 85.27/17.73  # ...of these trivial                  : 444
% 85.27/17.73  # ...subsumed                          : 4600
% 85.27/17.73  # ...remaining for further processing  : 4647
% 85.27/17.73  # Other redundant clauses eliminated   : 163
% 85.27/17.73  # Clauses deleted for lack of memory   : 0
% 85.27/17.73  # Backward-subsumed                    : 207
% 85.27/17.73  # Backward-rewritten                   : 121
% 85.27/17.73  # Generated clauses                    : 97344
% 85.27/17.73  # ...of the previous two non-redundant : 95136
% 85.27/17.73  # ...aggressively subsumed             : 0
% 85.27/17.73  # Contextual simplify-reflections      : 358
% 85.27/17.73  # Paramodulations                      : 97165
% 85.27/17.73  # Factorizations                       : 0
% 85.27/17.73  # NegExts                              : 0
% 85.27/17.73  # Equation resolutions                 : 163
% 85.27/17.73  # Disequality decompositions           : 0
% 85.27/17.73  # Total rewrite steps                  : 8725
% 85.27/17.73  # ...of those cached                   : 7762
% 85.27/17.73  # Propositional unsat checks           : 0
% 85.27/17.73  #    Propositional check models        : 0
% 85.27/17.73  #    Propositional check unsatisfiable : 0
% 85.27/17.73  #    Propositional clauses             : 0
% 85.27/17.73  #    Propositional clauses after purity: 0
% 85.27/17.73  #    Propositional unsat core size     : 0
% 85.27/17.73  #    Propositional preprocessing time  : 0.000
% 85.27/17.73  #    Propositional encoding time       : 0.000
% 85.27/17.73  #    Propositional solver time         : 0.000
% 85.27/17.73  #    Success case prop preproc time    : 0.000
% 85.27/17.73  #    Success case prop encoding time   : 0.000
% 85.27/17.73  #    Success case prop solver time     : 0.000
% 85.27/17.73  # Current number of processed clauses  : 2994
% 85.27/17.73  #    Positive orientable unit clauses  : 259
% 85.27/17.73  #    Positive unorientable unit clauses: 28
% 85.27/17.73  #    Negative unit clauses             : 227
% 85.27/17.73  #    Non-unit-clauses                  : 2480
% 85.27/17.73  # Current number of unprocessed clauses: 91649
% 85.27/17.73  # ...number of literals in the above   : 393358
% 85.27/17.73  # Current number of archived formulas  : 0
% 85.27/17.73  # Current number of archived clauses   : 1595
% 85.27/17.73  # Clause-clause subsumption calls (NU) : 2322086
% 85.27/17.73  # Rec. Clause-clause subsumption calls : 829172
% 85.27/17.73  # Non-unit clause-clause subsumptions  : 2376
% 85.27/17.73  # Unit Clause-clause subsumption calls : 76113
% 85.27/17.73  # Rewrite failures with RHS unbound    : 0
% 85.27/17.73  # BW rewrite match attempts            : 223
% 85.27/17.73  # BW rewrite match successes           : 54
% 85.27/17.73  # Condensation attempts                : 9909
% 85.27/17.73  # Condensation successes               : 316
% 85.27/17.73  # Termbank termtop insertions          : 22073712
% 85.27/17.73  # Search garbage collected termcells   : 2014708
% 85.27/17.73  
% 85.27/17.73  # -------------------------------------------------
% 85.27/17.73  # User time                : 15.166 s
% 85.27/17.73  # System time              : 1.228 s
% 85.27/17.73  # Total time               : 16.394 s
% 85.27/17.73  # Maximum resident set size: 1256160 pages
% 85.27/17.73  
% 85.27/17.73  # -------------------------------------------------
% 85.27/17.73  # User time                : 15.172 s
% 85.27/17.73  # System time              : 1.335 s
% 85.27/17.73  # Total time               : 16.507 s
% 85.27/17.73  # Maximum resident set size: 2192 pages
% 85.27/17.73  % E---3.1 exiting
% 85.27/17.74  % E exiting
%------------------------------------------------------------------------------