TSTP Solution File: SCT170^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SCT170^2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7DgWDRcgue true

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:27:27 EDT 2023

% Result   : Theorem 88.81s 12.14s
% Output   : Refutation 88.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  205 (  55 unt;  37 typ;   0 def)
%            Number of atoms       :  781 ( 244 equ; 126 cnn)
%            Maximal formula atoms :   29 (   4 avg)
%            Number of connectives : 2702 ( 101   ~;  38   |;  61   &;2198   @)
%                                         (  58 <=>; 103  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   38 (   8 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  189 ( 189   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   43 (  33 usr;  14 con; 0-6 aty)
%                                         ( 143  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  306 (  53   ^; 241   !;   0   ?; 306   :)
%                                         (  12  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(list_A2115238852le_alt_type,type,
    list_A2115238852le_alt: $tType ).

thf(arrow_475358991le_alt_type,type,
    arrow_475358991le_alt: $tType ).

thf(produc1501160679le_alt_type,type,
    produc1501160679le_alt: $tType ).

thf(arrow_1429601828e_indi_type,type,
    arrow_1429601828e_indi: $tType ).

thf(c_type,type,
    c: arrow_475358991le_alt ).

thf(set_Ar577454304le_alt_type,type,
    set_Ar577454304le_alt: list_A2115238852le_alt > arrow_475358991le_alt > $o ).

thf(cons_A228743023le_alt_type,type,
    cons_A228743023le_alt: arrow_475358991le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).

thf(member84363362le_alt_type,type,
    member84363362le_alt: arrow_475358991le_alt > ( arrow_475358991le_alt > $o ) > $o ).

thf(member2052026769e_indi_type,type,
    member2052026769e_indi: arrow_1429601828e_indi > ( arrow_1429601828e_indi > $o ) > $o ).

thf(arrow_823908191le_Lin_type,type,
    arrow_823908191le_Lin: ( produc1501160679le_alt > $o ) > $o ).

thf(p_type,type,
    p: arrow_1429601828e_indi > produc1501160679le_alt > $o ).

thf(distin236324274le_alt_type,type,
    distin236324274le_alt: list_A2115238852le_alt > $o ).

thf(a_type,type,
    a: arrow_475358991le_alt ).

thf('#sk14_type',type,
    '#sk14': list_A2115238852le_alt > arrow_475358991le_alt ).

thf('#sk6_type',type,
    '#sk6': arrow_1429601828e_indi ).

thf(arrow_734252939e_Prof_type,type,
    arrow_734252939e_Prof: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).

thf('#sk15_type',type,
    '#sk15': list_A2115238852le_alt > list_A2115238852le_alt ).

thf(nil_Ar1286194111le_alt_type,type,
    nil_Ar1286194111le_alt: list_A2115238852le_alt ).

thf(produc1347929815le_alt_type,type,
    produc1347929815le_alt: arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt ).

thf(top_to988227749indi_o_type,type,
    top_to988227749indi_o: arrow_1429601828e_indi > $o ).

thf(member526088951_alt_o_type,type,
    member526088951_alt_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).

thf(last_A1217315288le_alt_type,type,
    last_A1217315288le_alt: list_A2115238852le_alt > arrow_475358991le_alt ).

thf(append179082452le_alt_type,type,
    append179082452le_alt: list_A2115238852le_alt > list_A2115238852le_alt > list_A2115238852le_alt ).

thf(member214075476le_alt_type,type,
    member214075476le_alt: produc1501160679le_alt > ( produc1501160679le_alt > $o ) > $o ).

thf(member377231867_alt_o_type,type,
    member377231867_alt_o: ( produc1501160679le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).

thf(pi_Arr1929480907_alt_o_type,type,
    pi_Arr1929480907_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).

thf(butlas274947851le_alt_type,type,
    butlas274947851le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).

thf(rev_Ar1106406943le_alt_type,type,
    rev_Ar1106406943le_alt: list_A2115238852le_alt > list_A2115238852le_alt ).

thf('#ty_enc51_type',type,
    '#ty_enc51': ( ( produc1501160679le_alt > $o ) > $o ) > arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ).

thf(hd_Arr1965683346le_alt_type,type,
    hd_Arr1965683346le_alt: list_A2115238852le_alt > arrow_475358991le_alt ).

thf(arrow_2098199487_below_type,type,
    arrow_2098199487_below: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).

thf(b_type,type,
    b: arrow_475358991le_alt ).

thf(s_comb_type,type,
    '#S': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).

thf(c_comb_type,type,
    '#C': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).

thf(b_comb_type,type,
    '#B': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).

thf(k_comb_type,type,
    '#K': 
      !>[A: $tType,B: $tType] : ( B > A > B ) ).

thf(i_comb_type,type,
    '#I': 
      !>[A: $tType] : ( A > A ) ).

thf(fact_4_dist,axiom,
    distin236324274le_alt @ ( cons_A228743023le_alt @ a @ ( cons_A228743023le_alt @ b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ) ).

thf(zip_derived_cl2,plain,
    distin236324274le_alt @ ( cons_A228743023le_alt @ a @ ( cons_A228743023le_alt @ b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ),
    inference(cnf,[status(esa)],[fact_4_dist]) ).

thf(fact_467_hd_Osimps,axiom,
    ! [X_26: arrow_475358991le_alt,Xs_44: list_A2115238852le_alt] :
      ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X_26 @ Xs_44 ) )
      = X_26 ) ).

thf(zip_derived_cl268,plain,
    ( !!
    @ ^ [Y0: arrow_475358991le_alt] :
        ( !!
        @ ^ [Y1: list_A2115238852le_alt] :
            ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ Y0 @ Y1 ) )
            = Y0 ) ) ),
    inference(cnf,[status(esa)],[fact_467_hd_Osimps]) ).

thf(zip_derived_cl269,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ hd_Arr1965683346le_alt ) @ cons_A228743023le_alt ) ) ) @ '#I' ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl268]) ).

thf(zip_derived_cl471,plain,
    ! [X2: arrow_475358991le_alt] : ( !! @ ( '#C' @ ( '#B' @ (=) @ ( '#B' @ hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X2 ) ) ) @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl269]) ).

thf(zip_derived_cl472,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
      = X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl471]) ).

thf(zip_derived_cl473,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl472]) ).

thf(fact_375_append__Nil,axiom,
    ! [Ys_45: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_45 )
      = Ys_45 ) ).

thf(zip_derived_cl189,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ Y0 )
        = Y0 ) ),
    inference(cnf,[status(esa)],[fact_375_append__Nil]) ).

thf(zip_derived_cl190,plain,
    !! @ ( '#S' @ ( '#B' @ (=) @ ( append179082452le_alt @ nil_Ar1286194111le_alt ) ) @ '#I' ),
    inference(lams2combs,[status(thm)],[zip_derived_cl189]) ).

thf(zip_derived_cl371,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ X2 )
      = X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl190]) ).

thf(zip_derived_cl372,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ X2 )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl371]) ).

thf(fact_589_hd__in__set,axiom,
    ! [Xs_9: list_A2115238852le_alt] :
      ( ( Xs_9 != nil_Ar1286194111le_alt )
     => ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ Xs_9 ) @ ( set_Ar577454304le_alt @ Xs_9 ) ) ) ).

thf(zip_derived_cl331,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( ( Y0 != nil_Ar1286194111le_alt )
       => ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ Y0 ) @ ( set_Ar577454304le_alt @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_589_hd__in__set]) ).

thf(zip_derived_cl332,plain,
    !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ != @ nil_Ar1286194111le_alt ) ) @ ( '#S' @ ( '#B' @ member84363362le_alt @ hd_Arr1965683346le_alt ) @ set_Ar577454304le_alt ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl331]) ).

thf(zip_derived_cl406,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 != nil_Ar1286194111le_alt )
     => ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ X2 ) @ ( set_Ar577454304le_alt @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl332]) ).

thf(zip_derived_cl407,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 != nil_Ar1286194111le_alt )
      | ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ X2 ) @ ( set_Ar577454304le_alt @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl406]) ).

thf(zip_derived_cl408,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 = nil_Ar1286194111le_alt )
      | ( member84363362le_alt @ ( hd_Arr1965683346le_alt @ X2 ) @ ( set_Ar577454304le_alt @ X2 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl407]) ).

thf(fact_373_append__Cons,axiom,
    ! [X_50: arrow_475358991le_alt,Xs_99: list_A2115238852le_alt,Ys_47: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( cons_A228743023le_alt @ X_50 @ Xs_99 ) @ Ys_47 )
      = ( cons_A228743023le_alt @ X_50 @ ( append179082452le_alt @ Xs_99 @ Ys_47 ) ) ) ).

thf(zip_derived_cl185,plain,
    ( !!
    @ ^ [Y0: arrow_475358991le_alt] :
        ( !!
        @ ^ [Y1: list_A2115238852le_alt] :
            ( !!
            @ ^ [Y2: list_A2115238852le_alt] :
                ( ( append179082452le_alt @ ( cons_A228743023le_alt @ Y0 @ Y1 ) @ Y2 )
                = ( cons_A228743023le_alt @ Y0 @ ( append179082452le_alt @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_373_append__Cons]) ).

thf(zip_derived_cl186,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ append179082452le_alt ) @ cons_A228743023le_alt ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ cons_A228743023le_alt ) ) @ append179082452le_alt ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl185]) ).

thf(zip_derived_cl679,plain,
    ! [X2: arrow_475358991le_alt] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ append179082452le_alt @ ( cons_A228743023le_alt @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ ( cons_A228743023le_alt @ X2 ) ) @ append179082452le_alt ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl186]) ).

thf(zip_derived_cl680,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( append179082452le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) ) ) @ ( '#B' @ ( cons_A228743023le_alt @ X2 ) @ ( append179082452le_alt @ X4 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl679]) ).

thf(zip_derived_cl681,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt,X6: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) @ X6 )
      = ( cons_A228743023le_alt @ X2 @ ( append179082452le_alt @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl680]) ).

thf(zip_derived_cl682,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt,X6: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) @ X6 )
      = ( cons_A228743023le_alt @ X2 @ ( append179082452le_alt @ X4 @ X6 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl681]) ).

thf(fact_394_last__snoc,axiom,
    ! [Xs_80: list_A2115238852le_alt,X_42: arrow_475358991le_alt] :
      ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Xs_80 @ ( cons_A228743023le_alt @ X_42 @ nil_Ar1286194111le_alt ) ) )
      = X_42 ) ).

thf(zip_derived_cl227,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( !!
        @ ^ [Y1: arrow_475358991le_alt] :
            ( ( last_A1217315288le_alt @ ( append179082452le_alt @ Y0 @ ( cons_A228743023le_alt @ Y1 @ nil_Ar1286194111le_alt ) ) )
            = Y1 ) ) ),
    inference(cnf,[status(esa)],[fact_394_last__snoc]) ).

thf(zip_derived_cl228,plain,
    !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ last_A1217315288le_alt ) @ ( '#C' @ ( '#B' @ '#B' @ append179082452le_alt ) @ ( '#C' @ cons_A228743023le_alt @ nil_Ar1286194111le_alt ) ) ) ) ) @ '#I' ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl227]) ).

thf(zip_derived_cl512,plain,
    ! [X2: list_A2115238852le_alt] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ last_A1217315288le_alt @ ( '#B' @ ( append179082452le_alt @ X2 ) @ ( '#C' @ cons_A228743023le_alt @ nil_Ar1286194111le_alt ) ) ) ) @ '#I' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl228]) ).

thf(zip_derived_cl513,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt] :
      ( ( last_A1217315288le_alt @ ( append179082452le_alt @ X2 @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) ) )
      = X4 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl512]) ).

thf(zip_derived_cl514,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt] :
      ( ( last_A1217315288le_alt @ ( append179082452le_alt @ X2 @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl513]) ).

thf(fact_268_mem__def,axiom,
    ! [X_66: produc1501160679le_alt,A_12: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) ).

thf(zip_derived_cl84,plain,
    ( !!
    @ ^ [Y0: produc1501160679le_alt] :
        ( !!
        @ ^ [Y1: produc1501160679le_alt > $o] :
            ( ( member214075476le_alt @ Y0 @ Y1 )
          <=> ( Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_268_mem__def]) ).

thf(zip_derived_cl85,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member214075476le_alt ) ) @ ( '#C' @ '#I' ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl84]) ).

thf(zip_derived_cl507,plain,
    ! [X2: produc1501160679le_alt] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member214075476le_alt @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl508,plain,
    ! [X2: produc1501160679le_alt,X4: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ X2 @ X4 )
    <=> ( X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl507]) ).

thf(zip_derived_cl509,plain,
    ! [X2: produc1501160679le_alt,X4: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl508]) ).

thf(fact_0__096P_A_058_AProf_096,axiom,
    member526088951_alt_o @ p @ arrow_734252939e_Prof ).

thf(zip_derived_cl0,plain,
    member526088951_alt_o @ p @ arrow_734252939e_Prof,
    inference(cnf,[status(esa)],[fact_0__096P_A_058_AProf_096]) ).

thf(conj_0,conjecture,
    ! [I: arrow_1429601828e_indi] :
      ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) )
    <=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [I: arrow_1429601828e_indi] :
        ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) )
      <=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) ),
    inference('cnf.neg',[status(esa)],[conj_0]) ).

thf(zip_derived_cl343,plain,
    ~ ( !!
      @ ^ [Y0: arrow_1429601828e_indi] :
          ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ Y0 ) )
        <=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ Y0 ) @ c @ b ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl344,plain,
    ~ ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) ) @ p ) ) @ ( '#B' @ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) ) @ ( '#C' @ ( '#C' @ ( '#B' @ arrow_2098199487_below @ p ) @ c ) @ b ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl343]) ).

thf(zip_derived_cl376,plain,
    ~ ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ '#sk6' ) )
    <=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ '#sk6' ) @ c @ b ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl344]) ).

thf(zip_derived_cl377,plain,
    ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ '#sk6' ) )
   != ( member214075476le_alt @ ( produc1347929815le_alt @ a @ c ) @ ( arrow_2098199487_below @ ( p @ '#sk6' ) @ c @ b ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl376]) ).

thf(zip_derived_cl509_001,plain,
    ! [X2: produc1501160679le_alt,X4: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl508]) ).

thf(zip_derived_cl509_002,plain,
    ! [X2: produc1501160679le_alt,X4: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl508]) ).

thf(zip_derived_cl510,plain,
    ( ( p @ '#sk6' @ ( produc1347929815le_alt @ a @ b ) )
   != ( arrow_2098199487_below @ ( p @ '#sk6' ) @ c @ b @ ( produc1347929815le_alt @ a @ c ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl377,zip_derived_cl509,zip_derived_cl509]) ).

thf(fact_37_list_Osimps_I2_J,axiom,
    ! [A_23: arrow_475358991le_alt,List_4: list_A2115238852le_alt] :
      ( nil_Ar1286194111le_alt
     != ( cons_A228743023le_alt @ A_23 @ List_4 ) ) ).

thf(zip_derived_cl34,plain,
    ( !!
    @ ^ [Y0: arrow_475358991le_alt] :
        ( !!
        @ ^ [Y1: list_A2115238852le_alt] :
            ( nil_Ar1286194111le_alt
           != ( cons_A228743023le_alt @ Y0 @ Y1 ) ) ) ),
    inference(cnf,[status(esa)],[fact_37_list_Osimps_I2_J]) ).

thf(zip_derived_cl35,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( list_A2115238852le_alt != nil_Ar1286194111le_alt ) ) @ cons_A228743023le_alt ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl387,plain,
    ! [X2: arrow_475358991le_alt] : ( !! @ ( '#B' @ ( list_A2115238852le_alt != nil_Ar1286194111le_alt ) @ ( cons_A228743023le_alt @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl388,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( nil_Ar1286194111le_alt
     != ( cons_A228743023le_alt @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl387]) ).

thf(zip_derived_cl389,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( nil_Ar1286194111le_alt
     != ( cons_A228743023le_alt @ X2 @ X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl388]) ).

thf(fact_376_Nil__is__append__conv,axiom,
    ! [Xs_97: list_A2115238852le_alt,Ys_44: list_A2115238852le_alt] :
      ( ( nil_Ar1286194111le_alt
        = ( append179082452le_alt @ Xs_97 @ Ys_44 ) )
    <=> ( ( Ys_44 = nil_Ar1286194111le_alt )
        & ( Xs_97 = nil_Ar1286194111le_alt ) ) ) ).

thf(zip_derived_cl191,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( !!
        @ ^ [Y1: list_A2115238852le_alt] :
            ( ( nil_Ar1286194111le_alt
              = ( append179082452le_alt @ Y0 @ Y1 ) )
          <=> ( ( Y1 = nil_Ar1286194111le_alt )
              & ( Y0 = nil_Ar1286194111le_alt ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_376_Nil__is__append__conv]) ).

thf(zip_derived_cl192,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ ( list_A2115238852le_alt = nil_Ar1286194111le_alt ) ) @ append179082452le_alt ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (&) @ ( '#C' @ (=) @ nil_Ar1286194111le_alt ) ) ) @ ( '#C' @ (=) @ nil_Ar1286194111le_alt ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl191]) ).

thf(zip_derived_cl608,plain,
    ! [X2: list_A2115238852le_alt] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ ( list_A2115238852le_alt = nil_Ar1286194111le_alt ) @ ( append179082452le_alt @ X2 ) ) ) @ ( '#C' @ ( '#B' @ (&) @ ( '#C' @ (=) @ nil_Ar1286194111le_alt ) ) @ ( X2 = nil_Ar1286194111le_alt ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl192]) ).

thf(zip_derived_cl609,plain,
    ! [X2: list_A2115238852le_alt,X4: list_A2115238852le_alt] :
      ( ( nil_Ar1286194111le_alt
        = ( append179082452le_alt @ X2 @ X4 ) )
    <=> ( ( X4 = nil_Ar1286194111le_alt )
        & ( X2 = nil_Ar1286194111le_alt ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl608]) ).

thf(zip_derived_cl610,plain,
    ! [X2: list_A2115238852le_alt,X4: list_A2115238852le_alt] :
      ( ( nil_Ar1286194111le_alt
        = ( append179082452le_alt @ X2 @ X4 ) )
      = ( ( X4 = nil_Ar1286194111le_alt )
        & ( X2 = nil_Ar1286194111le_alt ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl609]) ).

thf(fact_496_rev__eq__Cons__iff,axiom,
    ! [Xs_25: list_A2115238852le_alt,Y_3: arrow_475358991le_alt,Ys_7: list_A2115238852le_alt] :
      ( ( ( rev_Ar1106406943le_alt @ Xs_25 )
        = ( cons_A228743023le_alt @ Y_3 @ Ys_7 ) )
    <=> ( Xs_25
        = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Ys_7 ) @ ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) ) ) ) ).

thf(zip_derived_cl305,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( !!
        @ ^ [Y1: arrow_475358991le_alt] :
            ( !!
            @ ^ [Y2: list_A2115238852le_alt] :
                ( ( ( rev_Ar1106406943le_alt @ Y0 )
                  = ( cons_A228743023le_alt @ Y1 @ Y2 ) )
              <=> ( Y0
                  = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Y2 ) @ ( cons_A228743023le_alt @ Y1 @ nil_Ar1286194111le_alt ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_496_rev__eq__Cons__iff]) ).

thf(zip_derived_cl306,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=) @ rev_Ar1106406943le_alt ) ) ) @ cons_A228743023le_alt ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ append179082452le_alt @ rev_Ar1106406943le_alt ) ) @ ( '#C' @ cons_A228743023le_alt @ nil_Ar1286194111le_alt ) ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl305]) ).

thf(zip_derived_cl808,plain,
    ! [X2: list_A2115238852le_alt] :
      ( !!
      @ ( '#B' @ !!
        @ ( '#S'
          @ ( '#B' @ '#S'
            @ ( '#B' @ ( '#B' @ (<=>) )
              @ ( '#B'
                @ ( '#B'
                  @ ( list_A2115238852le_alt
                    = ( rev_Ar1106406943le_alt @ X2 ) ) )
                @ cons_A228743023le_alt ) ) )
          @ ( '#B' @ ( '#B' @ ( list_A2115238852le_alt = X2 ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ append179082452le_alt @ rev_Ar1106406943le_alt ) ) @ ( '#C' @ cons_A228743023le_alt @ nil_Ar1286194111le_alt ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl306]) ).

thf(zip_derived_cl809,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt] :
      ( !!
      @ ( '#S'
        @ ( '#B' @ (<=>)
          @ ( '#B'
            @ ( list_A2115238852le_alt
              = ( rev_Ar1106406943le_alt @ X2 ) )
            @ ( cons_A228743023le_alt @ X4 ) ) )
        @ ( '#B' @ ( list_A2115238852le_alt = X2 ) @ ( '#C' @ ( '#B' @ append179082452le_alt @ rev_Ar1106406943le_alt ) @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl808]) ).

thf(zip_derived_cl810,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt,X6: list_A2115238852le_alt] :
      ( ( ( rev_Ar1106406943le_alt @ X2 )
        = ( cons_A228743023le_alt @ X4 @ X6 ) )
    <=> ( X2
        = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X6 ) @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl809]) ).

thf(zip_derived_cl811,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt,X6: list_A2115238852le_alt] :
      ( ( ( rev_Ar1106406943le_alt @ X2 )
        = ( cons_A228743023le_alt @ X4 @ X6 ) )
      = ( X2
        = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X6 ) @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl810]) ).

thf(fact_495_rev_Osimps_I2_J,axiom,
    ! [X_17: arrow_475358991le_alt,Xs_26: list_A2115238852le_alt] :
      ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X_17 @ Xs_26 ) )
      = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Xs_26 ) @ ( cons_A228743023le_alt @ X_17 @ nil_Ar1286194111le_alt ) ) ) ).

thf(zip_derived_cl303,plain,
    ( !!
    @ ^ [Y0: arrow_475358991le_alt] :
        ( !!
        @ ^ [Y1: list_A2115238852le_alt] :
            ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ Y0 @ Y1 ) )
            = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ Y1 ) @ ( cons_A228743023le_alt @ Y0 @ nil_Ar1286194111le_alt ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_495_rev_Osimps_I2_J]) ).

thf(zip_derived_cl304,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ rev_Ar1106406943le_alt ) @ cons_A228743023le_alt ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ append179082452le_alt @ rev_Ar1106406943le_alt ) ) @ ( '#C' @ cons_A228743023le_alt @ nil_Ar1286194111le_alt ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl303]) ).

thf(zip_derived_cl570,plain,
    ! [X2: arrow_475358991le_alt] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2 ) ) ) @ ( '#C' @ ( '#B' @ append179082452le_alt @ rev_Ar1106406943le_alt ) @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl304]) ).

thf(zip_derived_cl571,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
      = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X4 ) @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl570]) ).

thf(zip_derived_cl572,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
      = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X4 ) @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl571]) ).

thf(zip_derived_cl812,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt,X6: list_A2115238852le_alt] :
      ( ( ( rev_Ar1106406943le_alt @ X2 )
        = ( cons_A228743023le_alt @ X4 @ X6 ) )
      = ( X2
        = ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X4 @ X6 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl811,zip_derived_cl572]) ).

thf(fact_79_list_Oexhaust,axiom,
    ! [Y_26: list_A2115238852le_alt] :
      ( ( Y_26 != nil_Ar1286194111le_alt )
     => ~ ! [A: arrow_475358991le_alt,List: list_A2115238852le_alt] :
            ( Y_26
           != ( cons_A228743023le_alt @ A @ List ) ) ) ).

thf(zip_derived_cl50,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( ( Y0 != nil_Ar1286194111le_alt )
       => ( (~)
          @ ( !!
            @ ^ [Y1: arrow_475358991le_alt] :
                ( !!
                @ ^ [Y2: list_A2115238852le_alt] :
                    ( Y0
                   != ( cons_A228743023le_alt @ Y1 @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_79_list_Oexhaust]) ).

thf(zip_derived_cl51,plain,
    !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ != @ nil_Ar1286194111le_alt ) ) @ ( '#B' @ (~) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ != ) ) @ cons_A228743023le_alt ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl602,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 != nil_Ar1286194111le_alt )
     => ( (~) @ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( list_A2115238852le_alt != X2 ) ) @ cons_A228743023le_alt ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl603,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 != nil_Ar1286194111le_alt )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( list_A2115238852le_alt != X2 ) ) @ cons_A228743023le_alt ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl602]) ).

thf(zip_derived_cl604,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 = nil_Ar1286194111le_alt )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( list_A2115238852le_alt != X2 ) ) @ cons_A228743023le_alt ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl603]) ).

thf(zip_derived_cl605,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ~ ( !! @ ( '#B' @ ( list_A2115238852le_alt != X2 ) @ ( cons_A228743023le_alt @ ( '#sk14' @ X2 ) ) ) )
      | ( X2 = nil_Ar1286194111le_alt ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl604]) ).

thf(zip_derived_cl606,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2
       != ( cons_A228743023le_alt @ ( '#sk14' @ X2 ) @ ( '#sk15' @ X2 ) ) )
      | ( X2 = nil_Ar1286194111le_alt ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl605]) ).

thf(zip_derived_cl607,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2
        = ( cons_A228743023le_alt @ ( '#sk14' @ X2 ) @ ( '#sk15' @ X2 ) ) )
      | ( X2 = nil_Ar1286194111le_alt ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl606]) ).

thf(fact_572_last__in__set,axiom,
    ! [As: list_A2115238852le_alt] :
      ( ( As != nil_Ar1286194111le_alt )
     => ( member84363362le_alt @ ( last_A1217315288le_alt @ As ) @ ( set_Ar577454304le_alt @ As ) ) ) ).

thf(zip_derived_cl325,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( ( Y0 != nil_Ar1286194111le_alt )
       => ( member84363362le_alt @ ( last_A1217315288le_alt @ Y0 ) @ ( set_Ar577454304le_alt @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_572_last__in__set]) ).

thf(zip_derived_cl326,plain,
    !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ != @ nil_Ar1286194111le_alt ) ) @ ( '#S' @ ( '#B' @ member84363362le_alt @ last_A1217315288le_alt ) @ set_Ar577454304le_alt ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl325]) ).

thf(zip_derived_cl403,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 != nil_Ar1286194111le_alt )
     => ( member84363362le_alt @ ( last_A1217315288le_alt @ X2 ) @ ( set_Ar577454304le_alt @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl326]) ).

thf(zip_derived_cl404,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 != nil_Ar1286194111le_alt )
      | ( member84363362le_alt @ ( last_A1217315288le_alt @ X2 ) @ ( set_Ar577454304le_alt @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl403]) ).

thf(zip_derived_cl405,plain,
    ! [X2: list_A2115238852le_alt] :
      ( ( X2 = nil_Ar1286194111le_alt )
      | ( member84363362le_alt @ ( last_A1217315288le_alt @ X2 ) @ ( set_Ar577454304le_alt @ X2 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl404]) ).

thf(fact_264_mem__def,axiom,
    ! [X_66: arrow_475358991le_alt,A_12: arrow_475358991le_alt > $o] :
      ( ( member84363362le_alt @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) ).

thf(zip_derived_cl78,plain,
    ( !!
    @ ^ [Y0: arrow_475358991le_alt] :
        ( !!
        @ ^ [Y1: arrow_475358991le_alt > $o] :
            ( ( member84363362le_alt @ Y0 @ Y1 )
          <=> ( Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_264_mem__def]) ).

thf(zip_derived_cl79,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member84363362le_alt ) ) @ ( '#C' @ '#I' ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl468,plain,
    ! [X2: arrow_475358991le_alt] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member84363362le_alt @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl469,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt > $o] :
      ( ( member84363362le_alt @ X2 @ X4 )
    <=> ( X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl468]) ).

thf(zip_derived_cl470,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt > $o] :
      ( ( member84363362le_alt @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl469]) ).

thf(fact_556_distinct_Osimps_I2_J,axiom,
    ! [X_8: arrow_475358991le_alt,Xs_13: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X_8 @ Xs_13 ) )
    <=> ( ( distin236324274le_alt @ Xs_13 )
        & ~ ( member84363362le_alt @ X_8 @ ( set_Ar577454304le_alt @ Xs_13 ) ) ) ) ).

thf(zip_derived_cl321,plain,
    ( !!
    @ ^ [Y0: arrow_475358991le_alt] :
        ( !!
        @ ^ [Y1: list_A2115238852le_alt] :
            ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ Y0 @ Y1 ) )
          <=> ( ( distin236324274le_alt @ Y1 )
              & ( (~) @ ( member84363362le_alt @ Y0 @ ( set_Ar577454304le_alt @ Y1 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_556_distinct_Osimps_I2_J]) ).

thf(zip_derived_cl322,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ distin236324274le_alt ) @ cons_A228743023le_alt ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (&) @ distin236324274le_alt ) ) @ ( '#B' @ ( '#B' @ (~) ) @ ( '#C' @ ( '#B' @ '#B' @ member84363362le_alt ) @ set_Ar577454304le_alt ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl321]) ).

thf(zip_derived_cl661,plain,
    ! [X2: arrow_475358991le_alt] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ distin236324274le_alt @ ( cons_A228743023le_alt @ X2 ) ) ) @ ( '#S' @ ( '#B' @ (&) @ distin236324274le_alt ) @ ( '#B' @ (~) @ ( '#B' @ ( member84363362le_alt @ X2 ) @ set_Ar577454304le_alt ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl322]) ).

thf(zip_derived_cl662,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
    <=> ( ( distin236324274le_alt @ X4 )
        & ( (~) @ ( member84363362le_alt @ X2 @ ( set_Ar577454304le_alt @ X4 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl661]) ).

thf(zip_derived_cl663,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
      = ( ( distin236324274le_alt @ X4 )
        & ( (~) @ ( member84363362le_alt @ X2 @ ( set_Ar577454304le_alt @ X4 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl662]) ).

thf(zip_derived_cl470_003,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt > $o] :
      ( ( member84363362le_alt @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl469]) ).

thf(zip_derived_cl664,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
      = ( ( distin236324274le_alt @ X4 )
        & ( (~) @ ( set_Ar577454304le_alt @ X4 @ X2 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl663,zip_derived_cl470]) ).

thf(fact_269_mem__def,axiom,
    ! [X_66: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_12: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) ).

thf(zip_derived_cl86,plain,
    ( !!
    @ ^ [Y0: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
        ( !!
        @ ^ [Y1: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
            ( ( member526088951_alt_o @ Y0 @ Y1 )
          <=> ( Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_269_mem__def]) ).

thf(zip_derived_cl87,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member526088951_alt_o ) ) @ ( '#C' @ '#I' ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl544,plain,
    ! [X2: arrow_1429601828e_indi > produc1501160679le_alt > $o] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member526088951_alt_o @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl545,plain,
    ! [X2: arrow_1429601828e_indi > produc1501160679le_alt > $o,X4: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ X2 @ X4 )
    <=> ( X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl544]) ).

thf(zip_derived_cl546,plain,
    ! [X2: arrow_1429601828e_indi > produc1501160679le_alt > $o,X4: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl545]) ).

thf(fact_270_mem__def,axiom,
    ! [X_66: produc1501160679le_alt > $o,A_12: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member377231867_alt_o @ X_66 @ A_12 )
    <=> ( A_12 @ X_66 ) ) ).

thf(zip_derived_cl88,plain,
    ( !!
    @ ^ [Y0: produc1501160679le_alt > $o] :
        ( !!
        @ ^ [Y1: ( produc1501160679le_alt > $o ) > $o] :
            ( ( member377231867_alt_o @ Y0 @ Y1 )
          <=> ( Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_270_mem__def]) ).

thf(zip_derived_cl89,plain,
    !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ member377231867_alt_o ) ) @ ( '#C' @ '#I' ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl88]) ).

thf(zip_derived_cl547,plain,
    ! [X2: produc1501160679le_alt > $o] : ( !! @ ( '#S' @ ( '#B' @ (<=>) @ ( member377231867_alt_o @ X2 ) ) @ ( '#C' @ '#I' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl548,plain,
    ! [X2: produc1501160679le_alt > $o,X4: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member377231867_alt_o @ X2 @ X4 )
    <=> ( X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl547]) ).

thf(zip_derived_cl549,plain,
    ! [X2: produc1501160679le_alt > $o,X4: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member377231867_alt_o @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl548]) ).

thf(fact_12_in__below,axiom,
    ! [X: arrow_475358991le_alt,Y: arrow_475358991le_alt,L_1: produc1501160679le_alt > $o,A_24: arrow_475358991le_alt,B_17: arrow_475358991le_alt] :
      ( ( A_24 != B_17 )
     => ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin )
       => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ ( arrow_2098199487_below @ L_1 @ A_24 @ B_17 ) )
        <=> ( ( ( Y != A_24 )
             => ( ( ( X != A_24 )
                 => ( member214075476le_alt @ ( produc1347929815le_alt @ X @ Y ) @ L_1 ) )
                & ( ( X = A_24 )
                 => ( ( member214075476le_alt @ ( produc1347929815le_alt @ B_17 @ Y ) @ L_1 )
                    | ( Y = B_17 ) ) ) ) )
            & ( ( Y = A_24 )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ X @ B_17 ) @ L_1 ) )
            & ( X != Y ) ) ) ) ) ).

thf(zip_derived_cl11,plain,
    ( !!
    @ ^ [Y0: arrow_475358991le_alt] :
        ( !!
        @ ^ [Y1: arrow_475358991le_alt] :
            ( !!
            @ ^ [Y2: produc1501160679le_alt > $o] :
                ( !!
                @ ^ [Y3: arrow_475358991le_alt] :
                    ( !!
                    @ ^ [Y4: arrow_475358991le_alt] :
                        ( ( Y3 != Y4 )
                       => ( ( member377231867_alt_o @ Y2 @ arrow_823908191le_Lin )
                         => ( ( member214075476le_alt @ ( produc1347929815le_alt @ Y0 @ Y1 ) @ ( arrow_2098199487_below @ Y2 @ Y3 @ Y4 ) )
                          <=> ( ( ( Y1 != Y3 )
                               => ( ( ( Y0 != Y3 )
                                   => ( member214075476le_alt @ ( produc1347929815le_alt @ Y0 @ Y1 ) @ Y2 ) )
                                  & ( ( Y0 = Y3 )
                                   => ( ( member214075476le_alt @ ( produc1347929815le_alt @ Y4 @ Y1 ) @ Y2 )
                                      | ( Y1 = Y4 ) ) ) ) )
                              & ( ( Y1 = Y3 )
                               => ( member214075476le_alt @ ( produc1347929815le_alt @ Y0 @ Y4 ) @ Y2 ) )
                              & ( Y0 != Y1 ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_12_in__below]) ).

thf(zip_derived_cl12,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( '#C' @ member377231867_alt_o @ arrow_823908191le_Lin ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ member214075476le_alt ) @ produc1347929815le_alt ) ) ) ) ) @ arrow_2098199487_below ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) ) @ ( '#B' @ ( '#B' @ member214075476le_alt ) @ produc1347929815le_alt ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ (=) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ member214075476le_alt ) @ ( '#C' @ produc1347929815le_alt ) ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ (=) ) ) ) ) ) @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ member214075476le_alt ) @ produc1347929815le_alt ) ) ) ) ) ) ) ) @ != ) ) ) ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl413,plain,
    ! [X2: arrow_475358991le_alt] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( '#C' @ member377231867_alt_o @ arrow_823908191le_Lin ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ member214075476le_alt @ ( produc1347929815le_alt @ X2 ) ) ) ) ) @ arrow_2098199487_below ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#B' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt != X2 ) ) ) ) @ ( '#B' @ member214075476le_alt @ ( produc1347929815le_alt @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt = X2 ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ member214075476le_alt ) @ ( '#C' @ produc1347929815le_alt ) ) ) ) ) ) @ (=) ) ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ (=) ) ) ) ) @ ( '#C' @ ( '#B' @ member214075476le_alt @ ( produc1347929815le_alt @ X2 ) ) ) ) ) ) ) ) @ ( arrow_475358991le_alt != X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl414,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( '#C' @ member377231867_alt_o @ arrow_823908191le_Lin ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) ) ) ) @ arrow_2098199487_below ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt != X4 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#C' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt != X2 ) ) ) @ ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt = X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#C' @ ( '#B' @ member214075476le_alt @ ( '#C' @ produc1347929815le_alt @ X4 ) ) ) ) ) @ ( arrow_475358991le_alt = X4 ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt = X4 ) ) ) ) @ ( '#C' @ ( '#B' @ member214075476le_alt @ ( produc1347929815le_alt @ X2 ) ) ) ) ) ) ) @ ( X2 != X4 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl413]) ).

thf(zip_derived_cl415,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ != ) ) @ ( '#B' @ ( '#B' @ ( (=>) @ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ ( '#B' @ ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) ) ) @ ( arrow_2098199487_below @ X6 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt != X4 ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (&) @ ( '#C' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt != X2 ) ) @ ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt = X2 ) ) ) @ ( '#S' @ ( '#B' @ (|) @ ( '#C' @ ( '#B' @ member214075476le_alt @ ( '#C' @ produc1347929815le_alt @ X4 ) ) @ X6 ) ) @ ( arrow_475358991le_alt = X4 ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt = X4 ) ) ) @ ( '#C' @ ( '#B' @ member214075476le_alt @ ( produc1347929815le_alt @ X2 ) ) @ X6 ) ) ) ) @ ( X2 != X4 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl414]) ).

thf(zip_derived_cl416,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt] :
      ( !!
      @ ( '#S' @ ( '#B' @ (=>) @ ( arrow_475358991le_alt != X8 ) )
        @ ( '#B' @ ( (=>) @ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin ) )
          @ ( '#S' @ ( '#B' @ (<=>) @ ( '#B' @ ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) ) @ ( arrow_2098199487_below @ X6 @ X8 ) ) )
            @ ( '#C'
              @ ( '#S'
                @ ( '#B' @ (&)
                  @ ( '#B' @ ( (=>) @ ( X4 != X8 ) )
                    @ ( '#B'
                      @ ( (&)
                        @ ( ( X2 != X8 )
                         => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) ) )
                      @ ( '#B' @ ( (=>) @ ( X2 = X8 ) ) @ ( '#S' @ ( '#B' @ (|) @ ( '#C' @ ( '#B' @ member214075476le_alt @ ( '#C' @ produc1347929815le_alt @ X4 ) ) @ X6 ) ) @ ( arrow_475358991le_alt = X4 ) ) ) ) ) )
                @ ( '#B' @ ( (=>) @ ( X4 = X8 ) ) @ ( '#C' @ ( '#B' @ member214075476le_alt @ ( produc1347929815le_alt @ X2 ) ) @ X6 ) ) )
              @ ( X2 != X4 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl415]) ).

thf(zip_derived_cl417,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X10: arrow_475358991le_alt] :
      ( ( X8 != X10 )
     => ( ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
       => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ ( arrow_2098199487_below @ X6 @ X8 @ X10 ) )
        <=> ( ( ( X4 != X8 )
             => ( ( ( X2 != X8 )
                 => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) )
                & ( ( X2 = X8 )
                 => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X10 @ X4 ) @ X6 )
                    | ( X4 = X10 ) ) ) ) )
            & ( ( X4 = X8 )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X10 ) @ X6 ) )
            & ( X2 != X4 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl416]) ).

thf(zip_derived_cl418,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X10: arrow_475358991le_alt] :
      ( ( X8 != X10 )
      | ( ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
       => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ ( arrow_2098199487_below @ X6 @ X8 @ X10 ) )
        <=> ( ( ( X4 != X8 )
             => ( ( ( X2 != X8 )
                 => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) )
                & ( ( X2 = X8 )
                 => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X10 @ X4 ) @ X6 )
                    | ( X4 = X10 ) ) ) ) )
            & ( ( X4 = X8 )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X10 ) @ X6 ) )
            & ( X2 != X4 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl417]) ).

thf(zip_derived_cl419,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X10: arrow_475358991le_alt] :
      ( ( X8 = X10 )
      | ( ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
       => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ ( arrow_2098199487_below @ X6 @ X8 @ X10 ) )
        <=> ( ( ( X4 != X8 )
             => ( ( ( X2 != X8 )
                 => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) )
                & ( ( X2 = X8 )
                 => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X10 @ X4 ) @ X6 )
                    | ( X4 = X10 ) ) ) ) )
            & ( ( X4 = X8 )
             => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X10 ) @ X6 ) )
            & ( X2 != X4 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl418]) ).

thf(zip_derived_cl420,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X10: arrow_475358991le_alt] :
      ( ~ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
      | ( ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ ( arrow_2098199487_below @ X6 @ X8 @ X10 ) )
      <=> ( ( ( X4 != X8 )
           => ( ( ( X2 != X8 )
               => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) )
              & ( ( X2 = X8 )
               => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X10 @ X4 ) @ X6 )
                  | ( X4 = X10 ) ) ) ) )
          & ( ( X4 = X8 )
           => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X10 ) @ X6 ) )
          & ( X2 != X4 ) ) )
      | ( X8 = X10 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl419]) ).

thf(zip_derived_cl421,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X10: arrow_475358991le_alt] :
      ( ~ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
      | ( ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ ( arrow_2098199487_below @ X6 @ X8 @ X10 ) )
        = ( ( ( X4 != X8 )
           => ( ( ( X2 != X8 )
               => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) )
              & ( ( X2 = X8 )
               => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X10 @ X4 ) @ X6 )
                  | ( X4 = X10 ) ) ) ) )
          & ( ( X4 = X8 )
           => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X10 ) @ X6 ) )
          & ( X2 != X4 ) ) )
      | ( X8 = X10 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl420]) ).

thf(zip_derived_cl509_004,plain,
    ! [X2: produc1501160679le_alt,X4: produc1501160679le_alt > $o] :
      ( ( member214075476le_alt @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl508]) ).

thf(zip_derived_cl511,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X10: arrow_475358991le_alt] :
      ( ~ ( member377231867_alt_o @ X6 @ arrow_823908191le_Lin )
      | ( ( arrow_2098199487_below @ X6 @ X8 @ X10 @ ( produc1347929815le_alt @ X2 @ X4 ) )
        = ( ( ( X4 != X8 )
           => ( ( ( X2 != X8 )
               => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) )
              & ( ( X2 = X8 )
               => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X10 @ X4 ) @ X6 )
                  | ( X4 = X10 ) ) ) ) )
          & ( ( X4 = X8 )
           => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X10 ) @ X6 ) )
          & ( X2 != X4 ) ) )
      | ( X8 = X10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl421,zip_derived_cl509]) ).

thf(zip_derived_cl549_005,plain,
    ! [X2: produc1501160679le_alt > $o,X4: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member377231867_alt_o @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl548]) ).

thf(zip_derived_cl550,plain,
    ! [X2: arrow_475358991le_alt,X4: arrow_475358991le_alt,X6: produc1501160679le_alt > $o,X8: arrow_475358991le_alt,X10: arrow_475358991le_alt] :
      ( ~ ( arrow_823908191le_Lin @ X6 )
      | ( ( arrow_2098199487_below @ X6 @ X8 @ X10 @ ( produc1347929815le_alt @ X2 @ X4 ) )
        = ( ( ( X4 != X8 )
           => ( ( ( X2 != X8 )
               => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X4 ) @ X6 ) )
              & ( ( X2 = X8 )
               => ( ( member214075476le_alt @ ( produc1347929815le_alt @ X10 @ X4 ) @ X6 )
                  | ( X4 = X10 ) ) ) ) )
          & ( ( X4 = X8 )
           => ( member214075476le_alt @ ( produc1347929815le_alt @ X2 @ X10 ) @ X6 ) )
          & ( X2 != X4 ) ) )
      | ( X8 = X10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl511,zip_derived_cl549]) ).

thf(zip_derived_cl572_006,plain,
    ! [X2: arrow_475358991le_alt,X4: list_A2115238852le_alt] :
      ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X2 @ X4 ) )
      = ( append179082452le_alt @ ( rev_Ar1106406943le_alt @ X4 ) @ ( cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl571]) ).

thf(fact_316_UNIV__I,axiom,
    ! [X_55: arrow_1429601828e_indi] : ( member2052026769e_indi @ X_55 @ top_to988227749indi_o ) ).

thf(zip_derived_cl127,plain,
    ( !!
    @ ^ [Y0: arrow_1429601828e_indi] : ( member2052026769e_indi @ Y0 @ top_to988227749indi_o ) ),
    inference(cnf,[status(esa)],[fact_316_UNIV__I]) ).

thf(zip_derived_cl128,plain,
    !! @ ( '#C' @ member2052026769e_indi @ top_to988227749indi_o ),
    inference(lams2combs,[status(thm)],[zip_derived_cl127]) ).

thf(zip_derived_cl348,plain,
    ! [X2: arrow_1429601828e_indi] : ( member2052026769e_indi @ X2 @ top_to988227749indi_o ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl128]) ).

thf(fact_372_append__assoc,axiom,
    ! [Xs_100: list_A2115238852le_alt,Ys_48: list_A2115238852le_alt,Zs_5: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( append179082452le_alt @ Xs_100 @ Ys_48 ) @ Zs_5 )
      = ( append179082452le_alt @ Xs_100 @ ( append179082452le_alt @ Ys_48 @ Zs_5 ) ) ) ).

thf(zip_derived_cl183,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( !!
        @ ^ [Y1: list_A2115238852le_alt] :
            ( !!
            @ ^ [Y2: list_A2115238852le_alt] :
                ( ( append179082452le_alt @ ( append179082452le_alt @ Y0 @ Y1 ) @ Y2 )
                = ( append179082452le_alt @ Y0 @ ( append179082452le_alt @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_372_append__assoc]) ).

thf(zip_derived_cl184,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#B' @ ( '#B' @ append179082452le_alt ) @ append179082452le_alt ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ append179082452le_alt ) ) @ append179082452le_alt ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl183]) ).

thf(zip_derived_cl675,plain,
    ! [X2: list_A2115238852le_alt] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ append179082452le_alt @ ( append179082452le_alt @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ ( append179082452le_alt @ X2 ) ) @ append179082452le_alt ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl184]) ).

thf(zip_derived_cl676,plain,
    ! [X2: list_A2115238852le_alt,X4: list_A2115238852le_alt] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( append179082452le_alt @ ( append179082452le_alt @ X2 @ X4 ) ) ) @ ( '#B' @ ( append179082452le_alt @ X2 ) @ ( append179082452le_alt @ X4 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl675]) ).

thf(zip_derived_cl677,plain,
    ! [X2: list_A2115238852le_alt,X4: list_A2115238852le_alt,X6: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( append179082452le_alt @ X2 @ X4 ) @ X6 )
      = ( append179082452le_alt @ X2 @ ( append179082452le_alt @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl676]) ).

thf(zip_derived_cl678,plain,
    ! [X2: list_A2115238852le_alt,X4: list_A2115238852le_alt,X6: list_A2115238852le_alt] :
      ( ( append179082452le_alt @ ( append179082452le_alt @ X2 @ X4 ) @ X6 )
      = ( append179082452le_alt @ X2 @ ( append179082452le_alt @ X4 @ X6 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl677]) ).

thf(fact_289_Prof__def,axiom,
    ( arrow_734252939e_Prof
    = ( pi_Arr1929480907_alt_o @ top_to988227749indi_o
      @ ^ [Uu: arrow_1429601828e_indi] : arrow_823908191le_Lin ) ) ).

thf(zip_derived_cl92,plain,
    ( arrow_734252939e_Prof
    = ( pi_Arr1929480907_alt_o @ top_to988227749indi_o
      @ ^ [Y0: arrow_1429601828e_indi] : arrow_823908191le_Lin ) ),
    inference(cnf,[status(esa)],[fact_289_Prof__def]) ).

thf(zip_derived_cl93,plain,
    ( arrow_734252939e_Prof
    = ( pi_Arr1929480907_alt_o @ top_to988227749indi_o @ ( '#K' @ arrow_823908191le_Lin ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl10116,plain,
    ( arrow_734252939e_Prof
    = ( pi_Arr1929480907_alt_o @ top_to988227749indi_o @ ( '#ty_enc51' @ arrow_823908191le_Lin ) ) ),
    inference(remove_ty_args,[status(thm)],[zip_derived_cl93]) ).

thf(fact_114_funcset__mem,axiom,
    ! [X_71: arrow_1429601828e_indi,F_13: arrow_1429601828e_indi > produc1501160679le_alt > $o,A_18: arrow_1429601828e_indi > $o,B_15: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ F_13
        @ ( pi_Arr1929480907_alt_o @ A_18
          @ ^ [Uu: arrow_1429601828e_indi] : B_15 ) )
     => ( ( member2052026769e_indi @ X_71 @ A_18 )
       => ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ) ).

thf(zip_derived_cl54,plain,
    ( !!
    @ ^ [Y0: arrow_1429601828e_indi] :
        ( !!
        @ ^ [Y1: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
            ( !!
            @ ^ [Y2: arrow_1429601828e_indi > $o] :
                ( !!
                @ ^ [Y3: ( produc1501160679le_alt > $o ) > $o] :
                    ( ( member526088951_alt_o @ Y1
                      @ ( pi_Arr1929480907_alt_o @ Y2
                        @ ^ [Y4: arrow_1429601828e_indi] : Y3 ) )
                   => ( ( member2052026769e_indi @ Y0 @ Y2 )
                     => ( member377231867_alt_o @ ( Y1 @ Y0 ) @ Y3 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_114_funcset__mem]) ).

thf(zip_derived_cl55,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ member526088951_alt_o ) ) @ ( '#C' @ ( '#B' @ '#B' @ pi_Arr1929480907_alt_o ) @ '#K' ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ member2052026769e_indi ) ) ) ) @ ( '#B' @ ( '#B' @ member377231867_alt_o ) @ ( '#C' @ '#I' ) ) ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl899,plain,
    ! [X2: arrow_1429601828e_indi] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ member526088951_alt_o ) ) @ ( '#C' @ ( '#B' @ '#B' @ pi_Arr1929480907_alt_o ) @ '#K' ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( member2052026769e_indi @ X2 ) ) ) ) @ ( '#B' @ member377231867_alt_o @ ( '#C' @ '#I' @ X2 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl900,plain,
    ! [X2: arrow_1429601828e_indi,X4: arrow_1429601828e_indi > produc1501160679le_alt > $o] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ ( member526088951_alt_o @ X4 ) ) @ ( '#C' @ ( '#B' @ '#B' @ pi_Arr1929480907_alt_o ) @ '#K' ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( member2052026769e_indi @ X2 ) ) ) @ ( member377231867_alt_o @ ( X4 @ X2 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl899]) ).

thf(zip_derived_cl901,plain,
    ! [X2: arrow_1429601828e_indi,X4: arrow_1429601828e_indi > produc1501160679le_alt > $o,X6: arrow_1429601828e_indi > $o] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ ( member526088951_alt_o @ X4 ) @ ( '#B' @ ( pi_Arr1929480907_alt_o @ X6 ) @ '#K' ) ) ) @ ( '#B' @ ( (=>) @ ( member2052026769e_indi @ X2 @ X6 ) ) @ ( member377231867_alt_o @ ( X4 @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl900]) ).

thf(zip_derived_cl902,plain,
    ! [X2: arrow_1429601828e_indi,X4: arrow_1429601828e_indi > produc1501160679le_alt > $o,X6: arrow_1429601828e_indi > $o,X8: ( produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ X4 @ ( pi_Arr1929480907_alt_o @ X6 @ ( '#K' @ X8 ) ) )
     => ( ( member2052026769e_indi @ X2 @ X6 )
       => ( member377231867_alt_o @ ( X4 @ X2 ) @ X8 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl901]) ).

thf(zip_derived_cl546_007,plain,
    ! [X2: arrow_1429601828e_indi > produc1501160679le_alt > $o,X4: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
      ( ( member526088951_alt_o @ X2 @ X4 )
      = ( X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl545]) ).

thf(zip_derived_cl903,plain,
    ! [X2: arrow_1429601828e_indi,X4: arrow_1429601828e_indi > produc1501160679le_alt > $o,X6: arrow_1429601828e_indi > $o,X8: ( produc1501160679le_alt > $o ) > $o] :
      ( ( pi_Arr1929480907_alt_o @ X6 @ ( '#K' @ X8 ) @ X4 )
     => ( ( member2052026769e_indi @ X2 @ X6 )
       => ( member377231867_alt_o @ ( X4 @ X2 ) @ X8 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl902,zip_derived_cl546]) ).

thf(zip_derived_cl904,plain,
    ! [X2: arrow_1429601828e_indi,X4: arrow_1429601828e_indi > produc1501160679le_alt > $o,X6: arrow_1429601828e_indi > $o,X8: ( produc1501160679le_alt > $o ) > $o] :
      ( ~ ( pi_Arr1929480907_alt_o @ X6 @ ( '#K' @ X8 ) @ X4 )
      | ( ( member2052026769e_indi @ X2 @ X6 )
       => ( member377231867_alt_o @ ( X4 @ X2 ) @ X8 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl903]) ).

thf(zip_derived_cl905,plain,
    ! [X2: arrow_1429601828e_indi,X4: arrow_1429601828e_indi > produc1501160679le_alt > $o,X6: arrow_1429601828e_indi > $o,X8: ( produc1501160679le_alt > $o ) > $o] :
      ( ~ ( member2052026769e_indi @ X2 @ X6 )
      | ( member377231867_alt_o @ ( X4 @ X2 ) @ X8 )
      | ~ ( pi_Arr1929480907_alt_o @ X6 @ ( '#K' @ X8 ) @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl904]) ).

thf(zip_derived_cl10127,plain,
    ! [X2: arrow_1429601828e_indi,X4: arrow_1429601828e_indi > produc1501160679le_alt > $o,X6: arrow_1429601828e_indi > $o,X8: ( produc1501160679le_alt > $o ) > $o] :
      ( ~ ( member2052026769e_indi @ X2 @ X6 )
      | ( member377231867_alt_o @ ( X4 @ X2 ) @ X8 )
      | ~ ( pi_Arr1929480907_alt_o @ X6 @ ( '#ty_enc51' @ X8 ) @ X4 ) ),
    inference(remove_ty_args,[status(thm)],[zip_derived_cl905]) ).

thf(fact_365_snoc__eq__iff__butlast,axiom,
    ! [Xs_106: list_A2115238852le_alt,X_51: arrow_475358991le_alt,Ys_54: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ Xs_106 @ ( cons_A228743023le_alt @ X_51 @ nil_Ar1286194111le_alt ) )
        = Ys_54 )
    <=> ( ( ( last_A1217315288le_alt @ Ys_54 )
          = X_51 )
        & ( ( butlas274947851le_alt @ Ys_54 )
          = Xs_106 )
        & ( Ys_54 != nil_Ar1286194111le_alt ) ) ) ).

thf(zip_derived_cl173,plain,
    ( !!
    @ ^ [Y0: list_A2115238852le_alt] :
        ( !!
        @ ^ [Y1: arrow_475358991le_alt] :
            ( !!
            @ ^ [Y2: list_A2115238852le_alt] :
                ( ( ( append179082452le_alt @ Y0 @ ( cons_A228743023le_alt @ Y1 @ nil_Ar1286194111le_alt ) )
                  = Y2 )
              <=> ( ( ( last_A1217315288le_alt @ Y2 )
                    = Y1 )
                  & ( ( butlas274947851le_alt @ Y2 )
                    = Y0 )
                  & ( Y2 != nil_Ar1286194111le_alt ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_365_snoc__eq__iff__butlast]) ).

thf(zip_derived_cl174,plain,
    !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (<=>) ) ) @ ( '#B' @ ( '#B' @ (=) ) @ ( '#C' @ ( '#B' @ '#B' @ append179082452le_alt ) @ ( '#C' @ cons_A228743023le_alt @ nil_Ar1286194111le_alt ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ (=) @ last_A1217315288le_alt ) ) ) ) ) @ ( '#C' @ ( '#B' @ (=) @ butlas274947851le_alt ) ) ) ) ) @ ( '#C' @ != @ nil_Ar1286194111le_alt ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl173]) ).

thf(zip_derived_cl823,plain,
    ! [X2: list_A2115238852le_alt] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (<=>) ) @ ( '#B' @ (=) @ ( '#B' @ ( append179082452le_alt @ X2 ) @ ( '#C' @ cons_A228743023le_alt @ nil_Ar1286194111le_alt ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#C' @ ( '#B' @ (=) @ last_A1217315288le_alt ) ) ) ) @ ( '#C' @ ( '#B' @ (=) @ butlas274947851le_alt ) @ X2 ) ) ) @ ( '#C' @ != @ nil_Ar1286194111le_alt ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl174]) ).

thf(zip_derived_cl824,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt] :
      ( !!
      @ ( '#S'
        @ ( '#B' @ (<=>)
          @ ( list_A2115238852le_alt
            = ( append179082452le_alt @ X2 @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) ) ) )
        @ ( '#S' @ ( '#S' @ ( '#B' @ (&) @ ( '#C' @ ( '#B' @ (=) @ last_A1217315288le_alt ) @ X4 ) ) @ ( '#C' @ ( '#B' @ (=) @ butlas274947851le_alt ) @ X2 ) ) @ ( '#C' @ != @ nil_Ar1286194111le_alt ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl823]) ).

thf(zip_derived_cl825,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt,X6: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ X2 @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) )
        = X6 )
    <=> ( ( ( last_A1217315288le_alt @ X6 )
          = X4 )
        & ( ( butlas274947851le_alt @ X6 )
          = X2 )
        & ( X6 != nil_Ar1286194111le_alt ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl824]) ).

thf(zip_derived_cl826,plain,
    ! [X2: list_A2115238852le_alt,X4: arrow_475358991le_alt,X6: list_A2115238852le_alt] :
      ( ( ( append179082452le_alt @ X2 @ ( cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt ) )
        = X6 )
      = ( ( ( last_A1217315288le_alt @ X6 )
          = X4 )
        & ( ( butlas274947851le_alt @ X6 )
          = X2 )
        & ( X6 != nil_Ar1286194111le_alt ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl825]) ).

thf(zip_derived_cl10133,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl2,zip_derived_cl473,zip_derived_cl372,zip_derived_cl408,zip_derived_cl682,zip_derived_cl514,zip_derived_cl509,zip_derived_cl0,zip_derived_cl510,zip_derived_cl389,zip_derived_cl610,zip_derived_cl812,zip_derived_cl607,zip_derived_cl405,zip_derived_cl470,zip_derived_cl664,zip_derived_cl546,zip_derived_cl549,zip_derived_cl550,zip_derived_cl572,zip_derived_cl348,zip_derived_cl678,zip_derived_cl10116,zip_derived_cl10127,zip_derived_cl826]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SCT170^2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.12  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7DgWDRcgue true
% 0.16/0.34  % Computer : n020.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Thu Aug 24 14:58:30 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.16/0.34  % Running portfolio for 300 s
% 0.16/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.34  % Number of cores: 8
% 0.16/0.35  % Python version: Python 3.6.8
% 0.16/0.35  % Running in HO mode
% 0.21/0.65  % Total configuration time : 828
% 0.21/0.65  % Estimated wc time : 1656
% 0.21/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.69  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.70  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.70  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.21/0.85  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 88.81/12.14  % Solved by lams/40_b.comb.sh.
% 88.81/12.14  % done 428 iterations in 11.342s
% 88.81/12.14  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 88.81/12.14  % SZS output start Refutation
% See solution above
% 88.81/12.15  
% 88.81/12.15  
% 88.81/12.15  % Terminating...
% 88.81/12.23  % Runner terminated.
% 88.81/12.23  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------