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Zipperpin---2.1.9999.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV102^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qSqCIyXTh8 true

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Oct  2 04:57:11 PM UTC 2025

% Result   : Theorem 65.78s 8.93s
% Output   : Refutation 65.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   78 (   4 unt;   0 typ;   0 def)
%            Number of atoms       :  523 ( 219 equ;   0 cnn)
%            Maximal formula atoms :   24 (   6 avg)
%            Number of connectives : 1092 (  81   ~;  65   |; 111   &; 626   @)
%                                         (   0 <=>;  88  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   73 (  73   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  12 usr;   3 con; 0-2 aty)
%                                         (  64  !!;  57  ??;   0 @@+;   0 @@-)
%            Number of variables   :  332 ( 201   ^; 113   !;  18   ?; 332   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf('#sk16_type',type,
    '#sk16': ( a > a ) > a ).

thf('#_fresh_sk42_type',type,
    '#_fresh_sk42': ( a > a ) > a > a ).

thf('#sk2_type',type,
    '#sk2': a > $o ).

thf('#sk1_type',type,
    '#sk1': a > $o ).

thf('#sk10_type',type,
    '#sk10': ( a > a ) > a ).

thf('#sk5_type',type,
    '#sk5': a > a ).

thf('#sk20_type',type,
    '#sk20': a > a ).

thf('#l_lift27176_type',type,
    '#l_lift27176': ( a > a ) > a > a ).

thf('#sk19_type',type,
    '#sk19': a > a ).

thf('#sk4_type',type,
    '#sk4': a > a ).

thf('#sk3_type',type,
    '#sk3': a > $o ).

thf('#_fresh_sk61_type',type,
    '#_fresh_sk61': ( a > a ) > a > a ).

thf(cEQP_1C_pme,conjecture,
    ! [Xx: a > $o,Xy: a > $o,Xz: a > $o] :
      ( ( ? [Xs: a > a] :
            ( ! [Xy0: a] :
                ( ( Xy @ Xy0 )
               => ? [Xy_52: a] :
                    ( ( ^ [Xx0: a] :
                          ( ( Xx @ Xx0 )
                          & ( Xy0
                            = ( Xs @ Xx0 ) ) ) )
                    = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
                      @ Xy_52 ) ) )
            & ! [Xx0: a] :
                ( ( Xx @ Xx0 )
               => ( Xy @ ( Xs @ Xx0 ) ) ) )
        & ? [Xs: a > a] :
            ( ! [Xy0: a] :
                ( ( Xz @ Xy0 )
               => ? [Xy_53: a] :
                    ( ( ^ [Xx0: a] :
                          ( ( Xy @ Xx0 )
                          & ( Xy0
                            = ( Xs @ Xx0 ) ) ) )
                    = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
                      @ Xy_53 ) ) )
            & ! [Xx0: a] :
                ( ( Xy @ Xx0 )
               => ( Xz @ ( Xs @ Xx0 ) ) ) ) )
     => ? [Xs: a > a] :
          ( ! [Xy0: a] :
              ( ( Xz @ Xy0 )
             => ? [Xy_55: a] :
                  ( ( ^ [Xx0: a] :
                        ( ( Xx @ Xx0 )
                        & ( Xy0
                          = ( Xs @ Xx0 ) ) ) )
                  = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
                    @ Xy_55 ) ) )
          & ! [Xx0: a] :
              ( ( Xx @ Xx0 )
             => ( Xz @ ( Xs @ Xx0 ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: a > $o,X6: a > $o,X8: a > $o] :
      ( ( ? [X18: a > a] :
            ( ! [X24: a] :
                ( ( X6 @ X24 )
               => ( X8 @ ( X18 @ X24 ) ) )
            & ! [X20: a] :
                ( ( X8 @ X20 )
               => ? [X22: a] :
                    ( ( ^ [V_3: a] :
                          ( ( X20
                            = ( X18 @ V_3 ) )
                          & ( X6 @ V_3 ) ) )
                    = ( ^ [V_4: a] : ( X22 = V_4 ) ) ) ) )
        & ? [X10: a > a] :
            ( ! [X16: a] :
                ( ( X4 @ X16 )
               => ( X6 @ ( X10 @ X16 ) ) )
            & ! [X12: a] :
                ( ( X6 @ X12 )
               => ? [X14: a] :
                    ( ( ^ [V_1: a] :
                          ( ( X12
                            = ( X10 @ V_1 ) )
                          & ( X4 @ V_1 ) ) )
                    = ( ^ [V_2: a] : ( X14 = V_2 ) ) ) ) ) )
     => ? [X26: a > a] :
          ( ! [X32: a] :
              ( ( X4 @ X32 )
             => ( X8 @ ( X26 @ X32 ) ) )
          & ! [X28: a] :
              ( ( X8 @ X28 )
             => ? [X30: a] :
                  ( ( ^ [V_5: a] :
                        ( ( X28
                          = ( X26 @ V_5 ) )
                        & ( X4 @ V_5 ) ) )
                  = ( ^ [V_6: a] : ( X30 = V_6 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: a > $o,X6: a > $o,X8: a > $o] :
        ( ( ? [X18: a > a] :
              ( ! [X24: a] :
                  ( ( X6 @ X24 )
                 => ( X8 @ ( X18 @ X24 ) ) )
              & ! [X20: a] :
                  ( ( X8 @ X20 )
                 => ? [X22: a] :
                      ( ( ^ [V_3: a] :
                            ( ( X20
                              = ( X18 @ V_3 ) )
                            & ( X6 @ V_3 ) ) )
                      = ( ^ [V_4: a] : ( X22 = V_4 ) ) ) ) )
          & ? [X10: a > a] :
              ( ! [X16: a] :
                  ( ( X4 @ X16 )
                 => ( X6 @ ( X10 @ X16 ) ) )
              & ! [X12: a] :
                  ( ( X6 @ X12 )
                 => ? [X14: a] :
                      ( ( ^ [V_1: a] :
                            ( ( X12
                              = ( X10 @ V_1 ) )
                            & ( X4 @ V_1 ) ) )
                      = ( ^ [V_2: a] : ( X14 = V_2 ) ) ) ) ) )
       => ? [X26: a > a] :
            ( ! [X32: a] :
                ( ( X4 @ X32 )
               => ( X8 @ ( X26 @ X32 ) ) )
            & ! [X28: a] :
                ( ( X8 @ X28 )
               => ? [X30: a] :
                    ( ( ^ [V_5: a] :
                          ( ( X28
                            = ( X26 @ V_5 ) )
                          & ( X4 @ V_5 ) ) )
                    = ( ^ [V_6: a] : ( X30 = V_6 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: a > $o] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( !!
              @ ^ [Y2: a > $o] :
                  ( ( ( ??
                      @ ^ [Y3: a > a] :
                          ( ( !!
                            @ ^ [Y4: a] :
                                ( ( Y1 @ Y4 )
                               => ( Y2 @ ( Y3 @ Y4 ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( ( Y2 @ Y4 )
                               => ( ??
                                  @ ^ [Y5: a] :
                                      ( ( ^ [Y6: a] :
                                            ( ( Y4
                                              = ( Y3 @ Y6 ) )
                                            & ( Y1 @ Y6 ) ) )
                                      = ( ^ [Y6: a] : ( Y5 = Y6 ) ) ) ) ) ) ) )
                    & ( ??
                      @ ^ [Y3: a > a] :
                          ( ( !!
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y4 )
                               => ( Y1 @ ( Y3 @ Y4 ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( ( Y1 @ Y4 )
                               => ( ??
                                  @ ^ [Y5: a] :
                                      ( ( ^ [Y6: a] :
                                            ( ( Y4
                                              = ( Y3 @ Y6 ) )
                                            & ( Y0 @ Y6 ) ) )
                                      = ( ^ [Y6: a] : ( Y5 = Y6 ) ) ) ) ) ) ) ) )
                 => ( ??
                    @ ^ [Y3: a > a] :
                        ( ( !!
                          @ ^ [Y4: a] :
                              ( ( Y0 @ Y4 )
                             => ( Y2 @ ( Y3 @ Y4 ) ) ) )
                        & ( !!
                          @ ^ [Y4: a] :
                              ( ( Y2 @ Y4 )
                             => ( ??
                                @ ^ [Y5: a] :
                                    ( ( ^ [Y6: a] :
                                          ( ( Y4
                                            = ( Y3 @ Y6 ) )
                                          & ( Y0 @ Y6 ) ) )
                                    = ( ^ [Y6: a] : ( Y5 = Y6 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ~ ( !!
      @ ^ [Y0: a > $o] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( !!
              @ ^ [Y2: a > $o] :
                  ( ( ( ??
                      @ ^ [Y3: a > a] :
                          ( ( !!
                            @ ^ [Y4: a] :
                                ( ( Y1 @ Y4 )
                               => ( Y2 @ ( Y3 @ Y4 ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( ( Y2 @ Y4 )
                               => ( ??
                                  @ ^ [Y5: a] :
                                      ( ( ^ [Y6: a] :
                                            ( ( Y4
                                              = ( Y3 @ Y6 ) )
                                            & ( Y1 @ Y6 ) ) )
                                      = ( a = Y5 ) ) ) ) ) ) )
                    & ( ??
                      @ ^ [Y3: a > a] :
                          ( ( !!
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y4 )
                               => ( Y1 @ ( Y3 @ Y4 ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( ( Y1 @ Y4 )
                               => ( ??
                                  @ ^ [Y5: a] :
                                      ( ( ^ [Y6: a] :
                                            ( ( Y4
                                              = ( Y3 @ Y6 ) )
                                            & ( Y0 @ Y6 ) ) )
                                      = ( a = Y5 ) ) ) ) ) ) ) )
                 => ( ??
                    @ ^ [Y3: a > a] :
                        ( ( !!
                          @ ^ [Y4: a] :
                              ( ( Y0 @ Y4 )
                             => ( Y2 @ ( Y3 @ Y4 ) ) ) )
                        & ( !!
                          @ ^ [Y4: a] :
                              ( ( Y2 @ Y4 )
                             => ( ??
                                @ ^ [Y5: a] :
                                    ( ( ^ [Y6: a] :
                                          ( ( Y4
                                            = ( Y3 @ Y6 ) )
                                          & ( Y0 @ Y6 ) ) )
                                    = ( a = Y5 ) ) ) ) ) ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: a > $o] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( ( ??
                  @ ^ [Y2: a > a] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( Y0 @ Y3 )
                           => ( Y1 @ ( Y2 @ Y3 ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( ( Y1 @ Y3 )
                           => ( ??
                              @ ^ [Y4: a] :
                                  ( ( ^ [Y5: a] :
                                        ( ( Y3
                                          = ( Y2 @ Y5 ) )
                                        & ( Y0 @ Y5 ) ) )
                                  = ( a = Y4 ) ) ) ) ) ) )
                & ( ??
                  @ ^ [Y2: a > a] :
                      ( ( !!
                        @ ^ [Y3: a] :
                            ( ( '#sk1' @ Y3 )
                           => ( Y0 @ ( Y2 @ Y3 ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( ( Y0 @ Y3 )
                           => ( ??
                              @ ^ [Y4: a] :
                                  ( ( ^ [Y5: a] :
                                        ( ( Y3
                                          = ( Y2 @ Y5 ) )
                                        & ( '#sk1' @ Y5 ) ) )
                                  = ( a = Y4 ) ) ) ) ) ) ) )
             => ( ??
                @ ^ [Y2: a > a] :
                    ( ( !!
                      @ ^ [Y3: a] :
                          ( ( '#sk1' @ Y3 )
                         => ( Y1 @ ( Y2 @ Y3 ) ) ) )
                    & ( !!
                      @ ^ [Y3: a] :
                          ( ( Y1 @ Y3 )
                         => ( ??
                            @ ^ [Y4: a] :
                                ( ( ^ [Y5: a] :
                                      ( ( Y3
                                        = ( Y2 @ Y5 ) )
                                      & ( '#sk1' @ Y5 ) ) )
                                = ( a = Y4 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ~ ( !!
      @ ^ [Y0: a > $o] :
          ( ( ( ??
              @ ^ [Y1: a > a] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk2' @ Y2 )
                       => ( Y0 @ ( Y1 @ Y2 ) ) ) )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( ( Y0 @ Y2 )
                       => ( ??
                          @ ^ [Y3: a] :
                              ( ( ^ [Y4: a] :
                                    ( ( Y2
                                      = ( Y1 @ Y4 ) )
                                    & ( '#sk2' @ Y4 ) ) )
                              = ( a = Y3 ) ) ) ) ) ) )
            & ( ??
              @ ^ [Y1: a > a] :
                  ( ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk1' @ Y2 )
                       => ( '#sk2' @ ( Y1 @ Y2 ) ) ) )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( ( '#sk2' @ Y2 )
                       => ( ??
                          @ ^ [Y3: a] :
                              ( ( ^ [Y4: a] :
                                    ( ( Y2
                                      = ( Y1 @ Y4 ) )
                                    & ( '#sk1' @ Y4 ) ) )
                              = ( a = Y3 ) ) ) ) ) ) ) )
         => ( ??
            @ ^ [Y1: a > a] :
                ( ( !!
                  @ ^ [Y2: a] :
                      ( ( '#sk1' @ Y2 )
                     => ( Y0 @ ( Y1 @ Y2 ) ) ) )
                & ( !!
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y2 )
                     => ( ??
                        @ ^ [Y3: a] :
                            ( ( ^ [Y4: a] :
                                  ( ( Y2
                                    = ( Y1 @ Y4 ) )
                                  & ( '#sk1' @ Y4 ) ) )
                            = ( a = Y3 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ~ ( ( ( ??
          @ ^ [Y0: a > a] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y1 )
                   => ( '#sk3' @ ( Y0 @ Y1 ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk3' @ Y1 )
                   => ( ??
                      @ ^ [Y2: a] :
                          ( ( ^ [Y3: a] :
                                ( ( Y1
                                  = ( Y0 @ Y3 ) )
                                & ( '#sk2' @ Y3 ) ) )
                          = ( a = Y2 ) ) ) ) ) ) )
        & ( ??
          @ ^ [Y0: a > a] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk1' @ Y1 )
                   => ( '#sk2' @ ( Y0 @ Y1 ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk2' @ Y1 )
                   => ( ??
                      @ ^ [Y2: a] :
                          ( ( ^ [Y3: a] :
                                ( ( Y1
                                  = ( Y0 @ Y3 ) )
                                & ( '#sk1' @ Y3 ) ) )
                          = ( a = Y2 ) ) ) ) ) ) ) )
     => ( ??
        @ ^ [Y0: a > a] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y1 )
                 => ( '#sk3' @ ( Y0 @ Y1 ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk3' @ Y1 )
                 => ( ??
                    @ ^ [Y2: a] :
                        ( ( ^ [Y3: a] :
                              ( ( Y1
                                = ( Y0 @ Y3 ) )
                              & ( '#sk1' @ Y3 ) ) )
                        = ( a = Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl6,plain,
    ~ ( ??
      @ ^ [Y0: a > a] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y1 )
               => ( '#sk3' @ ( Y0 @ Y1 ) ) ) )
          & ( !!
            @ ^ [Y1: a] :
                ( ( '#sk3' @ Y1 )
               => ( ??
                  @ ^ [Y2: a] :
                      ( ( ^ [Y3: a] :
                            ( ( Y1
                              = ( Y0 @ Y3 ) )
                            & ( '#sk1' @ Y3 ) ) )
                      = ( a = Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl9,plain,
    ! [X2: a > a] :
      ~ ( ( !!
          @ ^ [Y0: a] :
              ( ( '#sk1' @ Y0 )
             => ( '#sk3' @ ( X2 @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( ( '#sk3' @ Y0 )
             => ( ??
                @ ^ [Y1: a] :
                    ( ( ^ [Y2: a] :
                          ( ( Y0
                            = ( X2 @ Y2 ) )
                          & ( '#sk1' @ Y2 ) ) )
                    = ( a = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl12,plain,
    ! [X2: a > a] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( '#sk1' @ Y0 )
             => ( '#sk3' @ ( X2 @ Y0 ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( '#sk3' @ Y0 )
             => ( ??
                @ ^ [Y1: a] :
                    ( ( ^ [Y2: a] :
                          ( ( Y0
                            = ( X2 @ Y2 ) )
                          & ( '#sk1' @ Y2 ) ) )
                    = ( a = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl17,plain,
    ! [X2: a > a] :
      ( ~ ( ( '#sk1' @ ( '#sk10' @ X2 ) )
         => ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( '#sk3' @ Y0 )
             => ( ??
                @ ^ [Y1: a] :
                    ( ( ^ [Y2: a] :
                          ( ( Y0
                            = ( X2 @ Y2 ) )
                          & ( '#sk1' @ Y2 ) ) )
                    = ( a = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl22,plain,
    ! [X2: a > a] :
      ( ( '#sk1' @ ( '#sk10' @ X2 ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( '#sk3' @ Y0 )
             => ( ??
                @ ^ [Y1: a] :
                    ( ( ^ [Y2: a] :
                          ( ( Y0
                            = ( X2 @ Y2 ) )
                          & ( '#sk1' @ Y2 ) ) )
                    = ( a = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl28,plain,
    ! [X2: a > a] :
      ( ~ ( ( '#sk3' @ ( '#sk16' @ X2 ) )
         => ( ??
            @ ^ [Y0: a] :
                ( ( ^ [Y1: a] :
                      ( ( ( '#sk16' @ X2 )
                        = ( X2 @ Y1 ) )
                      & ( '#sk1' @ Y1 ) ) )
                = ( a = Y0 ) ) ) )
      | ( '#sk1' @ ( '#sk10' @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl32,plain,
    ! [X2: a > a] :
      ( ( '#sk3' @ ( '#sk16' @ X2 ) )
      | ( '#sk1' @ ( '#sk10' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl5,plain,
    ( ( ??
      @ ^ [Y0: a > a] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y1 )
               => ( '#sk3' @ ( Y0 @ Y1 ) ) ) )
          & ( !!
            @ ^ [Y1: a] :
                ( ( '#sk3' @ Y1 )
               => ( ??
                  @ ^ [Y2: a] :
                      ( ( ^ [Y3: a] :
                            ( ( Y1
                              = ( Y0 @ Y3 ) )
                            & ( '#sk2' @ Y3 ) ) )
                      = ( a = Y2 ) ) ) ) ) ) )
    & ( ??
      @ ^ [Y0: a > a] :
          ( ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y1 )
               => ( '#sk2' @ ( Y0 @ Y1 ) ) ) )
          & ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y1 )
               => ( ??
                  @ ^ [Y2: a] :
                      ( ( ^ [Y3: a] :
                            ( ( Y1
                              = ( Y0 @ Y3 ) )
                            & ( '#sk1' @ Y3 ) ) )
                      = ( a = Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl7,plain,
    ( ??
    @ ^ [Y0: a > a] :
        ( ( !!
          @ ^ [Y1: a] :
              ( ( '#sk2' @ Y1 )
             => ( '#sk3' @ ( Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y1: a] :
              ( ( '#sk3' @ Y1 )
             => ( ??
                @ ^ [Y2: a] :
                    ( ( ^ [Y3: a] :
                          ( ( Y1
                            = ( Y0 @ Y3 ) )
                          & ( '#sk2' @ Y3 ) ) )
                    = ( a = Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl10,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( ( '#sk2' @ Y0 )
         => ( '#sk3' @ ( '#sk4' @ Y0 ) ) ) )
    & ( !!
      @ ^ [Y0: a] :
          ( ( '#sk3' @ Y0 )
         => ( ??
            @ ^ [Y1: a] :
                ( ( ^ [Y2: a] :
                      ( ( Y0
                        = ( '#sk4' @ Y2 ) )
                      & ( '#sk2' @ Y2 ) ) )
                = ( a = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl13,plain,
    ( !!
    @ ^ [Y0: a] :
        ( ( '#sk2' @ Y0 )
       => ( '#sk3' @ ( '#sk4' @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl18,plain,
    ! [X2: a] :
      ( ( '#sk2' @ X2 )
     => ( '#sk3' @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl24,plain,
    ! [X2: a] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#sk3' @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl23,plain,
    ! [X2: a > a] :
      ( ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( '#sk3' @ Y0 )
             => ( ??
                @ ^ [Y1: a] :
                    ( ( ^ [Y2: a] :
                          ( ( Y0
                            = ( X2 @ Y2 ) )
                          & ( '#sk1' @ Y2 ) ) )
                    = ( a = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl29,plain,
    ! [X2: a > a] :
      ( ~ ( ( '#sk3' @ ( '#sk16' @ X2 ) )
         => ( ??
            @ ^ [Y0: a] :
                ( ( ^ [Y1: a] :
                      ( ( ( '#sk16' @ X2 )
                        = ( X2 @ Y1 ) )
                      & ( '#sk1' @ Y1 ) ) )
                = ( a = Y0 ) ) ) )
      | ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl34,plain,
    ! [X2: a > a] :
      ( ( '#sk3' @ ( '#sk16' @ X2 ) )
      | ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl53,plain,
    ! [X0: a > a] :
      ( ~ ( '#sk2'
          @ ( X0
            @ ( '#sk10'
              @ ^ [Y0: a] : ( '#sk4' @ ( X0 @ Y0 ) ) ) ) )
      | ( '#sk3'
        @ ( '#sk16'
          @ ^ [Y0: a] :
              ( '#sk4'
              @ ( ^ [Y1: a] : ( X0 @ Y1 )
                @ Y0 ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl34]) ).

thf(zip_derived_cl54,plain,
    ! [X0: a > a] :
      ( ~ ( '#sk2'
          @ ( X0
            @ ( '#sk10'
              @ ^ [Y0: a] : ( '#sk4' @ ( X0 @ Y0 ) ) ) ) )
      | ( '#sk3'
        @ ( '#sk16'
          @ ^ [Y0: a] : ( '#sk4' @ ( X0 @ Y0 ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl54_001,plain,
    ! [X0: a > a] :
      ( ~ ( '#sk2'
          @ ( X0
            @ ( '#sk10'
              @ ^ [Y0: a] : ( '#sk4' @ ( X0 @ Y0 ) ) ) ) )
      | ( '#sk3'
        @ ( '#sk16'
          @ ^ [Y0: a] : ( '#sk4' @ ( X0 @ Y0 ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl23505,plain,
    ! [X0: a > a,X1: a] :
      ( ( '#l_lift27176' @ X0 @ X1 )
      = ( '#sk4' @ ( X0 @ X1 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl23505_002,plain,
    ! [X0: a > a,X1: a] :
      ( ( '#l_lift27176' @ X0 @ X1 )
      = ( '#sk4' @ ( X0 @ X1 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl23506,plain,
    ! [X0: a > a] :
      ( ~ ( '#sk2' @ ( X0 @ ( '#sk10' @ ( '#l_lift27176' @ X0 ) ) ) )
      | ( '#sk3' @ ( '#sk16' @ ( '#l_lift27176' @ X0 ) ) ) ),
    inference(lambda_lifting,[status(thm)],[zip_derived_cl54,zip_derived_cl23505,zip_derived_cl23505]) ).

thf(zip_derived_cl14,plain,
    ( !!
    @ ^ [Y0: a] :
        ( ( '#sk3' @ Y0 )
       => ( ??
          @ ^ [Y1: a] :
              ( ( ^ [Y2: a] :
                    ( ( Y0
                      = ( '#sk4' @ Y2 ) )
                    & ( '#sk2' @ Y2 ) ) )
              = ( a = Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a] :
      ( ( '#sk3' @ X2 )
     => ( ??
        @ ^ [Y0: a] :
            ( ( ^ [Y1: a] :
                  ( ( X2
                    = ( '#sk4' @ Y1 ) )
                  & ( '#sk2' @ Y1 ) ) )
            = ( a = Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl25,plain,
    ! [X2: a] :
      ( ~ ( '#sk3' @ X2 )
      | ( ??
        @ ^ [Y0: a] :
            ( ( ^ [Y1: a] :
                  ( ( X2
                    = ( '#sk4' @ Y1 ) )
                  & ( '#sk2' @ Y1 ) ) )
            = ( a = Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl30,plain,
    ! [X2: a] :
      ( ( ( ^ [Y0: a] :
              ( ( X2
                = ( '#sk4' @ Y0 ) )
              & ( '#sk2' @ Y0 ) ) )
        = ( a
          = ( '#sk19' @ X2 ) ) )
      | ~ ( '#sk3' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl36,plain,
    ! [X2: a] :
      ( ( ( ^ [Y0: a] :
              ( ( X2
                = ( '#sk4' @ Y0 ) )
              & ( '#sk2' @ Y0 ) ) )
        = ( a
          = ( '#sk19' @ X2 ) ) )
      | ~ ( '#sk3' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl37,plain,
    ! [X2: a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( X2
                = ( '#sk4' @ Y0 ) )
              & ( '#sk2' @ Y0 ) )
          @ X4 )
        = ( ( '#sk19' @ X2 )
          = X4 ) )
      | ~ ( '#sk3' @ X2 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl38,plain,
    ! [X2: a,X4: a] :
      ( ( ( ( X2
            = ( '#sk4' @ X4 ) )
          & ( '#sk2' @ X4 ) )
        = ( ( '#sk19' @ X2 )
          = X4 ) )
      | ~ ( '#sk3' @ X2 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl87,plain,
    ! [X2: a,X4: a] :
      ( ~ ( ( X2
            = ( '#sk4' @ X4 ) )
          & ( '#sk2' @ X4 ) )
      | ( ( '#sk19' @ X2 )
        = X4 )
      | ~ ( '#sk3' @ X2 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl90,plain,
    ! [X2: a,X4: a] :
      ( ~ ( ( X2
            = ( '#sk4' @ X4 ) )
          & ( '#sk2' @ X4 ) )
      | ( ( '#sk19' @ X2 )
        = X4 )
      | ~ ( '#sk3' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl121,plain,
    ! [X2: a,X4: a] :
      ( ( X2
       != ( '#sk4' @ X4 ) )
      | ~ ( '#sk2' @ X4 )
      | ~ ( '#sk3' @ X2 )
      | ( ( '#sk19' @ X2 )
        = X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl122,plain,
    ! [X2: a,X4: a] :
      ( ( X2
       != ( '#sk4' @ X4 ) )
      | ~ ( '#sk2' @ X4 )
      | ~ ( '#sk3' @ X2 )
      | ( ( '#sk19' @ X2 )
        = X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl121]) ).

thf(zip_derived_cl123,plain,
    ! [X4: a] :
      ( ( ( '#sk19' @ ( '#sk4' @ X4 ) )
        = X4 )
      | ~ ( '#sk3' @ ( '#sk4' @ X4 ) )
      | ~ ( '#sk2' @ X4 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl122]) ).

thf(zip_derived_cl24_003,plain,
    ! [X2: a] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#sk3' @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl124,plain,
    ! [X4: a] :
      ( ~ ( '#sk2' @ X4 )
      | ( ( '#sk19' @ ( '#sk4' @ X4 ) )
        = X4 ) ),
    inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl24]) ).

thf(zip_derived_cl38_004,plain,
    ! [X2: a,X4: a] :
      ( ( ( ( X2
            = ( '#sk4' @ X4 ) )
          & ( '#sk2' @ X4 ) )
        = ( ( '#sk19' @ X2 )
          = X4 ) )
      | ~ ( '#sk3' @ X2 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl127,plain,
    ! [X0: a,X1: a] :
      ( ( ( ( ( '#sk4' @ X0 )
            = ( '#sk4' @ X1 ) )
          & ( '#sk2' @ X1 ) )
        = ( X0 = X1 ) )
      | ~ ( '#sk2' @ X0 )
      | ~ ( '#sk3' @ ( '#sk4' @ X0 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl124,zip_derived_cl38]) ).

thf(zip_derived_cl24_005,plain,
    ! [X2: a] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#sk3' @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl2176,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk2' @ X0 )
      | ( ( ( ( '#sk4' @ X0 )
            = ( '#sk4' @ X1 ) )
          & ( '#sk2' @ X1 ) )
        = ( X0 = X1 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl127,zip_derived_cl24]) ).

thf(zip_derived_cl2189,plain,
    ! [X0: a,X1: a] :
      ( ~ ( ( ( '#sk4' @ X0 )
            = ( '#sk4' @ X1 ) )
          & ( '#sk2' @ X1 ) )
      | ( X0 = X1 )
      | ~ ( '#sk2' @ X0 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2176]) ).

thf(zip_derived_cl2194,plain,
    ! [X0: a,X1: a] :
      ( ~ ( ( ( '#sk4' @ X0 )
            = ( '#sk4' @ X1 ) )
          & ( '#sk2' @ X1 ) )
      | ( X0 = X1 )
      | ~ ( '#sk2' @ X0 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl2189]) ).

thf(zip_derived_cl2280,plain,
    ! [X0: a,X1: a] :
      ( ( ( '#sk4' @ X0 )
       != ( '#sk4' @ X1 ) )
      | ~ ( '#sk2' @ X1 )
      | ~ ( '#sk2' @ X0 )
      | ( X0 = X1 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2194]) ).

thf(zip_derived_cl2281,plain,
    ! [X0: a,X1: a] :
      ( ( ( '#sk4' @ X0 )
       != ( '#sk4' @ X1 ) )
      | ~ ( '#sk2' @ X1 )
      | ~ ( '#sk2' @ X0 )
      | ( X0 = X1 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl2280]) ).

thf(zip_derived_cl8,plain,
    ( ??
    @ ^ [Y0: a > a] :
        ( ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y1 )
             => ( '#sk2' @ ( Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y1: a] :
              ( ( '#sk2' @ Y1 )
             => ( ??
                @ ^ [Y2: a] :
                    ( ( ^ [Y3: a] :
                          ( ( Y1
                            = ( Y0 @ Y3 ) )
                          & ( '#sk1' @ Y3 ) ) )
                    = ( a = Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl11,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( ( '#sk1' @ Y0 )
         => ( '#sk2' @ ( '#sk5' @ Y0 ) ) ) )
    & ( !!
      @ ^ [Y0: a] :
          ( ( '#sk2' @ Y0 )
         => ( ??
            @ ^ [Y1: a] :
                ( ( ^ [Y2: a] :
                      ( ( Y0
                        = ( '#sk5' @ Y2 ) )
                      & ( '#sk1' @ Y2 ) ) )
                = ( a = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl15,plain,
    ( !!
    @ ^ [Y0: a] :
        ( ( '#sk1' @ Y0 )
       => ( '#sk2' @ ( '#sk5' @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl20,plain,
    ! [X2: a] :
      ( ( '#sk1' @ X2 )
     => ( '#sk2' @ ( '#sk5' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl26,plain,
    ! [X2: a] :
      ( ~ ( '#sk1' @ X2 )
      | ( '#sk2' @ ( '#sk5' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl16,plain,
    ( !!
    @ ^ [Y0: a] :
        ( ( '#sk2' @ Y0 )
       => ( ??
          @ ^ [Y1: a] :
              ( ( ^ [Y2: a] :
                    ( ( Y0
                      = ( '#sk5' @ Y2 ) )
                    & ( '#sk1' @ Y2 ) ) )
              = ( a = Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl21,plain,
    ! [X2: a] :
      ( ( '#sk2' @ X2 )
     => ( ??
        @ ^ [Y0: a] :
            ( ( ^ [Y1: a] :
                  ( ( X2
                    = ( '#sk5' @ Y1 ) )
                  & ( '#sk1' @ Y1 ) ) )
            = ( a = Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl27,plain,
    ! [X2: a] :
      ( ~ ( '#sk2' @ X2 )
      | ( ??
        @ ^ [Y0: a] :
            ( ( ^ [Y1: a] :
                  ( ( X2
                    = ( '#sk5' @ Y1 ) )
                  & ( '#sk1' @ Y1 ) ) )
            = ( a = Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl31,plain,
    ! [X2: a] :
      ( ( ( ^ [Y0: a] :
              ( ( X2
                = ( '#sk5' @ Y0 ) )
              & ( '#sk1' @ Y0 ) ) )
        = ( a
          = ( '#sk20' @ X2 ) ) )
      | ~ ( '#sk2' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl39,plain,
    ! [X2: a] :
      ( ( ( ^ [Y0: a] :
              ( ( X2
                = ( '#sk5' @ Y0 ) )
              & ( '#sk1' @ Y0 ) ) )
        = ( a
          = ( '#sk20' @ X2 ) ) )
      | ~ ( '#sk2' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl40,plain,
    ! [X2: a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( X2
                = ( '#sk5' @ Y0 ) )
              & ( '#sk1' @ Y0 ) )
          @ X4 )
        = ( ( '#sk20' @ X2 )
          = X4 ) )
      | ~ ( '#sk2' @ X2 ) ),
    inference(arg_cong_simpl,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl41,plain,
    ! [X2: a,X4: a] :
      ( ( ( ( X2
            = ( '#sk5' @ X4 ) )
          & ( '#sk1' @ X4 ) )
        = ( ( '#sk20' @ X2 )
          = X4 ) )
      | ~ ( '#sk2' @ X2 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl23505_006,plain,
    ! [X0: a > a,X1: a] :
      ( ( '#l_lift27176' @ X0 @ X1 )
      = ( '#sk4' @ ( X0 @ X1 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl24_007,plain,
    ! [X2: a] :
      ( ~ ( '#sk2' @ X2 )
      | ( '#sk3' @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl35,plain,
    ! [X2: a > a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ( ^ [Y1: a] :
                    ( ( ( '#sk16' @ X2 )
                      = ( X2 @ Y1 ) )
                    & ( '#sk1' @ Y1 ) ) )
              = ( a = Y0 ) ) )
      | ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl43,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( ( '#sk16' @ X2 )
                = ( X2 @ Y0 ) )
              & ( '#sk1' @ Y0 ) ) )
       != ( a = X4 ) )
      | ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl47,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( ( '#sk16' @ X2 )
                = ( X2 @ Y0 ) )
              & ( '#sk1' @ Y0 ) ) )
       != ( a = X4 ) )
      | ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl48,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( ( '#sk16' @ X2 )
                = ( X2 @ Y0 ) )
              & ( '#sk1' @ Y0 ) )
          @ ( '#_fresh_sk61' @ X2 @ X4 ) )
       != ( X4
          = ( '#_fresh_sk61' @ X2 @ X4 ) ) )
      | ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) ),
    inference(neg_ext_simpl,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl49,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ( ( '#sk16' @ X2 )
            = ( X2 @ ( '#_fresh_sk61' @ X2 @ X4 ) ) )
          & ( '#sk1' @ ( '#_fresh_sk61' @ X2 @ X4 ) ) )
       != ( X4
          = ( '#_fresh_sk61' @ X2 @ X4 ) ) )
      | ~ ( '#sk3' @ ( X2 @ ( '#sk10' @ X2 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl38_008,plain,
    ! [X2: a,X4: a] :
      ( ( ( ( X2
            = ( '#sk4' @ X4 ) )
          & ( '#sk2' @ X4 ) )
        = ( ( '#sk19' @ X2 )
          = X4 ) )
      | ~ ( '#sk3' @ X2 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl33,plain,
    ! [X2: a > a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ( ^ [Y1: a] :
                    ( ( ( '#sk16' @ X2 )
                      = ( X2 @ Y1 ) )
                    & ( '#sk1' @ Y1 ) ) )
              = ( a = Y0 ) ) )
      | ( '#sk1' @ ( '#sk10' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl42,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( ( '#sk16' @ X2 )
                = ( X2 @ Y0 ) )
              & ( '#sk1' @ Y0 ) ) )
       != ( a = X4 ) )
      | ( '#sk1' @ ( '#sk10' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl44,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( ( '#sk16' @ X2 )
                = ( X2 @ Y0 ) )
              & ( '#sk1' @ Y0 ) ) )
       != ( a = X4 ) )
      | ( '#sk1' @ ( '#sk10' @ X2 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl45,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ^ [Y0: a] :
              ( ( ( '#sk16' @ X2 )
                = ( X2 @ Y0 ) )
              & ( '#sk1' @ Y0 ) )
          @ ( '#_fresh_sk42' @ X2 @ X4 ) )
       != ( X4
          = ( '#_fresh_sk42' @ X2 @ X4 ) ) )
      | ( '#sk1' @ ( '#sk10' @ X2 ) ) ),
    inference(neg_ext_simpl,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl46,plain,
    ! [X2: a > a,X4: a] :
      ( ( ( ( ( '#sk16' @ X2 )
            = ( X2 @ ( '#_fresh_sk42' @ X2 @ X4 ) ) )
          & ( '#sk1' @ ( '#_fresh_sk42' @ X2 @ X4 ) ) )
       != ( X4
          = ( '#_fresh_sk42' @ X2 @ X4 ) ) )
      | ( '#sk1' @ ( '#sk10' @ X2 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl23527,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl32,zip_derived_cl23506,zip_derived_cl2281,zip_derived_cl26,zip_derived_cl41,zip_derived_cl23505,zip_derived_cl24,zip_derived_cl49,zip_derived_cl38,zip_derived_cl46]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV102^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.qSqCIyXTh8 true
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Oct  1 15:41:08 EDT 2025
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Running portfolio for 300 s
% 0.12/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  % Number of cores: 8
% 0.12/0.34  % Python version: Python 3.6.8
% 0.19/0.35  % Running in HO mode
% 0.50/0.63  % Total configuration time : 828
% 0.50/0.63  % Estimated wc time : 1656
% 0.50/0.63  % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.72  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.74  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.74  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.56/0.75  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 65.78/8.93  % Solved by lams/20_acsne_simpl.sh.
% 65.78/8.93  % done 1683 iterations in 8.158s
% 65.78/8.93  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 65.78/8.93  % SZS output start Refutation
% See solution above
% 65.78/8.93  
% 65.78/8.93  
% 65.78/8.93  % Terminating...
% 65.78/8.96  % Runner terminated.
% 65.78/8.98  % Zipperpin 1.5 exiting
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